Onboard Maneuver Planning for the Autonomous Vision Approach Navigation and Target Identification (AVANTI) experiment within the DLR FireBird mission G. Gaias, DLR/GSOC/Space Flight Technology Department Workshop on Advances in Space Rendezvous Guidance Slide1
Contents Overview of the AVANTI experiment Overall Concept of the MAneuver Planner (MAP) The Guidance Problem The Computation of the Maneuvers Example of a Rendezvous Conclusions and Current Development Status Slide 2
Contents Overview of the AVANTI experiment Overall Concept of the MAneuver Planner (MAP) The Guidance Problem The Computation of the Maneuvers Example of a Rendezvous Conclusions and Current Development Status Slide 3
The FireBird Mission DLR Scientific Mission, based on BIRD-TET s/c bus Expected launch: late 2014/early 2015 Orbit: Sun-synchronous, altitude 500-600 km Primary Objective: Earth observation, fire detection (infrared camera) Secondary Objectives: several scientific experiments Autonomous Vision Approach Navigation and Target Identification (AVANTI) demonstration of autonomous rendezvous to (and departure from) non-cooperative client using vision-based navigation 1 month of experiment campaign after in-orbit injection of a Picosat Slide 4
AVANTI motivations AVANTI is motivated by the following needs approach, identify, rendezvous with a non-cooperative, passive client from large distances (e.g., > 10 km) in an autonomous, fuel efficient, safe manner Angles-only navigation is an attractive solution low cost sensors (e.g., optical, infrared) star trackers often onboard (e.g., Biros!) simplicity, robustness, wide range but maneuvers are needed to reconstruct the relative state linearized-unperturbed relative motion unobservable without maneuvers Slide 5
AVANTI key functionalities Key functions to be proven handover from ground-operations to autonomous vision-based navigation & control onboard processing of camera images and target identification real-time relative navigation based on Line-Of-Sight (LOS) info autonomous maneuver planning to accomplish a rendezvous (RdV) Key performance to be proven LOS residuals below 40 arcsecs (half camera pixel size) relative orbit determination accuracy at 10% of range to client safe rendezvous operations between ±10 km and ±100 m Slide 6
Background August 2011, PRISMA - handover to OHB: Formation Re-Acquisition ground-in-the-loop, TLE + prototype of angles-only relative navigation filter April 2012, PRISMA - extended mission phase: ARGON Advanced Rendezvous Demonstration using GPS and Optical Navigation ground-in-the-loop, image processing, angles-only relative navigation man-in-the-loop, maneuver planning AVANTI new challenges onboard processing of camera images and identification of Picosat real-time relative navigation of Biros w.r.t. Picosat based on LOS info autonomous maneuver planning Slide 7
Contents Overview of the AVANTI experiment Overall Concept of the MAneuver Planner (MAP) The Guidance Problem The Computation of the Maneuvers Example of a Rendezvous Conclusions and Current Development Status Slide 8
MAP objectives Generation of the open-loop, impulsive maneuvers profile to accomplish a rendezvous (RdV) Operational conditions delta-v budget: fuel efficiency safety: safe approach during RdV system requirements: time constraints to cope with communication/power/thermal pointing requirements thrusters alignment Autonomy simplicity, preference to closed-form solutions Slide 9
Overall Concept - 1 Relative Orbital Elements (ROE) as state variables δα = {δa, δλ, δe x, δe y, δi x, δi y} T P = aδα description of each possible configuration δα = δa δλ δe x δe y δi x δi y = δa δλ δe cos ϕ δe sin ϕ δi cos θ δi sin θ = (a a d )/a d u u d + (Ω Ω d ) cos i d e cos ω e d cos ω d e sin ω e d sin ω d i i d (Ω Ω d ) sin i d a, e, i, Ω, and M: Keplerian elements u mean argument of latitude d servicer satellite Slide 10
ROE meaning and dynamics Radial a e a a Linearized motion + disturbances ( ) ( ) δȧ δȧ = Φ(t t δα 0) δα t t 0 Cross-Track a 2a e Along-Track a i 1 0 0 0 0 0 0 t 1 0 0 0 0 0 ν 2 t2 ν t 1 0 0 µ t 0 0 0 0 1 ϕ t 0 0 0 0 0 ϕ t 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 λ t 1 Along-Track differential drag mean J 2 Slide 11
Overall Concept - 2 ROE as state variables Layered approach RdV defined as P 0 P F through intermediate P i i-th times: solution of the scheduling problem in compliance with time constraints P i at i-th times computed to optimize a criterion MAP operatives modes: set a criterion, evaluation of the relevance of some operational conditions computation of the maneuvers to establish the P i Slide 12
Architecture Input: y 0, (P,t) 0, (P,t) F, Mode Time constraints Forbidden time intervals Minimum time to first maneuver Minimum time spacing between maneuvers Guidance (Scheduling, Planning, Safety) P 0 P 1 P 2 P F time Control (Maneuvers placement) t 0,2 t 2 maneuvers time Maneuvers profile Slide 13
Contents Overview of the AVANTI experiment Overall Concept of the MAneuver Planner (MAP) The Guidance Problem The Computation of the Maneuvers Example of a Rendezvous Conclusions and Current Development Status Slide 14
ROE sets planning: problem statement - 1 Evolution of the motion through Φ( t), effect of the maneuvers at t i: discontinuities in ROE P 1 = Φ 1,0 P 0 + a( δα) 1 P 2 = Φ 2,1 P 1 + a( δα) 2 End-conditions: achievement of P F at t F Φδ F,1 Φ δ F,m 1 Φ δ F,m Φ δ F,1 Φ δ F,m 1 Φ δ F,m }{{}}{{} first column last column b 0 = P F Φ F,0 P 0 x 1,1 x 1,m. x p,1 x p,m = b 0 (x 1,, x p) ( δȧ,a δa,a δλ,a δi x, a δi y) or (a δe x, a δe y) Slide 15
ROE sets planning: problem statement - 2 Functional cost, convex form of the ROE jumps over m steps: J plan = m i=1 ( δα)t i ( δα) i ROE variations not due to the natural dynamics describes delta-v cost (Gauss variational equations in ROE) Optimality conditions to minimize J plan reduce to a linear system in ROE due to: structure of Φ( t) property: Φ(t j, t i) Φ(t i, t k ) = Φ(t j, t k ) approximation in the relative eccentricity sub-problem (neglected terms of ϕ 2 t 2 and ϕ 3 t 3 after the 3rd jump) Slide 16
ROE sets planning: problem solution Optimal solution: m 1 opt. jumps ( δα) opt = M 1 b M and b function of (t i, ν, µ, λ) and (t i, ϕ) m end-cond. P F = Φ F,0 P 0 + Φ F,1 a( δα) opt 1 + + Φ F,m a( δα) m Generalization of a geometrical approach stepwise reconfiguration, disturbances compensation Suitable for automatic implementation Slide 17
Supported Operative Modes Modes Motivations Applicability minimum delta-v absolute min cost small reconfigurations direct P 0 P F accurate P 0 4 maneuvers maximum observability user defined t i P i (4) i maneuvers intensify maneuvers activity spread burns over horizon maneuver execution errors large reconfigurations uncertainty on P 0 Synergies criterion: minimum delta-v Slide 18
Contents Overview of the AVANTI experiment Overall Concept of the MAneuver Planner (MAP) The Guidance Problem The Computation of the Maneuvers Example of a Rendezvous Conclusions and Current Development Status Slide 19
Local control: problem statement - 1 Establishment of a (intermediate) reconfiguration P 0,i P i over a finite control window [u 0,i u F,i ] fixed time, fixed end-conditions problem Total ROE jump pre-corrected by disturbances effects over the window locally maneuvers computed with Φ of Kepler motion General framework for the p-pulses formulation: δv 1 ( ) ΦF,1 B 1 ΦF,p B p. δv p = n(p i Φ i F,0 P 0,i) = n δ α i Slide 20
Local control: problem solution - 1 Choice of δλ instead of δu and structure of control input matrix B: where δα = B(u M )δv out-of-plane and in-plane motions are decoupled Out-of-plane solution, deterministic: ( ) δĩy u oop = arctan δv n = na δĩ δĩ x two options per orbit In-plane solution, underdetermined: minimum 2 impulses required 6 unknowns in 4 equations Slide 21
In-plane reconfiguration: possible maneuvers schemes Reconfiguration: 0 F, u0, uf in-plane Enforcement of all End-conditions out-of-plane 000uoop, voop000 2-RT, 3-T, 3-T 000uip, vip000 generality a a a 2-RT, 3-T, 3-T 2-RT, 3-T, 3-T 2-RT, 3-T, 3-T 2-T 2-R 2-T Planning drivers: Thrusters duty cycle (# pulses) Attitude constraints (type of pulses) a 2-RT, 3-T, 3-T 2-RT, 2-T No-Type analytical No-Type numerical Safety & Visibility (ROE predictability) Determinism (computation of ui) Delta-v cost Slide 22
Local control: problem solution - 2 AVANTI design drivers for the choice of the in-plane scheme: autonomy, predictability maneuvers spacing constraints communication pointing constraints minimum delta-v 3-T analytical Maneuvers are located in: ( ( ) ) δẽy ū = mod arctan, π δẽ x u ipj = ū + k jπ, j = 1...3 k 1 < k 2 < k 3 Multiple (finite number) feasible solutions: one selected according to 1. preference to minor delta-v cost 2. preference to wider spacing between burns Slide 23
Contents Overview of the AVANTI experiment Overall Concept of the MAneuver Planner (MAP) The Guidance Problem The Computation of the Maneuvers Example of a Rendezvous Conclusions and Current Development Status Slide 24
Safety concept: ROE movement due to local control Out-of-plane control In-plane control optimal / sub-optimal Slide 25
Safety concept: ROE movement due guidance passive safety related to φ = ϕ θ keep (anti) parallel δe/δi during RdV guidance to minimize the total ROE P i distribute along the direction of ROE total variation Slide 26
Example of a Rendezvous - 1 400 200 Scenario 500 km high, inclination 98 deg B target: 0.01 m 2 /kg B/B: 2% normal [m] 0 200 400 15000 10000 along track [m] 5000 0 400 200 0 200 radial [m] 400 Input to MAP P 0 = [5, 10000, 50, 250, 30, 200] m P F = [0, 3000, 0, 100, 0, 100] m t F : 18 orbits after t 0 time constraints mode: max-observability delta v, δv t δv n [m/s] Normalized δe/δi plane 1 1 1 1 Total delta v: 0.2168 [m/s] 0.04 0.02 0 0.02 0.04 0 2 4 6 8 10 12 14 16 Slide 18 2720 time [orbital periods]
Example of a Rendezvous - 2 Relative eccentricity and inclination vectors Drift and mean relative longitude over time aδe y aδi y [m] 300 200 100 0 100 200 start target 300 300 200 100 0 100 200 300 aδe aδi [m] x x aδλ [m] aδa [m] 80 60 40 20 0 20 0 2 4 6 8 10 12 14 16 18 20 time [orbital periods] 12000 10000 8000 6000 4000 2000 0 2 4 6 8 10 12 14 16 18 20 time [orbital periods] Slide 28
Contents Overview of the AVANTI experiment Overall Concept of the MAneuver Planner (MAP) The Guidance Problem The Computation of the Maneuvers Example of a Rendezvous Conclusions and Current Development Status Slide 29
Conclusions and current development status Impulsive MAaneuvers Planner for formation reconfigurations and rendezvous for the AVANTI experiment (DLR/FireBird mission) experiment operational conditions (onboard functioning, space segment requirements,...) design concept (simplicity and determinism) provided an example of the MAP output Current work flight software implementation performance assessment in realistic simulation environment Future work design of the AVANTI experiment campaign Slide 30
ROE parameterization and safety concept D Amico, S., Autonomous Formation Flying in Low Earth Orbit, Ph.D. Dissertation, Technical University of Delft, The Netherlands, 2010. D Amico, S., and Montenbruck, O., Proximity Operations of Formation Flying Spacecraft using an Eccentricity/Inclination Vector Separation, Journal of Guidance, Control, and Dynamics, Vol. 29, No. 3, 2006, pp. 554 563. ARGON development and flight results Gaias, G., D Amico, S., Ardaens, J. -S., Angles-only Navigation to a Noncooperative Satellite Using Relative Orbital Elements, Journal of Guidance, Control, and Dynamics (accepted for publication). D Amico, S., Ardaens, J. -S., Gaias, G., Benninghoff, H., Schlepp, B, and Jørgensen, J. L., Noncooperative Rendezvous Using Angles-only Optical Navigation: System Design and Flight Results, Journal of Guidance, Control, and Dynamics, accessed September 13, 2013. doi: 10.2514/1.59236. MAP development Gaias, G., D Amico, S., Ardaens, J. -S., Generalized Multi-Impulsive Maneuvers for Optimum Spacecraft Rendezvous, International Conference on Spacecraft Formation Flying Missions & Technologies (SFFMT), Munich, Germany, 2013. Slide 31
Onboard Maneuver Planning for the AVANTI experiment within the DLR FireBird mission AVANTI experiment Guidance Solution Example MAP Concept Control Solution Conclusions gabriella.gaias@dlr.de