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Seminar 11 Project Management & System Design Spacecraft Guidance Robert Stengel FRS 148, From the Earth to the Moon Princeton University Project Management & Spacecraft Design Fundamentals of Space Systems, Ch 1 NASA-SP-2016-6105 Spacecraft Guidance: Understanding Space Sec 12.3

Copyright 2019 by Robert Stengel. All rights reserved. For educational use only. 1 http://www.princeton.edu/~stengel/FRS.html

Systems Engineering and Management § Introduction § Fundamentals of System Engineering § Concepts in Systems Engineering § Project Development Process § Management of the Development of Space Systems § Organization

Pisacane, V., Fundamentals of Space System Design, Ch. 1

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Systems Engineering

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Product Development

Pisacane, V., Fundamentals of Space System Design, Ch. 1

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NASA-2016-6105 5

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Spacecraft Mission Objectives and Requirements

Fortescue 7

Requirements Definition

• What must the system accomplish? • Why must it be done? • How do we achieve the design goal? • What are the alternatives? • What sub-systems perform what functions? • Are all functions technically feasible? • How can the system be tested to show that it satisfies requirements?

Wertz and Larson 8

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Program Management: Gantt Chart

• Project schedule • Task breakdown and dependency • Start, interim, and finish elements • Time elapsed, time to go

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Program Evaluation and Review Technique (PERT) Chart

• Milestones • Path descriptors • Activities, precursors, and successors • Timing and coordination • Identification of critical path • Optimization and constraint

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PERT Charts

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Project Phases

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Life Cycle Cost Impacts

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Spacecraft Subsystems

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Satellite Systems

• Power and •Structure •Electronics Propulsion –Skin, frames, ribs, –Payload –Solar cells stringers, –Control bulkheads –Kick motor/ –Radio payload assist –Propellant tanks transmitters and module (PAM) –Heat/solar/ receivers –Attitude-control micrometeoroid –Radar shields, insulation –orbit-adjustment transponders –Articulation/ –Antennas –station-keeping deployment –Batteries, fuel mechanisms cells –Gravity-gradient –Pressure tanks tether –De-orbit systems –Re-entry system (e.g., sample return)

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Functional Requirements of Spacecraft Subsystems

1. Payload must be pointed in the right direction 2. Payload must be operable 3. Data must be communicated to the ground 4. Desired orbit for the mission must be maintained 5. Payload must be held together and mounted on the spacecraft structure 6. Payload must operate reliably over some specified period 7. Adequate power must be provided

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LADEE Typical Satellite Mass Breakdown

• Satellite without on-orbit/de-orbit propulsion • Kick motor/ PAM can add significant mass 17

Communications Satellite Mass Breakdown

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Recommended Mass Growth Margins

Pisacane, V., Fundamentals of Space System Design, Ch. 1 19

Guidance, Navigation, and Control

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Guidance, Navigation, and Control

• Navigation: Where are we? • Guidance: How do we get to our destination? • Control: What do we tell our vehicle to do?

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First Apollo Program Contract MIT Instrumentation Laboratory August 9, 1961

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Components of Apollo CSM Primary Navigation Guidance and Control System (“PNGCS”)

Mindell, D., Digital Apollo, Ch. 5 23

Landmark Tracking for Apollo Guidance

Mindell, D., Digital Apollo, Ch. 5 24

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IMU Alignment and State Update

Mindell, D., Digital Apollo, Ch. 5

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Apollo Guidance Computer

• Parallel processor • 16-bit word length (hexadecimal) • Memory – 36,864 words (fixed) – 2,048 words (variable) • 1st operational solid-state computer • Identical computers in CSM and LM – Different software (with many identical subroutines) http://klabs.org/history/build_agc/ 26

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Apollo Guidance Computer Magnetic Core Memory Ropes

1 core = 1 bit 1 Kiloword Memory Bank

§ No built-in redundancy § No redundant computers § No failures § Mean time between failures = ∞

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Apollo Lunar Module Radars • Landing radar • Rendezvous radar – 3-beam Doppler – continuous-wave radar altimeter tracking radar – LM descent stage – LM ascent stage

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Apollo Guidance Computer Commands • Display/Keyboard (DSKY) • Sentence – Subject and predicate – Subject is implied • Astronaut, or • GNC system – Sentence describes action to be taken employing or involving an object • Predicate – Verb = Action – Noun = Variable or Program (i.e., the object)

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Numerical Codes for Verbs and Nouns in Apollo Guidance Computer Programs

Verb Code Description Remarks 01 Display 1st component of Octal display of data on REGISTER 1 02 Display 2nd component of Octal display of data on REGISTER 1 03 Display 3rd component of Octal display of data on REGISTER 1

Noun Code Description Scale/Units 01 Specify machine address XXXXX 02 Specify machine address XXXXX 03 (Spare) 04 (Spare) 05 Angular error XXX.XX degrees 06 Pitch angle XXX.XX degrees Heads up-down +/- 00001 07 Change of program or major mode 11 Engine ON enable 30

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Verbs and Nouns in Apollo Guidance Computer Programs

• Verbs (Actions) • Selected Nouns • Selected Programs – Display (Variables) (CM) – Enter – Checklist – AGC Idling – Monitor – Self-test ON/OFF – Gyro Compassing – Write – Star number – LET Abort – Terminate – Failure register – Landmark Tracking – Start code – Ground Track – Change – Event time Determination – Align – Inertial velocity – Return to Earth – Lock – Altitude – SPS Minimum – Set – Latitude Impulse – CSM/IMU Align – Return – Miss distance – Test – Delta time of burn – Final Phase – First Abort Burn – Calculate – Velocity to be gained – Update 31

A Little AGC Digital Autopilot Code

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Apollo GNC Software Testing and Verification

• Major areas of testing – Computational accuracy – Proper logical sequences • Testing program – Comprehensive test plans – Specific initial conditions and operating sequences – Performance of tests – Comparison with prior simulations, evaluation, and re-testing • Levels of testing – 1: Specifications coded in higher-order language for non-flight hardware (e.g., mainframe then, PCs now) – 2: Digital simulation of flight code – 3: Verification of complete programs or routines on laboratory flight hardware – 4: Verification of program compatibility in mission scenarios – 5: Repeat 3 and 4 with flight hardware to be used for actual mission – 6: Prediction of mission performance using non-flight computers and laboratory flight hardware 33

Lunar Module Navigation, Guidance, and Control Configuration

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Lunar Descent Guidance

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Lunar Module Transfer Ellipse to Powered Descent Initiation

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Lunar Module Powered Descent

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Lunar Module Descent Events

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Lunar Module Descent Targeting Sequence

• Braking Phase (P63) • Approach Phase (P64) 39 • Terminal Descent Phase (P66)

Characterize Braking Phase By Five Points

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Lunar Module Descent Guidance Logic (Klumpp, Automatica, 1974)

• Reference (nominal) trajectory, rr(t), from target position back to starting point (Braking Phase example) – Calculated before mission – Three 4th-degree polynomials in time – 5 points needed to specify each polynomial ⎡ x(t)⎤ t 2 t 3 t 4 ⎢ ⎥ r (t) = r + v t + a + j + s r(t) = y(t) r t t t 2 t 6 t 24 ⎢ ⎥ ⎣⎢ z(t)⎦⎥

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Coefficients of the Polynomials

t 2 t 3 t 4 r (t) = r + v t + a + j + s r t t t 2 t 6 t 24

• r = position vector • v = velocity vector ⎡ ⎤ • a = acceleration vector ⎡ x⎤ ⎡ x! ⎤ vx ⎢ ⎥ dr ⎢ ⎥ • j = jerk vector (time v ⎢ y ⎥ v r = y = = ⎢ ! ⎥ = ⎢ y ⎥ derivative of acceleration) ⎢ ⎥ dt ⎢ z⎥ ⎢ z! ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ vz • s = snap vector (time ⎣⎢ ⎦⎥ derivative of jerk)

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ax jx sx dv ⎢ ⎥ da ⎢ ⎥ dj ⎢ ⎥ a = = a j = = j s = = s dt ⎢ y ⎥ dt ⎢ y ⎥ dt ⎢ y ⎥ ⎢ a ⎥ ⎢ j ⎥ ⎢ s ⎥ ⎣⎢ z ⎦⎥ ⎣⎢ z ⎦⎥ ⎣⎢ z ⎦⎥ 42

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Corresponding Reference Velocity and Acceleration Vectors t 2 t 3 v (t) = v + a t + j + s r t t t 2 t 6 t 2 a (t) = a + j t + s r t t t 2

• ar(t) is the reference control vector – Descent engine thrust / mass = total acceleration – Vector components controlled by orienting yaw and pitch angles of the Lunar Module 43

Guidance Logic Defines Desired Acceleration Vector • If initial conditions, dynamic model, and thrust control were perfect, ar(t) would produce rr(t)

t 2 a (t) = a + j t + s ⇒ r t t t 2 t 2 t 3 t 4 r (t) = r + v t + a + j + s r t t t 2 t 6 t 24

• ... but they are not • Therefore, feedback control is required to follow the reference trajectory

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Guidance Law for the Lunar Module Descent

Linear feedback guidance law (real time

acommand (t) =

ar (t) + KV [v measured (t) − vr (t)]+ KR [rmeasured (t) − rr (t)]

KV :velocity error gain

KR :position error gain • Nominal acceleration profile is corrected for measured differences between actual and reference flight paths • Considerable modifications made in actual LM implementation (see Klumpps paper on Blackboard) 45

LM Manual Control Response During Simulated Landing

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Simulated LM Manual Control Response To Rate Command

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Next Time: The Future of Space Flight Telemetry, Communications & Tracking

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Supplemental Material

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Apollo GNC Software Specification Control

• Guidance System Operations Plan (GSOP) – NASA-approved specifications document for mission software – Changes must be approved by NASA Software Control Board • Change control procedures – Program Change Request (NASA) or Notice (MIT) – Anomaly reports – Program and operational notes • Software control meetings – Biweekly internal meetings – Joint development plan meetings – First Article Configuration Inspection – Customer Acceptance Readiness Review – Flight Software Readiness Review

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Apollo GNC Software Documentation and Mission Support

• Documentation generation and review – GSOP: 1: Prelaunch 2: Data links 3: Digital autopilots 4: Operational modes 5: Guidance equations 6: Control data – Functional description document: H/W-S/W interfaces, flowcharts of procedures – Computer listing of flight code – Independently generated program flowchart – Users Guide to AGC – NASA program documents: Apollo Operations Handbook, Flight Plans and Mission Rules, various procedural documents • Mission support – Pre-flight briefings to the crew – Personnel in Mission Control and at MIT during mission

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Ascent (Launch) Guidance

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Gravity-Turn Flight Path

Hermann Oberth

• “Oberth’s Synergy Curve” • Gravity-turn flight path is function of 3 variables – Initial pitchover angle (from vertical launch) – Velocity at pitchover – Acceleration profile, T(t)/m(t) • Gravity-turn program closely approximated by tangent steering laws

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Tangent Steering Laws Approximate Gravity Turn

• Neglecting surface curvature

⎛ t ⎞ tanθ(t) = tanθo ⎜1− ⎟ ⎝ tBO ⎠

• Open-loop command, i.e., no feedback of vehicle state • Accounting for effect of Earth surface curvature on burnout flight path angle

⎡ t ⎛ t ⎞ ⎤ tanθ(t) = tanθo ⎢1− − tanβ ⎜ ⎟ ⎥ ⎣ tBO ⎝ tBO ⎠ ⎦ 54

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Feedback Guidance Law Errors due to disturbances and modeling errors corrected by feedback control with damping

Thrust Angle(t) = cθ [θc (t) −θ(t)]− cqq(t) dθ q = = pitch rate dt

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Phases of Ascent Guidance

• Vertical liftoff • Roll to launch azimuth • Pitch program to atmospheric exit – Jet stream penetration – Booster cutoff and staging • Explicit guidance to desired orbit – Booster separation – Acceleration limiting – Orbital insertion

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Jet Stream Profiles

• Launch vehicle must able to fly through strong wind profiles • Design profiles assume 95th-99th-percentile worst winds and wind shear

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Thrust Vector Control During Launch

• Attitude control – Attitude and rate feedback • Drift-minimum control – Attitude and accelerometer feedback – Increased loads • Load relief control – Rate and accelerometer feedback – Increased drift

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Explicit Guidance Law ~Lunar Module Ascent, Space Shuttle Launch (Brand, Brown, Higgins, and Pu, CSDL, 1972)

• Initial conditions – End of pitch program, outside atmosphere • Final condition – Insertion in desired orbit • Initial inputs – Desired radius – Desired velocity magnitude – Desired flight path angle – Desired inclination angle – Desired longitude of the ascending/descending node • Continuing outputs – Unit vector describing desired thrust direction – Throttle setting 59

Guidance Program Initialization

• Thrust acceleration estimate • Mass/mass flow rate • Acceleration limit (~ 3g) • Effective exhaust velocity • Various coefficients • Unit vector normal to desired orbital plane, iq

⎡ sinid sinΩd ⎤ ⎢ ⎥ iq = sinid cosΩd i :desired inclination angle ⎢ ⎥ d

⎣⎢ cosid ⎦⎥ Ωd :desired longitude of descending node 60

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Guidance Program Operation: Position and Velocity

• Thrust acceleration estimate, aT, from guidance system • Compute corresponding mass/flow rate and throttle setting, δT • Position ⎡ r⎤ ⎡ r ⎤ ⎢ ⎥ ⎢ 1 ⎥ y rsin− i i ⎢ ⎥ = ⎢ ( r • q )⎥ ⎣⎢ z⎦⎥ ⎣⎢ open ⎦⎥

• Velocity ⎡ r˙ ⎤ ⎡ vIMU •ir ⎤ ⎢ ⎥ ⎢ ⎥ y˙ = v •i ⎢ ⎥ ⎢ IMU q ⎥ v IMU :velocity estimate in IMU frame ⎣⎢ z˙ ⎦⎥ ⎣⎢ vIMU •iz ⎦⎥ 61

Guidance Program: Velocity and Time to Go • Effective gravitational acceleration 2 µ r × v g = − + eff r2 r3 • Time to go (to burnout) t = t − Δt gonew goold Δt :guidance interval • Velocity to be gained ⎡ ⎤ (r!d − r!) − geff tgo / 2 ⎢ ⎥ v go = ⎢ −y! ⎥ ⎢ ⎥ z!d − z! ⎣⎢ ⎦⎥ • Time to go prediction (prior to acceleration limiting)

m −vgo / ceff t 1 e ceff :effective exhaust velocity go = ( − ) m˙ 62

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Guidance Program Commands • Guidance law produces required radial and cross-range accelerations a = a A + B t − t − g Tr T [ ( o )] eff a = a C + D t − t Ty T [ ( o )]

aT = net available acceleration, accounting for limit • Guidance coefficients, A, B , C, and D are functions of ˙ (rd ,r,r, tgo ) ˙ (y,y ,tgo) plus c ,m m! , acceleration limit eff 63

Guidance Program Commands

• Required thrust direction, iT (i.e., vehicle orientation in (ir, iq, iz) frame

⎡ a ⎤ Tr ⎢ ⎥ a a a ; i T T = ⎢ Ty ⎥ T = ⎢ ⎥ aT what's left over ⎣⎢ ⎦⎥ • Guidance philosophy • Force spacecraft into desired orbital plane • Climb toward desired 2-D orbit • Achieve orbital velocity 64

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