Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 2007-12 Distributed autonomous control of multiple spacecraft during close proximity operations McCamish, Shawn B. Monterey, California. Naval Postgraduate School, 2007. http://hdl.handle.net/10945/10213 NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA DISSERTATION DISTRIBUTED AUTONOMOUS CONTROL OF MULTIPLE SPACECRAFT DURING CLOSE PROXIMITY OPERATIONS by Shawn B. McCamish December 2007 Dissertation Supervisors: Xiaoping Yun Marcello Romano Approved for public release; distribution is unlimited. THIS PAGE INTENTIONALLY LEFT BLANK REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188) Washington DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED December 2007 Dissertation 4. TITLE AND SUBTITLE Distributed Autonomous Control of Multiple 5. FUNDING NUMBERS Spacecraft During Close Proximity Operations 6. AUTHOR(S) Shawn B. McCamish 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING Naval Postgraduate School ORGANIZATION REPORT Monterey, CA 93943-5000 NUMBER 9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING / MONITORING N/A AGENCY REPORT NUMBER 11. SUPPLEMENTARY NOTES The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. 12a. DISTRIBUTION / AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Approved for public release; distribution is unlimited. 13. ABSTRACT (maximum 200 words) This dissertation reports the development of an autonomous distributed control algorithm for multiple spacecraft during close proximity operations, including rendezvous and docking. The proposed control algorithm combines the efficiency of Linear Quadratic Regulator (LQR) and robust collision avoidance capability of Artificial Potential Function method (APF). The LQR control effort serves as attractive force toward goal positions, while the APF-based repulsive functions provide collision avoidance for obstacles. The combination of the LQR and APF multiple spacecraft close proximity control algorithms yielded promising results as demonstrated by the simulations reported in this dissertation. The multiple spacecraft close proximity control algorithm was developed, refined, and thoroughly simulated using high fidelity six DOF spacecraft models. A versatile multiple spacecraft model validation and simulation visualization technique using a MATLAB-STK (Satellite Tool Kit) interface was created to propagate spacecraft models, compare against STK generated ephemeris, and animate for analysis. The MATLAB-STK interface efficacy was demonstrated during the evaluation and analysis of the innovative control algorithm. Additionally, the LQR/APF multiple spacecraft control algorithm was thoroughly analyzed via Monte-Carlo simulations to validate its stability and robustness. Finally, the LQR/APF multiple spacecraft control algorithm was evaluated by virtual hardware-in-the-loop implementation at the NPS Spacecraft Robotics Laboratory. 14. SUBJECT TERMS APF, LQR, control, multiple spacecraft, rendezvous, docking, 15. NUMBER OF assembly, maneuver, close proximity operations, simulation, STK, virtual hardware-in-the- PAGES loop. 281 16. PRICE CODE 17. SECURITY 18. SECURITY 19. SECURITY 20. LIMITATION CLASSIFICATION OF CLASSIFICATION OF THIS CLASSIFICATION OF OF ABSTRACT REPORT PAGE ABSTRACT Unclassified Unclassified Unclassified UU NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. 239-18 i THIS PAGE INTENTIONALLY LEFT BLANK ii Approved for public release; distribution is unlimited. DISTRIBUTED AUTONOMOUS CONTROL OF MULTIPLE SPACECRAFT DURING CLOSE PROXIMITY OPERATIONS Shawn B. McCamish Major, United States Air Force B.S., Electrical Engineering, Iowa State University, 1994 M.S., Electrical Engineering, Air Force Institute of Technology, 1995 Submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY IN ELECTRICAL ENGINEERING from the NAVAL POSTGRADUATE SCHOOL December 2007 Author: __________________________________________________ Shawn B. McCamish Approved by: ______________________ _______________________ Xiaoping Yun Marcello Romano Professor of ECE Assistant Professor of MAE Dissertation Committee Chair Dissertation Co-Advisor ______________________ _______________________ Roberto Cristi Tri Ha Professor of ECE Professor of ECE ______________________ Ravi Vaidyanathan Assistant Professor of SE Approved by: __________________________________________________ Jeffrey Knorr, Chair, Department of Electrical and Computer Engineering Approved by: __________________________________________________ Julie Filizetti, Associate Provost for Academic Affairs iii THIS PAGE INTENTIONALLY LEFT BLANK iv ABSTRACT This research contributes to multiple spacecraft control by developing an autonomous distributed control algorithm for close proximity operations of multiple spacecraft systems, including rendezvous and docking scenarios. The proposed control algorithm combines the efficiency of the Linear Quadratic Regulator (LQR) and the robust collision avoidance capability of the Artificial Potential Function (APF) method. The LQR control effort serves as the attractive force toward goal positions, while the APF-based repulsive functions provide collision avoidance for both fixed and moving obstacles. The combination of the LQR and APF control logics, referred to as the LQR/APF control algorithm, yielded promising results as demonstrated by the numerous multiple spacecraft maneuver simulations reported in this dissertation. In order to validate the proposed control approach, a multiple spacecraft model validation and visualization technique was developed using a versatile MATLAB- Satellite Toll Kit (STK) interface to propagate the spacecraft models, compare against STK generated ephemeris, and animate for analysis. The MATLAB-STK interface efficacy was demonstrated during the evaluation and analysis of the innovative LQR/APF multiple spacecraft control algorithm. The LQR/APF multiple spacecraft close proximity control algorithm was developed, refined, and thoroughly simulated using high fidelity six Degree of Freedom (DOF) spacecraft models. In order to evaluate the stability and robustness of the control approach a Monte-Carlo simulations set was run. The LQR/APF control algorithm was further evaluated by virtual hardware-in-the-loop implementation at the NPS Spacecraft Robotics Laboratory. The laboratory hosts the Autonomous Docking and Spacecraft Servicing testbed which allows for on-the-ground testing of close proximity multiple spacecraft control concepts. v THIS PAGE INTENTIONALLY LEFT BLANK vi TABLE OF CONTENTS I. INTRODUCTION........................................................................................................1 A. MOTIVATION AND BACKGROUND ........................................................1 B. RESEARCH GOALS ......................................................................................3 C. MAIN CONTRIBUTIONS .............................................................................4 II. OVERVIEW OF MULTIPLE SPACECRAFT MISSIONS ...................................7 A. MULTIPLE SPACECRAFT CONTROL .....................................................7 B. MULTIPLE SPACECRAFT MISSIONS......................................................8 1. Homogenous and Heterogeneous Spacecraft ..................................11 2. Orbiting Spacecraft Mission Phases.................................................12 3. Multiple Spacecraft Groups..............................................................13 III. SINGLE SPACECRAFT KINEMATICS AND DYNAMICS MODELING.......17 A. INTRODUCTION..........................................................................................17 B. KEPLERIAN ORBITAL DYNAMICS .......................................................19 1. Two Body Problem ............................................................................19 2. Orbital Elements ................................................................................20 C. REFERENCE FRAMES AND TRANSFORMATIONS ...........................22 1. Earth and Body Centered Reference Frames .................................23 2. Transformations.................................................................................27 D. ATTITUDE DYNAMICS..............................................................................29 1. Spacecraft Rotational Dynamics ......................................................29 2. Gravity Gradient................................................................................30 E. ORBITAL PERTURBATIONS....................................................................31 1. Non-Symmetrical Earth ....................................................................32