Updated July 31, 2015 #ASC2015

Updated July 31, 2015 #ASC2015

AAS/AIAA ASTRODYNAMICS SPECIALIST CONFERENCE CONFERENCE INFORMATION

GENERAL INFORMATION Welcome to the 2015 Astrodynamics Specialist Conference, hosted by the American Astronautical Society (AAS) and co-hosted by the American Institute of Aeronautics and Astronautics (AIAA), August 9 – 13, 2015 (#ASC2015 on social media). This meeting is organized by the AAS Space Flight Mechanics Committee and the AIAA Astrodynamics Technical Committee, and held at the Vail Cascade Resort & Spa, 1300 Westhaven Dr, Vail, CO 81657, (970) 476-7111, http://www.vailcascade.com/. REGISTRATION Registration Site ( https://www.xcdsystem.com/aas/index.cfm ) In order to encourage early registration, we have implemented the following conference registration rate structure: Register by July 1, 2015, and save $70!

Category Early Registration Registration (after Late Registration (through July 1, 2015) July 1, 2015) (after July 27, 2015)

Full - AAS or AIAA Member $520 $590 $690

Full - Non-member $620 $690 $790

Retired or Student* - Member $190 $260 $360

Retired or Student* - Non-member $290 $360 $460

*does not include proceedings CD

Refunds will be issued in full until July 27, 2015. A 10% fee will be assessed for all refunds issued after that date and until 8:00 am EST August 10. No refunds will be issued after 8:00 am EST August 10. The Colorado buffet dinner on Tuesday evening is included with all registrations. Guest tickets for the dinner may be purchased for $25. Children under 5 eat free. More information about the Colorado buffet dinner is included below. All registrants and guests are invited to the Luge welcome reception on Sunday evening A conference registration and check-in table will be located on the Ballroom Foyer of the Vail Cascade Resort & Spa and will be staffed according to the following schedule: Sunday Aug. 9 3:00 PM – 6:00 PM Monday Aug. 10 7:30 AM – 2:00 PM Tuesday Aug. 11 8:00 AM – 2:00 PM Wednesday Aug. 12 8:00 AM – 2:00 PM Thursday Aug. 13 8:00 AM – 10:00 AM We will accept registration and payment on-site for those who have not pre-registered online, but we strongly recommend online registration before the conference in order to avoid delays (see URL above). Pre- registration also gives you free access to pre-print technical papers. On-site payment by credit card will be

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Updated July 31, 2015 #ASC2015 only through the AAS website using a computer at the registration table. Any checks should be made payable to the “American Astronautical Society.” SCHEDULE OF EVENTS Technical sessions begin on Monday, 10 August, at 8 AM. The last technical sessions end at noon on Thursday, 13 August. Presentations are limited to 15 minutes with an additional 5 minutes for questions and answers. Each session has a 20-minute morning (9:40 to 10:00 am) or afternoon (3:10 to 3:30 pm) break. Nominally, five presentations precede the break and six follow the break. On Monday through Thursday, conference registration and badge pickup will be held from 7:30 am through 2 pm (10:00 am Thursday) in the Rocky Mountain Foyer.

Sunday, August 10, 2015

Early Bird Reception Cascade Ballroom Hosted Bar 4:30 PM - 8:30 PM Luge Welcome Reception (i.e., food) 6:00 PM - 7:30 PM

Monday, August 11, 2015

Space Situational Awareness - 1 8:00 AM - 12:00 PM Rocky Ballroom A/B Astrodynamics - 1 8:00 AM - 12:00 PM Rocky Ballroom C/D Attitude Dynamics and Control - 1 8:00 AM - 12:00 PM Primrose Trajectory Design and Optimization - 1 8:00 AM - 12:00 PM Larkspur AAS/AIAA Joint Technical Committee Meeting 12:00 PM - 1:30 PM Mountain View Spacecraft GNC 1 1:30 PM - 5:30 PM Primrose Space Missions: New Horizons, MESSENGER and Mars 1:30 PM - 5:30 PM Rocky Ballroom A/B Reconnaissance Orbiter Trajectory Design and Optimization - 2 1:30 PM - 5:30 PM Larkspur High Performance Computing in Astronautics 1:30 PM - 5:30 PM Rocky Ballroom C/D AAS Conference Administration Subcommittee Meeting 5:30 PM - 6:30 PM Blue Spruce AAS Technical Activities Subcommittee Meeting 5:30 PM - 6:30 PM Juniper Room AAS Web Administration Subcommittee Meeting 5:30 PM - 6:30 PM Rocky Ballroom A/B

Tuesday, August 12, 2015

Space Situational Awareness 2 8:00 AM - 12:00 PM Rocky Ballroom A/B Astrodynamics 2 8:00 AM - 12:00 PM Rocky Ballroom C/D Attitude Dynamics and Control - 2 8:00 AM - 12:00 PM Primrose Trajectory Design and Optimization - 3 8:00 AM - 12:00 PM Larkspur AIAA Technical Committee Meeting 12:00 PM - 1:30 PM Mountain View Spacecraft GNC - 2 1:30 PM - 5:30 PM Primrose Formation Flying and Relative Motion 1:30 PM - 5:30 PM Rocky Ballroom A/B Trajectory Design and Optimization - 4 1:30 PM - 5:30 PM Larkspur Asteroid and Non Earth Orbiting Missions - 1 1:30 PM - 5:30 PM Rocky Ballroom C/D Buffet Dinner Centennial Ballroom Hosted Bar 5:00 PM - 9:00 PM Colorado Buffet Dinner 6:30 PM - 8:00 PM

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Updated July 31, 2015 #ASC2015 Wednesday, August 12, 2015

Space Situational Awareness - 3 8:00 AM - 12:00 PM Rocky Ballroom A/B Astrodynamics - 3 8:00 AM - 12:00 PM Rocky Ballroom C/D Attitude Dynamics and Control - 3 8:00 AM - 12:00 PM Primrose Trajectory Design and Optimization - 5 8:00 AM - 12:00 PM Larkspur AAS Technical Committee Meeting 12:00 PM - 1:30 PM Mountain View Spacecraft GNC - 3 1:30 PM - 5:30 PM Primrose Orbital Debris and Conjunction Analysis 1:30 PM - 5:30 PM Rocky Ballroom A/B Trajectory Design and Optimization - 6 1:30 PM - 5:30 PM Larkspur Asteroid and Non Earth Orbiting Missions 1:30 PM - 5:30 PM Rocky Ballroom C/D

Thursday, August 13, 2015

Spacecraft GNC - 4 8:00 AM - 12:00 PM Blue Spruce Astrodynamics - 4 8:00 AM - 12:00 PM Juniper Room Orbital Debris Analysis and Uncertainty Propagation 8:00 AM - 12:00 PM Rocky Ballroom A/B Space Environment and Spacecraft GNC 8:00 AM - 12:00 PM Rocky Ballroom C/D

A map of Vail Cascade and the relevant meeting rooms appears on the next page.

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Updated July 31, 2015 #ASC2015

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Updated July 31, 2015 #ASC2015

SPECIAL EVENTS

EARLY BIRD RECEPTION Sunday, 9 August 4:30 – 8:30 pm, Open Bar 6:00 – 7:30 pm, Reception Location: Vail Cascade Resort & Spa (Room TBA)

Menu: The Luge Grilled Shrimp and Chorizo, Marcona Almond Romesco Seared Rare Tuna Wonton with Egg Yolk, Egg White, Mustard Cream and Chive Colorado Bison and Mozzarella Stuffed Meatballs, Fresh Basil Pesto Colorado Farmhouse Cheese Board Fire Roasted Vegetable Plate Display of Seasonal Sliced Fresh Fruits Wild Mushroom Tartlet, Mascarpone, Tomato Basil Salsa Mini Cuban Sandwiches, Roasted Pork, Ham, Pickles, Swiss, Mustard Sliced Turkey, Home Baked Miniature Rolls and Condiments Wild Mushroom Ravioli, Asparagus, Porcini Truffle Cream Sauce Cheese Tortellini, Baby Spinach, Parmesan Cheese, Chardonnay Cream Sauce Pastry Chef’s Selection of Assorted Miniature Desserts Fresh Brewed Coffee, Decaffeinated Coffee and a Selection of Gourmet Hot Tea Served With Milk, Honey and Lemon

BUFFET DINNER Tuesday, 11 August 5:00 – 9:00 pm, Open Bar 6:30 – 8:00 pm, Buffet Dinner Location Vail Cascade Resort & Spa (Room TBA)

Menu: Colorado Fresh Baked Bread with Whipped Butter High Plains Buffalo Chili, Windsor Dairy Cheddar Caramelized Onion and Mushroom Soup, Toasted Barley Field Greens, Butternut Squash, Pumpkin Seeds, Haystack Farms Chevre, Riesling Pear Vinaigrette

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Updated July 31, 2015 #ASC2015 Fingerling Potatoes, Bacon, Roasted Apple, Caramelized Onions, Blue Cheese, Mustard Dressing Pan Seared Rocky Mountain Trout, Toasted Pine Nut Beurre Blanc Pork Tenderloin, Onion Cherry Compote Grilled Vegetable Barley Risotto, Balsamic Glazed Portobello Basil Pesto, Crispy Leeks Chef’s Choice Seasonal Vegetables Smoked Cheddar Mashed Potatoes Chocolate Bourbon Bread Pudding, Apple Crumble Cake, Pecan Tartlets

Guests should indicate any dietary restrictions on their completed registrations prior to 27 July so that the caterer can be informed. All conference registrations will receive an event ticket. Guest tickets are available for $25 each on the conference registration site. Children under 5 are free.

VAIL SUMMER BLUEGRASS SERIES The Vail Summer Bluegrass Series brings national level bluegrass talent as well as local/regional acts to Vail Square at the Arrabelle Hotel in Lionshead Village. Grant Farm & Dead Winter Carpenters play on 12 August at 6 p.m. The concert is free with an option to purchase preferred seating tickets .

VAIL JAZZ FESTIVAL The Vail Jazz Festival is a 12-week program that brings the best talent in the jazz world to the ultimate summer destination in the Colorado Rockies: Vail. The Festival consists of five distinctive series that run from June – September:  Vail Jazz @ Vail Square (Thursdays, 6-8 pm, $15)  Vail Jazz @ The Market (Sundays, noon-3 pm, FREE)  Vail Jazz Club Series (Cucina, Lodge at Vail, Wednesdays, 8 pm, $30)  Vail Jazz @ Sweet Basil (Sundays, 9 pm, FREE)  All events take place in the Town of Vail, which allows guests to stay, dine, and play just a short walk from world-class jazz performances. With over 40 performances and 150 artists, join us this summer as we fill the streets of Vail with the sounds of swing, salsa, blues, Latin, bebop, the American Songbook, and more! Concerts are Sundays , Wednesdays, and Thursdays

VAIL FARMERS’ MARKET & ART SHOW Get a taste of Vail, Colorado summer with the Vail Farmers’ Market and Art Show. Colorado’s finest locally grown produce, international dishes, fresh baked goods and even Colorado wine, all ready for you to enjoy during your summer in Vail. Once you have sated your hunger, enjoy even more local creativity at the Art Show. You can find everything from beautiful clothing and jewelry to handmade home items. Held on Sundays, 10 am to 3:30 pm.

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Updated July 31, 2015 #ASC2015 CONFERENCE LOCATION

VAIL CASCADE RESORT & SPA

Vail Cascade Resort & Spa 1300 Westhaven Drive Vail, CO 81657 Telephone number for AAS reservations: 800-420-2424 http://www.vailcascade.com/

From the moment you arrive at Vail Cascade you feel the inviting warmth of a true mountain retreat. Roaring fireplaces, stimulating meeting spaces and personalized service come together to create unmatched comfort and a sense of home year-round. Vail Cascade is a true reflection of its guests - refined yet relaxed, sophisticated yet understated, upscale yet accessible. Picture-perfect for creating memorable experiences and located overlooking Gore Creek, Vail Cascade is a destination where families bond, where mind, body and spirit are balanced, and where a majestic mountain backdrop is the setting for meaningful connections among families, couples, groups and adventure-seekers alike.

Vail Cascade's ideal location and breathtaking mountain surroundings create the perfect natural playground for all-season adventure. With pleasantly warm summers and cool falls, you can enjoy hiking, biking, fishing, strolling through the Villages and soaking up sun poolside. Conveniently located at the base of Vail Mountain and along the banks of Gore Creek, Vail Cascade is 30 minutes from Eagle County Airport and less than two hours from Denver International Airport. Group arrival is 8/9/2015 and Group Departure is 8/13/2015. Government Per Diem Hotel rate ($151 per night) is guaranteed for reservations made up to 21 days prior to arrival (i.e., 7/18/2015) and is valid three days before group arrival and three days after group departure based on availability. Currently, the tax rate is 9.8%. Mention that you are with the American Astronautical Society. Daily resort fee of $27.00 per room is waived (includes shuttle service, high-speed internet, etc.),

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Updated July 31, 2015 #ASC2015 Aria Spa and Club access of $15.00 per day is waived. Cancellations must be made in advance of 48 hours of intended arrival. Complimentary internet access in guest rooms and meeting space is available to all conference attendees. Complimentary parking is included for all guests.

TRANSPORTATION INFO Vail Cascade Resort and Spa is a convenient 35 minute drive from Eagle County Regional Airport (EGE) or less than 2 hours from Denver International Airport (DEN). The Eagle County Airport, http://www.eaglecounty.us/airport/, is served by American Airlines (daily summer non-stop from Dallas/Ft. Worth, DFW) and United Express (daily from DEN) and United Airlines (Thu – Mon from Houston, IAH). The Denver International Airport, http://www.flydenver.com/, is served by most domestic and international carriers. Both airports host a variety of rental car agencies. DIRECTIONS FROM AIRPORTS From DEN - Take I-70 West. Exit 176 (main Vail). At end of ramp, enter roundabout and go to the left under the Interstate. Enter the 2nd roundabout and turn right onto South Frontage Road (toward Lionshead). Follow the frontage road signs that direct you to the ‘Cascade Village.' The resort is approximately 1.75 miles on the left. Public ground transportation can be arranged through www.coloradomountainexpress.com/vail. From Eagle County Airport - Take I-70 East for approximately 30 minutes. Exit 173 (West Vail). Enter roundabout and follow signs to South Frontage Road/Vail Village/Lionshead. Follow the frontage road signs that direct you to the ‘Cascade Village.' The resort is located one mile on the right. Public ground transportation can be arranged through www.coloradomountainexpress.com/vail or www.hmtaxi.com. Bus service is also available via Eagle County’s transit service, ECO Transit, www.eaglecounty.us/transit/. VAIL GROUND TRANSPORTATION  Shuttle from Vail Cascade Resort & Spa to Vail and Lionshead, running in a continuous loop every 20 minutes from 7 a.m. to midnight, 7 days a week  Town of Vail Buses are FREE and run regularly between the eastern end of Vail Village and the western end of Lionshead. Scheduled buses to East Vail and West Vail run frequently as well. The town's NextBus system gives you immediate real-time bus arrival information from any stop on Vail's in-town out outlying bus routes. For information on Vail's Bus Service, call 970-479-2358.  Eagle County’s transit service, ECO Transit, www.eaglecounty.us/transit/.  Private Taxi service 24 hours a day o www.hmtaxi.com, (970) 476-8294 o www.vailmpg.com, (970) 390-1235 o www.vailtaxiservice.com, (970) 401-0825  A pleasant, one-mile footpath along Gore Creek leads to Lionshead village from the resort.

ARRIVAL INFORMATION

Check-In and Checkout  Check-in: 4:00 PM  Check-out: 11:00 PM

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Updated July 31, 2015 #ASC2015 Parking Valet parking is available at a rate of $25.00 plus tax per night. Self-parking is complimentary.

HOTEL SERVICES AND AMENITIES Cascade is a sophisticated yet understated destination in itself, offering all the services and amenities you'd expect in a AAA Four-Diamond ski retreat in Vail, Colorado. In addition to an award-winning spa and health club, unforgettable dining and Vail's only ski-in/ski-out accommodations, Vail Cascade provides:  24-hour front desk and concierge services  In-room dining: 7am-9pm  Daily housekeeping services  Valet parking for hotel guests  Self-parking for hotel guests  Shuttle to Lionshead and Vail Village  Shuttle from the condominiums and private homes to the hotel  Children's amenities and activities, including Cascade KidVenture. (Sample schedules posted. KidVenture runs in the summer and winter seasons only)  Launderette  Dry cleaning  Business services

HOTEL RESTAURANTS AND LOUNGES  Atwater on Gore Creek, Vail Cascade's signature creekside restaurant, is an authentic Colorado grill offering a journey through the world of creative cuisine, handcrafted brews, customized beer flights and artisan food pairings.  Cozy and relaxed, the Fireside Bar invites you to sit by a roaring fire or tall picturesque windows while enjoying hand crafted beers, signature cocktails, wine and shared plates on our tapas-style menu. Take it all in while letting it all go with a great atmosphere, entertainment, and stunning views of Gore Creek and Vail Mountain.  For on-the-go snacks and sundries, visit the Cascade Village Market & Cafe. The Market offers a delicious assortment of pastries, sandwiches, salads, along with a wide selection of soft drinks, coffees and other beverages including beer and wine. The Cafe also provides complimentary Wi-Fi to surf the Internet, check email or print boarding passes. The Market also offers "Build Your Own Lunch" options.

HOTEL RECREATION AND LEISURE Enjoy a wide variety of intriguing on-site events, adventurous activities and family-oriented programs year- round, including:  Onsite chairlift to Vail Mountain  Two heated outdoor swimming pools and three hot tubs  Three indoor and three outdoor tennis courts  Racquetball and squash courts  Indoor volleyball and basketball courts  Vail's largest fitness and athletic training facility

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Updated July 31, 2015 #ASC2015  Award-winning Aria Spa  Gold Medal fly-fishing on Gore Creek  Walking, running or cycling the Gore Creek Trail  Multiple dining options and restaurants  Children's amenities and activities, including Cascade KidVenture. KidVenture runs in the summer and winter seasons only. Sample schedule posted.  Vail concerts, programs and special events KidVenture

It's great to be a kid at Vail Cascade! Children ages 5-12 are invited to take part in fun and exciting daily activities through our Cascade KidVenture program. Each activity is supervised by the hotel staff and designed to be both entertaining and educational. *KidVenture runs in the summer and winter seasons only. Sample schedule posted.

For more information and to make advance reservations, please contact Vail Cascade’s Recreation Department at 970.476.7400.

AREA ATTRACTIONS Vail isn’t just a fabulous ski resort; it’s a scenic wonder all year round. Hiking, fishing, rafting, golfing, biking, and dozens of summer events await those who make a trip back after the snow melts. If you’d like to see how the mountain transforms in the summer, try one of these warm-weather activities: Take a scenic gondola ride In the winter, it carries people up the mountain for skiing or riding epic powder, but you can take the Eagle Bahn gondola up to the top of Vail Mountain in summer for some truly breathtaking views and perhaps lunch. Take a trip to Adventure Ridge The summer party starts at Adventure Ridge in Vail. Get your adrenaline flowing with a zipline tour, test your strength with some rock climbing or just chill out and play some disc golf. In between activities, be sure to grab some BBQ at Talon’s right next door. There are so many things to do in Vail during the summer that we can’t even possibly begin to list them all right here. Contact your concierge desk for even more great recommendations for events, activities and general sun-soaking fun. Get on your bike and ride With scenic trails all around Vail and technical singletrack on the mountain, you can get your fill of cycling no matter what the speed. Make sure to take a guided tour to discover all the best riding. If you’re feeling speedy, hitch your bike to the gondola and they’ll haul it up the mountain so you can ride it down. Hike one of our many beautiful trails With trails ranging from a walk in the park to a trek up the mountain, you can take it easy or challenge yourself. If you want to learn a little more about the local flora and fauna, you can take a guided hike. Vail offers several different types to make sure it’s fun for the whole family. You can download a hiking guide and a summer trail map.

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Updated July 31, 2015 #ASC2015 Raft one of the rivers in the area In the summer, all that beautiful snow melts and runs into the Eagle and Colorado rivers, creating some great rapids. Come enjoy Vail's snow once again in the summer. Get in 18 holes or more With more than one golf course in Eagle County, you’ll have more than enough choices to schedule several tee times during your vacation. Choose from the Vail Golf Club, Eagle-Vail Golf Club, Beaver Creek Golf Club, Red Sky Ranch & Golf Club and Eagle Ranch Golf Club. Cast a fly in one of the great fishing spots For something a bit more meditative, those same rivers provide some fantastic fly-fishing. Vail offers casting clinics so you can improve your technique. And local guides can show you the best secret holes. The suggestions above are a partial list of the many things to do and see in Vail. For more information and suggestions visit the concierge desk. The Vail Valley Visitor’s Bureau also has a very informative website, www.visitvailvalley.com, as does Vail Mountain Resort, www.vail.com. Other attractions include  Bol (Upscale Bowling Alley w/ Food) www.bolvail.com **Reservations are required to accommodate large parties.  Cinebistro (Upscale Movie Theatre w/Food) www.cobbcinebistro.com/solaris/ **Reservations are required to accommodate large parties.  Bistro 14 (On Mountain Dining) www.vail.com/summer **Requires lift ticket-Horseback Riding w/ Lunch available  Vail Events (Events around Town) www.visitvailvalley.com/events  Vail Pass Bike Tour www.chartersports.com **Located at our property - separate entity  4 Eagle Ranch www.4eagleranch.com -provides Horseback Riding through Triple G Outfitters (970-926-1234) -provides Zip Line Adventures www.zipadventures.com ***will need transportation  Nova Guides www.novaguides.com (Jeep Tours, White Water Rafting, ATV Tours, Guided Fishing)  Golf www.eaglevailgolfclub.com **will need transportation for Eagle-Vail www.vailgolfclub.net  Botanical Gardens www.bettfordalpinegardens.org And Mountain Biking | Road Biking | Hiking & Backpacking | Rafting & Kayaking | Performing Arts & Cultural Events | Golf | Fishing & Hunting | Nature Center & Alpine Garden | Tennis | Shopping | Spas | Nightlife

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Updated July 31, 2015 #ASC2015 ADDITIONAL INFORMATION

SPEAKER ORIENTATION Authors should email a draft version of their presentations and a brief (approximately 50 words or 3 sentences) speaker’s bio to their session chairs no later than noon on Friday, August 7. Authors are allowed update their presentations with their session chairs up to 5 pm the day before their presentation. Authors are required to be in their session room 30 minutes prior to the start of their sessions. No speakers’ breakfast will be served. Authors are reminded that the deadline to upload pre-prints to the https://www.xcdsystem.com/aas/ website before August 5, 2015, 06:00 AM (Mountain Time).

VOLUNTEERS Volunteers that would like to staff the registration table may sign up at the registration table.

PRESENTATIONS Each presentation is limited to 15 minutes. An additional five minutes is allotted between presentations for audience participation and transition. Session chairs shall maintain the posted schedule to allow attendees the option of joining a parallel session. Each room is equipped with a laser pointer, an electrical outlet, and a video projector that can be driven by a computer. Presenters shall coordinate with their Session Chairs regarding the computing equipment, software, and media requirements for the session; however, each presenter is ultimately responsible for having the necessary computer and software available to drive the presentation. Microsoft PowerPoint and PDF are the most common formats. "No-Paper, No-Podium" Policy Completed manuscripts shall be electronically uploaded to the submission site before the conference, limited to 20 pages in length, and conform to the AAS conference paper format. If the completed manuscript is not contributed on time, it will not be presented at the conference. If there is no conference presentation by an author, the contributed manuscript shall be withdrawn. Each author is also acknowledges that he or she is releasing technical information to the general public and that respective papers and presentations have been cleared for public release. If any author of a paper is a US person (citizen or permanent resident), he or she acknowledges that the release of these data and content of the paper and presentation conforms to ITAR and are not on the USML. The information contained in these documents is neither classified, SBU, FOUO, nor proprietary to any sponsoring organization.

PREPRINTED MANUSCRIPTS Physical copies of preprinted manuscripts are no longer available or required for the Space Flight Mechanics Meetings or the Astrodynamics Specialist Conferences. Electronic preprints are available for download at least 72 hours before the conference at https://aas.pxi.com/registration/reg/ for registrants who use the online registration system. The hotel provides conference guests with complimentary wireless internet access in guest rooms and the conference meeting space. Registrants without an internet-capable portable computer, or those desiring traditional paper copies should download and print preprint manuscripts before arriving at the conference.

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Updated July 31, 2015 #ASC2015 CONFERENCE PROCEEDINGS All full registrants will receive a CD of the proceedings mailed to them after the conference (extra copies are available for $50 during the conference). However, the hardbound volume of Advances in the Astronautical Sciences covering this conference will be available to attendees at a reduced pre-publication cost, if ordered at the registration desk. After the conference, the hardbound proceedings will more than double in price, although authors will still receive a special 50% discount off the post-conference rate even if they delay their order until after the conference. Cost of Proceedings: Conference Rate $290 domestic ($380 international) Post-Conference Rate $600 (approx.) Authors (post-conference) $300 (approx.) Although the availability of hardcopy proceedings enhances the longevity of your work and elevates the importance of your conference contribution, please note that conference proceedings are not considered an archival publication. Authors are encouraged to submit their manuscripts after the meeting to one of the relevant journals, such as: Journal of the Astronautical Sciences Editor-in-Chief: Kathleen C. Howell School of Aeronautics and Astronautics 3233 Armstrong Hall Purdue University West Lafayette, IN 47907 (765) 494-5786 [email protected]

Journal of Guidance, Control and Dynamics Editor-in-Chief: Dr. Ping Lu, Iowa State University Manuscripts can be submitted via: www.writetrack.net/aiaa/

Journal of Spacecraft and Rockets Editor-in-Chief: Dr. Robert D. Braun, NASA Langley Research Center Manuscripts can be submitted via: www.writetrack.net/aiaa/

SATISFACTION SURVEY Registrants are highly encouraged to record their level of satisfaction and conference preferences in an anonymous survey taken throughout the time of the conference. Please return the survey form included in this program to the registration table before departing from the conference.

COMMITTEE MEETINGS Committee seating is limited to committee members and invited guests. Committee and subcommittee meetings will be held according to the schedule at the beginning of the program.

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Updated July 31, 2015 #ASC2015 CONFERENCE SCHEDULE

MONDAY, AUGUST 10, 2015

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Updated July 31, 2015 #ASC2015 Monday Session 1 Space Situational Awareness – 1

Session Chairs: Simon Julier, University College London, Islam Hussein, Applied Defense Solutions Room: Rocky Ballroom A/B

8:00 AAS The Probabilistic Admissible Region with Additional Constraints 15-577 Christopher Roscoe, Applied Defense Solutions; Islam Hussein, Applied Defense Solutions; Matthew Wilkins, Applied Defense Solutions; Paul Schumacher, Air Force Research Laboratory The admissible region is defined as the set of physically acceptable orbits (e.g., orbits with negative energies). Given additional constraints on semimajor axis, eccentricity, etc., the region is further constrained, resulting in the constrained admissible region (CAR). Based on known measurement statistics, constraints are replaced by a probabilistic representation, resulting in the probabilistic admissible region (PAR). Additional constraints are incorporated, by considering given statistics over inclination and right ascension, resulting in a four-dimensional PAR. Noting that the concepts presented are general and can be applied to any measurement scenario, the idea is illustrated using a short-arc, angles-only observation scenario.

8:20 AAS Collision Risk Metrics for Large Dispersion Clouds During the Launch COLA Gap 15-579 Alan Jenkin A method for computing collision risk metrics during the COLA gap based on kernel density estimation has been developed. The method enables the determination of a smooth analytical representation of the distribution of conjunctions from a Monte Carlo representation of the dispersion cloud. Two COLA gap metrics are computed: containment inside the dispersion cloud and probability of collision. The basic theory behind the method is first discussed. Results are then presented for sample launch cases.

8:40 AAS Volumetric Encounter Analysis Enhancements 15-581 Salvatore Alfano, Center for Space Standards and Innovation; Daniel Oltrogge, Center for Space Standards and Innovation (CSSI) We present several enhancements to our original approaches for multi-year encounter screening of any pair of satellites. In our previous work, a spherical encounter volume is moved along the second satellite’s orbit to determine encounter probability while also estimating the average number of encounters over a given time span. Our first enhancement replaces the moving sphere with a moving ellipsoid of arbitrary orientation to emulate current conjunction screening procedures for some operators. Another enhancement is to allow public use of the original encounter rate method through a non-subscriber website Graphical User Interface, limited at this time to LEO

9:00 AAS Track-to-Track Data Association Using Mutual Information 15-583 Islam Hussein, Applied Defense Solutions; Christopher Roscoe, Applied Defense Solutions; Matthew Wilkins, Applied Defense Solutions; Paul Schumacher, Air Force Research Laboratory There are three primary types of data association of interest in space surveillance: the observation- to-track association (OTTA) problem, the track-to-track association (TTTA) problem, and the observation-to-observation association (OTOA) problem. In this paper, we build on recent work to further investigate the use of mutual information to solve the TTTA problem, in which we have multiple tracks at different time instances from one or more sensors and wish to determine whether any of the tracks belong to the same resident space object (RSO). We will demonstrate the main

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Updated July 31, 2015 #ASC2015 result in simulation for LEO, MEO, GTO, and GEO orbital regimes.

9:20 AAS A Correctness Ratio Metric for Assessing Data Association Methods in Space 15-673 Surveillance Joshua Horwood, Numerica Corporation; Jeffrey Aristoff, Numerica Corporation; David Beach, Numerica Corporation; Alex Ferris, Numerica Corporation; Alex Mont, Numerica Corporation; Navraj Singh, Numerica Corporation; Aubrey Poore, Numerica Corporation This paper describes a metric for assessing the performance of data association methods used in space surveillance tracking systems that facilitates regression testing, benchmark trade studies, and comparisons between the many different paradigms for data association brought forth by the community. The proposed correctness ratio metric gives a macro perspective on how a tracking system is performing, provides an honest assessment of performance since it penalizes both for incorrectly associated observations (cross-tags) as well as for missing observations, and streamlines the communication of results and performance to decision makers.

9:40 Break

10:00 AAS Application of Probability Transformation Mappings to the Admissible Region 15-733 Method Johnny Worthy; Marcus Holzinger, Georgia Institute of Technology This paper presents work showing how the probability distribution function of an admissible region can be transformed into different state spaces. Using a mathematical derivation, the general probability transformation theory is applied to the admissible region problem. This analysis imposes that the transformation mapping must be a one-to-one and onto mapping and thus must preserve probability across the transformation. This condition implies that a uniform admissible region is preserved independent of the state space it is transformed to.

10:20 AAS BOUNDING COLLISION PROBABILITY UPDATES 15-571 W. Todd Cerven, The Aerospace Corporation Over the last couple decades, the probability of collision (Pc) has been established as the dominant metric for evaluating satellite close approaches. However, the use of Pc by decision-makers has been limited due at least partially to its non-intuitive often wild variations between catalog updates. It simply does not show the same consistency that relative miss geometry updates show relative to predicted uncertainties. This paper presents a method for predictively computing probabilities and confidence bounds on how the Pc will change with an update.

10:40 AAS Multiple Frame Assignment Space Tracker (MFAST): Results on UCT Processing 15-675 Jeffrey Aristoff, Numerica Corporation; David Beach, Numerica Corporation; Alex Ferris, Numerica Corporation; Joshua Horwood, Numerica Corporation; Alex Mont, Numerica Corporation; Navraj Singh, Numerica Corporation; Aubrey Poore, Numerica Corporation Numerica's Multiple Frame Assignment Space Tracker (MFAST) is a multi-sensor multi-regime space object tracking system that is presently undergoing transition to an operational environment to support improved uncorrelated track (UCT) processing. This paper communicates recent results from MFAST that were obtained by processing real-world historical radar and optical data from the Space Surveillance Network (SSN) in a "UCT processing mode." The results demonstrate that MFAST generally achieves a correctness ratio of 95% or higher, with no cross-tags, and is able to process the data on a consumer-grade laptop computer in real-time or faster.

Page 16 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 11:00 AAS An Upper Bound on Orbital Debris Collision Probability When Only One Object has 15-717 Position Uncertainty Information Joseph Frisbee, SGT (NASA/JSC) Upper bounds on high speed satellite collision probability, Pc, have been investigated. Previous methods assume a position error covariance matrix is available for each object. The two matrices being combined into a relative error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum PC. If error covariance information for only one of the objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain a useful upper bound to the Pc.

11:20 AAS Realistic Covariance Generation in the Presence of Maneuvers 15-725 Travis Lechtenberg, SpaceNav LLC; Joshua Wysack, SpaceNav; Syed Hasan, Honeywell Technologies; John Nidhiry, ASRC Aerospace Corporation; William Guit Operational collision threat characterization is now an essential component of space mission operations. As the size of the space object catalog increases, more sophisticated collision threat characterization and collision avoidance strategies must be implemented. In order to accurately characterize the collision risk, a realistic covariance must be used when computing the collision probability. In order to generate realistic covariance, expected maneuver performance must be incorporated while modelling the spacecraft’s predicted state uncertainty. This paper describes an approach for generating realistic predictive covariance for NASA’s Earth Science Mission Operations (ESMO) satellite fleet.

11:40 AAS Multi-Static Radar for Space Situation Awareness 15-763 Simon Julier, University College London; John Crassidis, University at Buffalo, State University of New York; Hugh Griffiths Space Situational Awareness (SSA) is often developed using high accuracy optical or radar systems. However, these can be difficult and expensive to maintain. An alternative is to use signals of opportunity from systems not explicitly designed for SSA. The measurements from such systems are often be both noisy and highly nonlinear. In this paper, we explore the use of bi-static systems for SSA. We examine a case study which considers a transmitter system in France and a receiver in the UK. We explore the formulation of the nonlinear observation model and explore several different formulations of nonlinear estimators.

Page 17 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Monday Session 2 Astrodynamics - 1

Session Chairs: Ossama Abdelkhalik, Michigan Tech., Felix Hoots, The Aerospace Corporation Room: Rocky Ballroom C/D

8:00 AAS Performance of variable step numerical integration across eclipse boundary crossings 15-506 for HAMR objects Andre Horstmann, Institute for Aerospace Systems; Vitali Braun; Heiner Klinkrad, TU Braunschweig The numerical integration process across eclipse boundaries will experience a rapid change in lighting condition, which may introduce large numerical errors due to the rapid gain or loss of acceleration due to the solar radiation pressure. A typical behavior of variable-step multi-step integrators is the strong reduction of step size in the region of these shadow crossing. By adapting a correction algorithm for a fixed step integrator to a variable step integrator, it allows to cross the shadow crossing without the need of a very small step or even an integrator restart. Consequently, the overall performance of the integrator was increased by 1% to 5%.

8:20 AAS Semi-analytical spacecraft dynamics around planetary moons 15-511 Josué Cardoso dos Santos, Universidade Estadual Paulista (UNESP); Jean Paulo S. Carvalho, UNIFESP - Instituto de Ciéncia e Tecnologia; Rodolpho Moraes, UNIFESP; Antonio Fernando Prado Several missions that proposes to explore systems of planetary moons will require low-altitude, high-inclined orbits for gravity and surface mapping. In this context, this work aims to perform a search for these orbits considering gravitational disturbances on a spacecraft's orbit around different planetary moons. An analytical model for the third-body perturbation is developed considering it in an eccentric-inclined orbit. The non-sphericity of some planetary moons is also considered. The dynamic of these orbits is explored by numerical simulations. The results satisfied the requirements for missions and complement the analytical studies found in the literature.

8:40 AAS East-West GEO Satellite Station-keeping with Degraded Thruster Response 15-512 Stoian Borissov, Texas A&M University Higher harmonic terms of Earth's gravitational potential slowly modify the nominal longitude of GEO satellites while the third-body presence (Moon and Sun) mainly affects its latitude. For this reason GEO satellites periodically need to perform station-keeping maneuvers, namely, East-West and North-South to compensate longitudinaland latitudinal variations, respectively. During the operational lifetime of GEO satellites, the thrusters' response to perform these maneuvers slowly departs from the optimal nominal impulsive behavior. This paper addresses the practical problem of how to perform reliable East-West station-keeping maneuvers when thruster response is degraded. The corrections are particularly important near the end of lifetime of GEO

9:00 AAS Trajectory and State Transition Matrix Analytic Continuation Algorithms 15-516 James Turner, Khalifa University, Abu Dhabi; Abdullah Alnaqeb, Khalifa University, Abu Dhabi; Ahmad Bani Younes, Khalifa University, Abu Dhabi Series-based analytic continuation models have rcently been shown to provide highly efficient and accurate trajectory propagation algorithms for two-body applications. Taylor expansion models are enabled by introducing two nonlniear variable, where the resulting vector nth order time derivative models are gneerated by Leibnitz product rule. The prosition and velocity vectors are propagated by

Page 18 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 summing Taylor series models. This work addresses the algorithm extensions required for simltaneously generating the trajetory and state transition matrix solutions. Both first and second order state transition matrix calculatins are tested. Numerical examles are presented that demonstrate the accuracy and effectiveness of the new series algorithm.

9:20 AAS Optimal Formation Design of a Miniaturized Distributed Occulter/Telescope in Earth 15-799 Orbit Adam Koenig, Space Rendezvous Laboratory, Stanford University; Simone D'Amico, Stanford Space Rendezvous Laboratory; Bruce Macintosh, Department of Physics This paper presents a novel design methodology for the absolute and relative orbits of a miniaturized distributed occulter/telescope (DOT) in earth orbit. Compared to large-scale missions, DOTs based on micro- and nano-satellites in earth orbit reduce estimated costs by orders of magnitude, but require greater instrument integration time in an environment with larger relative accelerations. It follows that the delta-v cost associated with formation keeping during observations must be minimized. The formation design strategy presented in this work optimizes the delta-v cost of observations by allowing the spacecraft to freely drift along the observation axis.

9:40 Break

10:00 AAS An Analytic Perturbed Lambert Algorithm for Short and Long Durations 15-538 Gim Der, DerAstrodynamics This paper presents an analytic perturbed multi-rev Lambert algorithm for any duration using a targeting technique with analytic perturbed state transition matrices. Since state transition matrices are commonly used in linear motion, it is intuitive not to use state transition matrices for long duration. When targeting by one step for the whole long duration is not possible, the given long duration can be divided into multiple small steps. As long as the perturbed state transition matrices can provide accurate targeting solutions with smaller time steps, an analytic perturbed multi-rev Lambert algorithm for long durations can be developed.

10:20 AAS Hybrid methods around the critical inclination 15-540 Juan Félix San-Juan, University of LA Rioja; Montserrat SanMartin; Ivan Perez In this work we apply a new approach, hybrid perturbation theory, to the problem of orbit propagation near the critical inclination. The critical inclination is a singular value which appears in both the direct and inverse transformation of the elimination of the perigee when the zonal harmonic $J_2$ of the geopotential is considered, thus preventing its application. We consider four different hybrid orbit propagators based on a closed-form second-order Brouwer-like analytical theory of the main problem, with different orders of approximation in $J_2$, complemented with an additive Holt-Winters method, and analyze their behavior near the critical inclination.

10:40 AAS Analytical approximations to the generalization of the Kepler Equation 15-541 Juan Félix San-Juan, University of LA Rioja; Rosario Gomez; Denis Hautesserres, Centre National d'`Etudes Spatiales (CNES) The generalized Kepler equation is a transcendental non-linear equation which appears in the zonal problem of the artificial satellite theory when the Krylov-Bogoliubov-Mitropolsky method is applied. In this work, the Lie-Deprit method is used to apply the Lagrange inversion theorem in order to solve the generalized Kepler equation. For small eccentricities, this analytical approximated solution yields similarly accurate results to numerical methods. Finally, for the rest of eccentricities, we discuss the applicability of this approximation as initial guess in the numerical

Page 19 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 method used to solve the generalized Kepler equation.

11:00 AAS AN INTRUSIVE APPROACH TO UNCERTAINTY PROPAGATION IN ORBITAL 15-544 MECHANICS BASED ON TCHEBICHEFF POLYNOMIAL ALGEBRA Massimiliano Vasile, University of Strathclyde; Annalisa Riccardi, University of Strathclyde; Chiara Tardioli, Strathclyde University The paper presents an intrusive approach to propagate uncertainty in orbital mechanics. The approach is based on an expansion of the uncertain quantities in Tchebicheff series and a propagation through the dynamics using a generalised polynomial algebra. Tchebicheff series expansions offer a fast uniform convergence with relaxed continuity and smoothness requirements. The paper details the proposed approach and illustrates its applicability through a set of test cases considering both parameter and model uncertainties. This novel intrusive technique is then compared against its non-intrusive counterpart in terms of approximation accuracy and computational cost.

11:20 AAS Design and Applications of Solar Sail Periodic Orbits in the Non-Autonomous Earth- 15-626 Moon System Jeannette Heiligers, Advanced Space Concepts Laboratory, University of Strathclyde; Malcolm Macdonald, University of Strathclyde; Jeff Parker, University of Colorado Solar sailing has been demonstrated to enable a wide range of applications in the Sun-Earth system. This paper extends these applications by finding new families of solar sail periodic orbits in the non- autonomous Earth-Moon system. Through a differential correction scheme and suitable in-plane and out-of-plane steering laws, solar sail orbits are found that are periodic with the Sun’s motion around the Earth-Moon system. Found orbits include those that bifurcate from the natural Lyapunov, halo and eight-shaped orbit families at the L1 and L2 points and show potential for high-latitude Earth observations, lunar South Pole coverage and lunar far-side communications.

11:40 AAS Dynamical Evolution about Asteroids with High Fidelity Gravity Field and 15-637 Perturbations Modeling Andrea Colagrossi, Politecnico di Milano; Fabio Ferrari, Politecnico di Milano; Michèle Lavagna, Politecnico di Milano; Kathleen Howell, Purdue University The paper presents a model of the dynamical field in the vicinity of an irregular celestial body, built through accurate gravity field modeling and perturbations evaluation. The gravitational attraction of an irregular object has been modeled with a constant density polyhedron or an ensemble of point masses. The accurate shape representation is used to compute the contribution of the relevant perturbing effects, including both gravitational and non-gravitational (YORP, SRP, internal dissipation of energy) terms. The high fidelity model is used to compute trajectories near these bodies. The different perturbations are compared and their influence on the resulting dynamics is studied.

Page 20 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Monday Session 3 Attitude Dynamics and Control - 1

Session Chairs: Kyle DeMars, Missouri University of S&T, Maruthi Akella, The University of Texas at Austin Room: Primrose

8:00 AAS Undamped Passive Attitude Stabilization and Orbit Management of a 3U CubeSat 15-502 with Drag Sails Siddharth Kedare, Carleton University; Steve Ulrich, Carleton University The effectiveness of drag sails on maintaining a ram-facing orientation for a 3U CubeSat in Equatorial Low Earth Orbit is examined through computational modeling of the spacecraft dynamics. The influences of varying drag sail area and the satellite inertia tensor on the aerostabilization characteristics and orbit of the spacecraft are investigated. In addition, the capability of a commercially available attitude control system to slew the spacecraft into a low-drag orientation to extend orbital lifetime is evaluated.

8:20 AAS Influence analysis of the impacts and frictions of the joints of the vibration isolation 15-509 platform for control moment gyroscope Zixi Guo, Beijing institute of technology; Yao Zhang; Jingrui Zhang; Xin Guan; Liang Tang Isolation struts and vibration isolation platforms are commonly used in the Earth observation spacecrafts for high stability attitude control. In this paper, the author would focus on the impacts and frictions of the clearances of the spherical hinges and universal joints of these isolation struts. To analysis characteristics of the impacts and frictions, a dynamic model considering the spherical hinges and universal joints of the isolation struts was built, the pattern of the impacts are analyzed, and the kinematics analysis of the spherical hinges and universal joints are done.

8:40 AAS A Neural Network Approach to Fault Detection in Spacecraft Attitude Determination 15-525 and Control Systems John Schreiner; Rees Fullmer, Utah State University This paper proposes a neural network-based method of fault detection in spacecraft attitude determination and control systems (ADCS). The proposed method works by deploying a trained neural network to analyze a set of residuals that is defined based on available ADCS telemetry. A series of neural networks were trained with simulated telemetry using various backpropagation algorithms, and the results of each were analyzed to determine accuracy with respect to detecting and isolating faults at the system, subsystem, and component level.

9:00 AAS FRACTIONAL ORDER CAYLEY TRANSFORMS FOR DUAL QUATERNIONS 15-549 BASED POSE REPRESENTATION Daniel Condurache, Technical University of Iasi; Adrian Burlacu, Techical University of Iasi This main goal of this research is the development of a new pose parameterization technique based on fractional order Cayley transforms for dual quaternions. Our study is based on the properties of maps that link dual vectors with unitary dual quaternions. For the first time a complete representation framework is constructed, embedding multiple of the reported attitude parameterization Cayley maps and extending them towards pose parameterization.The novelty of our methods over existing solutions is discussed and the main advantages are revealed.

Page 21 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 9:20 AAS SPACECRAFT ATTITUDE TRACKING CONTROL BASED ON DIFFERENTIAL 15-558 GEOMETRY THEORY Jianjun Luo; Zeyang Yin; Jianping Yuan This paper presents a novel methodology to solve the attitude tracking control problem for a spacecraft system with external disturbances and parameters uncertainties. For spacecraft attitude tracking error equations, exact linearization is realized through state feedback based on differential geometry theory.The linearized system is controlled by means of Active Disturbance Rejection Control, which is effective in external disturbances rejection. In order to solve the problem of parameter uncertainties, this approach is developed using Improved Particle Swarm Optimization algorithm to realize on- line parameters identification. Numerical simulations are finally given to demonstrate the performance of the methodology.

9:40 Break

10:00 AAS LYAPUNOV BASED ATTITUDE CONSTRAINED CONTROL OF A 15-601 SPACECRAFT Monimoy Bujarbaruah, Indian Institute of Technology, Bombay; Srikant Sukumar, Indian Institute of Technology Bombay The article deals with the problem of imposing attitude constraints during trajectory tracking for a spacecraft. A Lyapunov function based approach is utilized to develop a novel nonlinear backstepping controller for implementation of the imposed attitude constraints, while guaranteeing reference attitude tracking. The result combines a static optimization and a Lyapunov funcion based approach to ensure that initial conditions starting within the attitude constraint boundary, stay within the same for all time.

10:20 AAS Analysis of the Gauss-Bingham Distribution for Attitude Uncertainty Propagation 15-605 Jacob Darling, Missouri University of Science and Technology; Kyle DeMars, Missouri University of Science and Technology Attitude uncertainty quantification typically requires a small angle assumption, and thus an inherent small uncertainty assumption, to quantify the attitude uncertainty. This small angle assumption can be obviated by employing the Bingham distribution to represent the attitude uncertainty using quaternions. Moreover, an extension to the Bingham distribution, termed the Gauss-Bingham distribution, can be used to represent correlated quaternion and angular velocity uncertainty to enable attitude uncertainty propagation. Uncertainty propagation using the Gauss-Bingham distribution is compared to more conventional methods which require the small angle assumption by mapping the propagated uncertainty to a common attitude parameterization through transformation of variables theory.

10:40 AAS APPLICATION OF THE REGULARIZED PARTICLE FILTER FOR ATTITUDE 15-614 DETERMINATION USING REAL MEASUREMENTS OF CBERS-2 SATELLITE William Reis Silva, National Institute for Space Research (INPE); Hélio Koiti Kuga, Instituto Nacional de Pesquisas Espaciais; Maria Zanardi, Federal University of ABC (UFABC) In this work, the attitude determination and the gyros drift estimation using the Regularized Particle Filter (RPF) with Roughening for nonlinear systems will be described. The application uses the real measurement data for orbit and attitude of the CBERS-2 (China Brazil Earth Resources Satellite) that are compared with the simulated measurements, with low and high sampling rate, emulating the real conditions of CBERS-2 satellite.The results show that one can reach accuracies in attitude

Page 22 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 determination within the prescribed requirements using the Regularized Particle Filter, although at extra computational cost when compared to conventional nonlinear filter approaches like Extende Kalman Filter.

11:00 AAS Velocity-free attitude stabilization with measurement errors 15-685 Sungpil Yang, The University of Texas at Austin; Frederic Mazenc; Maruthi Akella, The University of Texas at Austin This paper addresses the rigid-body attitude stabilization problem with the quaternion representation. Specifically, a passivity-based output feedback controller is considered in the presence of measurement errors. With the perfect measurements, it is known that the body orientation can be stabilized using a first-order stable filter. Once the filter is driven by a noise- corrupted quaternion and the controller employs both the imperfect attitude measurements and the output of the filter, the stability properties of the system are weakened. Using the strictification technique, a strict Lyapunov-like function is built and certain conditions ensuring boundedness of the closed-loop trajectories are established.

11:20 AAS Nonlinear Tracking Attitude Control of Spacecraft On Time Dependent Trajectories 15-704 Ozan Tekinalp, METU Aerospace Engineering Dept.; Mohammad Mehdi Gomroki, METU Aerospace Engineering Dept.; Omer Atas, Middle East Technical University, Aerospace Engineering Department The spacecraft attitude control is carried out using the to-go quaternion. A derivative of the to-go quaternion is derived where the desired attitude is a time dependent function. Based on this new attitude formulation, a proper state dependent coefficient matrix expression is obtained. Then the nonlinear tracking attitude control is realized using the state dependent Riccati equation method. The simulation results are given and discussed.

11:40 AAS Ergodicity of the Euler-Poinsot Problem 15-781 Andrew Sinclair, Auburn University; John Hurtado, Texas A&M University This paper illustrates the possibility of ergodic motion in the Euler-Poinsot problem. In the traditional polhode/herpolhode interpretation, ergodicity corresponds to a specific location on the polhode never repeating points of contact on the herpolhode. In the case of axisymmetric bodies, this condition corresponds to the commensurability of the radii of the circular polhode and herpolhode. For general asymmetric bodies, the condition is difficult to investigate. The alternative motion-constant interpretation provides a more direct condition, with ergodicity being related to the commensurability of the periods of the angular-momentum vector and Poinsot’s chronometric vector.

Page 23 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Monday Session 4 Trajectory Design and Optimization - 1

Session Chairs: Kohei Fujimoto, Utah State University, David B. Spencer, Penn State Room: Larkspur

8:00 AAS Trajectory Designs for a Mars Hybrid Transportation Architecture 15-522 Min Qu, AMA NASA’s Evolvable Mars Campaign (EMC) team is developing a reusable hybrid transportation architecture in which both chemical and electric propulsion systems are used to send crew and cargo to various Mars destinations. By combining chemical and electrical propulsions and applying each where it is the most effective, the hybrid architecture enables a series of Mars trajectories that are more fuel-efficient than an all chemical architecture without significant increases in flight times. This paper documents the methods and techniques used for the trajectory designs of the architecture, some of which have shown to provide propellant or delta-V savings over traditional methods.

8:20 AAS Multi-Objective Hybrid Optimal Control for Multiple-Flyby Interplanetary Mission 15-523 Design using Chemical Propulsion Jacob Englander, NASA Goddard Space Flight Center; Matthew Vavrina, a.i. solutions Preliminary design of high-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys and the bodies at which those flybys are performed. For some missions, such as surveys of small bodies, the mission designer also contributes to target selection. In addition, real-valued decision variables, such as launch epoch, flight times, maneuver and flyby epochs, and flyby altitudes must be chosen. This work presents an automated solution to the high-thrust mission design problem by posing it as a multiobjective hybrid optimal control problem.

8:40 AAS EARTH-MARS TRANSFERS THROUGH MOON DISTANT RETROGRADE 15-588 ORBIT Davide Conte, The Pennsylvania State University; Koki Ho, University of Illinois, Urbana- Champaign; Marilena Di Carlo, University of Strathclyde; David Spencer, The Pennsylvania State University; Massimiliano Vasile, University of Strathclyde This paper focuses on trajectory design which is relevant for missions that would follow NASA's Asteroid Redirect Mission (ARM) to further explore and utilize asteroids and eventually human Mars exploration. Assuming that a refueling “gas station” is present at a given DRO, we analyze ways of departing from the Earth to Mars via that DRO. Porkchop plots depicting the required C3 at launch, v_infinity at arrival, Time of Flight (TOF), and total delta-V for various DRO departure and Mars arrival dates are created.

9:00 AAS MANY-REVOLUTION LOW-THRUST ORBIT TRANSFER COMPUTATION 15-590 USING EQUINOCTIAL Q-LAW INCLUDING J2 AND ECLIPSE EFFECTS Jose Manuel Sanchez Perez, ESA; Gábor Varga, European Space Agency Mission designers addressing the computation of low-thrust many-revolution transfers need versatile and reliable tools for solving the problem with efficient computational times. This paper proposes a Lyapunov feedback control method, Q-law by Petropoulos, with algorithm modifications to accommodate for the singularities in the original equations and to include the most relevant perturbations, such as the J2 perturbation and the effect of coasting during eclipse periods. The optimization of the control-law parameters via a multi-objective evolutionary algorithm (NSGA-II) improves the results significantly and permits to easily compute the minimum time transfer and a

Page 24 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 well-spread Pareto front, trading transfer time versus propellant.

9:20 AAS OPTIMIZING THE SOLAR ORBITER 2018 OCTOBER TRAJECTORY TO 15-591 INCREASE THE DATA RETURN Jose Manuel Sanchez Perez, ESA; Waldemar Martens, ESA / ESOC; Yves Langevin, IAS The ESA-NASA Solar Orbiter mission has recently delayed the launch date to October 2018. Further analysis of the planned trajectory has revealed an inferior data downlink capability than all previous trajectories regarded for the mission. Being the data bit rate inversely proportional to the squared Earth distance, it becomes critical to phase the science orbit such that several of the aphelia are close to the Earth providing extended periods with maximum downlink capability. This paper describes alternative trajectories providing a significant improvement of the data return overall and reaching a factor over 2 during the core science period.

9:40 Break

10:00 AAS Analytical low-thrust transfer design based on velocity hodograph 15-594 David Gondelach, University of Southampton; Ron Noomen, Delft University of Technology Shape-based models are used to represent approximations of low-thrust transfer orbits between celestial bodies. Here, we propose a new model, which is based on simple analytical base functions that together represent the velocity of the spacecraft. After integration, these base functions also yield analytical expressions for distances traveled. As a result, both the velocity and the trajectory of a transfer can be modeled analytically with a series of such base functions, which can be chosen and scaled at will. The technique is tested on a number of cases: transfers to Mars, asteroid 1989ML, comet Temple 1 and Mercury.

10:20 AAS Periapsis Poincaré Maps for Preliminary Trajectory Design in Planet-Moon Systems 15-600 Diane Davis, a.i. solutions, Inc.; Sean Phillips; Brian McCarthy Spaceflight in regimes where multiple gravitational bodies simultaneously affect a spacecraft trajectory is increasingly common. However, preliminary trajectory design in the presence of two or more large bodies is challenging due to the complicated nature of such orbits. In this investigation, periapsis Poincaré maps are employed to characterize the design space in the vicinity of planetary moons. Using an interactive JavaFX visualization tool, initial conditions are easily selected to satisfy a variety of mission applications in multi-body systems. In particular, long-term orbits around the smaller primary in planet-moon systems are considered.

10:40 AAS Unscented Optimization 15-607 Isaac M. Ross; Ronald Proulx; Mark Karpenko, Naval Postgraduate School Unscented optimization combines the concept of the unscented transform with standard optimization to produce a new approach for addressing uncertainties. Every practical optimization problem can be unscented; hence, the concepts introduced here can be applied to a wide range of problems in astrodynamics. If unscented optimization techniques are used during the early phases of a mission design, it can provide quick results on estimates of risk, reliability and associated costs so that “optimal missions” do not suffer from overruns due to requirements creep. We show how it is possible to reduce risk from 50% all the way down to 1%.

11:00 AAS High-Fidelity Low-thrust SEP Trajectories From Earth to Jupiter Capture 15-609 Sean Patrick; Alfred Lynam, West Virginia University

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Updated July 31, 2015 #ASC2015 Triple Satellite aided capture sequences use gravity-assists at three of Jupiter’s four massive Galilean moons to reduce the ΔV required to enter into Jupiter orbit. In this paper, a solar electric propulsion (SEP), low-thrust trajectory from Earth to Jupiter capture is optimized using JPL’s high- fidelity Mystic software. A Mars gravity assist is used to augment the heliocentric trajectory. Gravity assist flybys of Callisto, Ganymede, and Io are used to capture into Jupiter Orbit. With a 100-day period, an orbit that is shorter than most capture orbits, the main satellite tour of the Jupiter mission could begin sooner using this strategy.

11:20 AAS Trajectory Design of the Time Capsule To Mars Student Mission 15-658 Jonathan Aziz, University of Colorado Boulder; Stijn De Smet, University of Colorado; Jeff Parker, University of Colorado; Sean Napier, University of Colorado Boulder Time Capsule to Mars (TC2M) is a student-led mission that will deliver a time capsule containing digital media to Mars. Mission architecture considers the deployment of a 6U CubeSat as a secondary launch payload from geosynchronous orbit. The low-thrust ion Electrospray Propulsion System for CubeSats (iEPS) enables TC2M to escape Earth orbit and reach the Martian atmosphere on its own propellant. This work highlights the TC2M trajectory design and optimization for a target launch in 2020. A trade study of mission event dates and propulsion system performance is presented with consideration of a Venus gravity assist and a missed-thrust analysis.

11:40 AAS Evolutionary Optimization of a Rendezvous Trajectory for a Satellite Formation with 15-668 a Space Debris Hazard Darren Hitt, University of Vermont; David Hinckley Orbital debris continues to pose a serious threat to space assets in low Earth orbit (LEO). In response, active debris mitigation approaches have been proposed - including the coordinated activities of satellite formations. A critical first step is the determination of the optimal trajectory for the satellite formation to rendezvous with the debris subject to prescribed mission constraints. Motivated by this scenario, differential evolution is used to optimize multi-satellite rendezvous trajectory problems with topological constraints. Initial impulsive maneuvers are sought for a group of five satellites that lead to debris rendezvous in the form of a trigonal bipyramid.

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Updated July 31, 2015 #ASC2015 Monday Session 5 Spacecraft GNC 1

Session Chairs: Minh Q. Phan, Dartmouth College, Mark Karpenko, Naval Postgraduate School Room: Primrose

13:30 AAS DYNAMIC RECURSIVE APPROACH TO MULTIBODY SYSTEMS WITH 15-589 DOUBLE-GIMBAL VARIABLE-SPEED CONTROL MOMENT GYROSCOPES Shiyuan Jia; Yinghong Jia; Shijie Xu This paper presents a comprehensive recursive formulation of dynamic equations for multibody systems with double-gimbal variable-speed control moment gyroscopes (DGVs). It permits any rigid or flexible body with DGVs in a generic configuration as actuators. The detailed dynamics of the actuators is taken into consideration. Motion equations for a single body with n-DGVs are derived by Kane’s method. The recursive algorithm is obtained through analyzing the kinematics and dynamics between two adjacent bodies. The recursive algorithm of rigid-rigid and flexible- flexible connections is written in a unified form by transformation matrix. The recursive dynamics is verified by numerical simulations.

13:50 AAS GENETIC ALGORITHM FOR THE OPTIMAL PLACEMENT OF SENSORS AND 15-703 ACTUATORS FOR GYROELASTIC BODY Shiyuan Jia; Yinghong Jia; Shijie Xu This paper presents the optimal placement of sensors and actuators for gyroelastic body based on genetic algorithm. First, the vibration control model of the gyroelastic body is introduced; Based on the concept of the controllability and the observability of the controlled system, the objective functions are proposed aiming at the maximization of the controllability and the observability of the controlled modes. For a comprehensive optimization of the number of actuators and sensors and their locations, genetic algorithm is introduced. Numerical examples are presented, which shows that the proposed method is feasible.

14:10 AAS MULTIBODY DYNAMICS DRIVING GNC AND SYSTEM DESIGN IN 15-530 TETHERED NETS FOR ACTIVE DEBRIS REMOVAL Riccardo Benvenuto, Politecnico di Milano - DAER; Samuele Salvi, Politecnico di Milano; Michèle Lavagna, Politecnico di Milano Debris removal in Earth orbits is an urgent issue to be faced for space exploitation durability. Among different techniques, tethered-nets present appealing benefits and some open points to fix. Former and latter are discussed in the paper, supported by the exploitation of a multibody dynamics tool. Critical phases as impact and wrapping are analysed to address the tethered-stack controllability. The critical modes prevention by means of a closed-loop control synthesis is shown and the connection between flexible dynamics and capture system design is highlighted, giving engineering answers to most challenging open points to lead to a ready to flight solution.

14:30 AAS Fast and Efficient Sail-Assisted Deorbiting Strategy for LEO Satellites in Orbits 15-595 Higher Than 700 km Sergey Trofimov, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences; Mikhail Ovchinnikov, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences A novel efficient deorbiting strategy for LEO satellites is proposed. The attitude motion of a spacecraft with a flat solar sail resembling the Likins-Pringle hyperbolic relative equilibrium can be stabilized by a damping control torque an order of magnitude smaller than the three environmental

Page 27 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 torques. As a result, there appears a secular decrease in the semimajor axis induced by the solar pressure. For a series of 900 km sun-synchronous orbits with different mean local times of ascending node, numerical simulation of coupled orbit-attitude dynamics reveals a dramatic reduction in deorbit time as compared with the aerostabilized sail deorbiting mode.

14:50 AAS SOLAR SAIL SPACECRAFT BOOM VIBRATION DURING DEPLOYMENT AND 15-797 DAMPING MECHANISMS Ozan Tekinalp, METU Aerospace Engineering Dept.; Omer Atas, Middle East Technical University, Aerospace Engineering Department; Ertan Demiral, Middle East Technical University Boom deployment vibration analysis is presented for a solar sail 3U Cubesat. The damping mechanism of the boom vibration, using shape memory alloys is examined. It is found that shape memory alloys do not reduce vibration below a certain level. Vibration damping via inherent friction in the deployment system is also considered. The analysis showed that the vibration may be completely damped due to the inherent friction in the deployment system.

15:10 Break

15:30 AAS Agility Envelopes for Reaction-Wheel Spacecraft 15-620 Mark Karpenko, Naval Postgraduate School; Jeffery King, U.S. Naval Academy This paper presents the concept of the agility envelope as a means to identify “hidden agility” that can be exploited to maximize the slew performance of a conventional attitude control system. This hidden agility can significantly reduce slew times or relax slew torque requirements in new spacecraft designs. The agility envelope for a reaction wheel attitude control system is an n- dimensional hypercube projected into three-dimensional space. Therefore, simple expressions exist for determining the maximal agility envelope. These expressions are developed and used to find the reaction wheel skew angles that maximize agility for a given spacecraft configuration.

15:50 AAS Superspace and Subspace Identification of Bilinear Models by Discrete-Level Inputs 15-559 Minh Phan, Dartmouth College; Francesco Vicario, Philips Research North America; Richard Longman, Columbia University; Raimondo Betti, Columbia University When excited by an input consisting of a number of discrete levels, a bilinear system becomes a linear time-varying system whose dynamics switches from one linear subsystem to another depending on the input level. This paper describes an identification method that uses the concept of a superstate of a linear switching system as a superstate of the bilinear system. In a superspace method, these superstates are used directly to identify a bilinear system model. In a subspace method, two or more superstate representations are intersected to find a reduced dimension subspace prior to identification of a bilinear model.

16:10 AAS Mass, Stiffness, and Damping Matrices from an Identified State-Space Model By 15-562 Sylvester Equations Dong-Huei Tseng; Minh Phan, Dartmouth College; Richard Longman, Columbia University This paper presents a method to identify the mass, stiffness, and damping matrices of a dynamical system from an identified state-space model. The mass, stiffness, and damping matrices are solved from three independent Sylvester equations. Position, velocity, acceleration measurements or any combination can be used. The proposed solution represents a major improvement over a Kronecker product based solution that is computationally prohibitive for large dimensional problems. The

Page 28 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Observer/Kalman filter identification method (OKID) is used as a pre-processing step for optimal identification of a state-space model prior to the recovery of the mass, stiffness, and damping matrices.

16:30 AAS Modified Polynomial Guidance Law for Lunar Landing 15-715 Donghun Lee In this paper, a modified polynomial guidance law is studied for a powered terminal descent of a lunar lander. Also, Zero-Effort-Miss/Zero-Effort-Velocity (ZEM/ZEV) and modified Apollo guidance laws including off-line trajectory op-timization approach are analyzed. Because each guidance law has advantages and drawbacks, modified polynomial guidance laws is proposed. The modified guidance law is derived quasi-analytically after taking advantages of previous real-time guidance laws for onboard application. In the numerical simulation section, performance will be compared from several points of view such as avoiding surface collision and fuel consumption.

16:50 AAS Simultaneous Iterative Learning and Feedback Control Design 15-722 Anil Chinnan, Columbia University; Minh Phan, Dartmouth College; Richard Longman, Columbia University Iterative Learning Control (ILC) applies to control systems performing a maneuver repeatedly. It learns from previous repetitions aiming for zero tracking error at all time steps. Spacecraft applications include repeated scanning maneuvers. ILC also requires feedback control action to address random disturbances. In contrast to typical feedback control design, previous research developed finite-time feedback control methods based on a desired trajectory, giving feedback appropriate for addressing error during transients. The present paper develops a cost function based design to combine this feedback with ILC, allowing the designer to adjust the emphasis placed on repeating versus random disturbances.

17:10 AAS A NOVEL UNIFIED MODELING AND ADAPTIVE SLIDING MODE CONTROL 15-556 BASED ON DIFFERENTIAL INCLUSION FOR HYPERSONIC RE-ENTRY VEHICLE Jianjun Luo; Caisheng Wei; Jianping Yuan A novel unified modeling approach is proposed to model the multi- model control system for hypersonic re- entry vehicle in wide flight envelope based on differential inclusion. Then the real- time compensation for the system parameters with the weight based on coefficient of variation is implemented to prevent the aged model, which is under fast estimation for the un- modeled system parameters online. Afterwards, a modified adaptive nonsingular terminal sliding mode controller by introducing integral sliding mode surface is devised to realize the high precise robust control for hypersonic re- entry vehicle. Finally, numerical simulation results verify the efficiency of the modeling approach and controller.

Page 29 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Monday Session 6 Space Missions: New Horizons, MESSENGER and Mars Reconnaissance Orbiter

Session Chairs: Bobby Williams, KinetX Inc., James McAdams, The Johns Hopkins University Applied Physics Laboratory. Room: Rocky Ballroom A/B

13:30 AAS NAVIGATION STRATEGY AND RESULTS FOR NEW HORIZONS’ APPROACH 15-636 AND FLYBY OF THE PLUTO SYSTEM Bobby Williams, KinetX SNAFD; Frederic Pelletier, KinetX Inc.; Dale Stanbridge, KinetX Aerospace, Inc.; Jeremy Bauman, KinetX inc.; Kenneth Williams, KinetX Aerospace, Inc.; Coralie Jackman, KinetX, Inc.; Derek Nelson, KinetX, Inc.; Philip Dumont, KinetX, Inc.; Peter Wolff, KinetX Aerospace, Inc.; Christopher Bryan, KinetX Aerospace, Inc.; Anthony Taylor, KinetX Aerospace, Inc.; Bob Jensen, JHUAPL; Gabe D. Rogers, The Johns Hopkins University Applied Physics Laboratory The New Horizons mission, the first mission in NASA’s New Frontiers Program, is also the first mission with primary science objectives to explore the Pluto/Charon system. After launch in January 2006 and an interplanetary cruise of more than 9 years, New Horizons has completed the approach and flyby of Pluto. This paper presents an overview of the analysis and operational constraints that led to the navigation strategy used. Also presented are operational results for that strategy during this final phase of the prime mission.

13:50 AAS Mars Reconnaissance Orbiter Navigation Strategy for Dual Support of InSight and 15-532 ExoMars Entry, Descent and Landing Demonstrator Module in 2016 Sean Wagner, NASA/JPL; Premkumar Menon, NASA/JPL; Min-Kun Chung, NASA/JPL; Jessica Williams, NASA/JPL The Mars Reconnaissance Orbiter (MRO) will support NASA's InSight Mission and ESA's ExoMars Entry, Descent and Landing Demonstrator Module (EDM) during the Entry, Descent and Landing (EDL) sequences in late 2016. MRO provided relay support during the EDL sequences of Mars Phoenix Lander in 2008 and the Mars Science Laboratory in 2012. Unlike these missions, MRO will coordinate between two EDL events separated by only three weeks: InSight on September 28, 2016 and EDM on October 19, 2016. This paper describes MRO Navigation's maneuver plan to move MRO's ascending node to meet the InSight EDL phasing requirement and support EDM.

14:10 AAS Mars Reconnaissance Orbiter Navigation Strategy for the Comet Siding Spring 15-551 Encounter Premkumar Menon, NASA/JPL; Sean Wagner, NASA/JPL; Tomas Martin-Mur, NASA/JPL; David Jefferson, NASA / Caltech JPL; Shadan Ardalan, NASA / Caltech JPL; Min-Kun Chung, NASA/JPL; Kyong Lee, NASA/JPL; William Schulze, NASA/JPL On October 19, 2014, Comet Siding Spring encountered Mars at a distance of about 141,000 km, the nearest comet flyby of a planet in recorded history. Mars Reconnaissance Orbiter (MRO) was able to detect the comet and capture images with its HiRISE camera as it approached Mars. To help protect MRO from the incoming comet particles, two propulsive maneuvers were performed to position the spacecraft behind Mars at the time of the expected peak particle fluence. This paper documents the Navigation Team's maneuver plan to mitigate risk from the comet particles while allowing observations of the comet flyby.

14:30 AAS Design, Implementation, and Outcome of MESSENGER's Trajectory from Launch to

Page 30 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 15-608 Mercury Impact Dawn Moessner, Johns Hopkins University Applied Physics Laboratory; James McAdams, Johns Hopkins University Applied Physics Laboratory MESSENGER was launched on 3 August 2004, entered orbit about Mercury on 18 March 2011 (UTC), and impacted Mercury’s surface on 30 April 2015. After a 6.6-year cruise phase with one Earth, two Venus, and three Mercury flybys, MESSENGER spent 4.1 years in Mercury orbit. Initially in a 12-h orbit, MESSENGER maintained periapsis altitudes of 200–505 km before transferring to an 8-h orbit on 20 April 2012. During the mission's final year MESSENGER’s low- altitude campaign included periapsis altitudes between 15 and 200 km. In its final 44 days, MESSENGER maintained unprecedented minimum altitudes below 38 km above Mercury’s terrain before impact.

14:50 AAS Engineering MESSENGER's Grand Finale at Mercury - the Low-Altitude Hover 15-634 Campaign James McAdams, Johns Hopkins University Applied Physics Laboratory; Christopher Bryan, KinetX Aerospace, Inc.; Stewart Bushman, Johns Hopkins University Applied Physics Laboratory; Andrew Calloway, Johns Hopkins University Applied Physics Laboratory; Eric Carranza, Johns Hopkins University Applied Physics Laboratory; Sarah Flanigan, The Johns Hopkins University Applied Physics Laboratory; Madeline N. Kirk, The Johns Hopkins University Applied Physics Laboratory; Haje Korth, Johns Hopkins University Applied Physics Laboratory ; Dawn Moessner, Johns Hopkins University Applied Physics Laboratory; Daniel O'Shaughnessy, Johns Hopkins University Applied Physics Laboratory ; Kenneth Williams, KinetX Aerospace, Inc. Having completed its primary and first extended missions by mid-March 2013, the MESSENGER Mercury orbiter began a 2.1-year final mission extension that brought significant opportunity for low-altitude science, along with many technical challenges that the flight operations and science teams worked together to successfully overcome. After four orbit-correction maneuvers (OCMs) from June 2014 to January 2015 targeted minimum altitudes near 25 km and 15 km, five OCMs in March and April 2015 maintained minimum altitude between 5 km and 37 km. Engineering challenges at the end included efficiently utilizing usable propellant and helium gas pressurant to delay Mercury impact.

15:10 Break

15:30 AAS MESSENGER Maneuver Performance in the Low-Altitude Hover Campaign 15-652 Madeline N. Kirk, The Johns Hopkins University Applied Physics Laboratory; Sarah Flanigan, The Johns Hopkins University Applied Physics Laboratory; Daniel O'Shaughnessy, Johns Hopkins University Applied Physics Laboratory ; Stewart Bushman, Johns Hopkins University Applied Physics Laboratory; Paul Rosendall, Johns Hopkins University Applied Physics Lab Helium gas pressurant from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft's near-empty main fuel tanks will be used as a propellant to delay the spacecraft's surface impact on Mercury until late April 2015 and enable a one-month "hover" campaign with periapsis altitudes as low as 6 km. The final six maneuvers of the mission have unique challenges, including using helium as a propellant, firing thrusters that have not been used in more than eight years, and executing multiple maneuvers within a short time frame that if unsuccessful lead to impact times as little as 30 hours later.

Page 31 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 15:50 AAS Navigation and Dispersion Analysis of the First Orion Exploration Mission 15-768 Christopher DSouza, NASA/JSC; Renato Zanetti, NASA JSC The navigation and dispersion performance of the first Orion Exploration Mission (EM-1) to a Distant Retrograde Orbit (DRO) will be presented. Both the autonomous optical navigation system performance and the ground navigation system performance will be evaluated. In addition the DV performance for all of the correction and deterministic maneuvers will be evaluated. The results will be presented mapped to the final epoch of each phase of the mission.

16:10 AAS Navigation Analysis for the JUICE Jupiter Moon Tour 15-651 Tomohiro Yamaguchi, GMV at ESA/ ESOC; Arnaud Boutonnet, ESA / ESOC This paper presents the results of the navigation analysis for the Jupiter moon tour of the Jupiter Icy Moon Explorer mission (JUICE). Many moon flybys are planned during the Jupiter tour, thus justifying a detail navigation analysis to evaluate the required propellant in the spacecraft. The manoeuvres sequencing has been optimized to minimize the stochastic delta-V cost while fulfilling the spacecraft flyby delivery dispersions requirements. The target parameters for each manoeuvre are investigated in order to keep the spacecraft on the reference trajectory. Several manoeuvre strategies are analysed and compared to understand the optimal strategy considering the operational constraints.

Page 32 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Monday Session 7 Trajectory Design and Optimization - 2

Session Chairs: Roby Wilson, Jet Propulsion Laboratory, Jacob Williams, NASA Johnson Space Center Room: Larkspur

13:30 AAS WHOLE SUPERIOR PLANETS RENDEZVOUS WITH CONTINUOUS 15-501 PROPULSION Dong-sun Kim This paper relates to design deep space optimal orbit of continuous propulsion spaceship that rendezvous with whole superior planets in solar system. It is slighty different with traditional orbit that only use planet gravity, but can be possible to make unconstraint free and correct spacecraft optimal rendezvous orbit by continuous propulsion with clohessy-wiltshire equation. In this paper, numerical analysis with MATLAB program show an example of sequential optimal rendezvous orbit with Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. It is considered that about 15 years sequential optimal rendezvous deep space orbit which departure from Earth on January 1, 2020.

13:50 AAS IMPULSIVE HALO TRANSFER TRAJECTORY DESIGN AROUND SEL1 POINT 15-507 WITH MULTIPLE CONSTRAINTS Hao Zeng, Beijing Institute of Technology; Jingrui Zhang; Mingtao Li; Zixi Guo, Beijing institute of technology In this paper, impulsive Halo transfer trajectories are studied in the Sun-Earth system with multiple constraints. In order to solve the orbit transfer problem with multiple constraints and sensitive initial values, the methodology based on differential corrections and initial value polynomial is presented, where the relationship between launch epoch constraints and RAAN constraints is introduced to ensure algorithm convergence and initial value polynomial is got to solve the initial value problem of differential corrections. This paper has researched the transfer trajectory from an Earth parking orbit to L1 Halo orbit with launch opportunities in different months and launch sites.

14:30 AAS Lisa Pathfinder - Robust Launch Window Design for a Transfer towards a Large 15-519 Amplitude Orbit about the Sun-Earth Libration Point 1 Florian Renk, European Space Agency; Markus Landgraf, European Space Agency; Bram de Vogeleer, GMV at ESOC The LISA-Pathfinder mission is scheduled for launch toward the Sun-Earth Libration Point 1 (SEL1) end of 2015. The launch will be on Europe’s VEGA launcher. The performance of VEGA does not allow for a direct injection towards the SEL1 region. Consequently LPF must propel itself towards its operational orbit. This injection cannot be done in one manoeuvre without accepting significant gravity loss. A sequence of apogee raising manoeuvres is required to finally inject LPF onto a suitable SEL1 orbit. These manoeuvres must be optimized in order to minimize the received radiation dose for the nominal trajectory and several contingency cases.

14:50 AAS An Unconditionally Stable Method for Propagating Sailcraft Trajectories 15-521 Alex Karwas; Ray Taghavi, University of Kansas A new method for propagating the trajectories of solar sail spacecraft is presented. The new method provides unconditionally stable calculations that arrive at a unqiue numerical solution to the sailcraft equations of motion. The numerical framework uses the least squares hpk finite element method to solve the equations of motion. Details of the numerical solver and the implementation of the sailcraft equations of motion are presented. When compared to flight data, the new method shows an increase in accuracy over other common trajectory propagation methods. Results are presented

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Updated July 31, 2015 #ASC2015 for two-dimensional and three-dimensional trajectory simulations.

15:10 Break

15:30 AAS Trajectory Optimization for Low-Thrust Time-Limited Multiple Asteroids 15-543 Rendezvous Mission Gao Tang; Fanghua Jiang; Junfeng Li Interplanetary mission in the future will be more meaningful and challenging if it’s planned to rendezvous with multiple targets. A mission consisting of multiple probes to rendezvous with as many as asteroids in the main-belt with low-thrust propulsion within a preset duration is investigated. A simple way of estimating the transfer cost is applied to find acceptable targets. Time optimal transfer is solved to obtain the minimum transfer time. It’s applied recursively to generate feasible sequences. Indirect methods with homotopic form and switching function detection are implemented to reduce fuel consumption and realize the transfer.

15:50 AAS Mission Analysis for a Human Exploration Architecture in the Earth-Moon System 15-552 and Beyond Florian Renk, European Space Agency; Markus Landgraf, European Space Agency In the frame of the International Space Exploration Coordination Working Group (ISECG) the European Space Agency is participating in the planning of future exploration architectures. The paper gives an overview of existing research on some of the topics, the currently known pros and cons of the options and will explain on which aspects of the system engineering as well as the mission analysis the focus is currently put on. It is the intention of this paper to foster the discussion and exchange on the link between architecture design and trajectory design.

16:10 AAS Fractionated Satellite Systems for Earth Observation Missions: Feasibility and 15-759 Performances Analysis Daniele Filippetto, Politecnico di Milano; Michèle Lavagna, Politecnico di Milano This paper aims at investigating the feasibility of fractionated satellite architecture for Earth observation missions. The payload fractionation, consisting in the physical distribution of the payload over a cluster of satellites flying in formation or constellation can be obtained using either the same or a different payload in each satellite. Issues, possible solutions and applications (visible/infrared and synthetic aperture radar remote sensing) of both of these approaches are analysed in this study. In particular, the problems of deployment, configuration maintenance and reconfiguration are addressed for various formations in different orbits. The results are critically discussed in the paper.

Page 34 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Monday Session 8 High Performance Computing in Astronautics

Session Chairs: Nitin Arora, Jet Propulsion Laboratory, Sergey Tanygin, Analytical Graphics, Inc. Room: Rocky Ballroom C/D

13:30 AAS INFRARED, VISUAL, AND RADAR SENSOR CHARACTERIZATION AND GPU- 15-563 BASED SIMULATIONS FOR ASTEROID INTERCEPT OR RENDEZVOUS MISSIONS (Submit to special session) Joshua Lyzhoft As demonstrated before, NASA's Deep Impact mission, Raytheon's EKV, and NEOWISE telescope, have used instrumentation to impact or detect objects in space. This paper explores the use of infrared, visual, and radar devices to be used in rendezvous or intercept applications. Signal-to- noise ratio and detection distance calculations are performed for small asteroid bodies (50-100 meter diameter). These asteroids are polyhedron models of Bennu, Comet 67P/C-G, and 433 Eros, which undergo ray trace shadow algorithms and solid angle approximations using a GPU. Simulations using the GPU are conducted, which incorcorporates sensor parameters, to determine asteroid mission feasibility.

13:50 AAS A GPU-Accelerated Computational Tool for Asteroid Disruption Modeling and 15-568 Simulation Ben Zimmerman, Iowa State University; Bong Wie, Iowa State University In this paper, a computational tool for studying the effectiveness of hypervelocity kinetic impactors and nuclear subsurface explosions applied to asteroid disruption is presented. Solutions are completed with high-order methods on GPUs (Graphics Processing Units), to take advantage of the computationally efficient framework of high-order methods and the architecture of GPUs. Several hypervelocity kinetic impact scenarios are explored, which vary the impactors mass, shape, and number. Nuclear options are also of interest. For these simulations, we demonstrate the effects of utilizing surface and subsurface nuclear explosions on the target. The overall goal is to study target damage from the aforementioned disruption methods.

14:10 AAS A Massively Parallel Bayesian Approach to Planetary Protection Trajectory Analysis 15-535 and Design Mark Wallace, Jet Propulsion Laboratory, California Institute of Technology The NASA Planetary Protection Office has levied a requirement that the upper stage of future planetary launch vehicles have a less than 10-4 chance of impacting Mars for 50 years after launch. A brute-force approach requires over a year of computer time to demonstrate compliance. By applying Bayes Theorem to the problem and taking advantage of the demonstrated reliability of the upper stage, the required number of fifty-year propagations can be massively reduced. By spreading the remaining embarrassingly parallel Monte Carlo simulations across multiple computers, compliance can be demonstrated in a reasonable time frame. The method used is described here.

14:30 AAS Paramat: Parallel Processing with the General Mission Analysis Tool 15-587 Darrel Conway, Thinking Systems, Inc. Paramat, a threaded, parallel processing tool built on the General Mission Analysis Tool (GMAT), is a system designed to use modern, multi-core computer platforms for orbit modeling. Examples of the problems targeted by Paramat are Monte Carlo analysis of spacecraft mission parameters, parametric studies, trajectory dispersion analyses, and phase space analysis problems. Paramat has been demonstrated as a proof of concept prototype system to drive Monte Carlo analyses for orbital

Page 35 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 transfers. In this paper, the Paramat system is described. Examples of the performance gains seen in the Paramat system are presented. Paramat runs on Windows, Linux, and Mac workstations.

14:50 AAS EXPERIMENTS WITH JULIA FOR ASTRODYNAMICS APPLICATIONS 15-795 Nitin Arora, JPL; Anastassios Petropoulos, NASA / Caltech JPL; Nathan Strange, Jet Propulsion Laboratory / California Institute of Technology Julia's potential for solving complex astrodynamics problems is studied. Julia is a new dynamic (MATLAB like) programming language with performance approaching C/FORTRAN and has features like inbuilt parallelism, variable accuracy, integrated numerical libraries, and direct C and FORTRAN interfaces. Three astrodynamics problems are solved in Julia: 1) Lambert's problem, using the vercosine formulation, 2) impulsive-broad-search for interplanetary trajectory and tour design, and 3) low thrust optimization using Julia’s optimization packages. Implemented algorithms are compared with C and FORTRAN based counterparts on key performance parameters (speed, development effort etc). Using Julia for implementing fast and reliable astrodynamics software is also discussed.

15:10 Break

15:30 AAS A Non-Linear PARallel OPTimization Tool (NLPAROPT) for solving spacecraft 15-808 trajectory problems Alexander Ghosh, University of Illinois at Urbana-Champaign; Victoria Coverstone, University of Illinois at Urbana-Champaign; Ryne Beeson, University of Illinois at Urbana- Champaign; Donald Ellison, University of Illinois at Urbana-Champaign Aerospace Engineering Department; David Carroll, CU Aerospace; Laura Richardson, University of Illinois A new Non-Linear Parallel Optimization Tool (NLPAROPT) is being developed that will be capable of solving the same nonlinear programming problems as current state-of-the-art serial solvers, but in a rapid parallel fashion. Preliminary results have already shown that NLPAROPT significantly reduces the total runtime of a trajectory optimization problem, and by adding more parallel implementations and refining the core algorithm will continue to reduce time to optimal solutions.

15:50 AAS Parallel Generation of Extremal Field Maps for Optimal Multi-Revolution 15-791 Continuous Thrust Orbit Transfers Robyn Woollands We simulate hybrid thrust transfers to rendezvous with orbital debris. The hybrid thrust transfer consists of a two-impulse maneuver at the terminal boundaries, augmented with continuous low- thrust sustained throughout the flight. The optimal control problem is formulated using the path approximation numerical integrator, Modified Chebyshev Picard Iteration. This two-point boundary value problem is solved in a shooting manner using the Method of Particular Solutions, thus allowing multi-revolution orbit transfers to be computed. We utilize a parallel architecture for computing the delta V cost associated with each transfer. Parallel implementation reduces the computation time

16:10 AAS GPU-Based Uncued Surveillance from LEO to GEO with Small Optical Telescopes 15-735 Peter Zimmer, J.T. McGraw and Associates, LLC; John McGraw, University of New Mexico/JTMA; Mark Ackermann, J.T. McGraw and Associates, LLC J.T. McGraw and Associates, LLC (JTMA) operates two proof-of-concept wide-field imaging

Page 36 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 systems to test novel techniques for uncued surveillance of LEO/MEO/GEO/HEO and, in collaboration with the University of New Mexico (UNM), uses a third small telescope for rapidly queued same-pass follow-up observations. Using our GPU-accelerated detection methods, the proof-of-concept systems operating at sites near and within Albuquerque, NM, have detected objects fainter than V=13 at greater than 6 sigma significance moving at apparent rates in excess of 0.75 degrees per second. Dozens of objects are measured during each operational twilight period, many of which have no corresponding catalog object.

16:30 AAS GPU-ACCELERATED COMPUTATION OF DRAG AND SRP FORCES AND 15-688 TORQUES WITH GRAPHICAL ENCODING OF SURFACE NORMALS Sergei Tanygin, Analytical Graphics, Inc.; Gregory M. Beatty, Analytical Graphics, Inc. The analysis of forces and torques due to atmospheric drag and solar radiation pressure (SRP) acting on a 3D model are efficiently calculated by utilizing the highly parallelized hardware available in commodity desktop PC graphics processing units. The calculations are using general- purpose computing on graphics processing units (GPGPU) techniques via OpenCL. In cases when the forces and torques include contributions that depend on surface normals, their directions are encoded as pseudo-colors which allows OpenCL kernel methods to efficiently unpack this additional information and perform the necessary computations.By utilizing the highly parallelized processing units available in commodity GPUs, the time required run the calculations is significantly reduced.

16:50 AAS Massively Parallel Implementation of Modified Chebyshev Picard Iteration for 15-793 Perturbed Orbit Propagation Austin Probe; Julie Read; John Junkins, Texas A&M University Future Space Situational Awareness (SSA) capabilities will greatly increase the population of trackable space objects and consequently the need for accurate and efficient orbital propagation. The serial formulation Modified Chebyshev Picard Iteration (MCPI) has proven to be an efficient and accurate method for propagating perturbed orbital motion; however, the performance is comparable to other state-of-practice numerical integrators. One significant advantage of MCPI is that the forcing function evaluations and much of the quadrature can be performed independently, resulting in a high degree of parallelizability. This paper details a graphics card based massively parallel implementation of perturbed orbit propagation with MCPI.

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Updated July 31, 2015 #ASC2015

TUESDAY, AUGUST 11, 2015

Page 38 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Tuesday Session 1 Space Situational Awareness 2

Session Chairs: David Vallado, Center for Space Standards and Innovation, Ryan Weisman, Air Force Research Laboratory. Room: Rocky Ballroom A/B

8:00 AAS New Consolidated Files for Earth Orientation Parameters and Space Weather Data 15-500 David Vallado, Center for Space Standards and Innovation; T.S. Kelso Earth Orientation Parameter (EOP) and Space Weather data are critical data elements for numerical propagation and space operations. Since CSSI first began assembling consolidated files of EOP and space weather data in 2005, we have continually sought to improve the accuracy of that process. A recent effort reexamined all the sources and added additional logic to permit quick estimation of long range solar cycle values and providing missing indices where they could be reliably estimated. This paper provides detailed documentation concerning the assembly and rationale for choices made as well as accuracy plots for predicted values.

8:20 AAS Angles-only algorithms for Initial Orbit Determination Revisited 15-539 Gim Der, DerAstrodynamics This paper presents numerical results to address the historical questions:

1. How accurate was the 1801 Ceres data of Piazzi? 2. Did Laplace compute any Ceres orbit? 3. How accurate was the 1801 Ceres orbit computed by Gauss? 4. Why the angle-only problem remains a great challenge over 200 years?

The author's 2012 AMOS paper provided 10 numerical examples and marked a new range-solving angles-only algorithm that can consistently determine the correct range and initial perturbed orbit of any unknown object in all orbit regimes without guessing. This new algorithm allows optical sensors to be used for efficient and cost effective catalog maintenance and catalog building.

8:40 AAS Updating Position Data from Full Serendipitous Satellite Streaks 15-555 Charlie Bellows, Air Force Institute of Technology; Gary Goff; Jonathan Black; Richard Cobb, Air Force Institute of Technology; Alan Jennings Reliable Space Situational Awareness (SSA) is a recognized requirement in the current congested, contested, and competitive environment of space operations. A shortage of available sensors and reliable data sources are some current limiting factors for maintaining SSA. Alternative methods are sought to enhance current SSA. This work examines the feasibility and utility of performing positional updates for a Resident Space Object (RSO) catalog using metric data obtained from from RSO streaks that cross completely through an astronomical image. The methodology developed can also be applied to dedicated SSA sensors to extract data from serendipitous streaks gathered while observing other RSOs.

9:00 AAS Gaussian Mixture Approximation of the Bearings-Only Initial Orbit Determination 15-575 Likelihood Function Mark Psiaki, Cornell University; Ryan Weisman, Air Force Research Laboratory; Moriba Jah, Air Force Research Laboratory A method is developed to approximate the bearings-only orbit determination likelihood function using a Gaussian mixture. The resulting probability density function can provide the a priori

Page 39 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 information for a Gaussian mixture orbit determination filter. The new technique starts with the diffuse prior assumption, and it forms a Gaussian mixture approximation of this prior in the interesting region of position/velocity space. The algorithm finishes by applying the standard measurement update of a Gaussian mixture filter. The processed measurements are an initial batch of right-ascension and declination data from one or more optical observing stations.

9:20 AAS Uncertain Angles-Only Track Initiation for SSA using Different IOD Methods 15-578 Christopher Roscoe, Applied Defense Solutions; Islam Hussein, Applied Defense Solutions; Paul Schumacher, Air Force Research Laboratory; Matthew Wilkins, Applied Defense Solutions Uncertainty in initial orbit determination (IOD) resulting from sparse optical data is an underexplored topic in SSA. Uncertainty propagation has been investigated in detail for purposes of collision probability analysis, data association, and Bayesian estimation, but all of these investigations assume knowledge of the initial uncertainty. For optical observations with long arcs of data, uncertainty is usually assumed Gaussian. This paper continues previous work investigating characterization of uncertainty for short-arc data, including mapping uncertainty through the Gooding and Casotto methods, and investigating IOD uncertainty using derived angle-rates. Several examples are presented, with different observation geometries, orbit parameters, and error characterizations.

9:40 Break

10:00 AAS Minimization of the Kullback-Leibler Divergence for Nonlinear Estimation 15-639 Jacob Darling, Missouri University of Science and Technology; Kyle DeMars, Missouri University of Science and Technology A nonlinear quadrature filter is proposed in which the true probability density function of the state vector is approximated by an assumed Gaussian density. The parameters of the Gaussian density are found by minimizing the Kullback-Leibler divergence of the Gaussian density with respect to the true density, as defined by the Chapman-Kolmogorov equation and Bayes' rule. The corrector step of the proposed filter employs a nonlinear update in which the moments of Bayes' rule define the mean and covariance of the posterior Gaussian density. Results are shown which compare the proposed filter to the extended, unscented, and quadrature Kalman filters.

10:20 AAS Fragmentation Event Tracking with the GM-CPHD Filter 15-676 Daniel Bryant, University of Colorado Boulder; Brandon Jones, University of Colorado Boulder The tracking of space objects generated by fragmentation events has been a significant challenge for the space situational awareness community. In a multi-target framework, such events are ideally modeled as spawning processes and an implementation of the Cardinalized Probability Hypothesis Density (CPHD) filter has recently been derived for the explicit use of a spawning model. This paper presents the first application of the model to the tracking of space objects and demonstrates application of the CPHD filter to the tracking of fragmentation and similarly modeled events. Simulation results demonstrate the efficacy of the filter implementation for tracking low-Earth orbit objects.

10:40 AAS Orbit Determination for Partially Understood Object Via Matched Filter Bank 15-726 Timothy Murphy, Georgia Institute of Technology; Marcus Holzinger, Georgia Institute of Technology; Brien Flewelling, Air Force Research Laboratory

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Updated July 31, 2015 #ASC2015 The main result to be presented in this paper is a novel method to create a bank of matched filters for detection of space objects and subsequent orbit determination. When prior knowledge is only constrained to an arbitrary probability density function, two hypothesis orbits often produce different signals in subsequent images, necessitating a bank of matched filters. This paper develops the measurement dissimilarity metric, which is then applied to partition a general prior orbit set which defines a matched filter bank. A formulation for localized matched filtering is then developed. Simulation shows detection of dim space objects for sensor handoff.

11:00 AAS Efficient trajectory propagation for orbit determination problems 15-730 Javier Roa, Technical University of Madrid; Jesus Pelaez, Technical University of Madrid (UPM) Orbiting an unknown body is one of the most effective techniques to determine its mass, inertia properties and to estimate its gravity field. The accuracy of the estimation depends on the resolution of the instruments, but also on the accuracy of the propagated trajectory. This paper studies the evolution of the propagation error and its connection with orbit determination problems, especially during flybys. The potential limitations of the integration in Cartesian coordinates is discussed. Parametric studies are conducted to evaluate the sensitivity of the trajectory resulting from the flyby to errors in the initial conditions.

11:20 AAS Sensor Bias Estimation and Uncertainty Quantification Strategies for Space Object 15-767 Tracking Eamonn Moyer, University at Buffalo, State University of New York The problems of estimation and uncertainty quantification of sensor biases are investigated in this paper. Several approaches to these problems are explored, and their success in the mitigation of bias is investigated. ``De-biasing", augmented filtering, and consider filtering approaches are studied and their results are compared. In addition, smoothing results are presented. The approaches have their own merits and drawbacks, and their pros and cons are discussed within and recommendations are made as to when to use which approach. Statistical consistency checks are provided to show when the filter is not acting in an optimal fashion.

11:40 AAS Characterizing the Effects of Low Order Perturbations on Geodetic Satellite Precision 15-778 Orbit Determination John Warner; Annie Lum Satellite operations often rely on the ability to precisely determine and accurately predict the satellite's orbit. Thus, there are numerous papers dedicated to developing methodologies for successful orbit determination. However, there are numerous lower order forces that act upon satellites that are not directly studied in detail. Two such phenomenon are studied here; perturbations due to the Lunar geopotential, and lower order relativistic corrections. The affects of both on orbit determination are studied with US Naval Research Laboratory's Orbit Covariance Estimation and ANalysis (OCEAN) tool. High precision laser ranging data to geodetic satellites are used as test cases to evaluate.

Page 41 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Tuesday Session 2 Astrodynamics 2

Session Chairs: Angela Bowes, NASA Langley Research Center, Johnathan Brown, A.i. solutions, Inc. Room: Rocky Ballroom C/D

8:00 AAS USING TAYLOR DIFFERENTIAL ALGEBRA IN MISSION ANALYSIS: 15-518 BENEFITS AND DRAWBACKS Vincent Morand, CNES After having proved its potential in the field of particle beam physics, Taylor Differential Algebra (TDA) is being more and more used for space applications. As an example, the issues of Near Earth Objects encounters, orbital conjunctions and even long term orbit propagation can be analyzed using Taylor Differential Algebra. The field of mission analysis seems particularly suited for the use of TDA, since the uncertainty on inputs are generally high, parametrical studies are often required and computational efficiency is necessary. The paper details the TDA engine used in CNES and gives example of its applications for mission analysis.

8:20 AAS SEARCHING FOR MORE STABLE PERTURBED ORBITS AROUND THE 15-666 EARTH Antonio Fernando Prado; Thais Oliveira This goal of the present paper is to search for orbits around the Earth that are more stable, in the sense of presenting minimum variations with respect to a Keplerian initial orbit. This variation will be measured by the integral of the differences of the radius vector of the real perturbed orbit and the equivalent vector of the Keplerian orbit that starts at the same point. Those maps will be done based on the integral of the magnitude of the perturbation forces. Particularly, the effects of the inclination and the eccentricity of the orbit in those mappings are studied.

8:40 AAS Analytical Perturbation Theory for Dissipative Forces in Two-Point Boundary Value 15-684 Problems Oier Penagaricano Munoa, Alerion Technologies; Daniel Scheeres, University of Colorado Analytical perturbation technique for solving two-point boundary value problems. The technique builds on previous work done in the perturbation theory for Hamilton’s principal function and used to analytically solve for the velocities in the perturbed targeting problem. The method presented extends to dissipative forces such as aerodynamic drag, and only requires the nominal two-body solution.

9:00 AAS Expansion of Density Model Corrections Derived from Orbit Data to the ANDE 15-713 Satellite Series Travis Lechtenberg, SpaceNav LLC; Craig McLaughlin, University of Kansas; Harold Flanagan, University of Kansas: Department of Aerospace Engineering Current techniques to estimate corrections to atmospheric density are expanded to the ANDE satellite series. These are tracked using satellite laser ranging, while having firmly established drag characteristics. These corrections yield estimated density corrections which in turn lead to better drag estimates, improved orbit determination and prediction, as well as an enhanced understanding of density variations in the thermosphere and exosphere. This examination will give a better idea of obtainable improvements in atmospheric density. Consideration will also be given to the effects of varying levels of geomagnetic and solar activity.

9:20 AAS HIGH ORDER TRANSFER MAP METHOD AND GENERAL PERTURBATION

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Updated July 31, 2015 #ASC2015 15-731 TECHNIQUES APPLIED TO PERTURBED KEPLERIAN MOTION Roberto Armellin, Universidad de La Rioja; Alexander Wittig, Politecnico di Milano; Juan Félix San-Juan, University of LA Rioja The present international concern in space situational awareness (SSA) has produced a renewed interest in efficient methods for propagation of catalogs of data. Recently, Wittig et al. (2014) have proposed a new technique called high-order transfer map (HOTM) method. This technique is based on the numerical integration of a single orbital revolution in differential algebra arithmetic, yielding an analytical high order approximation of the true transfer map. It is then followed by its repeated analytical evaluation to advance the orbital propagation by several orbital periods. The main focus of this work is to compare the HOTM with high-order closed-form theory based on Lie transforms.

9:40 Break

10:00 AAS Investigating the Evolution of a Practical Distant Retrograde Orbit for Over 20,000 15-743 Years Collin Bezrouk, University of Colorado, Boulder; Jeff Parker, University of Colorado This paper discusses a survey of distant retrograde orbits (DROs) that are stable for thousands to tens of thousands of years. Several DROs of varying size and inclination are propagated with a high- fidelity dynamics model using quadruple precision. The long duration secular effects on each orbit are characterized and used to predict the stability duration in cases where trajectories cannot be integrated further. The dynamics responsible for these secular effects are identified and important frequencies related to these dynamics are discussed as well.

10:20 AAS Searching for periodic and quasi-periodic orbits of spacecrafts on the Haumea system 15-770 Diogo Sanchez, National Institute for Space Research - INPE; Antonio Fernando Prado; Tadashi Yokoyama, State University of São Paulo - Unesp The goal of the present paper is to provide options for optimal exploration of the Haumea system. We are seeking for periodic and quasi-periodic orbits around Haumea. The search for periodic orbits will be made by Poincaré maps, taking into account Haumea and Namaka, and Haumea and Hi’iaka system separately. The combination of these two sets of maps will provide the periodic orbits of the system. Therefore, with this method, we can find quasi-periodic orbits. The quasi-periodic orbits can close at some point and could have guaranteed their periodicity by applying an impulsive delta-V at the point of closure.

10:40 AAS Long term evolution of the eccentricity in the MEO region, with a perturbed harmonic 15-798 oscillator approach. Florent Deleflie, IMCCE; Jerome Daquin, IMCCE, Paris Observatory; Michel Capderou, LMD; Jérôme Pérez We study the long term evolution of the mean eccentricity of trajectories within the MEO region, in a model accounting for zonal and tesseral parameters of the Earth’s gravity field, and the luni solar attraction. Depending on the initial conditions, the two components o the eccentrity vector (as well as the inclination vector) follow an ellipse through the equations of a harmonic oscillator with two regimes: libration or circulation. The perturbed harmonic oscillators are written and are analytically interpretated. Some comparisons with the STELA propagator and TLE data sets are provided.

11:00 AAS Analytical conversion of mean orbital elements into osculating elements for frozen 15-803 orbit about asteroids Inkwan Park, University of Colorado at Boulder; Daniel Scheeres, University of Colorado

Page 43 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 The analytical conversion algorithm of mean orbital elements space is discussed in this study. In particular, we apply the algorithm to map a frozen or quasi-frozen orbit defined in mean orbital elements space about asteroids into osculating elements space. We expect that frozen orbits become more applicable, such as introducing control law, through the analytical conversion. For this study, a perturbation theory is exploited in order to derive both an averaged (normalized) equation and a generating function. The suggested algorithm is applied to two different perturbed Keplerian motions about asteroid 101955 Bennu.

11:20 AAS Seasonal Variations of the James Webb Space Telescope Orbital Dynamics 15-802 Jonathan Brown, a.i. solutions, Inc.; Jeremy Petersen, a.i. solutions; Benjamin Villac, a.i. solutions, Inc.; Wayne Yu, NASA GSFC While spacecraft orbital variations due to the Earth’s tilt and orbital eccentricity are well-known phenomena, the implications for the James Webb Space Telescope present unique features. We investigate the variability of the observatory trajectory characteristics with launch date, which includes transfer delta-v, geometry of the science orbit, orbit determination accuracy and overall sensitivity against model parameters, and impact on stationkeeping trends. After providing an overview of the magnitude of the observed changes, we present an explanation of some of these effects using invariant manifold theory and local approximation of the dynamics in terms of the restricted three-body problem.

11:40 AAS DEALING WITH UNCERTAINTIES IN INITIAL ORBIT DETERMINATION 15-734 Roberto Armellin, Universidad de La Rioja; Pierluigi Di Lizia, Politecnico di Milano; Renato Zanetti, NASA JSC A method for dealing with uncertainties in initial orbit determination (IOD) is presented. This is based on the use of Taylor differential algebra (DA) for nonlinearly mapping the uncertainties from the observation space to the state space. When a minimum set of observations is available DA is used to expand the solution of the IOD in Taylor series with respect to measurement errors. A filtering algorithm based on nonlinear mapping of statistics and a linear update scheme is then applied to update the knowledge of the initial orbit when additional observations are available.

Page 44 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Tuesday Session 3 Attitude Dynamics and Control - 2

Co Chair: Sergei Tanygin, Analytical Graphics, Inc., Mark Karpenko, Naval Postgraduate School. Room: Primrose

8:00 AAS ON-ORBIT EXPERIENCE OF FLYING TWO-WHEEL CONTROLLED 15-542 SATELLITES Johannes Hacker, Globalstar Inc; Peter Lai, Globalstar Inc; Jiongyu Ying, Globalstar, inc. Following several reaction wheel on-orbit anomalies and ensuing lifetime extension of the Globalstar 2nd generation fleet, a hybrid control algorithm using two wheels and magnetic torque bars was developed and implemented in the satellites on low Earth orbit. Since the control torque by magnetics is much smaller than that by reaction wheel and its strength varies with satellite position and attitude on the orbit, satellite operations engineers must take special care during station keeping, yaw slew, etc. The on-orbit data and lessons learned will be presented.

8:20 AAS Attitude Control of a Modular NPU-PhoneSat Based on Shape Actuation 15-573 Qiao Qiao; Jianping Yuan; Xin Ning, Northwestern Polytechnical University; Baichun Gong, Northwestern Polytechnical University Much like a falling cat can reorient itself in mid-air,this modular PhoneSat could reorient itself without changes in net angular momentum by altering the shape and instantaneous mass distribution during attitude maneuvers.Given size and cost constraints,this paper focuses on the under-actuated case.Optimal attitude control method to steer the PhoneSat to the desired posture is proposed,with the objective to minimize the input energy.Particle Swarm Optimization is employed to search the optimal control to achieve the reorientation .The input torques is parametrized by spline to satisfy the imposed constraints.Simulation results are presented and confirm the effectiveness of the proposed method.

8:40 AAS FIXED-TIME CONTROL DESIGN FOR SPACECRAFT ATTITUDE 15-596 STABILIZATION Boyan Jiang, Harbin Institute of Technology; Chuanjiang Li; Yanning Guo, Harbin Institute of Technology; LI Yuan Fixed-time controller features an upper bound of settling time, which does not depend on initial states of control system. In view of that nearly all the existing fixed-time control methods are based on the terminal sliding mode, a new fixed-time control law is developed by using a special Lyapunov function with a power integrator form for the spacecraft attitude stabilization in the presence of external disturbance. The bounded convergence time is given through a strictly theoretical deduction. Numerical simulations are performed to illustrate the effectiveness of the proposed fixed-time control scheme in the spacecraft attitude control system.

9:00 AAS CONSERVING FUEL FOR THE LUNAR RECONNAISSANCE ORBITER BY 15-599 USING ATTITUDE MANEUVERS TO CONTROL ANGULAR MOMENTUM AND DECREASE FREQUENCY OF MOMENTUM UNLOADS Russell DeHart; Milton Phenneger This analysis examines the use of attitude maneuvers to control the growth in reaction wheel angular momentum, thereby decreasing the fuel used by the Lunar Reconnaissance Orbiter (LRO) for momentum unloads. Changes in system angular momentum caused by past attitude maneuvers were analyzed to determine the feasibility of this approach. A simulation was developed to predict changes in angular momentum, which was calibrated and validated with real flight data. By

Page 45 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 examining historical trends in angular momentum and the predictive model output, methods are proposed for designing and timing operational slews to limit momentum unloads.

9:20 AAS A Motion Planning Method for Spacecraft Attitude Maneuvers Using Single 15-627 Polynomials Albert Caubet, University of Strathclyde; James Biggs, University of Strathclyde A path planning technique for generating smooth spacecraft attitude slew maneuvers is presented. The attitude trajectory is shaped with a polynomial determined by matching prescribed boundary conditions and maneuver time. This method allows constraints on velocity, acceleration, jerk, and torque. In the general case with arbitrary boundary conditions, the attitude is parametrized with quaternions. The special cases of rest-to-rest and spin-to-spin maneuvers are studied. The problem of time minimization is addressed, and a method for estimating the minimum time of a maneuver is proposed. Simulations with a flexible spacecraft model with feedback tracking control demonstrate the effect of trajectory smoothness.

9:40 Break

10:00 AAS A Micro-Slew Concept for Precision Pointing of the Kepler Spacecraft 15-628 Mark Karpenko, Naval Postgraduate School; Isaac M. Ross; Neil Dennehy, NASA Engineering and Safety Center In the Kepler K2 mission, a hybrid control architecture is used for pointing the now underactuated spacecraft in the ecliptic plane. Pointing precision is dictated by the minimum impulse bit of spacecraft’s thrusters. This paper describes a new control strategy called the micro-slew, which can be executed with the remaining reaction wheels only. The micro-slew utilizes optimal control concepts to repurpose the solar torque acting on Kepler as a disturbance into a control, thus reducing reliance on thrusters. The new idea enables wheels only control and could be used to improve Kepler’s pointing performance beyond the K2 mission.

10:20 AAS Hanging by a String: Attitude Control Methods and Reaction Wheel Sizing Analysis 15-643 for EyasSat^3 Daniel Jones This paper explores the use of a CubeSat, or a small, cube-shaped satellite, to provide an excellent learning and demonstration tool to students at the undergraduate level in attitude determination and control methods. The United States Air Force Academy uses a CubeSat program as a method for training future engineers in satellite design and operation. This new CubeSat, EyasSat3, is a three- unit demonstration CubeSat that contains many of the subsystems of a space-capable satellite.

10:40 AAS Quaternion-Based Finite-Time Angular Velocity Observers for Spacecraft Attitude 15-680 Tracking Maneuver Haichao Gui, Beihang University The attitude control without angular velocity measurements is addressed. A continuous but nonsmooth angular velocity is designed via homogeneous theory. It is proved that the proposed method achieves finite-time convergence of the estimation angular velocity to its true values independently of the control inputs. This significant feature ensures that the separation principle is satisfied for many certainty-equivalence attitude tracking laws. Moreover, the finite-time stability guarantees faster convergence and better robustness to disturbances and parametric uncertainties, compared to the smooth angular velocity observer.

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Updated July 31, 2015 #ASC2015 11:00 AAS Fuzzy Model-Based Attitude Control of Solar Sailcraft via Linear Matrix Inequalities 15-683 Joshua Baculi, Santa Clara University; Mohammad Ayoubi, Santa Clara University We present a fuzzy model-based attitude controller for a large-size solar sail. First, a Takagi- Sugeno fuzzy model is derived based on the existing equations of motion. Then, by using the Parallel Distributed Compensation technique, a nonlinear fuzzy control law is developed. The proposed controller stabilizes the attitude of the solar sail while it minimizes the L2 gain of the closed-loop system and satisfies actuator amplitude constraint. The fuzzy controller design problem is cast in the form of linear matrix inequalities. In the end, the stability and performance of the proposed controller is examined for a typical solar sail.

11:20 AAS UNIFIED APPROACH TO VARIABLE-STRUCTURE TRACKING CONTROL IN 15-686 VARIOUS ATTITUDE PARAMETERIZATIONS Sergei Tanygin, Analytical Graphics, Inc. The variable-structure control for attitude tracking is examined in general terms. Two alternative sliding mode surfaces are compared: one resulting in the kinematically optimal performance index and the other leading to the linear error dynamics. It is shown that the same control formulation can be viewed alternatively as optimal or as producing linear error dynamics depending on what underlying attitude parameterization is adopted. It is also shown how to achieve the closed-loop error dynamics that are both optimal and linear. Finally, the control laws are modified to guarantee that the closed-loop error dynamics evolve along the shortest arcs.

11:40 AAS UNIFIED APPROACH TO ADAPTIVE VARIABLE-STRUCTURE TRACKING 15-687 CONTROL IN VARIOUS ATTITUDE PARAMETERIZATIONS Sergei Tanygin, Analytical Graphics, Inc. The adaptive variable-structure control for attitude tracking is examined in general terms. The earlier formulation developed in terms of quaternion components is reexamined in a more general form suitable for other attitude parameterizations. The adaptive control laws are modified to address the unwinding phenomenon and to guarantee that the closed-loop error dynamics evolve along the shortest arcs. It is shown that various parameterizations can lead to notably different closed-loop behaviors particularly for the adaptation parameter

Page 47 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Tuesday Session 4 Trajectory Design and Optimization - 3

Session Chairs: Ryan Whitley, NASA Johnson Space Center, Jacob Williams, NASA Johnson Space Center Room: Larkspur

8:00 AAS Efficient Maneuver Placement for Automated Trajectory Design 15-585 Damon Landau, Jet Propulsion Laboratory When designing a mission, the addition of a maneuver at the right spot often improves the utility of an otherwise mediocre trajectory. However, the additional degrees of freedom of finding the best maneuver location can severely complicate automated broad-search algorithms. A computationally- efficient formulation that reduces the maneuver design space to a single dimension is presented, where the efficacy of additional maneuvers along previously computed transfers is calculated explicitly via Lawden’s “primer vector.” Examples include leveraging maneuvers to ease capture at Europa, phasing maneuvers to enable resonant-hopping among Saturn’s moons, and broken-plane maneuvers on transfers to Mars.

8:20 AAS A New Plugin Architecture for the Copernicus Spacecraft Trajectory Optimization 15-606 Program Jacob Williams, NASA Johnson Space Center This paper describes the design of a new plugin capability recently added to the Copernicus spacecraft trajectory design and optimization system. Details of the software architecture design and development are given, as well as examples of how the capability can be used to extend the tool in order to expand the type of trajectory optimization problems that can be solved. The inclusion of plugins is a significant update to Copernicus, allowing user-created algorithms to be incorporated into the tool for the first time.

8:40 AAS Combining Simulation Tools for End-to-End Trajectory Optimization 15-662 Ryan Whitley, NASA; Cesar Ocampo, Odyssey Space Research/NASA-JSC; Jacob Williams, NASA Johnson Space Center; Anthony Craig, ERC, Inc; Tim Dawn, NASA; Brett Starr, NASA; Daniel Litton, NASA; Min Qu, AMA Trajectory simulations with advanced optimization algorithms are invaluable tools in the process of designing spacecraft. Due to the need for complex models, simulations are often highly tailored to the needs of the particular program or mission. NASA’s Orion and SLS programs are no exception. While independent analyses are valuable to assess individual spacecraft capabilities, a complete end-to-end trajectory from launch to splashdown maximizes potential performance and ensures a continuous solution. In order to obtain end-to-end capability, Orion’s in-space tool (Copernicus) was modified to interface directly with the SLS’s ascent tool (POST2) and let the in-space tool become the full problem

9:00 AAS Creating an End-to-End Simulation for the Multi-Purpose Crewed Vehicle 15-641 Daniel Litton, NASA; Min Qu, AMA; Jeremy Shidner, Analytical Mechanics Associates, Inc.; Richard Powell, AMA; Anthony Craig, ERC, Inc; Richard Winski; Badejo Adebonojo, Jacobs (ESSSA)/NASA The NASA Engineering Safety Center (NESC) has commissioned a study to determine the benefits of combining the Multi-Purpose Crew Vehicle’s (MPCV) ascent, on-orbit operations, and entry back into Earth’s atmosphere using a Multidisciplinary Design Optimization (MDO) approach. A commercially available program, Isight, has been selected to combine all aspects of MPCV’s mission into one seamless MDO. The work to date has found that this MDO method helps

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Updated July 31, 2015 #ASC2015 determine the launch window and launch period faster and more successfully than previous methods. The particular case investigated is NASA’s Exploration Mission 1 (EM-1). Results detailing how EM-1 was setup and the resulting

9:20 AAS TARGETING THE MARTIAN MOONS VIA DIRECT INSERTION INTO MARS’ 15-580 ORBIT Davide Conte, The Pennsylvania State University; David Spencer, The Pennsylvania State University Here, we analyze interplanetary transfer maneuvers from Earth to Mars in order to target the Martian moons, Phobos and Deimos. Such analysis is done by solving Lambert’s Problem and investigating the necessary targeting upon arrival at Mars. Additionally, the orbital parameters of the arrival trajectories as well as the relative required delta-v's and times of flight were determined in order to define the optimal departure and arrival windows for a given range of dates.

9:40 Break

10:00 AAS Global Optimization of Interplanetary Trajectories in the Presence of Realistic 15-582 Mission Constraints David Hinckley; Jacob Englander, NASA Goddard Space Flight Center; Darren Hitt Interplanetary missions are often subject to difficult constraints, like solar phase angle upon arrival at the destination, velocity at arrival, and altitudes for flybys. Preliminary design of such missions is often conducted by solving the unconstrained problem and then filtering away solutions which do not naturally satisfy the constraints. However this can bias the search into non-advantageous regions of the solution space, so it can be better to conduct preliminary design with the full set of constraints imposed. In this work two stochastic global search methods are developed which are well suited to the constrained global interplanetary trajectory

10:20 AAS Early Mission Maneuver Operations for the Deep Space Climate Observatory Sun- 15-613 Earth L1 Libration Point Mission Craig Roberts, a. i. solutions, Inc.; Sara Case, a.i. solutions; John Reagoso, a .i. solutions, Inc.; Benjamin Villac, University of California, Irvine; Cassandra Alberding, NASA Goddard Space Flight Center The Deep Space Climate Observer (DSCOVR) mission launched on February 11, 2015, and was injected into a transfer trajectory toward a Lissajous orbit around the Sun-Earth L1 libration point. This paper presents an overview of the baseline transfer orbit and early mission maneuver operations leading up to the start of nominal science orbit operations. In particular, the analysis and performance of the transfer trajectory injection, the mid-course correction maneuvers, and the deep- space Lissajous orbit insertion maneuver will be discussed, comparing the baseline orbit with actual mission results and highlighting mission and operations constraints.

10:40 AAS Lissajous Orbit Control for the Deep Space Climate Observatory Sun-Earth L1 15-611 Libration Point Mission Craig Roberts, a. i. solutions, Inc.; Sara Case, a.i. solutions; John Reagoso, a .i. solutions, Inc. The DSCOVR mission—launched February 11, 2015—will become the first NOAA spacecraft to orbit the Sun-Earth L1 collinear point, a location ideal for its dual solar weather measurement and Earth full-disk imaging objectives. In addition to orbital stationkeeping maneuvers, long-term control of the Lissajous orbit such that it avoid a Solar Exclusion Zone (SEZ) of four degrees about

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Updated July 31, 2015 #ASC2015 the Sun is required. The ‘Z-axis control’ technique, which consists of maneuvers to freeze the Lissajous phase such that the same avoidance pattern is repeated continually, is described. Maneuver operations for both stationkeeping and SEZ avoidance are described.

11:00 AAS Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex 15-616 Optimization Robin Pinson, NASA MSFC; Ping Lu, Iowa State University Department of Aerospace Engineering This paper investigates a convex optimization based method that rapidly generates the fuel-optimal asteroid powered descent trajectory. The ultimate goal is to autonomously design the optimal powered descent trajectory on-board immediately prior to the descent burn. Compared to a planetary powered landing problem, the major difficulty is the complex gravity field near the surface of an asteroid that cannot be approximated by a constant gravity field. The paper uses relaxation techniques and a successive solution process that seeks the solution to the original nonlinear, non- convex problem through the solutions to a sequence of convex optimal control problems.

11:20 AAS Guidance and Navigation of a Callisto-Io-Ganymede Triple Flyby Jovian Capture 15-624 Alan Didion, West Virginia University; Alfred Lynam, West Virginia University Triple-satellite-aided capture maneuvers greatly reduce the ΔV required to insert into Jovian orbit and provide close flyby opportunities at three of Jupiter's four large Galilean moons. This paper focuses on the guidance and navigation of such trajectories in the presence of state errors, ephemeris errors, and maneuver execution errors. A powered-flyby trajectory-correction-maneuver is added to the nominal trajectory at Callisto and the nominal Jupiter orbit insertion maneuver is modified to complete capture and target the Ganymede flyby. A third correction is employed to act as a JOI cleanup maneuver. A Monte Carlo simulation shows that correction ΔV is manageable.

11:40 AAS SWITCHING PATHS AT THE LUNAR ‘ROUTER’: FINDING VERY LOW-COST 15-629 TRANSFERS BETWEEN USEFUL TRAJECTORY SEQUENCES IN THE EARTH- MOON SYSTEM Tim McElrath; Rodney Anderson The Earth-Moon system allows many types of transfers between lunar encounters, including those with low perigees. Combinations of transfers can produce several different useful ballistic trajectory sequences. With the right orbit types (particularly backflips) included, a vehicle can cheaply (using low thrust) switch between sequences that have very different characteristics. Several useful sequences are presented, and the transfer cost vs. time is examined in both the patched-conic and CR3BP models. These trajectory sequences would be particularly applicable for returned asteroids (in the near term) and lunar-derived resource transport (in the long term).

Page 50 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Tuesday Session 5 Spacecraft GNC - 2

Session Chairs: David C. Hyland, Texas A&M University, Nathan Strange, JPL Room: Primrose

13:30 AAS Power Star: A New Approach to Space Solar Power 15-503 David Hyland, Texas A&M University; Haithem Altwaijry, King Abdulaziz City for Science and Technology Space Solar Power refers to the concept of a space system that collects solar power via photovoltaics and transmits it to ground collection stations using visible or microwave radiation. Previous system designs developed over the past several decades entail gigantic structures with many moving parts and require on-orbit infrastructure and in-space construction. The concept advanced here combines new solar cell / microwave printing technology with well established inflatable satellite technology to form a design that has no moving parts, requires no in-space construction and can be packaged in many existing launch vehicle payload fairings.

14:10 AAS LAUNCH RESULTS OF GUIDANCE & CONTROL SYSTEM OF EPSILON 15-737 ROCKET Hirohito Ohtsuka, IHI AEROSPACE Co.,Ltd.; Yasuhiro Morita, Japan Aerospace Exploration Agency; Kensaku Tanaka, IHI Aerospace Co.,Ltd JAXA launched the first Epsilon launch vehicle with a small payload 'Sprint-A' on September 14, 2013 in Japan. Epsilon has a new absorber structure in Payload Attach Fitting to reduce the vibration condition for payload. We designed the robust control logic to satisfy the compatibility of robust stability and response against various disturbance. The 3rd Stage under spinning has a Rhumb-line Control function which reduces the pointing error at separation and ignition of solid motor. We could insert the payload into the orbit precisely by ‘LVIC’ guidance, suitable for low thrust propulsion in Post Boost Stage. We will present the flight results of the G&C system and dynamics of Epsilon rocket.

14:30 AAS NEURAL NETWORK BASED ADAPTIVE CONTROLLER FOR ATTITUDE 15-754 CONTROL OF ALL-ELECTRIC SPACECRAFT Suwat Sreesawet, Wichita State University; Venkatasubramani Subba Reddiar Pappu, Wichita State University; Atri Dutta, Wichita State University; James Steck, Wichita State University This paper considers the attitude control problem for an all-electric spacecraft during its transfer to the Geostationary Earth orbit. During the transfer, the spacecraft's solar arrays need to point towards the Sun, except in eclipses, in order to operate the onboard electric thrusters. We propose a neural- network based adaptive controller, utilizing a Modified State Observer methodology, for the attitude control of the all-electric spacecraft. We demonstrate the performance of the controller for the case of orbit-raising of both small (6-kW) and large (20-kW) class of telecommunication satellites employing one or more BPT-4000 thrusters.

14:50 AAS ATTITUDE DYNAMICS OF A NEAR-SYMMETRIC VARIABLE MASS 15-771 CYLINDER Angadh Nanjangud, UC, Davis This paper examines the attitude motion of a near-symmetric cylinder with uniform mass loss. Since the fundamental equations governing the motion of a nearsymmetric system are typically non-linear, it is often difficult, or even impossible, to generate analytical solutions. In this paper, an

Page 51 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 approximation approach to linearize the equations of motion for a class of such systems to obtain analytical solutions is presented. Results from the approximate analytical solution and the numerical simulation of the exact nonlinear equations of attitude motion are contrasted and a simplification to the linear model is briefly explored.

15:10 Break

15:30 AAS Satellite Magnetism: Torque Rods for EyasSat3 Attitude Control 15-777 Michael Hychko, USAFA; David Richie, USAFA When employed correctly, torque rods are an effective pointing and/or reaction wheel desaturation means of satellite control: both on orbit and in the classroom. The US Air Force Academy has recently developed a brand-new CubeSat classroom demonstrator known as EyasSat3, complete with various attitude control sensor and actuator systems. Thus, this paper investigates effective magnetic control actuation through CubeSat torque rod sizing, analysis, and construction methods. These improvements yielded promising results that were further analyzed, compared, and contrasted herein, leading to follow-on classroom use that will satisfactorily demonstrate torque rod- based CubeSat attitude control and wheel desaturation.

15:50 AAS Circulant Zero-Phase Low-Pass Filter Design for Improved Robustification of 15-784 Iterative Control Bing Song, Columbia University; Richard Longman, Columbia University Iterative learning control can produce zero tracking error to a command that is repeated, each time starting from the same initial condition. Spacecraft applications include repeated scanning maneuvers with fine pointing equipment. A zero-phase frequency cutoff of the learning is needed to robustify to residual modes or parasitic poles. A zero-phase Butterworth filter has transients at both beginning and end of the trajectory. Here a circulant non-causal digital filter is developed whose singular value decomposition is a precise equivalent of the desired frequency response. This design addresses the usual difficulties with transients, and trajectory extensions of zero phase designs.

16:10 AAS 15- Singularity Analysis of Control Moment Gyros on Gyroelastic Body 804 Quan Hu; Yao Zhang; Jingrui Zhang; Zixi Guo, Beijing institute of technology Control moment gyro (CMG) is a widely used device for generating control torques for spacecraft attitude control without expending propellant. Because of its effectiveness and cleanness, it has been considered to be mounted on a space structure to achieve vibration suppression. The resultant system is the so-called gyroelastic body. Since CMGs could exert both torque and modal force to the structure, it can also be used to simultaneously achieve attitude maneuver and vibration reduction of an flexible spacecraft. In this paper, we consider the singularity problem in such application of CMGs.

16:30 AAS OVERVIEW OF THE ATTITUDE CONTROL SYSTEM DESIGN FOR THE 15-814 MAGNETOSPHERIC MULTISCALE FORMATION Steven Queen, NASA GSFC; Dean Chai, NASA GSFC The Magnetospheric Multiscale (MMS) mission which launched in March 2015 consists of four identically instrumented observatories orbiting the Earth in a tetrahedron formation. Each spin- stabilized spacecraft possesses a suite of instruments on eight deployable booms of various lengths which span more that 120-meters when fully extended. A primary requirement for mission success is the ability for the on-board systems to deliver precise orbit maneuver-adjustments capable of maintaining the shape of the formation without an unsustainable maneuvering cadence. The

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Updated July 31, 2015 #ASC2015 conjunction of these two mission features resulted in a 6-DOF maneuvering and attitude control system (ACS) that was unique in many respects.

16:50 AAS Generalized Momentum Control of the Spin-Stabilized Magnetospheric Multiscale 15-816 Formation Suyog Benegalrao, NASA Goddard Space Flight Center, Code 591; Steven Queen, NASA GSFC; Neerav Shah The Magnetospheric Multiscale (MMS) mission which launched in March 2015 consists of four identically instrumented, spin-stabilized observatories orbiting the Earth in a tetrahedron formation. The on-board attitude control system adjusts the angular momentum of the system using a thruster-actuated control system that simultaneously manages precession, nutation and spin. Originally developed using Lyapunov control-theory of rate-feedback, the algorithm has been augmented to provide a balanced attitude/rate response using a single weighting parameter. This approach overcomes an orientation sign-ambiguity, and also allows for a smoothly tuned-response applicable to both a compact/agile spacecraft, as well as one with large articulating appendages.

17:10 AAS The Transverse Dynamic Motion Control of the Flexible Bare Electrodynamic Tether 15-801 System GAGNQIANG LI, Shanghai Jiaotong University In paper, a high-fidelity computer model is developed by using the nodal position finite element method and 3-stage and fourth-order Symplectic Explicit Runge-Kutta Nystrom time integrator with consideration the elastic, thermal, and electrical coupling effects on the transverse dynamic motion and stability of the flexible bare electrodynamic tether system. A practical control strategy based on libration energy of the virtual tether of the flexible tether model is derived, the comparison study with previous control strategy are conducted.

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Updated July 31, 2015 #ASC2015 Tuesday Session 6 Formation Flying and Relative Motion

Session Chairs: Srinivas R. Vadali, Texas A&M University, Hanspeter Schaub, University of Colorado. Room: Rocky Ballroom A/B

13:30 AAS Global Coverage for Large Lattice Flower Constellations 15-790 Sanghyun Lee, Texas A&M University; Martin Avendano, University of Zaragoza; Daniele Mortari, Texas A&M University This paper addresses the problem of designing optimal satellite constellations for observing applications with a large number of satellites. The 2-D and 3-D Lattice Flower Constellations theory is here applied to design a 200 satellite constellation using circular orbits and elliptical orbits. Optimization is performed using Genetic Algorithms to estimate the constellation performance. Analysis is performed to validate the capability to guarantee continuous communication between one (or two) ground station(s) and any satellite. Graph theory is used to measure connectivity in the constellation. The resulting constellation has been compared with the constellation designed by the Walker constellations theory.

14:10 AAS Nonlinear Reduced Order Dynamics of Spacecraft Relative Motion for a Circular 15-622 Chief Orbit Eric Butcher, University of Arizona; Thomas Lovell, Air Force Research Laboratory Nonlinear reduced order models are obtained for spacecraft relative motion in the case of circular chief orbits. First, a nonlinear third order extension of the CWH equations is obtained and a modal transformation is employed that decouples the linear dynamics. Then two techniques, linear-based order reduction and the methodology of nonlinear normal modes, are employed to obtain nonlinear reduced models corresponding to the three modes of the CWH equations. The resulting nonlinear models extend linear modal analysis of the CWH equations to the nonlinear regime valid for larger separation distances and allow for a geometric characterization of the nonlinear dynamics of relative motion.

14:30 AAS Use of Nonlinearities for Increased Observability in Relative Orbit Estimation 15-623 Jingwei Wang, University of Arizona; Eric Butcher, University of Arizona; Thomas Lovell, Air Force Research Laboratory In this paper, the effects of incorporating nonlinearities in sequential relative orbit estimation are studied for a chief spacecraft in a circular orbit, assuming either range or line-of-sight measurement of the deputy from the chief. The relative motion models used in an extended Kalman filter can be categorized into four cases: first order (HCW equation), second order, third order and full nonlinear. Observability is studied analytically using Lie derivatives and numerically with the observability index and condition number obtained from employing an extended Kalman filter. The results highlight the improving benefits of using higher order nonlinear models.

14:50 AAS Establishing a Formation of Small Satellites in a Lunar Flower Constellations 15-640 Hanspeter Schaub, University of Colorado; Lauren McManus The success of previous Lunar science missions can be improved upon by using a constellation of satellites to increase the Lunar surface coverage. A constellation could also serve as a communications or GPS network for a Lunar human base. Small-sats are proposed as an affordable way to achieve a Lunar constellation and the establishment of a constellation of small satellites at

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Updated July 31, 2015 #ASC2015 the Moon is investigated. Optimal methods of deploying this constellation, the constellation lifetime, and other challenges associated with a constellation of small satellites at the Moon are studied.

15:10 Break

15:30 AAS Analytic Solution For Satellite Relative Motion With Nonspherical Gravity Effects 15-705 Bharat Mahajan, Texas A&M University, College Station; Srinivas R. Vadali, Texas A&M University; Kyle T. Alfriend, Texas A&M University Accurate analytical relative motion models are indispensable for fast and reliable prediction, fuel efficient formation maintenance, space situational awareness, and proximity operations. In this work, an analytical solution in the form of a state transition matrix/tensor for relative motion is proposed taking into account higher-order Earth’s nonspherical gravitational effects from J2 to J6. The proposed solution includes third-order secular effects for J2, J4 and J6, as well as second- order short-period and long-period effects from J2 to J6 with no zero eccentricity or zero inclination singularity.

15:50 AAS Continuous-Time Modeling and Control Using Linearized Relative Orbit Elements 15-773 Trevor Bennett, University of Colorado; Hanspeter Schaub, University of Colorado Motivated by the breadth of applications for relative orbit control in formation flying and proximity operations, a new approach to the time-varying Clohessy-Wiltshire (CW) equations is developed. The Lagrangian Brackets variations enable study of invariants in the presence of perturbation accelerations. The Lagrangian Brackets are applied to the constants in the CW equations to provide equations of motion. Investigated are the geometrical insights present when drag perturbations are included. In addition, a LROE feedback control law to transition between relative orbits is developed and numerically assessed. The manuscript concludes with relative orbit reconfiguration optimization fundamentals and discussion of additional work.

16:10 AAS SPATIAL RESOLUTION IN DENSITY PREDICTION FOR DIFFERENTIAL 15-531 DRAG RELATIVE MANEUVERING GUIDANCE David Guglielmo, University of Florida; David Perez, University of Florida; Riccardo Bevilacqua, University of Florida; Leonel Mazal, University of Florida Atmospheric differential drag can be used to control, propellant-less, the coplanar relative motion of multiple spacecraft in Low Earth Orbit provided they can vary their ballistic coefficients. However, the variability of the atmospheric density, and therefore the drag acceleration, makes the generation of accurate drag-based guidance challenging. Currently available models to estimate density have bias in their results, causing errors in drag force estimation. In this work, a method exploiting spatial resolution in forecasted density for creating improved guidance for drag maneuvers is presented. This allows for the creation of more realistic guidance trajectories for spacecraft differential drag- based relative maneuvering.

16:30 AAS Improved Teardrop Hovering Formation Control Strategy Based on Relative Orbit 15-653 Elements Chen Huan; Yinrui Rao; Chao Han, Beihang University The optimal four-impulse control strategy based on ROE, which requires at least one orbit period, is improved when there is relative drift between the reference satellite and chaser satellite. The double- impulse control strategy based on ROE for orbital transfer, in which the impulse time can be designed, is derived and optimized. The teardrop formation movement and reconfiguration

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Updated July 31, 2015 #ASC2015 strategies based on both the optimal four-impulse and double-impulse control strategies are developed and compared. Several simulation cases are presented to demonstrate the control strategies proposed.

16:50 AAS Bridging Dynamical Modeling Effort and Sensor Accuracy in Relative Spacecraft 15-677 Navigation Kohei Fujimoto, Utah State University; Kyle T. Alfriend, Texas A&M University; Srinivas R. Vadali, Texas A&M University In current practice, the dynamical model in a spacecraft navigation algorithm is often set ad hoc without explicit regard for the level of measurement, guidance, or control errors expected. In this paper, we develop methods to quickly survey the trade space between navigation system parameters and dynamical model fidelity. We focus our efforts on forces that have precise deterministic physical models, e.g., the Earth's gravity, such that modeling errors may be regarded as biases. Our approach simplifies the workflow of designing GNC systems by mitigating the need to conduct a large-scale non-linear numerical validation of system performance.

17:10 AAS Libration Point Orbit Rendezvous Using Linearized Relative Motion Dynamics and 15-747 Nonlinear Differential Correction Sara Case, a.i. solutions This paper presents a technique for computing a rendezvous trajectory with a target satellite in a libration point orbit. The chaser satellite completes the rendezvous by executing a series of impulsive maneuvers to travel between waypoints approaching the target satellite. Linearized equations of relative motion of the chaser with respect to the target in the circular restricted three body problem are used to compute the required magnitude and direction of the maneuvers; these results are then refined using differential correction with the nonlinear equations of motion. The performance of this technique is discussed and several rendezvous strategies are evaluated.

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Updated July 31, 2015 #ASC2015 Tuesday Session 7 Trajectory Design and Optimization - 4

Session Chairs: Thomas Carter, Eastern Connecticut University, Christopher Spreen, Purdue University Room: Larkspur

13:30 AAS Interactive Node Placement Capability For Spacecraft Trajectory Targeting In An 15-638 Ephemeris Model Christopher Spreen; Kathleen Howell, Purdue University; Belinda Marchand, Progalaxia, LLC Targeting and guidance are nontrivial but frequently accomplished by employing discretized representations of a trajectory via nodes along the path, reflecting the full state at specific times and locations. In complex regimes, sensitivity to the startup arcs, through the nodes, requires experience and knowledge of the dynamical environment for efficient corrections. Given a feasible solution, modification of node placements is particularly challenging. A corrections scheme is augmented by updating node placements based upon leveraging the stability attributes via the local Lyapunov exponents. An interactive capability allows visual insight into the dynamical behavior and is applied in an ephemeris model.

13:50 AAS Planar Optimal Two-Impulse Transfers 15-644 Thomas Carter, Eastern Connecticut State University,; Mayer Humi, WPI The problem of finding a planar two-impulse transfer orbit between two known Keplerian Orbits that minimizes the total characteristic velocity of the transfer arc is examined. Using a transformation of the variables presented in previous work, necessary conditions for an optimal transfer are determined, followed by a proof that an optimal transfer exists, concluding with some sufficiency arguments. This analysis results in sets of algebraic nonlinear equations whose computional solution reveals the optimal two-impulse transfers.

14:10 AAS Planar Optimal Two-Impulse Closed-Form Solutions of Transverse Transfers 15-645 Thomas Carter, Eastern Connecticut State University,; Mayer Humi, WPI The problem of finding a planar two-impulse transfer orbit between two known Keplerian orbits that minimizes the total characteristic velocity of the transfer arc is examined. Closed-form minimizing solutions are found for all cases in which elliptical boundary orbits are coaxial and all cases in which apses of boundary elliptical orbits are equidistant from the center of attraction. For these cases the minimizing transfers are transverse, and the transfer orbits are tangent to the boundary orbits at apses. An example having no minimizing solution is also presented.

14:30 AAS OPTIMAL ENERGY MANAGEMENT STEERING FOR LAMBERT’S PROBLEM 15-647 USING HYBRID OPTIMIZATIONG METHOD SIHANG ZHANG; Chao Han, Beihang University For Lambert’s problem, the optimal energy management steering method and the general optimal energy management steering method have been proposed and utilized to minimize the maneuver of the thruster during the burn. In com-parison with existing method, the optimal energy management steering, with smaller maneuver angle of the thruster, is smoother and more accurate. A hybrid optimization method is implemented for the optimal steering solution whereby the costates are added to the vector of free parameters and the performance index is directly minimized. Numerical results are presented to demonstrate the efficiency, accuracy and stability of the method.

14:50 AAS AN ADAPTIVE APPROACH FOR MODIFFED CHEBYSHEV PICARD

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Updated July 31, 2015 #ASC2015 15-625 ITERATION Ahmad Bani Younes, Khalifa University, Abu Dhabi; John Junkins, Texas A&M University The demand of having fast and efficient numerical propagators to solve engineering problems has become essential. The level of system complexity increases the cost of obtaining the solution. Many real world problems require developing efficient, precise and fast solutions. For example, efficient, high precision orbit propagation has gained renewed impetus due to the rapidly escalating demands for improved Space Situational Awareness (SSA) and the challenges posed by the Kessler Syndrome, which hypothesizes that every collision of two space objects drastically increases the probability of subsequent collisions. The recent development Junkins et al. of Modiffed Chebyshev Picard Iteration (MCPI) has shown

15:10 Break

15:30 AAS Multi-Objective Search for Multiple Gravity Assist Trajectories 15-664 Demyan Lantukh, The University of Texas at Austin; Ryan Russell, The University of Texas at Austin A systematic multiple gravity assist grid search and multi-level pruning algorithm is presented. Explore, a trajectory pathsolving tool, implements this sequential breadth-first algorithm. Decomposing the problem into a sequence of subproblems enables the inclusion of different trajectory segment and patching condition types. Comparisons between performing the search with ballistic transfers, impulsive maneuvers, and low-thrust approximation are presented. Pruning is conducted using constraints and multi-objective Pareto ranking with performance indices. The solution storage structure allows solution space subdivision and reduces data duplication. An overview of current global search and optimization methods for multiple gravity assist trajectories provides context for the presented method.

15:50 AAS A New Method for Determining the Time of Flight on a Powered Flight Trajectory for 15-671 Mission Planning & Design Darren Garber, NXTRAC This paper details the utility of the Generalized Transfer Equation (GTE) to provide a unique and computational efficient method for accurately determining the time of flight on a powered flight trajectory to include continuous, low, high and variable thrust profiles. With the continuing increase in advanced propulsion techniques (e.g. electric propulsion, solar sail, etc.), the need for rapid and accurate modeling of powered flight trajectories is critical to fully exploiting these new technologies and enabling responsive operations for ensuring safety of flight and enabling mission success

16:10 AAS HIGH-ORDER STATE TRANSITION TENSOR MODELS FOR THE 15-698 UNCERTAINITY PROPAGATION OF PERTURBED ORBITAL MOTION Ahmad Bani Younes, Khalifa University, Abu Dhabi; James Turner, Khalifa University, Abu Dhabi Modeling and simulation for complex applications in science and engineering develop behavior predictions based on mechanical loads. Imprecise knowledge of the model parameters or external force laws alters the system response from the assumed nominal model data. As a result, one seeks algorithms for generating insights into the range of variability that can be the expected due to model uncertainty. Two issues complicate approaches for handling model uncertainty. First, most systems are fundamentally nonlinear, which means that closed-form solutions are not available for predicting

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Updated July 31, 2015 #ASC2015 the response or designing control and/or

16:30 AAS EXPLOITING SYMMETRY IN HIGH ORDER TENSOR-BASED SERIES 15-701 EXPANSION ALGORITHMS Mohammad Alhulayil, Khalifa University; Ahmad Bani Younes, Khalifa University, Abu Dhabi; James Turner, Khalifa University, Abu Dhabi; Rabeb Mizouni Many applications in science and engineering require the calculations of partial derivative models. Computational differentiation has been developed as a software technology to addressing this need. The goal of computational differentiation is to generate first, second, and higher order sensitivity models, where the output is numerical. Typical applications include problems in applied mathematics and computer science for stability and optimizations studies. Both initial condition and parameter sensitivity applications are of interest. A major challenge with computational differentiation is that the explosive growth in the required computer memory for handling problems at an engineering level of fidelity. To handle these effects,

16:50 AAS EXPLOITING SPARSITY IN TENSOR-BASED COMPUTATIONAL 15-702 DIFFERENTIATION ALGORITHMS Mohammad Alhulayil, Khalifa University; Ahmad Bani Younes, Khalifa University, Abu Dhabi; James Turner, Khalifa University, Abu Dhabi; Rabeb Mizouni High order tensor models for applications in science and engineering require the calculation of partial derivative models. It is well known that Jacobian sensitivity problems have sparse structures, for which many powerful and effective algorithms have been developed. This paper explores to extension of these sparse technologies for higher-order gradient calculations. All partial derivatives are generated by using Computational differentiation software. Computational differentiation develops numerical solutions for all partial derivative orders. The structure of the first and higher order partials is usually fixed and can be exploited to eliminate both the generation and computation with known

17:10 AAS Comparison of Overall Propulsion System Effectiveness for Orbit Insertion and 15-724 Escape Maneuvers Nathan Strange, NASA / JPL Although specific impulse is often used as the primary measure of propulsion system efficiency, lower specific impulse systems with a smaller inert mass fraction can often provide better performance higher specific impuse systems. In addition, chemical propulsion systems can out- perform much higher specific impulse electric propulsion systems when they can use the Oberth effect, i.e. an impulsive maneuver deep in a gravity well. We show that for many cases solid rockets would outperform higher specific impulse liquid systems. We also show that for low v-infinities, chemical systems would outperform electric propulsion systems for orbit insertion maneuvers.

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Updated July 31, 2015 #ASC2015 Tuesday Session 8 Asteroid and Non Earth Orbiting Missions - 1

Session Chairs: Brent Barbee, NASA Goddard, Bong Wei, Iowa State University Room: Rocky Ballroom C/D

13:30 AAS Near-Earth Asteroids 2006 RH120 and 2009 BD: Proxies For Maximally Accessible 15-526 Objects? Brent Barbee, NASA Goddard Space Flight Center; Paul Chodas, Jet Propulsion Laboratory NASA's Near-Earth Object Human Space Flight Accessible Targets Study (NHATS) has identified nearly 1400 of the currently known 12,400 near-Earth asteroids (NEAs) as more astrodynamically accessible, round-trip, than Mars. Hundreds of those 1400 NEAs can be visited round-trip for less change-in-velocity than the lunar surface, and dozens can be visited round-trip for less change-in-velocity than low lunar orbit. How accessible might the hundreds of millions of undiscovered NEAs be? We probe that question by investigating the hypothesis that NEAs 2006 RH120 and 2009 BD are proxies for the most accessible NEAs we would expect to find and describing future NEA population model studies.

13:50 AAS Rosetta: Imaging Tools, Practical Challenges and Evolution of Optical Navigation 15-533 around a Comet David Antal-Wokes, SciSys Deutschland GmbH; Francesco Castellini, European Space Agency One challenge of ESA's Rosetta mission was developing a generic navigation tool about unknown bodies. Optical navigation was fundamental, through manual and automatic processing of the comet images. The image processing GUIs exercising continuous manual optical navigation are examined: the first addresses initial defining of landmarks and enabling a heuristic reconstruction of the landmarks and camera; the second enables manual processing by deriving an appropriate subset of images to aid in identifying all visible landmarks; the third is designed for poor imaging conditions, exercising contour-shifting. The image selection processes, predictive tools and N-point correction algorithms are derived and examples given.

14:10 AAS Induced Fragmentation of Asteroids during Close Encounters 15-546 Bryan Tester, University of Strathclyde; Massimiliano Vasile, University of Strathclyde We consider the behaviour of rotating binary asteroids as they pass through Earth's Hill sphere, with primary interest in the effect the tidal force has on the interaction between the two components of the binary and their post-encounter trajectories. We focus on contact binary asteroids bound by a regolith bridge, using both direct numerical simulation and an analytical approach.

14:30 AAS Towing Asteroids with Gravity Tractors Enhanced by Tethers and Solar Sails 15-553 Haijun Shen, Analytical Mechanics Associates, Inc.; Carlos Roithmayr, NASA Langley Research Center Material collected from an asteroid's surface can be used to increase gravitational attraction between the asteroid and a Gravity Tractor (GT); the spacecraft therefore operates more effectively and is referred to as Enhanced (EGT). We investigate use of tethers and solar sails to further improve effectiveness and simplify operations. By employing a tether, the asteroidal material can be placed close to the asteroid while the spacecraft is stationed farther away, resulting in a better safety margin and improved thruster efficiency. A solar sail on a spacecraft can naturally provide radial offset and inter-spacecraft separation required for multiple EGTs.

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14:50 AAS Impact Risk Assessment and Planetary Defense Mission Planning for Near-Earth 15-564 Asteroids George Vardaxis, Iowa State University The accurate estimation of the impact probability of hazardous asteroids is extremely important for planetary defense mission planning. Feasible mission trajectories can be found to mitigate the impact threat of hazardous asteroids. A computational method is developed to estimate the impact probability of the hazardous asteroid, investigate the fragmentation of the asteroid due to a disruption mission, and analyze its effects on the current and future encounters. A fictional asteroid, 2015 PDC, is used as a reference asteroid to demonstrate the effectiveness and applicability of computational tools being developed for impact risk assessment and planetary defense mission planning.

15:10 Break

15:30 AAS Non-Nuclear MKIV (Multiple Kinetic Impactor Vehicle) Mission Concept for 15-567 Pulverizing Small (50-150 m) Asteroids with Short Warning Times Bong Wie, Iowa State University; Ben Zimmerman, Iowa State University; Pavithra Premaratne, Iowa State University; Joshua Lyzhoft; George Vardaxis, Iowa State University This paper presents a non-nuclear MKIV (Multiple Kinetic Impactor Vehicle) concept for pulverizing small (50-150 m) asteroids. The proposed MKIV system simply consists of multiple kinetic impactors, and it is intended mainly for disruption, not deflection, of asteroids for short warning time scenarios. Multiple kinetic impactors simultaneously hit different locations widely distributed across the surface area of a target asteroid to cause the more effective propagation of shock waves across the wider surface area, in comparison with a single heavier kinetic impactor (with the same total mass of the MKIV system).

15:50 AAS Organizing Ballistic Orbit Classes around Small Bodies 15-619 Benjamin Villac, a.i. solutions, Inc.; Rodney Anderson, NASA / Caltech JPL; Alex Pini, a.i. solutions, Inc. Orbital dynamics around small bodies are as varied as the shape and dynamical state of these bodies. While various classes of orbits have been analyzed in detail, the global overview of relevant ballistic orbits at such bodies is not easily computed or organized. Yet, correctly categorizing these orbits will ease their future use in the overall trajectory design process. This paper overviews methods that have been used to organize orbits, and introduces new methods based on clustering approaches. While providing a flexible approach to classification, clustering algorithms also provide the ability to relate orbit classes across model complexity levels.

16:10 AAS Contactless Ion Beam Asteroid Despinning 15-659 Claudio Bombardelli, Technical University of Madrid (UPM); Daniel Pastor-Moreno, Technical University of Madrid; Hodei Urrutxua, Technical University of Madrid (UPM) The paper analyses the performance of an ion beam shepherd (IBS) spacecraft as a contactless actuator to modify the rotational state of an asteroid. The beam is pointed towards the asteroid with a properly controlled offset distance that maximizes the torque trnsmitted to the celestial body. Analytical and numerical tools are employed to evaluate the despin performance of the method for asteroids of various shapes and sizes. A simple control strategy to minimize the residual tumbling motion at the end of the despin maneuver is proposed. Results show that the method can

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16:30 AAS Tethered Gravity Assisted Maneuvers in Close Approach Asteroids to Acelerate a 15-665 Spacecraft Antonio Fernando Prado The present paper proposes the use of a Tethered Gravity Assisted Maneuver in a Near-Earth- Asteroid that makes a close approach with the Earth to give enough energy for a spacecraft to escape the Solar System. So, the spacecraft has energy enough to reach any planet of the Solar System. The maneuver starts with a spacecraft approaching the asteroid, coming from the Earth, with a given velocity Vinf,. Then it is connected to the asteroid by a tether, with length l, using an anchor device. After that the spacecraft rotates around the asteroid by an angle 2d, guided by the tether.

16:50 AAS On the Projection of Covariance Ellipsoids onto Non-planar Surfaces for Small Body 15-667 Landing Analysis Jay McMahon, University of Colorado; Nicola Baresi; Daniel Scheeres, University of Colorado The goal of this paper is to present the results of a set of relatively simple tools for projecting a position covariance onto the surface of a small body represented by either an ellipsoid or a polyhedral shape model. This approach provides fast access to the shape of the landing footprint on a small body, as well as the correlations with the time of landing within this footprint. This has the ability to greatly speed up the analysis of landing scenarios for current and future small body missions.

17:10 AAS Asteroid Rendezvous Problem Part 1: Autonomous Rendezvous Guidance for 15-699 Neighboring Relative Motion around Vesta Jingyang Li, Tsinghua University; Hongwei Yang; Mingwei Yin; Hexi Baoyin, Tsinghua University

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WEDNESDAY, AUGUST 12, 2015

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Updated July 31, 2015 #ASC2015 Wednesday Session 1 Space Situational Awareness - 3

Session Chairs: Marcus Holzinger, Georgia Tech, David Vallado, Center for Space Standards and Innovation. Room: Rocky Ballroom A/B

8:00 AAS Updated Covariance Transformations for Satellite Flight Dynamics Operations 15-537 David Vallado, Center for Space Standards and Innovation; Salvatore Alfano Covariance estimates are becoming more widely available as flight dynamics operations work towards greater accuracy. Investigators have looked at how covariance matrices are propagated, to include orbital state formats and coordinate systems. Various equations to convert between orbital state formats and satellite coordinate systems are essential to correctly compare each approach. The literature contains many partial examples. Vallado (2003) presented a complete set of equations, but advised that a few inconsistencies were found. We have corrected those errors and provide the results. Test results are given for a variety of orbital regimes, and MatLab code is available.

8:20 AAS ANALYSIS AND COMPARISON ON LS AND UKF FOR ORBIT ESTIMATION 15-648 Lu Deng, Beihang University; Xiucong Sun; Chao Han, Beihang University According to different requirements, applicabilities of the two common methods, namely, batch least squares method and unscented Kalman filter, and their corresponding derivative algorithms are discussed. First, the principles of classical batch least squares method and the unscented Kalman filter are briefly reviewed, and then the research progresses of these two estimation methods are summarized in detail. Moreover, sensitivity analysis of orbit determination results to different initial errors, measurement data-sampling periods, and measurement errors are made with classical and their derivative estimation algorithms. By comparison, some conclusions can be drawn about the rate, accuracy, stability and robustness of these algorithms.

8:40 AAS Improving Geolocation Accuracy through Refined Satellite Ephemeris Estimation in 15-670 an Ill-Conditioned System Jeroen Geeraert, University of Colorado at Boulder CCAR; Brandon Jones, University of Colorado Boulder; Jay McMahon, University of Colorado Commercial geolocating systems claim a capability of estimating the position of an interfering signal to within 5 km. Ephemeris inaccuracies are generally the primary source of error in geolocation and is therefore a main focus of this paper's research. Using a two-satellite technique of time difference of arrival (TDOA) and frequency difference of arrival (FDOA) and an improved ephemeris estimate, we are able to show geolocating capabilities down to just several hundred meters using real data. High fidelity dynamic and measurement models are used with both a Batch and Square Root Information Filter (SRIF) in a two-step process. First, using known calibrator transmitters the ephemeris is estimated. Second, using this ephemeris an unknown transmitter is geolocated with a consider batch filter (CBF). Due to the geometry of the satellite, transmitter and receiver setup, however, the system is ill-conditioned and introduces sensitivities, especially in the AGOM parameters. In spite of those sensitivities, the reduced ephemeris error significantly improves the geolocation accuracy.

9:20 AAS Analytical Covariance Equations for Solutions to the Initial Relative Orbit 15-723 Determination For Close-in Orbital Proximity Operations Baichun Gong, Northwestern Polytechnical University; David Geller, Utah State

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Updated July 31, 2015 #ASC2015 University; Jianjun Luo This research furthers the development of a closed-form solution to the angles-only initial relative orbit determination problem for close-in proximity operations when the camera offset from the vehicle center-of-mass allows for range observability.Closed-form analytic estimates of the relative state covariance based on angle measurement errors, attitude knowledge errors and camera center-of-mass offset uncertainties for three and more observations are obtained. A Monte Carlo simulation system with J2 perturba- tions is used to evaluate the performance of the closed-form relative state estimation algorithms and associated closed-form covariance equations. The sensitivity of the solution accuracy to different conditions is presented and discussed.

9:40 Break

10:00 AAS Uncued Satellite Initial Orbit Determination Using Signals of Opportunity 15-738 Johnny Worthy; Marcus Holzinger, Georgia Institute of Technology This paper investigates the application of signal of opportunity based multilateration to generate initial orbit estimates. Using at least 3 observer stations, the time differential of arrival of signals of opportunity can be measured by using hypothesis testing and matched filtering to identify unique signals. Each signal can then be classified by its source dynamics using a proposed classification scheme. Admissible region theory can then be applied to space sources and generate an initial orbit estimate.

10:20 AAS Orbit Determination for Geosynchronous Spacecraft Across Unobserved Station- 15-746 Keeping Maneuvers John Warner; Bryan Brown Accurately determining the orbits of geosynchronous spacecraft is challenging at best, and is even more difficult when such a spacecraft undergoes a station-keeping maneuver during which no observations are taken. Often even the times and kind of maneuver are unknown (apse pair, node pair, hybrid, etc.), except in the spacecraft operations center. Even so, it is often desirable to be able to include both pre-maneuver and post-maneuver observations in the orbit determination process. We discuss one method for modeling and using such maneuver models in batch Weighted Least Squares orbit determination. It is shown that by generating multiple maneuver hypotheses

10:40 AAS On Comparing Precision Orbit Solutions of Geodetic Satellites Given Several 15-752 Atmospheric Density Models John Warner; Annie Lum Many aspects of a satellite mission is directly impacted by the ability to precisely determine and accurately predict the satellite's orbit through high precision orbit determination. While gravity forces are typically well understood, the precise modeling of conservative forces is often more challenging. The precise modeling of drag forces is critical to high precision orbit determination for low Earth orbiting satellites. A number of current and historically recommended atmospheric density models are examined using the Naval Research Laboratory's Orbit Covariance Estimation and ANalysis (OCEAN) tool. High precision laser ranging data to geodetic satellites are used as test cases to evaluate

11:00 AAS OBTAINING NAVIGATION OBSERVABLES FROM HIGH DEFINITION 15-776 TELEVISION TOWERS Ryan Handzo, University of Colorado - Boulder; Austin Anderson, University of Colorado -

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Updated July 31, 2015 #ASC2015 Boulder; Jeff Parker, University of Colorado; Dirk Grunwald, University of Colorado - Boulder; George Born, University of Colorado at Boulder This paper considers the navigation observables that can be obtained from HDTV signals using the ATSC transmission standard. The ATSC transmission standard has multiple com- ponents that allow for range and Doppler navigation observables to be extracted. This paper looks at the structure of these observables as well as the types of hardware that are needed to obtain these observations. In addition, the paper will present a comparison between sim- ulated signal data used in satellite navigation studies and real data collected using hardware on the ground.

11:20 AAS The Impact of Intersatellite Range Measurements on the Orbit Determination of 15-780 Satellite Constellations Byron Davis, Georgia Institute of Technology; Brian Gunter, Georgia Institute of Technology The focus of this study is to examine the impact that intersatellite range measurements would have on the overall positioning knowledge of a constellation/formation of satellites across a range of different scenarios. The results of a sensitivity study is presented in which the precision and availability (maximum distance, sampling rate, number of simultaneous observations allowed, etc.) of the intersatellite measurements, along with the number and distribution of satellites, are all varied and assessed in a simulation environment. The results will help quantify the benefit of such observations and drive the requirements for future implementations of such ranging systems.

11:40 AAS Interplanetary Orbit Uncertainty Propagation Using Polynomial Surrogates 15-807 Marc Balducci, CCAR - CU Boulder Approximations for the time-varying distribution of interplanetary orbit state uncertainty have traditionally relied on Gaussian assumptions or computationally expensive Monte Carlo (MC) methods. This generally leads to reduced accuracy of the propagated uncertainty in the first case, or an undesirable number of orbit propagations in the latter. This paper considers the application of polynomial chaos (PC) for interplanetary orbit uncertainty propagation when there is one or more planetary or natural satellite flybys. The presented PC-based method of approximating the a posteriori probability density function requires no fundamental simplifying assumptions, and reduces the computation time compared to MC.

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Updated July 31, 2015 #ASC2015 Wednesday Session 2 Astrodynamics - 3

Session Chairs: Kathleen Howell, Purdue University, Hanspeter Schaub, University of Colorado. Room: Rocky Ballroom C/D

8:00 AAS Geosynchronous Debris Conjunction Lead-Time Requirements for Autonomous Low- 15-514 Thrust Disposal Guidance Paul Anderson, University of Colorado Boulder; Hanspeter Schaub, University of Colorado Autonomous, low-thrust guidance for active disposal of geosynchronous debris, subject to collision avoidance with the local debris population, is studied. A bisection method is employed to determine trajectory modifications to avoid a conjuncting object by a range of distances, assuming a range of collision lead times. A parametric study is performed in which re-orbit thrust accelerations are varied from 10-6-10-3 m/s2, to demonstrate how the continuous-thrust level impacts the required lead time to achieve a desired debris miss distance. The lowest thrust levels considered show that a 6-12 hour lead time is required to achieve 1-10 km debris separation at the predicted collision time.

8:20 AAS Analytic Power Series Solutions for Two-Body and J2-J6 Trajectories and State 15-663 Transition Models Kevin Hernandez, Texas A&M University Recent work by Turner and Elgohary has shown that Two-Body and J2 gravity perturbation terms can be analytically modeled using analytic continuation models. This work has been extended by Turner and Kim to demonstrate a highly effective variable step-size control for the analytic continuation Taylor series model. The current work builds on these earlier results by extending the analytic power series approach to trajectory calculations for two-body and J2-J6 gravity perturbation terms. The series solution algorithm is compared using Modified Chebyshev Picard Iteration (MCPI) and other state-of-the-art numerical integrators for both accuracy and computational efficiency.

8:40 AAS Meridian Ellipse Continued Fraction Cartesian to Geodetic Transformation 15-515 James Turner, Khalifa University, Abu Dhabi; Abdullah Alnaqeb, Khalifa University, Abu Dhabi; Ahmad Bani Younes, Khalifa University, Abu Dhabi A standard problem in modern geodesy involves the numerical inversion of the ellipsoidal coordinates that define the transformation. The key step involves the use of the Earth's surface unit vector. the problem necessary condition is formulated using the meridian ellipse that defines the plane section that intercepts the Earth's ellipsoidal model. The continued fraction solution algorithm presented in this work jprovides three significant benefits over existing approaches for the problem: (1) No quartic polynomial solutions required; (2) One iteration for useful solution accuracy; and (3) Uniform solution accuracy is obtained everywhere, including the Equator and the Polar regions.

9:00 AAS Mode Analysis for Long-term Behavior in a Resonant Earth-Moon Trajectory 15-572 Cody Short, Purdue University; Kathleen Howell, Purdue University; Amanda Haapala, Purdue University; Donald Dichmann Trajectory design in chaotic regimes allows for exploitation of system dynamics to achieve certain behavior. For the Transiting Exoplanet Survey Satellite (TESS) mission, the selected science orbit represents a stable option well-suited to meet the mission objectives. Extended, long-term analysis of particular solutions nearby in the phase space reveals transitions into desirable terminal modes induced by natural dynamics. This investigation explores the trajectory behavior and borrows from flow-based Finite-Time Lyapunov Exponent (FTLE) strategies to characterize modes of the motion.

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Updated July 31, 2015 #ASC2015 The goal is to identify mechanisms that drive the spacecraft into a particular modes and supply conditions necessary for such transitions.

9:20 AAS Satellite Formation-Keeping about Libration Points in the Presence of System 15-610 Uncertainties Mai Bando, Kyushu University; Hamidreza Nemati, Kyushu University; Shinji Hokamoto, Kyushu University Recently formation flying along halo orbits near a libration point or simply formation flying in the vicinity of a libration point of the circular-restricted three-body problem (CR3BP) has been studied from the point of view of future missions. Utilizing the Jordan canonical form of the system, we develop the fuel efficient formation flying controller along a halo orbit via linear quadratic regulator (LQR) and nonlinear chattering attenuation sliding mode controller (CASMC). Then the performances of LQR and CASMC are evaluated in the presence of system uncertainties.

9:40 Break

10:00 AAS Isolating Blocks as Computational Tools in the Circular Restricted Three-Body 15-615 Problem Rodney Anderson, NASA / Caltech JPL; Robert Easton; Martin W. Lo Isolating blocks may be used as computational tools to search for the invariant manifolds of orbits and hyperbolic invariant sets associated with libration points while also giving insight into the dynamics in these regions. We use isolating blocks to investigate the dynamics of objects entering the Earth-Moon system in the circular restricted three-body problem with energies close to the energy of the L2 libration point. Specifically, the invariant manifolds of Lyapunov orbits and hyperbolic invariant sets around the libration points are first obtained numerically using isolating blocks. Invariant spheres of solutions in the spatial problem are then located using the manifolds.

10:20 AAS End of Life Disposal for Three Libration Point Missions through Manipulation of the 15-618 Jacobi Constant and Zero Velocity Curves Jeremy Petersen, a.i. solutions; Jonathan Brown, a.i. solutions, Inc. The aim of this investigation is to determine the feasibility of mission disposal by inserting the spacecraft into a heliocentric orbit along the unstable manifold and then manipulating the Jacobi Constant to prevent the spacecraft from returning to the Earth-Moon system. This investigation focuses around L1 orbits representative of ACE, WIND, and SOHO. It will model the impulsive dV necessary to close the zero velocity curves after escape through either the L1 or L2 gateway in the circular restricted three body model and also include full ephemeris force models and higher fidelity finite maneuver models for the three spacecraft.

10:40 AAS Space Partitioning Structures For Efficient Stability Map Generation 15-689 Navid Nakhjiri, California State Polytechnic University, Pomona Stable orbits are known candidates for designing long-term science missions in perturbed dynamical environments. Finding stable regions containing these orbits often requires a tedious investigation of phase-space. Traditionally, a uniform sampling of many points in the phase-space is needed to generate a stability map that reveals the stable regions. However, an adaptive non-uniform grid can significantly reduce the computation effort. In this paper, a series of space partitioning structures have been explored for the purpose of adaptively generate a non-uniform grid that is dense near the boundaries of the stable regions

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Updated July 31, 2015 #ASC2015 11:00 AAS TRANSFERRING TO THE MERCURY THROUGH PERIODIC LIBRATION 15-696 POINT ORBITS IN THE ELLIPTIC SYSTEM Hao Peng, Beihang University; Shijie Xu New periodic libration point orbits in the Sun-Mercury Elliptic Restricted Three-Body Problem (ERTBP) are investigated as transferring relays from the Earth to the Mercury. These orbits are generated through a tangential continuation method starting from halo orbits. The ERTBP is time- dependent, so it is difficult to construct a transfer trajectory. In this study a comparison between directly transferring to the Mercury and the approach through a libration point orbit is presented. It is estimated how effective taking advantage of the ERTBP model can be. Our results is expected to provide experiences of designing orbits in the ERTBP.

11:20 AAS Design of Optimal Transfer Trajectory from Earth to L2 Lyapunov Orbit via L1 15-749 Lagrange point Jin Haeng Choi, Chonbuk National University; Tae Soo No, Chonbuk National University; Okchul Jung, Korea Aerospace Research Institute; Jeong Bu Baek; Young Jae Park Since the concept of Interplanetary Superhighway was proposed, research efforts to find or design a trajectory for touring several planets are equilibrium points are relatively few. In this paper, we propose a method of designing an optimal transfer trajectory from the Earth to L2 Lagrange point via L1 point in the Earth-Moon three body system. As way of enforcing a natural transit through L1 point after leaving the Earth, the energy level of the spacecraft is controlled so that its Jacobi constant remains slightly below of L2-energy level. This paper will present and analyze the results of more representative examples.

11:40 AAS Convex Constraints on Stability for Impulsive Transfer Optimization 15-691 Eric Trumbauer, University of California, Irvine; Navid Nakhjiri, California State Polytechnic University, Pomona Stable transfers have been proposed as a transfer strategy to guarantee mission recovery under the risk of maneuver or modeling errors. These transfers consist of a sequence of impulses such that the trajectory stays within the stable region of the dynamics at all times. As convex optimization becomes increasingly popular for both autonomous and ground based design, it is possible to include stability constraints directly into the problem formulation.

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Updated July 31, 2015 #ASC2015 Wednesday Session 3 Attitude Dynamics and Control - 3

Session Chairs: Robert Melton, Penn State, David C. Hyland, Texas A&M University Room: Primrose

8:00 AAS An Epitaxial Device for Momentum Exchange with the Vacuum State 15-504 David Hyland, Texas A&M University This paper re-examines the dynamic Casimir effect as a possible mechanism for propulsion. Previous investigations assumed mechanical motion of a mirror to generate thrust. In this case, because of the finite strength of materials and the high frequencies necessary, the amplitudes of motion must be restricted to the nanometer range. Here, we propose an epitaxial stack of transparent semiconductor laminae. Voltage is rapidly switched to successive lamina, creating continuous, large amplitude motion of a reflective surface without mechanical contrivances. The paper provides correct relativistic results for large amplitude motion. With meter-level magnitudes, propulsive forces are raised to significant levels.

8:40 AAS Attitude Dynamics of Spinning Satellites in an Elliptical Orbit 15-646 Dayung Koh, University of Southern California; Henryk Flashner, University of Southern California The attitude dynamics of a spinning satellite in an elliptical orbit subjected on gravity gradient torque is studied. Previous studies considered satellites in circular orbit and assumed small motion dynamics. In this paper, a new approach that combines analytical and numerical techniques is used to study the global behavior of the full nonlinear system. Families of periodic solutions and rich dynamic phenomena are analyzed. Stability properties and bifurcations of periodic solutions as function of satellite's spin rate and inertial property are presented. Fast Fourier analysis is utilized to further characterize the motion by finding quasi-periodic behaviors.

9:00 AAS Generalized Attitude Model for Momentum-Biased Solar Sail Spacecraft 15-656 Yuichi Tsuda, Japan Aerospace Exploration Agency; Takanao Saiki, JAXA / ISAS; Naoko Ogawa, Japan Aerospace Exploration Agency; Yuya Mimasu, Japan Aerospace Exploration Agency; Go Ono, University of Tokyo; Kosuke Akatsuka; Fuyuto Terui, ISAS/JAXA This paper describes a method of modeling attitude dynamics of momentum-biased spacecraft under strong influence of solar radiation pressure (SRP). The authors developed the theory called “Generalized Spinning Sail Model (GSSM)”, in which the spinning sail dynamics under strong influence of SRP is formulated with a simple mathematical form. This paper extends the GSSM theory to handle biased-momentum non-spinning solar sail spacecraft. The theory is applied to the operation of Japanese interplanetary probe Hayabusa2. It is shown that this novel method enables interplanetery missions to realize passive and reliable sun- pointing attitude with single wheel only, without fuel for long period.

9:20 AAS ROBUST AND OPTIMAL FUZZY MODEL-BASED ATTITUDE CONTROL OF 15-672 SPACECRAFT WITH FUEL SLOSHING Lilit Mazmanyan, Santa Clara University; Mohammad Ayoubi, Santa Clara University We present a robust-optimal fuzzy controller to stabilize the attitude of the spacecraft with a partially-filled fuel tank. First, the nonlinear equations of motion of spacecraft containing a liquid fuel store are presented briefly and approximated by the Takagi-Sugeno (T-S) fuzzy model. Next, the robust-optimal controller is designed with the parallel distributed compensation control

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Updated July 31, 2015 #ASC2015 technique. The problem of designing robust-optimal controller based on the Takagi-Sugeno fuzzy model with quadratic cost function and actuator amplitude constraint is cast in the form of linear matrix inequalities. In the end, the performance of the proposed fuzzy controller is examined with numerical simulation.

9:40 Break

10:00 AAS Frequency Response Based Repetitive Control Design for Linear Systems with 15-714 Periodic Coefficients Henry Yau, Columbia University; Richard Longman, Columbia University Feedback control (FB) systems make deterministic errors following periodic commands, characterized by the system bandwidth. Repetitive Control (RC) applies to systems performing a periodic command, and aims to eliminate error adjusting the command based on error in previous period. Spacecraft applications include repeating scanning maneuvers. The FB control error is likely reasonably small, so linearization of nonlinear equations about the desired trajectory produces an accurate model that is linear with periodic coefficients. This paper develops RC theory to apply to such models. It develops their frequency response, then mimics the particularly effective heuristic stability condition for constant coefficient systems.

10:20 AAS Attitude Dynamics Modeling of Spinning Solar Sail under Optical Property Control 15-716 Takuro Furumoto, the University of Tokyo; Tomohiro Yamaguchi, GMV at ESA/ ESOC; Ryu Funase, The University of Tokyo This paper presents a novel attitude control for a spinning solar sail spacecraft with reflectivity control capability using an extended form of Generalized Spinning Sail Model. This model aims to express long periodic motion of a spin axis while controlling the attitude by changing the optical properties of the sail. It is shown that the problem of controlling optical properties can be expressed as the problem of controlling properties of the spiral attitude behavior. It is also shown that the control performance is governed by three parameters. The fidelity of the proposed model is discussed using in-flight data of IKAROS.

10:40 AAS Time-Optimal Reorientation via Inverse Dynamics A Quaternion and Particle Swarm 15-762 Formulation Kaushik Basu, Pennsylvania State University; Robert Melton, The Pennsylvania State University An inverse-dynamics method is used in conjunction with a particle swarm algorithm to find near- minimum-time reorientation maneuvers in the presence of path constraints. The method employs a quaternion formulation of the kinematics, using B-splines to represent the quaternions. Overall results are compared with a similar approach that uses the Modified Rodrigues Parameters.

11:00 AAS Using Quadratically Constrained Quadratic Programming to Design Repetitive 15-772 Controllers: Application to Nonminimum Phase Systems Pitcha Prasitmeeboom, Columbia University; Richard Longman, Columbia University Repetitive Control (RC) can eliminate the effects of a periodic disturbance to a control system. Spacecraft applications include active vibration isolation from slight imbalance in CMG’s or reaction wheels. A particularly effective design produces an FIR compensator minimizing a quadratic cost to mimic the frequency response inverse by solving a set of linear equations. This paper minimizes the maximum error, formulating as quadratically constrained quadratic programming. The original cost is likely preferred in most applications. However, examining RC

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Updated July 31, 2015 #ASC2015 designs for nonminimum phase systems, there is difficulty producing effective designs. The new cost function is seen to produce much improved designs.

11:20 AAS Spacecraft Attitude Determination Simulation 15-779 Nathan Houtz; Carolin Frueh, Purdue University Knowing the attitude is crucial for many functions of spacecraft. Non-constant environmental torques and uncertainty in attitude control systems make it difficult to predict a spacecraft's orientation. This work addresses the problem of determining the attitude of a spacecraft at any particular instant via a star tracker, utilizing an experimental lab setup. A camera with two degrees of rotational freedom observes virtual stars. Nonlinear Kalman filter estimation techniques use the images from the camera to make an estimate of how the attitude has changed, which is compared with the change measured by the camera mount's sensors.

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Updated July 31, 2015 #ASC2015 Wednesday Session 4 Trajectory Design and Optimization - 5

Session Chairs: Renato Zanetti, NASA Johnson Space Center, Jeffrey Stuart, JPL Room: Larkspur

8:00 AAS Asteroid Impact Mission: a Possible Approach to Design Effective Close Proximity 15-694 Operations to Release MASCOT-2 Lander Fabio Ferrari, Politecnico di Milano; Michèle Lavagna, Politecnico di Milano The paper presents a potential and effective strategy to release MASCOT-2 lander - part of the Asteroid Impact Mission (AIM) - on the secondary of Didymos binary asteroid system. Suitable landing solutions are investigated with a three-body approach, exploited to model the gravity field in the proximity of Didymos binary asteroid, the target of AIM mission. Compared to classical Keplerian solutions, three-body dynamics is shown to be effective to lower the risk of lander rebounding on the binary smaller asteroid surface after a purely ballistic landing, and to make safer the overall release maneuver to be performed by AIM orbiter.

8:20 AAS FAST SEARCH ALGORITHM OF HIGH-PRECISION EARTH-MOON FREE- 15-706 RETURN TRAJECTORY Kun Peng Free-return trajectory design is an important guarantee for the safety of manned lunar mission. This trajectory can ensure that the spacecraft returns to Earth without any maneuver when the mission goes wrong. A fast search algorithm of high-precision Earth-Moon free-return trajectory is proposed in this paper. It is consisted of four parts: (1) solution model establishment for high-precision free- return trajectory, (2) initial values estimation for control variables, (3) multilevel search for free- return trajectory, (4) extended search for multiple types of free-return trajectory. This algorithm can search the accurate free-return trajectory without any designer-provided prior information, and can converge rapidly.

8:40 AAS LOW-THRUST EARTH-ORBIT TRANSFER OPTIMIZATION USING 15-728 ANALYTICAL AVERAGING WITHIN A SEQUENTIAL METHOD DAVID MORANTE, University Carlos III (Madrid); Manuel Sanjurjo-Rivo, Universidad Carlos III; MANUEL SOLER ARNEDO, UNIVERSITY CARLOS III MADRID A robust and flexible tool for computing optimal low-thrust Earth orbit transfer is pro- posed. This approach is based on three sequential steps of growing complexity. Each of the steps is grounded on methods developed in the literature and attempts to obtain near-optimal solutions in an effective manner. They will be reviewed independently comparing their own partial outcome, advantages and disadvantages. At the first and second stage, analytical av- eraging is used to propagate efficiently the trajectory together with predefined control laws. Finally, basing on the previous near-optimal solutions, the direct

9:00 AAS Generalized logarithmic spirals for low-thrust trajectory design 15-729 Javier Roa, Technical University of Madrid; Jesus Pelaez, Technical University of Madrid (UPM) Shape-based approaches are practical for the preliminary design of low-thrust trajectories. Logarithmic spirals are the simplest, but of little practical use due to having a constant flight-path angle. We prove that logarithmic spirals are only a particular case of an entire family of generalized spirals that originates from the same tangential thrust profile. These new curves are obtained when solving rigorously the equations of motion. Analytic solutions for the trajectory and the time-of-

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Updated July 31, 2015 #ASC2015 flight are obtained, an important improvement with respect to more complex curves. Applications to transfers and targeting problems are discussed.

9:20 AAS Mission Design Analysis for the Martian Moon Phobos: Close Flybys, Missed Thrusts, 15-756 and other In-Flight Entertainment Jeffrey Stuart, Jet Propulsion Laboratory; Tim McElrath, JPL/Caltech; Anastassios Petropoulos, NASA / Caltech JPL A robotic mission to the Martian moons Phobos and Deimos would offer a wealth of scientific information and serve as a useful precursor to potential human missions. In this paper, we investigate a prospective mission enabled by solar electric propulsion that would explore Phobos via a series of flybys followed by capture into orbit around the moon. Of particular interest are low-cost options for capture and walkdown to the target science orbits aided by multi-body effects due to the mutual gravitational interaction of Phobos and Mars. We also consider contingency operations in the event of missed thrust or maneuver execution

9:40 Break

10:00 AAS TRAJECTORIES FOR A NEAR TERM MISSION TO THE INTERSTELLAR 15-758 MEDIUM Nitin Arora, JPL; Nathan Strange, Jet Propulsion Laboratory / California Institute of Technology; Leon Alkalai Trajectories for rapid access to the interstellar medium(ISM) with a Kuiper Belt Object(KBO) flyby, launching between 2020 and 2030, are described. An impulsive-patched-conic broad search algorithm combined with a local optimization strategy is used for the trajectory computations. Two classes of trajectories, 1)with a perihelion maneuver and 2)with a powered Jupiter flyby, are studied and compared. Planetary flybys combined with leveraging maneuvers reduce launch C3 requirements (by factor of 2 or more) and help satisfy mission-phasing constraints. Low launch C3 combined with leveraging and a perihelion maneuver is found to be enabling for a near term mission to the ISM.

10:20 AAS Optimal Low-Thrust Geostationary Transfer Orbit Design Using Legendre-Gauss- 15-766 Radau Collocation David Spencer, The Pennsylvania State University; Andrew Goodyear, The Pennsylvania State University Low-thrust trajectories for optimal geostationary transfer orbits provide significant mass savings compared to traditional transfers. A numerical solution to optimal low-thrust geostationary transfer orbits is presented. Using a direct, Legendre-Gauss-Radau collocation technique, the minimum time problem is solved by turning the orbital mechanics problem into a nonlinear programming problem. The trajectory is modeled in an Earth-Centered Inertial coordinate system, and includes oblateness and Sun-Moon gravitational perturbations. Thrust along the transfer is assumed to be constant, with the control parameters being two angles that describe the direction of the thrust. The results

10:40 AAS Piecewise Initial Trajectory Design Using Linearized Dynamic Models 15-817 Ossama Abdelkhalik, Michigan Technological University; Shadi Darani Several approximating approaches have been developed in the literature for initial planning of low- thrust space trajectories. This paper presents investigation efforts on using linearized equations of motion for piecewise trajectory planning. The preliminary results show potential for this approach in generating initial guess trajectories for very low thrust acceleration space trajectories. This approach

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Updated July 31, 2015 #ASC2015 enables handling constraints on the maximum thrust force as well as no-thrust eclipse periods.

11:00 AAS SYSTEMATIC DESIGN OF OPTIMAL LOW-THRUST TRANSFERS FOR THE 15-757 THREE-BODY PROBLEM Shankar Kulumani, George Washington University; Taeyoung Lee, George Washington University A computational approach is developed for the systematic design of low-thrust transfers in the planar circular restricted three-body problem. Computational geometric optimal control is applied to compute the reachability set on Poincare sections. This formulation of the optimal control problem preserves the underlying geometric features of the optimal trajectory. Necessary conditions for optimality are derived and an efficient discrete solution method is proposed to solve the two point boundary value problem. Maximization of the reachability set enables the use of an iterative method to design optimal transfers between.

11:20 AAS Solar Sail Transfers from Earth to the Lunar Vicinity in the Circular Restricted 15-719 Problem Ashwati Das, Purdue University; Kathleen Howell, Purdue University The lunar region enables a variety of mission scenarios that advance space exploration endeavors. Therefore, a return to this region implies the development of alternative strategies to support affordable mission design options, subject to limited resource utilization. Hence, a general solar sail framework is developed to probe the capabilities associated with transfer options employing natural pathways. Prior investigations related to Earth-escape strategies, low thrust regimes and the development of desirable destination orbits at/near a primary all contribute. But, realistic mission constraints such as current sail technology levels, sail inefficiencies, occultation events and limitations on sail maneuverability all impact performance.

11:40 AAS SIMPLE GRAVITATIONAL MODELS AND CONTROL LAWS FOR 15-693 AUTONOMOUS OPERATIONS IN PROXIMITY OF UNIFORMLY ROTATING ASTEROIDS Andrea Turconi, Surrey Space Centre Maintaining missions in proximity of small bodies requires extensive orbit determination and ground station time due to a ground-in-the-loop approach. Recent developments in on-board navigation paved the way for autonomous proximity operations. The missing elements for achieving this goal are a gravity model, simple enough to be easily used by the spacecraft to steer itself around the asteroid, and guidance laws that can make use of such inherently simple model. In this paper we derive a simple three point mass model and propose control laws that can take advantage of the characteristics of this approximate model.

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Updated July 31, 2015 #ASC2015 Wednesday Session 5 Spacecraft GNC - 3

Session Chairs: Daniel Litton, NASA Johnson Space Center, Rees Fullmer, Utah State University Room: Primrose

13:30 AAS AN EXTENDED KALMAN SMOOTHER FOR DETERMINING UPPER 15-751 ATMOSPHERE WIND VELOCITIES USING DATA FROM THE FALLING SPHERE PAYLOAD Rees Fullmer, Utah State University; Chad` Fish, Utah State University The in-situ measurement of neutral winds in the upper atmosphere represents a major challenge. The Falling Spheres sounding rocket ballistic payload uses aerodynamic accelerations on the sphere to estimate these winds. An Extended Kalman Smoother has been developed to extract these very small accelerations (10-6 m/s2) and hence wind velocities from the data. The filter design, results and accuracies are presented.

13:50 AAS Detection strategies for high-rate, low SNR star detections 15-782 John Enright, Ryerson University; Tom Dzamba, Ryerson University; Laila Kazemi, Ryerson University Emerging applications for nanosatellite star trackers requires that sensors maintain an attitude lock during rapid maneuvers. Slewing to track a ground target from a low earth orbit (LEO) spacecraft is a common operational scenario. For these applications the sensors must be tolerant of body rate of around 1-deg/s. Although some star trackers have been design to be tolerant of much faster rates, this scenario nevertheless presents challenges for many compact instruments. At these rates, stars show pronounced elongation in the detector images and degraded SNR characteristics. In this study we evaluate a number of parametric strategies for detection and localization

14:10 AAS A Multilayer Perceptron Hazard Detector for Vision-Based Autonomous Planetary 15-529 Landing Paolo Lunghi, Politecnico di Milano - Aerospace Science & Technology Dept.; Marco Ciarambino, Politecnico di Milano; Michèle Lavagna, Politecnico di Milano A hazard detection and target selection algorithm, based on Artificial Neural Networks, is presented. From a single frame acquired by a VIS camera, the system computes a hazard map, exploited to select the best target, in terms of safety, guidance constraints, and scientific interest. ANNs generalization properties allow the system to correctly operate also in conditions not explicitly considered during calibration. The net architecture design, training, verification and results are critically presented. Performances are assessed in terms of recognition accuracy and selected target safety. Results for different scenarios are discussed to highlight the effectiveness of the system.

14:30 AAS Single-point Position Estimation in Interplanetary Trajectories using Star Trackers 15-660 Daniele Mortari, Texas A&M University This study provides a closed-form single-point position estimation technique for interplanetary missions using visible planets observed by star trackers. The least-squares solution is obtained by minimizing the sum of the expected minimum square distances. A weighted least-squares solution is provided by an iterative procedure. The weights are evaluated using the distances to the planets estimated by the least-squares solution. It is shown that the weighted approach does not require more than one iteration to converge. The light time correction is taken into account while the stellar abberation cannot be implemented in single-point estimation as it requires knowledge of the velocity.

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14:50 AAS IMAGE PROCESSING OF EARTH AND MOON IMAGES FOR OPTICAL 15-744 NAVIGATION SYSTEMS Stoian Borissov, Texas A&M University; Francesco de Dilectis, Texas A&M University; Daniele Mortari, Texas A&M University This paper presents a detailed method for processing true and synthetic images of the Moon and Earth for the purposes of optical navigation of spacecraft. The method takes in an image of a celestial body along with a priori information regarding observer position, identity of observed celestial object and its geometric parameters, and finally, camera parameters. Image processing follows a five step processing which produces an estimate for the relative distance between observer and target. Results of this estimation are shown. We demonstrate that the apparent radius can be estimated to within 3-sigma = 1/3 pixel precision.

15:10 Break

15:30 AAS Affine Invariant Tracking of Image Features Utilizing IMU Data 15-813 Brian Bergh, University at Buffalo; Manoranjan Majji, University at Buffalo, State University of New York Increasing trends in unmanned technologies have prompted the need for robust tracking systems. Utilization of aerial platforms further introduces a layer of complexity to the accurate resolution and registration of image features for photogrammetry by a systematic introduction of environmental effects such as the changes in illumination, view point, pose and scale. In order to improve the performance of autonomous image feature tracking systems, it is imperative to account for effects of platform motion in the dense optical flow of the image features observed by the camera system.

15:50 AAS Feedback Tracking Control Based On A Trajectory-Specific Finite-Time Causal 15-547 Inverse Nermin Caber, Helmut-Schmidt-University; Anil Chinnan, Columbia University; Minh Phan, Dartmouth College; Richard Longman, Columbia University; Joachim Horn, Helmut-Schmidt-University Classical feedback control is typically designed for infinite time with a focus on steady- state performance. However, Iterative Learning Control (ILC) operates in finite time where the same tracking operation is repeated over and over again. This paper develops a finite- time formulation of feedback control based on a trajectory-specific causal inverse that is consistent with the finite-time framework of ILC so that both can later be optimized simultaneously. The performance of the finite- time feedback controller is illustrated on a highly flexible lightly damped dynamical system for tracking a very short trajectory. Disturbance and measurement error are also considered.

16:10 AAS Thrust Vector Control of Upper Stage with Uncertainty of the Centroid 15-548 Zhaohui Wang, Beihang University; Lei Jin, Beihang University; Shijie Xu; Ming Xu, Beihang University For the upper stage, the command direction of thrust vector determined by the guidance system should ideally pass through the centroid. However, it is hard to realize in actual operation. Moreover, the low identification accuracy and the changing of centroid position make the situation worse. TVC of upper stage without the consideration of uncertainty of the centroid is obtained by our previous work. On the basis, an observer and a control algorithm are introduced to draw the thrust vector tracks the position of the centroid and aligns with the command direction.

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Updated July 31, 2015 #ASC2015 16:30 AAS MULTI-CONSTRAINT HANDLING AND A MIXED INTEGER PREDICTIVE 15-554 CONTROLLER FOR SPACE ROBOTS WITH OBSTACLE AVOIDANCE Jianjun Luo; Lijun Zong; Jianping Yuan This paper develops a mixed integer predictive control approach for space robots to avoid obstacles. Firstly, a novel obstacle avoidance constraint of space robots is formulated based on propositional logic. Then, in the frame of Model Predictive Control, the priority of the constraints is established based on propositional logic, considering three kinds of constraints (joint input and output limits, as well as the developed obstacle avoidance constraint), so that can guarantee the problem is solved under the satisfaction of the maximum number of constraints. Numerical simulations are finally given to demonstrate the performance of the methodology.

16:50 AAS Incorporating Angular Rate Sensors for Derivative Control of an Educational 15-788 CubeSat Richard Phernetton; Brian Kester, United States Air Force Academy The United States Air Force Academy's EyasSat3 is a low cost platform aimed at providing students with hands-on experience in satellite operation and design as a part of an integrated space systems engineering curriculum. This paper discusses implementation of a single-axis controller in EyasSat3 using light sensors and reaction wheels to orient the spacecraft toward a light source and follow it. Next, an angular rate sensor is incorporated into the controller to provide derivative feedback.The single axis controller provides a baseline for future 3-axis control design and provides critical sensor and actuator characterizations to be used in upcoming control strategies.

17:10 AAS A Two-Tiered Approach to Spacecraft Positioning from Significantly Biased Gravity 15-593 Gradient Measurements Xiucong Sun; Pei Chen; Christophe Macabiau; Chao Han, Beihang University The gravity gradient information is proposed to fix a spacecraft’s position in GPS-denied environments. A two-tiered approach is developed to deal with significant biases in actual gravity gradient measurements. The navigation process includes a positioning stage and an error calibration stage. The calibrated full-tensor gravity gradients are used to resolve positions, from which smoothed orbits can be obtained. A least-squares calibration filter is then used to process the observation residuals and to estimate the error parameters. The algorithm is tested with real data from the ESA’s GOCE satellite, and position accuracies of hundreds of meters are achieved.

Page 78 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Wednesday Session 6 Orbital Debris and Conjunction Analysis

Session Chairs: Liam Healy, Naval Research Laboratories, Glenn Peterson, The Aerospace Corporation Room: Rocky Ballroom A/B

13:30 AAS EXAMINATION OF POTENTIAL SOURCES OF SMALL HIGH DENSITY 15-528 PARTICLES IN EARTH ORBIT Glenn Peterson, The Aerospace Corporation; Marlon Sorge, The Aerospace Corporation Evidence of high-density man-made steel particles has been observed in returned Shuttle radiators and windows. However, the true physical sources of these particles have not been conclusively identified. This paper examines several potential sources (surface degradation of orbiting intact objects, historical explosions, and engine firings) and their consequences for long-term modeling:. It was found that few intact objects have stainless steel surfaces with implications for any surface degradation model, and, if explosions are a source, then the small particles should have decayed out of the environment by the present time.

13:50 AAS Containment of Moderate-Eccentricity Breakup Debris Clouds within a Maximum 15-534 Isotropic Spreading Speed Boundary Brian Hansen, The Aerospace Corporation; Felix Hoots Following the energetic breakup of a satellite, it is important to determine if any other satellites will be at risk from the resulting debris cloud. One method for assessing this risk involves the determination of times when a satellite flies within the boundary of the debris cloud. This analysis seeks to prove that a certain set of boundary fragments will form a surface that continues to contain the interior fragments of a moderate-eccentricity debris cloud evolving over time. Thus, if a satellite is not inside this surface, it will not be at risk from any other debris fragments.

14:10 AAS Comparison of non-intrusive approaches to uncertainty propagation in orbital 15-545 mechanics Chiara Tardioli; Martin Kubicek; Aaron Del Rio Bellisco; Massimiliano Vasile, University of Strathclyde; Edmondo Minisci Non-intrusive approaches are based on high order polynomial representations built on sparse samples of the system response to the uncertain quantities. The paper presents four different non- intrusive approaches to the propagation of uncertainty in orbital dynamics with particular application to space debris orbit analysis: a standard Polynomial Chaos Expansion, an Uncertain Quantification-High Dimensional Model Representation, a Generalised Gradient Enhance Kriging model and an expansion with Tchebicheff polynomials on sparse grids. This work assesses the computational cost and the suitability of these methods to propagate different forms of uncertainties characterized by precise and imprecise probability measures.

14:30 AAS DEBRIS REENTRY MODELING USING HIGH DIMENSIONAL DERIVATIVE 15-557 BASED UNCERTAINTY QUANTIFICATION Piyush Mehta, University of Strathclyde; Martin Kubicek; Massimiliano Vasile, University of Strathclyde; Edmondo Minisci Well-known tools developed for satellite and debris re-entry perform break-up and trajectory simulations in a deterministic sense and do not perform any uncertainty treatment. In this work, we present work towards implementing uncertainty treatment into a Free Open Source Tool for Re- entry of Asteroids and Space Debris (FOSTRAD). The uncertainty treatment in this work is limited to aerodynamic trajectory simulation. Results for the effect of uncertain parameters on trajectory

Page 79 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 simulation of simple objects like sphere, cube, cylinder and flat plate will be presented. The work uses a novel high-dimensional derivative based uncertainty quantification approach developed at the University of Strathclyde.

14:50 AAS Petascale Discovery of Passively Controlled Satellite Constellations for Global 15-584 Coverage William Whittecar, The Aerospace Corporation Satellite mission designers have long sought solutions to the global coverage problem using a minimum number of vehicles. Draim designed a four-satellite constellation with elliptical orbits that continuously covers the globe, but orbit perturbations can degrade coverage up to 32% without significant stationkeeping. This study combines high-fidelity orbit propagation and coverage analysis with many-objective evolutionary algorithms to explore the design space of four-satellite constellations, seeking alternatives to Draim’s design that maintain continuous coverage with minimal propellant. Also leveraging massively parallel computing and advanced visual analytics, we have discovered families of sustainable, passively controlled constellations that provide near- continuous worldwide coverage.

15:10 Break

15:30 AAS Conjunction Assessment Risk Trending Using a Simple Functional Model in a 15-586 Bayesian Framework Jonathon Vallejo, Baylor University; Matthew Hejduk, Astrorum Consulting LLC; James Stamey, Baylor University Conjunction events tend to follow a canonical pattern in which the probability of collision (Pc) ascends to a peak and then falls off rapidly, and event risk assessment can greatly benefit from being able to surmise whether this peak has been reached. A Bayesian modeling technique using a second-degree characteristic function with parameters determined from informative priors is employed to determine as individual events develop whether the peak Pc has been reached. Model performance is quite satisfactory, with correct identification exceeding 50% after two Pc values and typically residing in the 75-90% range by the risk mitigation maneuver commit point.

15:50 AAS Posterior distribution of an orbital ensemble from position-only observations 15-602 Liam Healy, Naval Research Laboratory; Christopher Binz, Naval Research Laboratory Unassociated partial-state observations of orbits can provide probabilistic information on the earth orbital environment. A probability density function (pdf) of orbits may be constructed from position-only observations by assuming that velocities are all equally possible subject only to physical constraints. The eccentricity vector can be computed; combined with previously-presented results for other elements, this can be used to derive the pdf over a complete set of state variables. Unassociated position observations from an ensemble of orbits provide a joint pdf by orbital element. The location of sensors and the distribution of orbits affect the quality and utility of the results.

16:10 AAS Maneuver Detection with Event Representation using Thrust-Fourier-Coefficients 15-631 Hyun Chul Ko, University of Colorado at Boulder; Daniel Scheeres, University of Colorado A systematic way of detecting unknown maneuvers is developed by representing unknown acceleration tied to an event with Thrust-Fourier-Coeffieicnts (TFCs). Event representation using TFCs can rigorously represent an unknown maneuver by generating an equivalent maneuver with the same secular behavior. By appending 14 TFCs as solve-for states, the modified sequential filter

Page 80 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 processes observation data both forwards and backwards in time to detect maneuver onset and termination time respectively. Along with the represented perturbing acceleration, the detection algorithm provides more accurate post-maneuver orbit solutions. A case study of detecting unknown maneuvers with different types of simulated measurement data verifies our approach.

16:30 AAS NOISE QUANTIFICATION IN OPTICAL OBSERVATIONS OF RESIDENT 15-635 SPACE OBJECTS FOR PROBABILITY OF DETECTION AND LIKELIHOOD Francois Sanson; Carolin Frueh, Purdue University Charged Couple Device (CCD) technology is widely used in the observation of resident space objects despite the noise they generate. Analytical estimate of the Signal to Noise ratio have been carried by Newberry and Merline et al. but recent needs for highly reliable observations in satellite tracking lead us to look for improvements in the pre-existing CCD equations. This study aims at critically inspecting the hypotheses involved in the CCD equation to provide a rigorous derivation and to compare it with computer run simulations of CCDs. Finally probability of detection are derived for the use in multi-target tracking algorithms.

16:50 AAS REGULARISED METHODS FOR HIGH-EFFICIENCY PROPAGATION 15-697 Jacco Geul, Delft University of Technology; Ron Noomen, Delft University of Technology; Erwin Mooij, Delft University of Technology Although regularised propagation methods have a good performance (accuracy versus evaluations), they suffer from a number of practical difficulties, such as propagation to a fixed time, making them ill-suited for practical applications. Several solutions that address these limitations are proposed, thoroughly discussed, and analysed on diverse test cases. Dromo outperforms the conventional propagation methods significantly. It is shown that regularised methods, through some adaptations, can be successfully applied to different orbit problems. The proposed method is recommended especially for computationally demanding problems.

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Updated July 31, 2015 #ASC2015 Wednesday Session 7 Trajectory Design and Optimization - 6

Session Chairs: Alfred Lynam, West Virginia University, Ryan P. Russell, The University of Texas at Austin Room: Larkspur

13:30 AAS Conjugate Unscented Transformation Based Collocation Scheme to Solve the 15-812 Hamilton Jacobi Bellman Equation Manoranjan Majji, University at Buffalo, State University of New York; Nagavenkat Adurthi, University at Buffalo; Puneet Singla, University at Buffalo The objective of this paper is to present a non-product collocation method to efficiently solve the Hamilton- Jacobi-Bellman (HJB) equation for a general nonlinear system. Recently developed Conjugate Unscented Transformation (CUT) points will be used in conjunction with non-product quadrature rules to transcribe the optimal control problem and obtain a general solution methodology for the value function. Global solutions to the Hamilton-Jacobi-Bellman equations lead to the development of feedback control laws for nonliear dynamical systems with stability guarantees ensured by exploiting the relationships between the value function and the Lyapunov functions.

13:50 AAS PROGRADE LUNAR FLYBY TRAJECTORIES FROM DISTANT RETROGRADE 15-775 ORBITS Kathryn Davis, University of Colorado This paper examines trajectories from Distant Retrograde Orbits (DROs) that perform prograde lunar flybys. Nominal states on a DRO are given small perturbations and propagated forward in time. Perturbations as low as 20 m/s can initiate trajectories that leave the DRO in a retrograde fashion and later flyby the Moon in the prograde direction. For a perturbation of 100 m/s, 13% of all perturbations result in a prograde lunar flyby with a 55 day average time of flight. Topologically similar trajectories had correlated perturbation directions. The results presented here may aid in designing low-cost transfers from DROs to prograde orbits.

14:10 AAS Piece-wise Constant Charging Strategy For The Reconfiguration Of A 3-Craft 15-783 Coulomb Formation Yinan Xu, UMich This paper investigates the non-equilibrium fixed-shape three-craft Coulomb formation reconfiguration problem and proposes a trajectory program approach to accomplish the reconfiguration. The entire maneuver trajectories are divided into multiple phases. During each phase, only two of the three craft are charged. In this way the relative trajectory of the charged spacecraft during a certain phase is a conic section. The entire trajectories are composed of patched conics and/or straight lines. The procedures determining the three-phase maneuver strategy is developed, including a preadjusting phase and two transition phases.

14:30 AAS On the Accuracy of Trajectory State Transition Matrices 15-785 Etienne Pellegrini, The University of Texas at Austin Accurate partial derivatives are of the utmost importance for optimization and root-solving algorithms, but can prove challenging and computationally expensive to obtain. In the case of trajectory state transition matrices, integration tolerances often have to be tightened for the sole purpose of obtaining accurate derivatives, slowing the algorithms down unnecessarily. This paper presents different techniques for computing accurate state transition matrices while using low- fidelity propagation. Analytical methods are compared to the complex step approximation and finite

Page 82 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 differences methods, for a variety of problems and integration techniques. The complex step approximation proves to be the most versatile, yielding accurate derivatives in all scenarios. Other subtleties of partials computation are addressed.

14:50 AAS IDENTIFYING ACCESSIBLE NEAR-EARTH OBJECTS FOR CREWED 15-598 MISSIONS WITH SOLAR ELECTRIC PROPULSION Stijn De Smet, University of Colorado; Jeff Parker, University of Colorado; Jonathan F.C. Herman; Jonathan Aziz, University of Colorado Boulder; Brent Barbee, NASA Goddard Space Flight Center; Jacob Englander, NASA Goddard Space Flight Center This paper discusses the expansion of the Near-Earth Object Human Space Flight Accessible Targets Studies (NHATS) with Solar Electric Propulsion (SEP). The research will investigate the existence of new launch seasons that would have been impossible to achieve using only chemical propulsion. Furthermore, this paper will investigate to what extent SEP can be used to reduce the launch mass of potential missions as compared to the current, purely chemical trajectories identified by the NHATS project.

15:10 Break

15:50 AAS Fast and robust optimization of high fidelity low thrust transfer orbits with 15-800 constraints David Mostaza Prieto, SES Engineering; Georges Krier, SES Engineering This paper presents the development and validation of an original method to optimize low and medium thrust trajectories between two orbits. The main difference with respect to previous approaches is a great improvement in robustness and speed. The method is able to solve any high fidelity minimum time or minimum fuel problem in a few seconds, without convergence issues and without the need for an initial guess. These features allow supporting both studies and real time operations, such as low-thrust transfer orbits to GEO. Several interesting results and findings regarding low-trust orbits are also provided.

16:30 AAS Fuel-efficient Planetary Landing Guidance with Hazard Avoidance 15-682 Yanning Guo, Harbin Institute of Technology; Hutao Cui; Guangfu Ma, Harbin Institute of Technology; Yao Zhang In order to satisfy real-time, low-fuel consumption and hazard avoidance requirements, an improved guidance strategy for planetary precise landing is proposed based on ZEM/ZEV guidance algorithm and potential method. Several key problems, including the assessment strategy of the collision possibility, the relocation of the waypoints and landing site, the hazard avoidance guidance algorithm in the context of control force magnitude constraint, will be presented in details. The feasibility of the proposed strategy will be evaluated through a variety of simulations for a typical Mars landing scenario.

16:50 AAS A Free-Return Earth-Moon Cycler Orbit for an Interplanetary Cruise Ship 15-794 Anthony Genova; Buzz Aldrin A periodic circumlunar orbit is presented that can be used by an interplanetary cruise ship for regular travel between Earth and the Moon. This Earth-Moon cycler orbit was revealed by introducing solar gravity and modest phasing maneuvers (average of 39 m/s per month) which yields close-Earth encounters every 7 or 10 days. Lunar encounters occur every 26 days and offer the chance for a smaller craft to depart the cycler and enter lunar orbit, or head for a Lagrange point (e.g., EM-L2 halo orbit), distant retrograde orbit (DRO), or interplanetary destination such as a near-

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Updated July 31, 2015 #ASC2015 Earth object (NEO) or Mars.

17:10 AAS ORBIT TYPE SELECTION AND ORBIT KEEPING ANALYSES FOR RELAY 15-708 SATELLITES AROUND THE EARTH-MOON L2 Fenglei WU; Weiguang Liang; Peng Zhang; Weihua HAN The Service Module of Chinese Chang'e 5-T1 spacecraft circled the Earth-Moon L2 libration point successfully. Spacecrafts flying around L2 have the advantage of serving as the relay satellites for the lunar far-side communications. Firstly, the candidate relay satellite orbits are discussed. Secondly, the orbital parameters of the relay satellites are further discussed. The smaller the distance away from L2 is, the better the orbit is. Finally, orbital control strategy during the long-term operation has been analyzed. The delta-V requirement for keeping the relay satellite orbit is approximately 0.16m/s per day.

Page 84 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Wednesday Session 8 Asteroid and Non Earth Orbiting Missions

Session Chairs: Jay McMahon, University of Colorado at Boulder, Jeffrey S. Parker, University of Colorado at Boulder. Room: Rocky Ballroom C/D

13:30 AAS Passive vs. Parachute System Trade For Robotic Sample Return Mission Studies 15-550 Robert Maddock, NASA Langley Research Center Describes the development of a simplified parametric parachute sizing model for the Multi-Mission Earth Entry Vehicle concept and the utilization of that model in a system trade analysis to determine under what conditions might a fully passive vehicle be more desireable (e.g. has the greater payload mass to EEV system mass ratio) than one which utilizes a parachute system. Dimensional analysis of data provided by the MMEEV System Analysis for Planetary EDL (M-SAPE) trade space tool, over an extensive span of likely robotic sample return mission constraints, including entry conditions, payload mass, vehicle size, and payload landing requirements, is then used to evaluate this system performance trade.

13:50 AAS Sensitivity Analysis of the OSIRIS-REx Terminator Orbits to Random De-sat 15-565 Maneuvers Siamak Hesar, University of Colorado Boulder; Daniel Scheeres, University of Colorado; Jay McMahon, University of Colorado OSIRIS-REx is NASA's asteroid sample return mission and is aimed for launch in the year 2016 to the asteroid 1999 RQ36. The nominal orbit considered for the science phase of the mission is a sun- terminator circular orbit. Sun-terminator orbits are quasi-stable orbits in a solar radiation pressure dominated environment. However, due to highly non-Keplerian dynamics that exist in such an environment, small perturbations can lead to large deviations from the nominal trajectory. Such perturbations arise from errors in de-saturation maneuvers. In this study we analyze the sensitivity of the terminator orbits to the maneuver execution errors and their uncertainties.

14:10 AAS Shape Dependence of Kinetic Deflection for a Survey of Real Asteroids 15-642 Juliana Feldhacker, University of Colorado at Boulder; Brandon Jones, University of Colorado Boulder; Alireza Doostan, University of Colorado; Daniel Scheeres, Colorado Center for Astrodynamics Research; Jay McMahon, University of Colorado The change in velocity imparted on an asteroid via a kinetic impactor is a function of uncertain system inputs so that the change in velocity itself is stochastic. This paper considers uncertainties in impact location and surface material properties in a survey of real asteroid shapes to determine the effect of shape on the resulting change in velocity. For each case, an analytic solution is computed for the distribution of the change in velocity resulting from impact, and this posterior distribution is decomposed into relative contributions by the system inputs using analysis of variance parameters known as the Sobol' indices.

14:30 AAS A POLYHEDRAL-POTENTIAL APPROACH FOR EDUCATIONAL 15-655 SIMULATIONS OF SPACECRAFT IN ORBIT ABOUT COMET 67P/Churyumov-- Gerasimenko Darren Hitt, University of Vermont; Jason Pearl, University of Vermont The European Space Agency's Rosetta Mission to comet 67P/Churyumov-Gerasimenko (67P/CG) has provided a wealth of detailed, 3-D topological data enabling the reconstruction a digital version of the body. Using this information, a discrete `polyhedra potential' approach has been taken to

Page 85 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 develop an a computational testbed for students in advanced astrodynamics courses to examine the irregular 3-D potential field of 67P/CG and the corresponding motion of a spacecraft in its orbit. These computational activities provide students with a valuable experience in appreciating the complexities associated with actual mission trajectory planning in stark contrast to idealized two- body models.

14:50 AAS Optimizing Small Body Gravity Field Estimation over Short Arcs 15-669 Jay McMahon, University of Colorado; Daniel Scheeres, University of Colorado Many current and future missions wish to target small bodies where challenging dynamics and weak gravity make estimation of the gravity field very difficult. The purpose of this paper is to investigate various orbit designs and measurement combinations in order to maximize the amount of gravity field information obtained over constrained timeframes. There are many drivers to this problem, however this paper attempts to illustrate the key components in reducing the gravity field uncertainty under common constraints, including time in orbit and limits on measurement cadence and/or quantity.

15:10 Break

15:30 AAS ORBITAL STABILITY REGIONS FOR HYPOTHETICAL NATURAL 15-681 SATELLITES OF 101955 BENNU (1999 RQ36) Samantha Rieger; Daniel Scheeres, University of Colorado; Brent Barbee, NASA Goddard Space Flight Center The OSIRIS- REx mission to return a sample from potentially hazardous near-Earth asteroid Bennu will occupy two distinct Sun-terminator plane orbits: one at a radius of 1 km, and another at a radius of 1.5 km. This research investigates whether Bennu might possess any natural satellites in long- term stable orbits that could interfere with spacecraft operations in Bennu’s vicinity. To investigate whether stable orbits exist for natural satellites of 10 meters or less, we consider known stable orbits such as terminator plane orbits and orbits that reside in what we refer to as the modified Laplace plane.

15:50 AAS Orbit Stability of OSIRIS-REx in the Vicinity of Bennu Using a High-Fidelity Solar- 15-690 Radiation Model Trevor Williams, NASA/Goddard Space Flight Center; Kyle Hughes, Purdue University; Alinda Mashiku, NASA GSFC; James Longuski, Purdue University Solar radiation pressure (SRP) is one of the largest perturbing forces on the OSIRIS-REx trajectory as it orbits the asteroid Bennu. In this work, we investigate how forces due to SRP perturb the OSIRIS-REx trajectory in a high-fidelity model. The model accounts for Bennu’s non-spherical gravity field, third-body gravity forces from the Sun and Jupiter, as well as for SRP forces acting on a simplified spacecraft model. Such high-fidelity simulations indicate significant SRP perturbations from the nominal orbit. Modifications to the nominal orbit are found using variation of parameters, and reduce the perturbation in eccentricity by a factor of one-half.

16:10 AAS Inflatable Sail for Asteroid Capture 15-721 Samuel Ximenes, XArc Exploration Architecture Corp; Barney Gorin, GoVentures, Inc.; Roy Hartfield, Auburn University; David Cicci, Auburn University; Bruce Tatarchuk, Auburn University; Marek Teichmann, CMLabs Simulations Inc. Discussed is a unique and innovative approach for robotically capturing an irregularly shaped asteroid, spinning in its lowest energy state. The concept permits capture of higher-aspect ratio

Page 86 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 asteroids outside of a mean 4-10m diameter. The concept employs an innovative, large “Sail” capture mechanism. The Sail is deployed beyond the spacecraft envelope and can adapt to an asteroid with a long dimension significantly larger than 10 meters. A “Spindle” configuration concept rotates the Sail capture mechanism with respect to the overall spacecraft allowing the spacecraft as a whole to remain inertially stable during the capture event and the subsequent asteroid de-spin process.

16:30 AAS The European Asteroid Impact Mission: phase A design and Mission Analysis 15-739 Michele Lavagna, Politecnico di Milano; Fabio Ferrari, Politecnico di Milano; Marc Scheper, OHB Systems AG; Bastian Burmann, OHB Systems AG; Ian Carnelli, European Space Agency The design of the mission analysis for the Asteroid Impact Mission (AIM), currently in phase A, is here presented. AIM is the European part of the joint cooperation between ESA and NASA on the Asteroid Impact & Deflection Assessment (AIDA) mission the target of which is the Apollo NEA binary system 65803 Didymos, to be reached at its close approach with Earth in late 2022 (less than 0.1 AU). Strategies adopted to design each mission phase are critically discussed, starting from the launch window selection, the interplanetary transfer tuning, the far-approach sizing, to the rendezvous and close-proximity maneuvering at Didymos.

16:50 AAS PREDICTION OF ASTEROID TRAJECTORY DEFLECTION DUE TO ALBEDO 15-786 CHANGE: An APPLICATION TO APOPHIS DEFLECTION Reza Raymond Karimi, Texas A&M University Permanent deflection of asteroid Apophis from a potential impact in 2036 can be achieved using an albedo manipulation technique by which the Yarkovsky acceleration components are changed and consequently the trajectory of the asteroid can be altered to avoid any potential conjunction. Since the spin axis and geometrical shape of the asteroid is unknown, the known spin axes of few other asteroids were used for the purpose of the study. A spin axis Monte Carlo analysis was performed to account for all possible axis orientations. This technique could be applied to mitigate other small NEAs and Earth-crossing objects.

17:10 AAS Asteroid Rendezvous Problem Part 2: Autonomous Rendezvous Guidance for Distant 15-700 Relative Motion around Vesta Jingyang Li, Tsinghua University; Hongwei Yang; Mingwei Yin; Hexi Baoyin, Tsinghua University Not Provided

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Updated July 31, 2015 #ASC2015

THURSDAY, AUGUST 13, 2015

Page 88 2015 AAS/AIAA Astrodynamics Specialist Meeting, Vail, Colorado

Updated July 31, 2015 #ASC2015 Thursday Session 1 Spacecraft GNC - 4

Session Chairs: Christopher Roscoe, Applied Defense Solutions, Roberto Furfaro, University of Arizona Room: Blue Spruce

8:00 AAS Close-Maneuvering Spacecraft Formation Flying via Immersion and Invariance 15-654 Adaptive Control Leonel Palacios, University of Glasgow; Gianmarco Radice, University of Glasgow; Arun Misra The objective of this paper is to develop a noncertainty-equivalence analytically-oriented adaptive control scheme for spacecraft formation flying, in both circular and eccentric reference orbits, via a novel geometric nonlinear control methodology called Immersion and Invariance Adaptive Control. The proposed approach commands the dynamical performance of one or several followers with respect to a leader to asymptotically track a time-varying nominal trajectory, while uncertainty in the modelling of perturbation forces is present. Test cases are simulated in order to compare the proposed controller performance with a classic adaptive control framework and results are presented in terms of fuel consumption.

8:20 AAS Stationkeeping control of real Earth-Moon collinear libration points using NMPC 15-692 Yanning Guo, Harbin Institute of Technology; Boyan Jiang, Harbin Institute of Technology; Guangfu Ma, Harbin Institute of Technology; Gang Liu, Harbin Institute of Technology; Jing Huang, Harbin Institute of Technology The problem of the station keeping control for periodic orbits around the libration points of the real Earth-Moon system is investigated. Considering all the gravitational forces of the planets, the periodic orbits are obtained in a complete Solar System model instead of conventional restricted three-body model. The station keeping control of the spacecraft on halo orbits is performed via the use of the nonlinear model predictive control. The closed-form solution for the control is relatively simple to calculate and well suited to the real-time embedded computing environment. Both control strategy and simulation results are based on a complete Solar System

8:40 AAS Optimal Low Thrust Orbit Correction in Curvilinear Coordinates 15-695 Juan Luis Gonzalo, Technical University of Madrid (UPM); Claudio Bombardelli, Technical University of Madrid (UPM) The minimum-time, low-constant-thrust transfer between two close, coplanar, quasi-circular orbits is studied using a novel non-linear formulation of relative motion in curvilinear coordinates. The Optimal Control Problem in the thrust orientation angle is treated from a quantitative and qualitative point of view, using the Direct and Indirect methods respectively. The former yields numerical solutions for a wide range of thrust parameters, while a better understanding of the physics is achieved seeking for approximate solution of the latter with perturbation techniques. Fundamental changes in the structure of the solution with the thrust parameter are identified.

9:00 AAS PID Tuning Using Genetic Algorithm in Three Axis Stabilized CubeSats 15-707 Kendrick Amezquita Three-axis Stabilization is widely used in the Attitude Determination and Control System (ADCS) of CubeSats, typically by using reaction wheels (RW). To implement such a stabilization, a robust controller is required in order to cope with perturbations and uncertainties that arise from the interaction with the space environment and physical variations such as inertia matrix deviation. A PID controller is suitable for this kind of applications when the controller's parameters are properly

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Updated July 31, 2015 #ASC2015 tuned. Therefore, in this paper we propose a Genetic Algorithm (GA) for tuning the PID controller's parameters, using MATLAB/Simulink.

9:20 AAS Optimal Collision-Avoidance Guidance for Rendezvous in Cluttered Environments 15-711 via Extreme Learning Machines Roberto Furfaro, The University of Arizona In this paper, we present the development of innovative relative guidance and control algorithms for safe, fuel-efficient autonomous rendezvous in highly cluttered environments that substantially improve performance and robustness while minimizing computational requirements.The guidance approach implements the next generation of Artificial Potential Function Guidance (APFG) which synthesizes path and time-constrained fuel effi-cient velocity fields via Extreme Learning Machines (ELM).

9:40 Break

10:00 AAS Relative Optical Navigation Around Small Bodies via Extreme Learning Machines: 15-712 Preliminary Results Roberto Furfaro, The University of Arizona; Andrew Law, University of Arizona A novel machine learning-based approach for relative optical navigation around small bodies is proposed. The algorithm is based on Extreme Learning Machine (ELM) theories which are built on the predicate that hidden-layers weights and biases can be randomly assigned and do not need to be tuned. As a result, training of a Single Layer Forward Network (SLFN) occurs by only determining the outer layer weights. ELM theories are employed to d-sign SLFNs that can estimate the relative spacecraft position from optical images taken from the navigation camera.

10:20 AAS CubeSat Proximity Operations Demonstration (CPOD) Mission: End-to-End 15-720 Integration and Mission Simulation Testing Christopher Roscoe, Applied Defense Solutions; Jason Westphal, Applied Defense Solutions; John Bowen, Tyvak Nano-Satellite Systems The CPOD mission will demonstrate rendezvous, proximity operations, and docking with a pair of 3U CubeSats using miniaturized components and sensors. The mission goal is to validate new small spacecraft technologies via spaceflight. Several systems were designed for this program: next generation miniature star trackers, reaction wheels, cold-gas propulsion, relative navigation sensors, power management electronics, and intelligent software solutions. We present an overview of the spacecraft and mission Concept of Operations, then describe recent end-to-end integration and simulation testing. The test campaign demonstrates the readiness of the integrated system for the flight mission, scheduled for launch in fall 2015.

10:40 AAS DIRECTIVE POSITIONING AND AUTONOMOUS NAVIGATION ALGORITHM 15-732 BASED ON DUAL CONE-SCANNING HORIZON SENSOR/STAR SENSOR Weihua Ma, Northwestern Polytechnical University; Jinwen Tan; Malcolm Macdonald, University of Strathclyde; Jianjun Luo Infrared Scanning Horizon Sensors (ISHS) could construct the Autonomous Integrated Navigation System (AINS) with other sensors. However, Jacobin matrix of filter’s observation equation is complex because the observations are always constructed with the angle from ISHS. Based on the horizon crossing vectors from ISHS and absolute attitude from star sensor (SS), a new directive positioning algorithm converting the ISHS outputs from angle to inertial position is constructed. The positioning error model is deduced, too. Thus new AINS filter chooses the inertial position from

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Updated July 31, 2015 #ASC2015 ISHS/SS as the observation and simplify the observation Jacobin matrix greatly. Simulation validates the idea.

11:00 AAS Autonomous Observation Planning with Flash LIDAR around Small Bodies 15-736 Ann Dietrich, University of Colorado Boulder; Jay McMahon, University of Colorado A flash LIDAR instrument, which returns a three-dimensional image of its subject, is investigated here for spacecraft autonomous navigation. Previous work found this instrument can provide high accuracy for navigation; however processing power was large. This study investigates the capabilities of flash LIDAR and techniques to reduce processing power. Edge detection matching within the image can provide a quick initial estimate of the spacecraft state to initialize the filter and determine safety. The observation planning algorithm developed maximizes the information content of a subset of image pixels through the Fisher Information Matrix, and reduces processing power without reducing accuracy.

11:20 AAS Random Matrix based Approach for Statistical Analysis of the Optimal Linear 15-810 Attitude Estimator Manoranjan Majji, University at Buffalo, State University of New York; Kumar Vishwajeet, University at Buffalo; Puneet Singla, University at Buffalo This paper focuses on the development of analytical methods for uncertainty quantification of the attitude estimates obtained by the Optimal Linear Attitude Estimator (OLAE) algorithm to quantify the effect of noise in the observation data. Starting from first principles, analytical expressions will be presented for the distribution of OLAE estimate by application of standard results in random matrix theory. Assuming the observations to be corrupted by zero mean Gaussian noise, the distribution of the linear model for the OLAE algorithm will be represented by the non-symmetric Wishart distribution. From the Wishart

11:40 AAS Differential geometry for Motion Along a rotating ellipse for Remote Sensing 15-517 James Turner, Khalifa University, Abu Dhabi; Fatima Hammadi, Khalifa University, Abu Dhabi; Maithah Hashemi, Khalifa University, Abu Dhabi; Ahmad Bani Younes, Khalifa University, Abu Dhabi Satellite Remote sensing aplicatons generate 2D map projectoins for observed points on the Earth's surface. When a phyiscal point on the Earth's surface is jprojected onto the map plane length distortions are introduced. A differential geometry approach is jpresented for rigorously computing displacement along arbitray arcs on the Earth's surface. A Taylor series based approach is developed. Arbitrary satellite motion in assumed. The ground track point is recovered from a cartesian to geodetic transformation algorithm. Arbitrary points off the ground track are accessed by locall rotating the Taylor expansion in the direction of the surface point.

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Updated July 31, 2015 #ASC2015 Thursday Session 2 Astrodynamics - 4

Session Chairs: Atri Dutta, Wichita State University, Thomas Starchville, The Aerospace Corporation Room: Juniper

8:00 AAS Equilibrium Points of Elongated Celestial Bodies as The Perturbed Rotating Mass 15-508 Dipole Xiangyuan Zeng, Tsinghua University; Junfeng Li; Hexi Baoyin, Tsinghua University; Kyle T. Alfriend, Texas A&M University; Shengping Gong, Tsinghua University The rotating mass dipole is adopted in this paper to approximate the gravitational field of the elongated celestial bodies. The equations of motion of the perturbed dipole model with oblateness of both primaries are derived to allow the existence of additional equilibrium points, including the points in the equatorial plane and in the plane xoz. Numerical simulations are performed to show the distribution of these equilibrium points along with zero-velocity curves around the dipole model. The effects of the oblateness of the primaries on the topological structure are also discussed based on the variation of zero-velocity curves.

8:20 AAS FORMATION FLYING CONSTANT LOW-THRUST CONTROL MODEL BASED 15-510 ON RELATIVE ORBIT ELEMENTS Xinwei Wang, Beihang University; Yinrui Rao; SIHANG ZHANG; Chao Han, Beihang University A new set of relative orbit elements (ROE) is used to establish a piecewise constant low-thrust control model for the satellites formation flying. An optimal objective function is defined in the control strategies of initialization, reconfiguration and configuration maintenance, which could be modified by the transfer error. The function extreme value has been solved by a nonlinear programming algorithm for the purpose of determining the propulsion time and scale. Furthermore, considering the impact of perturbations, a closed-loop feedback control law for configuration maintenance is derived. Numerical results indicate that the formation reconfiguration and configuration maintenance have been achieved.

8:40 AAS Orbit Determination and Differential-Drag Control of Planet Labs Cubesat 15-524 Constellations Cyrus Foster, Planet Labs; Henry Hallam, Planet Labs; James Mason, Planet Labs We present methodology and mission results from orbit determination of Planet Labs nanosatellites and differential-drag control of their relative motion. Orbit determination (OD) is required on Planet Labs satellites to accurately predict the positioning of satellites during downlink passes and we present a scalable OD solution for large fleets of small satellites utilizing two-way ranging. In the second part of this paper, we present mission results from relative motion differential-drag control of a constellation of satellites deployed in the same orbit.

9:00 AAS Review of Mission Design and Navigation for the Van Allen Probes Primary Mission 15-603 Justin Atchison, Johns Hopkins University Applied Physics Laboratory; Fazle Siddique, The Johns Hopkins University Applied Physics Laboratory The Van Allen Probes completed their primary mission on November 1, 2014 following two years of successful operation. The mission consists of two spacecraft in highly elliptical (e = 0.68), 9 hour orbits. This paper reviews their operations with respect to mission design and navigation. In terms of mission design, all requirements were met with no trajectory correction maneuvers. Three unplanned collision avoidance maneuvers were performed. In terms of navigation,

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Updated July 31, 2015 #ASC2015 overlap comparisons indicate that the 7 day prediction accuracy is better than 9 km for 95% of the samples, and the mission’s 22 km accuracy requirement is always satisfied.

9:20 AAS ORBIT AND ATTITUDE STABILITY CRITERIA OF SOLAR SAIL ON THE 15-604 DISPLACED ORBIT Junquan Li, Clyde Space Ltd; Mark Post, University of Strathclyde; George Vukovich, York University The polar regions of the Earth are of particular interest to spacecraft missions in terms of monitoring, provision of communications and resource exploration, and biasing the coverage provided in northern latitudes also has commercial advantages. This paper will study orbit and attitude stability criteria for a solar sail spacecraft that could serve this region and possible strategies for acquisition using the limited resources to miniaturized spacecraft without a propulsion system. An example of a coupled orbit and attitude stability analysis for a spacecraft using solar radiation pressure for displaced orbits will provide results based on stability and controllability criteria.

9:40 Break

10:00 AAS SEP Mission Design Space for Mars Orbiters 15-632 Ryan Woolley, NASA / Caltech JPL; Austin Nicholas, Jet Propulsion Laboratory/Caltech The advancement of solar-electric propulsion (SEP) technologies and larger, light-weight solar arrays offer a tremendous advantage to Mars orbiters in terms of both mass and timeline flexibility. These advantages are multiplied for round-trip orbiters (e.g. potential Mars sample return) where a large total ΔV would be required. In this paper we investigate the mission design characteristics of missions concepts utilizing various combinations and types of SEP thrusters, solar arrays, launch vehicles, launch dates, arrival dates, etc. We also present the SEP analog to the ballistic Porkchop plot – the “Bacon” plot.

10:20 AAS Europa Clipper Mission Concept: Trajectory Design Trades and Challenges 15-657 Try Lam, Jet Propulsion Laboratory; Juan Arrieta, NASA / Caltech JPL; Brent Buffington, NASA / Caltech JPL With potential sources of water, energy and other chemicals essential for life, Europa is a top candidate for finding life outside of Earth. This paper describes the current trajectory design concept for a multiple Europa flyby mission and discusses several trajectory design challenges. The reference trajectory utilizes multiple flybys to enable global coverage of Europa while orbiting Jupiter and balancing science requirements, radiation dose, propellant usage, and flight time. Trajectory design trades and robustness are also discussed.

10:40 AAS Compact Solution of Circular Orbit Relative Motion in Curvilinear Coordinates 15-661 Claudio Bombardelli, Technical University of Madrid (UPM); Juan Luis Gonzalo, Technical University of Madrid (UPM); Javier Roa, Technical University of Madrid (UPM) An exact solution of the relative motion in cylindrical curvilinear coordinates is provided in compact form starting from the solution of the individual Keplerian orbits of the chief and the follower spacecraft. An approximate solution valid for small inclination and small to moderate eccentricity of the follower is then obtained, which allows a rarther compact and accurate description of the highly nonlinear relative motion with no need to solve Kepler's Equation.

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Updated July 31, 2015 #ASC2015 11:00 AAS GRASP ALGORITHM FOR MULTI-RENDEZVOUS MISSION PLANNING WITH 15-761 OPTIMIZED TRIP TIMES Atri Dutta, Wichita State University The paper considers the Greedy Random Adaptive Search Procedure to optimize a sequence of rendezvous maneuvers by a spacecraft with multiple targets. The algorithm consists of two phases: the first phase constructs feasible solutions of the problem, and the second phase performs local search about the constructed solution. In this paper, we propose an improvement over prior work by considering optimization of the individual trip times during the mission. We consider multi- revolution solutions to the Lambert's problem in order to determine the optimal transfers corresponding to individual trips. Finally, we demonstrate our methodology using numerical examples for planar targets.

11:20 AAS Applications of Relative Satellite Motion Modeling using Curvilinear Coordinate 15-678 Frames Alex Perez, Utah State University; Thomas Lovell, Air Force Research Laboratory; David Geller, Utah State University This paper compares various satellite relative motion solutions previously derived via nonlinear transformations from a curvilinear coordinate frame to a Cartesian frame. The solutions can be compared by creating difference contour plots that show the difference of the maximum position error between two solutions. A relative maneuver targeting algorithm based on Lambert’s problem is developed using a cylindrical coordinate frame and compared with known Cartesian and second order relative motion maneuver targeting algorithms.

11:40 AAS Relative Satellite Motion Optimal Control using Convex Optimization 15-679 Alex Perez, Utah State University; David Geller, Utah State University; Jacob Gunther, Utah State University Convex optimization theory is applied to relative satellite motion to determine the optimal control profile for satellite rendezvous scenarios. The relative satellite rendezvous problem is shown to be convex when using the Hill-Clohessy Wiltshire linearized ordinary differential equations as the governing dynamics. Several inequality constraints are imposed on the convex problem in order to simulate keep-out zones, rendezvous corridors and navigation line-of-sight constraints. Several cases of satellite rendezvous are presented with varying initial conditions and times of flight to briefly show the utility and robustness of the convex optimization algorithm applied to relative satellite rendezvous.

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Updated July 31, 2015 #ASC2015 Thursday Session 3 Orbital Debris Analysis and Uncertainty Propagation

Session Chairs: Carolin Frueh, Purdue University, Suman Chakravorty, Texas A&M University Room: Rocky Ballroom A/B

8:00 AAS COLLISION AND RE-ENTRY ANALYSIS UNDER ALEATORY AND EPISTEMIC 15-709 UNCERTAINTY Massimiliano Vasile, University of Strathclyde; Chiara Tardioli, Strathclyde University The paper presents an approach to the design of optimal collision avoidance and reentry manoeuvres considering different types of uncertainty in the initial conditions and model parameters. The uncertainty is propagated, with a non-intrusive approach based on Tchebicheff high order expansions, through the system and dynamic models to form a high order polynomial representation of the uncertainty region enclosing the state of the spacecraft at the predicted collision time. The collision probability both in the case of precise and imprecise probability measures is computed considering the intersection between the uncertainty region of the impactor with the one of the target.

8:20 AAS Impacts of debris removal on future near-Earth-orbit population & Selection of 15-710 targets at short and long terms Melissa Zemoura, Kyushu University; Sonali Batra, Kyushu University; Toshiya Hanada, Kyushu University; Satomi Kawamoto, JAXA This proposed research aims to evaluate the effects of remediation activities on the future evolution of the near-Earth environment, both on long-term and short-term periods, depending on the nature and/or the number of removed objects. Using an analytical evolutionary model, 100 Monte-Carlo simulations were run over the various periods of analysis. In each scenario, the origins of the expected debris were identified, and the impacts of their removal were established through double- check simulations where the targeted objects were removed. Therefore, this study tries to suggest a way to classify the most adapted targets according to a particular aim or need.

8:40 AAS Observability of Space Debris 15-576 Carolin Frueh, Purdue University The knowledge of space objects, which are not operational and communicating any more re- lies solely on observations. Recently various authors have spent a lot of effort to develop better models for the space object propagation. Although the models were inspired by observations, it is hard to close the loop back and have a reliable falsification or confirmation procedure, as orbital motion, attitude motion, material properties etc are strongly coupled. This paper investigates the theoretical observability of different model parameters in optical observations. A consider-like approach is used in the observability analysis.

9:00 AAS A UKF-PF based Hybrid Estimation Scheme for Space Object Tracking 15-740 Dilshad Veettil, Texas A&M University; Suman Chakravorty A UKF-PF based hybrid filtering framework for space object tracking is presented. The hybrid filtering scheme is designed to provide accurate and consistent estimates when measurements are sparse without incurring a large computational cost. It employs an unscented Kalman filter (UKF) for state estimation when measurements are available. When the target moves out of the field of view of the sensor, the state probability density function is updated via a sequential Monte Carlo method. Three variants of the hybrid filter are considered by modifying UKF-PF transition. The hybrid filters are employed in two test cases to demonstrate their estimation performance.

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9:20 AAS A Randomized Sampling based Approach to Multi-Object Tracking with comparison 15-745 to HOMHT Weston Faber, Texas A&M University; Suman Chakravorty; Islam Hussein, Applied Defense Solutions In this paper, we present a randomized version of the finite set statistics (FISST) Bayesian recursions for multi-object tracking problems with application to the space situational awareness (SSA) problem. We introduce a hypothesis level derivation of the FISST equations that shows that the multi-object tracking problem may be considered as a finite state space Bayesian filtering problem, albeit with a growing state space. It further allows us to propose a randomized scheme, termed randomized FISST (R-FISST), where we choose the highly likely children hypotheses using Markov Chain Monte Carlo (MCMC) methods which allows us to keep the problem computationally tractable.

9:40 Break

10:00 AAS Singular Maneuvers in Angles-Only Initial Relative-Orbit Determination 15-769 Laura Hebert, Auburn University; Andrew Sinclair, Auburn University; Thomas Lovell, Air Force Research Laboratory A maneuver performed by either the chief or deputy spacecraft can provide observability in relative- orbit determination using angles-only measurements and linear, Cartesian dynamics model. This paper, however, presents solutions for maneuvers that result in singular measurement equations and therefore do not provide full-state observability. The singular maneuvers produce changes in the relative position that are proportional to the expected line of sight, and thus produce no changes in the measurements. These solutions for singular maneuvers provide insight into desirable maneuvers that improve the accuracy of the initial relative-orbit determination.

10:40 AAS DISTRIBUTED COMPUTATION FOR REAL-TIME FOOTPRINT GENERATION 15-617 Christopher McGrath, Naval Postgraduate School; Mark Karpenko, Naval Postgraduate School; Ronald Proulx It is computationally expensive to solve the series of highly non-linear optimal control problems required to generate landing footprints for reentry vehicles. Techniques that utilize parallel computation in conjunction with psuedospectral optimal control theory can significantly decrease the time required to generate high-fidelity landing footprints for reusable launch vehicles. These distributed computing techniques can calculate an entire footprint in almost the same time that it takes a serial method to generate a single optimal trajectory. The resulting speedup is a significant step towards real-time footprint generation.

11:00 AAS Analysis of Hyper-pseudospectral Transformation of Random Variables 15-630 Paul Frontera, Naval Postgraduate School; Ronald Proulx; Mark Karpenko, Naval Postgraduate School; Isaac M. Ross Accurate transformation of random variables is required for many estimation algorithms applications including guidance, navigation, and control (GNC). While the linear transformation of random variables is well understood, nonlinear transformations remain challenging as analytic solutions frequently do not exist and numeric approximation techniques must be employed. Existing approximation methods for nonlinear systems include linearization, Monte Carlo analysis using a sufficiently large number of samples, and numeric integration using the Unscented Transform. This paper demonstrates the use of Hyper-pseudospectral points, HS points,

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Updated July 31, 2015 #ASC2015 to approximate nonlinear transformation of random variables with greater accuracy than the existing Unscented Transform.

11:20 AAS Observability Assessment of Angles-Only Relative Navigation Using Different State 15-755 Representations Joshua Sullivan, Stanford Space Rendezvous Laboratory; Simone D'Amico, Stanford Space Rendezvous Laboratory This paper presents a novel comparative assessment of observability in angles-only relative navigation using three different state representations. A rigorous formulation of the relative dynamics as well as linear and nonlinear measurement sensitivity is presented in the framework of rectilinear, curvilinear, as well as relative orbital elements state representations. The associated observability matrices and observability Gramians are assessed analytically and numerically via iterative simulations to evaluate the conditioning characteristics of the dynamic system. Conclusions are drawn on the efficacy of the chosen dynamics and measurement sensitivity models for use in a novel estimation filter specifically designed for angles-only navigation.

11:40 AAS USING IN-FLIGHT NAVIGATION INFORMATION TO CREATE A DEFINED 3- 15-536 D FORMATION OF TWENTY-FOUR DEPLOYED SUB-PAYLOADS Ernest Bowden; Charles Kupelian; Brian Tibbetts The C-REX (Cusp Region EXperiment) sounding rocket mission launched November 24th, 2014, successfully demonstrating a new technique for deploying and detonating a formation of trackable chemicals in a defined 3-dimensional spatial grid comprised of twenty-four sub-payloads. This paper describes the new systems required to create this 3-D formation of sub-payloads in the face of the large trajectory dispersions associated with high altitude sounding rockets and achieve adequate separation within the short 12 minute total flight time. Preliminary results from the C-REX mission show separations of upwards of 40km from the main body, with the formation of sub-payloads being successfully implemented.

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Updated July 31, 2015 #ASC2015 Thursday Session 4 Space Environment and Spacecraft GNC

Session Chairs: Craig McLaughlin, Kansas University, Marcin Pilinski, ASTRA LLC. Room: Rocky Ballroom C/D

8:00 AAS Physics-Based Assimilative Atmospheric Modeling for Satellite Drag Specification and 15-818 Forecasts Marcin Pilinski, ASTRA LLC.; Geoff Crowley, ASTRA LLC.; Jonathan Wolfe, ASTRA LLC.; Tim Fuller-Rowell, CIRES Space Weather Prediction Center; Tomoko Matsuo, CIRES; Mariangel Fedrizzi, UCAR; Stan Solomon, UCAR; Liying Qian, UCAR; Jeffrey Thayer, Colorado Center for Astrodynamics Research; Mihail Codrescu, NOAA Space Weather Prediction Center We describe ongoing work to build a comprehensive nowcast and forecast system for specifying orbital drag conditions. The Atmospheric Density Assimilation Model (ADAM) is based on three state-of-the-art coupled models of the thermosphere-ionosphere running in real-time and uses assimilative techniques to produce a thermospheric nowcast. ADAM will also produce 72 hour predictions of the global thermosphere-ionosphere system using the nowcast as the initial condition and using near real-time and predicted space weather data and indices as the inputs. In this presentation, we will review the system requirements, describe the system design challanges and solutions, and present preliminary modeling results.

8:20 AAS Analytic models for drag-assisted rendezvous and proximity maneuvers 15-592 Vladimir Martinusi, University of Liège; Lamberto Dell'Elce, University of Liège; Gaetan Kerschen, University of Liège The paper offers an analytic method to determine and achieve the boundedness of the relative motion of two spacecraft orbiting at low altitudes. The method is based on the previous analytic results obtained by the authors, that introduced time-explicit propagators for the absolute and relative motion of satellites. It is proven that, under certain conditions, it is possible to acquire proximity flying and rendezvous only by adjusting the ballistic coefficients of the satellites. To that purpose, a maneuvering algorithm is developed, that is based on the analytic model of the relative motion under the assumption of a constant atmospheric density distribution model.

8:40 AAS Drag Coefficients and Neutral Density Estimation for the ANDE Satellites 15-741 Craig McLaughlin, University of Kansas; Harold Flanagan, University of Kansas: Department of Aerospace Engineering; Travis Lechtenberg, SpaceNav LLC The drag coefficients for the spherical Atmospheric Neutral Density Experiment (ANDE) satellites are calculated using different theories and assumptions to characterize the possible variations. Drag coefficients vary with altitude, solar activity, accommodation, and other factors. Satellite laser ranging data are used as observations in a precision orbit determination scheme to estimate density along the ANDE satellite orbits. The effects of using different drag coefficients on the estimated density are examined.

9:00 AAS Model Predictive Control of Planetary Aerocapture Using Takagi-Sugeno Fuzzy 15-742 Model Benjamin Margolis, Santa Clara University; Mohammad Ayoubi, Santa Clara University In this paper, we present a guidance and control algorithm for a planetary entry vehicle during an aerocapture maneuver. The proposed algorithm utilizes the model predictive control (MPC) technique with Takagi-Sugeno (T-S) fuzzy model of the vehicle to control the velocity and position

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Updated July 31, 2015 #ASC2015 of the entry vehicle using bank angle and angle-of-attack modulation. Finally, a Mars aerocapture case study is presented to evaluate the performance of the proposed algorithm.

9:20 AAS Analytical Assessment of Drag-Modulation Trajectory Control for Planetary Entry 15-748 with Application to Real-Time Guidance Zachary Putnam, Georgia Institute of Technology; Robert Braun, Georgia Institute of Technology Drag-modulation trajectory control is assessed for planetary entry using the analytical Allen-Eggers approximate solution to the equations of motion. A control authority metric for drag-modulation trajectory control systems is derived. Closed-form relationships are developed to assess range divert capability, identify jettison condition constraints for limiting peak acceleration and peak heat rate, and compute partial derivatives of interest. The closed-form relationships are used to build an analytical real-time guidance and targeting scheme for planetary entry. The guidance scheme is shown to be effective in the presence of expected day-of-flight uncertainty through example application to a notional Mars lander.

9:40 Break

10:00 AAS Hyperbolic Rendezvous at Mars: Risk Assessments and Mitigation Strategies 15-753 Ricky Jedrey, NASA - Johnson Space Center; Damon Landau, Jet Propulsion Laboratory; Ryan Whitley, NASA Given the current interest in the use of flyby trajectories for human Mars exploration, a key requirement is the capability to execute hyperbolic rendezvous. Hyperbolic rendezvous is used to transport crew from a Mars centered orbit, to a transiting Earth bound habitat that does a flyby. Representative cases are taken from future potential missions of this type, and a thorough sensitivity analysis of the hyperbolic rendezvous phase is performed. This includes early engine cut-off, missed burn times, and burn misalignment. A finite burn engine model is applied that assumes the hyperbolic rendezvous phase is done with at least two burns.

10:20 AAS EFFECTS OF ATMOSPHERIC DENSITY MODELS AND ESTIMATION 15-760 TECHNIQUES ON UNCONTROLLED RE-ENTRY PREDICTION Jin Haeng Choi, Chonbuk National University; Deok Jin Lee, Kunsan National University; Tae Soo No, Chonbuk National University; Dae-Won Chung; Okchul Jung, Korea Aerospace Research Institute; Hyeon Jung Yim, Korea Aerospace Research Institute The research is focused on the effects of the atmospheric density model and estimation techniques on the atmospheric re-entry prediction of an uncontrolled space object. For an accurate estimation of the orbital decay, an effective orbit determination approach is used to estimate the states of the object with a dynamic model compensation approach with radar observation data. For the analysis of the effects of the density model on re-entry prediction, three difference density models were used in the lifetime computation. Then, a break-up event that generates a group of break-up parts is simply modeled using the statistical model.

10:40 AAS PRELIMINARY DESIGN OF A MULTI-SPACECRAFT MISSION TO 15-765 INVESTIGATE SOLAR SYSTEM EVOLUTION USING SOLAR ELECTRIC PROPULSION Carlos Marc Alberto Deccia, CU Boulder; Jeff Parker, University of Colorado; Stijn De Smet, University of Colorado; Jonathan F.C. Herman; Ron Noomen, Delft University of Technology

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Updated July 31, 2015 #ASC2015 This paper discusses a preliminary mission design in order to study solar system evolution. Existing models trace the processes that formed planets starting from a protoplanetary disc. Despite the high fidelity of these models many aspects of planetary formation remain unclear and of great scientific interest. In order to validate these models and gain further insight in the involved processes, we propose a multi spacecraft approach. This concept will determine the uncertainty in the asteroids targeted orbit in order to deflect its course using solar electric propulsion (SEP), allowing terminal navigation upon impact. Impacts with a relative velocity below 10 km/s will allow direct observations to study solar system dynamics.

11:00 AAS DYNAMICAL SUBSTITUTES OF EQUILIBRIUM POINTS OF ASTEROIDS 15-787 UNDER SOLAR RADIATION PRESSURE Xiaosheng Xin, Nanjing University; Xiyun Hou Previous works have focused on the hovering points or periodic motion for an imperfect solar sail near an asteroid with the Hill approximation. In the current study, we analysed the equivalent equilibrium points, i.e., dynamical substitutes, of an asteroid under solar radiation pressure (SRP) in the asteroid rotating frame. The uniformly rotating triaxial ellipsoid is adopted to model the gravitation of the asteroid. Different orientations of the solar panel together with the varied parameters of the ellipsoid model are investigated to study the stability of the dynamical substitues and the corresponding invariant manifolds that could possibly intersect with the asteroid.

11:20 AAS ORBITAL MANEUVERING SYSTEM DESIGN AND PERFORMANCE FOR THE 15-815 MAGNETOSPHERIC MULTISCALE FORMATION Dean Chai, NASA GSFC; Steven Queen, NASA GSFC The Magnetospheric Multiscale (MMS) mission which launched in March 2015 consists of four identically instrumented, spin-stabilized observatories elliptically orbiting the Earth in a tetrahedron formation. A requirement for the operational success of the mission was the ability for the on-board systems to deliver precise maneuver adjustments. A 6DOF, closed-loop control system was developed that tracks a time-varying, inertial velocity-target with less than 1% error down to a millimeter-per-second lower-threshold. This level of performance is achieved in-part through integrated and dynamically-compensated accelerometer feedback with micro-gravity resolution. System performance is bounded through an extensive Monte Carlo simulation campaign that explores the multi-body dynamics and non-linear sensitivities, and demonstrated with flight results.

11:40 AAS Rendezvous via Differential Drag with Uncertainties in the Drag Model 15-520 Leonel Mazal, University of Florida; David Perez, University of Florida; Riccardo Bevilacqua, University of Florida; Fabio Curti Differential-drag relative maneuvers have been actively explored in the last decades, as they provide a method to drive two spacecraft into close-proximity configurations, reducing the need for propellant expenditure. However, drag force models bear significant levels of uncertainty in the Earth's atmospheric density and in the ballistic coefficients, which might jeopardize the maneuver performance. This work presents two approaches for differential-drag maneuvers, aimed at achieving rendezvous between two satellites. The proposed approaches explicitly consider and deal with the aforementioned uncertainties, ensuring the performance of the maneuvers. The attitude of the satellite is used as the control input.

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