# An Autonomous Onboard Targeting Algorithm using Finite Thrust Maneuvers

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Published on March 21, 2014

Author: BelindaMarchand

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Talk charts for presentation at the 2009 AIAA Guidance, Navigation, and Control Conference & Exhibit, held
August 10-13, 2009, Chicago, IL

An Autonomous Onboard Targeting Algorithm using Finite Thrust Maneuvers Sara K. Scarritt, Belinda G. Marchand, MichaelW.Weeks AIAA Guidance, Navigation, and Control Conference & Exhibit 10-13August 2009, Chicago, IL AIAA 2009-6104 1

Introduction  Onboard guidance for Orion lunar return  Two-level targeting algorithm  Based on linear system theory  Designed for impulsive maneuvers  In a main engine failure scenario, impulsive approximation invalid  Adapt two-level targeter to incorporate finite burns while retaining its simplicity 22

Classical Impulsive Level I Process Goal: Position Continuity Only Control Variables: DV’s BEFORE LEVEL I AFTER LEVEL I

Classical Level II Process: Goal: Meet Specified Constraints (e.g. Velocity Continuity), Control Variables: Time & Position of Patch States BEFORE LEVEL II IMPLEMENTATION IN THE N/L SYSTEM LEVEL II: LINEAR CORRECTION

T kr 1k  k T Level 1: Impulsive vs. Finite Burn 5 1 Constraint: Control Variables: , k k Tt    r 0 u1 Constraint: Control Variables: k k    D r 0 v IMPULSIVE FINITE BURN kr 1kDv 1k  k 11 1 g m m                  r v x u 6 1        r x v

Variational Equations: Impulsive vs. Finite Burn 6 , 1 , 1 1 1 1 , 1 , 1 1 1 1 k k k kk k k k k k k k k kk kk k k k A Bt t C Dt t                                          r v r v v a v a IMPULSIVE FINITE BURN , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 T T T T T k T k T k T k T kT T T T k T k T k T k T kT T T T k T k T k T k T kT g T T k T k T k T k T kg g T T g T A B E F Gt C D H I Jt K L M N Om m t P Q R S Tm m t t                                                        r v v a u u 1 1 1 1 1 1 1 1 1 1 1 1 , 1 , 1 , 1 , 1 , 1 1 1 1 k k k k k k k k k k g k g g k T k T k T k T k T k k k k t t m m t m m t U V W X Y t                                                                 r v v a u u , 1 , 1 1 1 1 , 1 , 1 1 1 1 k k k kk k k k k k k k k kk kk k k k A Bt t C Dt t                                          r v r v v a v a , 1 , 1 1 1 1 , 1 , 1 1 1 1 k k k kk k k k k k k k k kk kk k k k A Bt t C Dt t                                          r v r v v a v a , , , , k T k Tk k k T T T k T k Tk k T Tk T A Bt t C Dt t                                r v r v v a v a

Level 1 Targeting  Direct fromTEI-3 to Earth entry  Entry targets:  GeodeticAltitude (km) 121.92  Longitude (deg) 175.6365  GeocentricAzimuth (deg) 49.3291  Geocentric Flight PathAngle (deg) -5.86 7

Level II Algorithm: Impulsive vs. Finite Burn 8 k  v k  v 1k  k 1k      1 2 1 0 0 1 1 Constraints: , , , , , , , , , , v Control Var , ,iables: , , ,, jn TEI j n n h t t t              D D D D D    V = v v v A = b = r r r k  v k  v 1k  k 1k  T IMPULSIVE FINITE BURN   1T M T M MM      D   D D                    V V Vb A A b bb A

Variational Equations: Impulsive vs. Finite Burn 9 , 1 , 1 1 1 1 , 1 , 1 1 1 1 k k k kk k k k k k k k k kk kk k k k A Bt t C Dt t                                          r v r v v a v a IMPULSIVE FINITE BURN , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 , 1 T T T T T k T k T k T k T kT T T T k T k T k T k T kT T T T k T k T k T k T kT g T T k T k T k T k T kg g T T g T A B E F Gt C D H I Jt K L M N Om m t P Q R S Tm m t t                                                        r v v a u u 1 1 1 1 1 1 1 1 1 1 1 1 , 1 , 1 , 1 , 1 , 1 1 1 1 k k k k k k k k k k g k g g k T k T k T k T k T k k k k t t m m t m m t U V W X Y t                                                                 r v v a u u , 1 , 1 1 1 1 , 1 , 1 1 1 1 k k k kk k k k k k k k k kk kk k k k A Bt t C Dt t                                          r v r v v a v a , 1 , 1 1 1 1 , 1 , 1 1 1 1 k k k kk k k k k k k k k kk kk k k k A Bt t C Dt t                                          r v r v v a v a , , , , k T k Tk k k T T T k T k Tk k T Tk T A Bt t C Dt t                                r v r v v a v a

Total Cost Constraint: Impulsive vs. Finite Burn 10 v | |k k k   D  v v   0v ln 1 kg T k k sp k m t t I g m   D        v , ,k k T kf t t mD      1 1 1 1 , , , , , , k k k k k k k k k k k k t t t t           v v r r v v r r IMPULSIVE FINITE BURN 1 0 1 [ ] n k g burn j j m m m t     D

Main Engine Simulation  Initial guess data  Epoch: 4-Apr-2024 15:30:00TDT  Initial mass: 20339.9 kg (total fuel = 8063.65 kg)  Main EngineThrust: 33,361.6621 N  Main Engine Isp: 326 sec  State (J2000 Moon-centered inertial frame):  X: -1236.7970783385588 km  Y: 1268.1142350088496 km  Z: 468.38317094160635 km  Vx: 0.0329108058365355 km/sec  Vy: 0.589269803607714 km/sec  Vz -1.528058717568413 km/sec  Entry constraints:  GeodeticAltitude (km): 121.92  Longitude (deg): 175.6365  GeocentricAzimuth (deg): 49.3291  Geocentric Flight PathAngle (deg): - 5.86 11

Results (1/2) 12 MCI Frame Perspective Earth Moon

Results (2/2)  Comparison of finite burn and impulsive algorithms: 13

Auxiliary Engine Simulation  Same initial guess data and constraints  Assume main engine failure afterTEI-1  TEI-2 andTEI-3 performed using auxiliary engines:  Auxiliary EngineThrust: 4,448.0 N  Auxiliary Engine Isp: 309 sec 1414

Results  Maneuver and final constraint data: 1515

Lunar Cycle Simulations  Simulations run for 10 different days spanning February 2024  Patch points from converged impulsive runs  Initial lunar orbit of 100 km, targeting altitude (121.9 km) and flight path angle (-5.86o)  Auxiliary engines used forTEI-2 andTEI-3

Results

Delayed Patch Points  Patch points associated with specific epoch  Targeter must converge even if the patch points are not current  Using February 1 input file from previous example, initial epoch delayed for (a) 3 hours and (b) 12 hours

Results

Conclusions and Future Work  Two-level targeting algorithm developed for finite burn maneuvers  Algorithm successfully targets lunar return trajectory  Using main engines  Using auxiliary engines following simulated failure of main engines afterTEI-1  Future work  Implementing thruster steering law  Automated patch point selection 20

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