Applications of Artificial Potential Function Methods to Autonomous Space Flight

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Information about Applications of Artificial Potential Function Methods to Autonomous...
Technology

Published on March 21, 2014

Author: BelindaMarchand

Source: slideshare.net

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Talk charts from AAS/AIAA Astrodynamics Specialist Conference, held July 31 - Aug. 4 2011 in
Girdwood, Alaska

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Applications of Artificial Potential Function Methods to Autonomous Space Flight Sara K. Scarritt∗ and Belinda G. Marchand† AAS/AIAA Astrodynamics Specialist Conference July 31 - Aug. 4 2011 Girdwood, Alaska ∗Graduate Student, Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, 210 E. 24th St., Austin, TX 78712. †Assistant Professor, Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, 210 E. 24th St., Austin, TX 78712. Sara K. Scarritt and Belinda G. Marchand 1

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Background Artificial Potential Function (APF) Methods ◮ Extensive use in path planning applications ◮ Global minimum at goal, peaks at constraints ◮ Vehicle follows steepest descent of potential ◮ Extendable to more general trajectory planning Sara K. Scarritt and Belinda G. Marchand 2

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Background Modification for General Trajectory Design ◮ Discrete control parameter (∆v) vs. continuous control ◮ Formation flight problem - time derivative of Φ to define switching time ◮ Minimum of Φ → lowest available maneuver cost ◮ Potential as a function of velocity error 1 (i.e. ∆v) ◮ Dynamical model to calculate desired velocity field 1Neubauer, J., Controlling Swarms of Micro-Utility Spacecraft, Ph.D. dissertation, Washington University in St. Louis, August 2002 Sara K. Scarritt and Belinda G. Marchand 3

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Maneuver Planning Potential Function Construction ◮ Desired state/desired orbit (transfer time constraint) ◮ Two distinct cases: (1) intersecting orbits, and (2) non-intersecting orbits ◮ Initial orbit intersects target orbit → maneuver at intersection point: Φint = (rintersect − r0)T (rintersect − r0), ◮ For non-intersecting orbits, Φ = Φ(∆v): Φvel = ∆v2 , Sara K. Scarritt and Belinda G. Marchand 4

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Maneuver Planning APF Maneuver Planning Sara K. Scarritt and Belinda G. Marchand 5

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Desired Velocity Field Coplanar Transfer Lunar Example The Desired Velocity Field ◮ Desired velocity depends on target point rf along final orbit ◮ Target point assumed to be ◮ apoapsis of the transfer orbit, if transferring to higher altitude ◮ periapsis of the transfer orbit, if decreasing altitude ◮ Gives eccentricity vector direction, leads to desired velocity vector: rf → ˆet → et → vt Sara K. Scarritt and Belinda G. Marchand 6

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Desired Velocity Field Coplanar Transfer Lunar Example Coplanar Transfer: Desired Velocity Field ◮ Target point: 180◦ from current position ˆrf = − r0 r0 . −8000 −6000 −4000 −2000 0 2000 4000 6000 8000 −6000 −4000 −2000 0 2000 4000 6000 x (km) y(km) (a) Velocity Field (b) Resulting Potential Figure: Coplanar Velocity Field and Potential Function Sara K. Scarritt and Belinda G. Marchand 7

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Desired Velocity Field Coplanar Transfer Lunar Example Coplanar Transfer ◮ Total ∆v: 1.25 km/s ◮ Doubly cotangential 180◦ transfer - matches analytical optimal result Table: Coplanar Transfer Initial and Target States Parameter Initial Target x (km) -6478.145 0.000 y (km) 0.000 12587.983 z (km) 0.000 0.0000 vx (km/s) 0.000 -4.708 vy (km/s) -7.844 0.000 vz (km/s) 0.000 0.000 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 x (×104 ) y(×104 ) Target Orbit Initial Orbit Transfer Orbit Maneuvers Initial Position Figure: Coplanar Transfer Sara K. Scarritt and Belinda G. Marchand 8

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Desired Velocity Field Coplanar Transfer Lunar Example The Desired Velocity Field: Inclined Transfer ◮ Target point: intersection of initial and desired orbit planes ◮ Higher altitude solution to minimize cost of the plane change −8000 −6000 −4000 −2000 0 2000 4000 6000 8000 −6000 −4000 −2000 0 2000 4000 6000 x (km) y(km) (a) Velocity Field (b) Resulting Potential Figure: Non-Coplanar Velocity Field and Potential Function Sara K. Scarritt and Belinda G. Marchand 9

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Desired Velocity Field Coplanar Transfer Lunar Example Inclined Transfer ◮ Total ∆v: 3.46 km/s → Compare to 6.11 km/s for Lambert solution ◮ Consider three-maneuver sequence to reduce plane change Table: Inclined Transfer Initial and Target States Parameter Initial Target x (km) -5610.238 190.512 y (km) 0.000 12396.744 z (km) 3239.073 2177.562 vx (km/s) 0.000 -4.690 vy (km/s) -7.844 0.000 vz (km/s) 0.000 0.410 −0.5 0 0.5 −0.5 0 0.5 1 −0.2 0 0.2 x (×104 ) y (×104 ) z(×104 ) Desired Orbit Initial Orbit Transfer Orbit Maneuvers Initial Position Figure: Non-Coplanar Transfer Sara K. Scarritt and Belinda G. Marchand 10

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Desired Velocity Field Coplanar Transfer Lunar Example Lunar Example (1/3) ◮ More complex test of APF algorithm ◮ Specific time needed at target state; not guaranteed by APF method as-is ◮ Offset targeting to do timing match, typically converges in 3-4 iterations Table: Initial Conditions Epoch 2-Aug-2018 17:16:06 TDT x (km) -1834.7155 y (km) -66.2361 z (km) -73.9653 vx (km/s) -0.0864 vy (km/s) 0.8139 vz (km/s) 1.4136 Table: Estimated Arrival Conditions Epoch 7-Aug-2018 00:52:08 TDT Geocentric Altitude (km) 121.92 Longitude (deg) -134.5456 Geocentric Latitude -19.20410 Geocentric Azimuth (deg) 13.9960 Geocentric Flight Path Angle (deg) -5.8600 Sara K. Scarritt and Belinda G. Marchand 11

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Desired Velocity Field Coplanar Transfer Lunar Example Lunar Example (2/3) ◮ Total ∆v: 1.9483 km/s Figure: APF Lunar Return, 1.9483 km/s Sara K. Scarritt and Belinda G. Marchand 12

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Desired Velocity Field Coplanar Transfer Lunar Example Lunar Example (3/3) ◮ Investigate phasing effects on total cost ◮ Shift departure/arrival epoch by n revolutions −15 −10 −5 0 5 10 15 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 # of Revolutions ∆v(km/s) Figure: ∆v of Time-Shifted Transfers vs. # of Revolutions Sara K. Scarritt and Belinda G. Marchand 13

Introduction Artificial Potential Function Trajectory Design Examples Conclusions Conclusions ◮ Preliminary exploration of artificial potential function methods as a design tool for generating startup arcs ◮ Candidate potential function construction presented ◮ Method for calculating a desired velocity field developed based on two-body analysis ◮ APF trajectory design algorithm developed and tested ◮ APF method is promising, but room for improvement in design of potential field ◮ Future work will focus on constructing more complex potentials for use in multi-body regimes Sara K. Scarritt and Belinda G. Marchand 14

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