onboard maneuver planning for the autonomous vision...
TRANSCRIPT
Onboard Maneuver Planning for theAutonomous Vision Approach Navigation andTarget Identification (AVANTI) experimentwithin the DLR FireBird mission
G. Gaias, DLR/GSOC/Space Flight Technology Department
Workshop on Advances in Space Rendezvous Guidance
Slide1Toulouse > 2013/10/31
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 2Toulouse > 2013/10/31
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 3Toulouse > 2013/10/31
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 4Toulouse > 2013/10/31
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 relativestate
linearized-unperturbedrelative motionunobservable
without maneuvers
Slide 5Toulouse > 2013/10/31
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 6Toulouse > 2013/10/31
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: ARGONAdvanced 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 7Toulouse > 2013/10/31
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 8Toulouse > 2013/10/31
MAP objectives
∠
Generation of the open-loop, impulsive maneuvers’ profile to accomplish arendezvous (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 9Toulouse > 2013/10/31
Overall Concept - 1
∠
Relative Orbital Elements (ROE) as state variables
δα = δa, δλ, δex, δey, δix, δiyT
P = aδα description of each possible configuration
δα =
δaδλδexδeyδixδiy
=
δaδλ
δe cosϕδe sinϕδi cos θδi sin θ
=
(a− ad)/ad
u− ud + (Ω− Ωd) cos ide cosω − ed cosωd
e sinω − ed sinωd
i− id(Ω− Ωd) sin id
a, e, i, Ω, and M : Keplerian elements u mean argument of latitude
“d” servicer satellite
Slide 10Toulouse > 2013/10/31
ROE meaning and dynamics
Along-Track
Radial
Along-Track
Cross-Track
a e
a a
a i
2a ea
Linearized motion + disturbances(δaδα
)t
= Φ(t− t0)
(δaδα
)t0
↓
1 0 0 0 0 0 0∆t 1 0 0 0 0 0ν2
∆t2 ν∆t 1 0 0 µ∆t 00 0 0 1 −ϕ∆t 0 00 0 0 ϕ∆t 1 0 00 0 0 0 0 1 00 0 0 0 0 λ∆t 1
differential drag mean J2
Slide 11Toulouse > 2013/10/31
Overall Concept - 2
∠
ROE as state variables
∠
Layered approach
∠
RdV defined as P0 → PF through intermediate Pi∠
i-th times: solution of the scheduling problem in compliance with timeconstraints
∠
Pi at i-th times computed to optimize a criterion
∠
MAP operatives modes:
∠
set a criterion, evaluation of the relevance of some operationalconditions
∠
computation of the maneuvers to establish the Pi
Slide 12Toulouse > 2013/10/31
Architecture
Guidance(Scheduling, Planning, Safety)
Control(Maneuvers placement)
Maneuvers’ profile
Forbidden time intervals
Minimum time to first maneuver
Minimum time spacing between maneuvers
Input:
y0, (P,t)0, (P,t)F, Mode Time constraints
time
time
P0 PFP1 P2
t0,2 t2
maneuvers
Slide 13Toulouse > 2013/10/31
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 14Toulouse > 2013/10/31
ROE sets planning: problem statement - 1
∠
Evolution of the motion through Φ(∆t), effect of the maneuvers at ti:discontinuities in ROE
P1 = Φ1,0 P0 + a(∆δα)1 P2 = Φ2,1 P1 + a(∆δα)2 · · ·
∠
End-conditions: achievement of PF at tF
Φδ∗F,1 · · · Φδ∗
F,m−1 Φδ∗F,m︸ ︷︷ ︸
first column
· · · Φδ∗F,1 · · · Φδ∗
F,m−1 Φδ∗F,m︸ ︷︷ ︸
last column
x1,1·
x1,m...
xp,1·
xp,m
= b0
b0 = PF −ΦF,0P0
(x1, · · · ,xp)→ (∆δa,a∆δa,a∆δλ,a∆δix, a∆δiy) or (a∆δex, a∆δey)
Slide 15Toulouse > 2013/10/31
ROE sets planning: problem statement - 2
∠
Functional cost, convex form of the ROE jumps over m steps:
Jplan =∑mi=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 Jplan reduce to a linear systemin ∆ROE due to:
∠
structure of Φ(∆t)→ property: Φ(tj , ti) ·Φ(ti, tk) = Φ(tj , tk)
∠
approximation in the relative eccentricity sub-problem(neglected terms of ϕ2∆t2 and ϕ3∆t3 after the 3rd jump)
Slide 16Toulouse > 2013/10/31
ROE sets planning: problem solution
∠
Optimal solution:
m− 1 opt. jumps (∆δα)opt = M−1b
M and b function of (ti, ν, µ, λ) and (ti, ϕ)
m end-cond. PF = ΦF,0P0 + ΦF,1a(∆δα)opt1 + · · ·+ ΦF,ma(∆δα)m
∠
Generalization of a geometrical approach stepwise reconfiguration,disturbances compensation
∠
Suitable for automatic implementation
Slide 17Toulouse > 2013/10/31
Supported Operative Modes
Modes Motivations Applicability
∠
minimum delta-v
direct P0 → PF
4 maneuvers
absolute min cost small reconfigurations
accurate P0
∠
maximum observability
user defined ti ⇒ Pi
(4)× i maneuvers
intensify maneuvers’ activity
spread burns over horizon
maneuver execution errors
large reconfigurations
uncertainty on P0
Synergies
∠
criterion: minimum delta-v
Slide 18Toulouse > 2013/10/31
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 19Toulouse > 2013/10/31
Local control: problem statement - 1
∠
Establishment of a (intermediate) reconfiguration P0,i → Pi
over a finite control window [u0,i uF,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:
(ΦF,1B1 · · · ΦF,pBp
) δv1
...δvp
= n(Pi −ΦiF,0P0,i)
= n∆δαi
Slide 20Toulouse > 2013/10/31
Local control: problem solution - 1
∠
Choice of δλ instead of δu and structure of control input matrix B:where ∆δα = B(uM )δv
∠
out-of-plane and in-plane motions are decoupled
∠Out-of-plane solution, deterministic:
uoop = arctan
(∆δiy
∆δix
)|δvn| = na
∥∥∥∆δi∥∥∥ two options per orbit
∠
In-plane solution, underdetermined:minimum 2 impulses required⇒ 6 unknowns in 4 equations
Slide 21Toulouse > 2013/10/31
In-plane reconfiguration: possible maneuvers’ schemes
a
a
a
a
2-RT, 3-T, 3-T
2-R
generality
in-plane
Reconfiguration: 0 F, u0, uF
Enforcement of all End-conditions
out-of-plane
Planning drivers:
Thrusters’ duty cycle (# pulses)
Attitude constraints (type of pulses)
Safety & Visibility (ROE predictability)
Determinism (computation of ui)
Delta-v cost
000uoop, voop000
000uip, vip000
No-Type analytical
No-Type numerical
2-T
2-T
2-RT, 3-T, 3-T
2-RT, 3-T, 3-T
2-RT, 3-T, 3-T
2-RT, 3-T, 3-T 2-RT, 2-T
Slide 22Toulouse > 2013/10/31
Local control: problem solution - 2
∠
AVANTI design drivers for the choice of the in-plane scheme:
∠
autonomy, predictabilitymaneuvers’ spacing constraintscommunication pointing constraintsminimum delta-v
3-T analytical
∠Maneuvers are located in:
u = mod(
arctan
(∆δey∆δex
), π
)uipj = u+ kjπ, j = 1...3
k1 < k2 < k3
∠
Multiple (finite number) feasible solutions: one selected according to1. preference to minor delta-v cost2. preference to wider spacing between burns
Slide 23Toulouse > 2013/10/31
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 24Toulouse > 2013/10/31
Safety concept: ROE movement due to local control
Out-of-plane control In-plane control
optimal / sub-optimal
Slide 25Toulouse > 2013/10/31
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
∠
Pi distribute along the direction ofROE total variation
Slide 26Toulouse > 2013/10/31
Example of a Rendezvous - 1
∠
Scenario
∠
500 km high, inclination 98 deg
∠
Btarget: 0.01 m2/kg
∠∆B/B: 2%
∠
Input to MAP
∠
P0 = [5, 10000, −50, −250, −30, 200] m
∠
PF = [0, 3000, 0, −100, 0, 100] m
∠
tF: 18 orbits after t0
∠
time constraints
∠
mode: max-observability
−400−200
0200
400
0
5000
10000
15000−400
−200
0
200
400
radial [m]along−track [m]
norm
al [m
]−1 1
−1
1
Normalized δe/δi plane
0 2 4 6 8 10 12 14 16 18 20−0.04
−0.02
0
0.02
0.04Total delta−v: 0.2168 [m/s]
time [orbital periods]
de
lta
−v, δv
t δv
n [
m/s
]
Slide 27Toulouse > 2013/10/31
Example of a Rendezvous - 2
Relative eccentricity andinclination vectors
Drift and mean relative longitudeover time
−300 −200 −100 0 100 200 300−300
−200
−100
0
100
200
300
aδex aδi
x [m]
aδe
y a
δi y
[m
]
start
target
0 2 4 6 8 10 12 14 16 18 20−20
0
20
40
60
80
time [orbital periods]
aδa [m
]
0 2 4 6 8 10 12 14 16 18 202000
4000
6000
8000
10000
12000
time [orbital periods]
aδλ [m
]
Slide 28Toulouse > 2013/10/31
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 29Toulouse > 2013/10/31
Conclusions and current development status
∠
Impulsive MAaneuvers Planner for formation reconfigurations and rendezvousfor the AVANTI experiment (DLR/FireBird mission)
∠
experiment operational conditions (onboard functioning, space segmentrequirements, ...)
∠
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 30Toulouse > 2013/10/31
∠
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 FlyingSpacecraft 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 NoncooperativeSatellite Using Relative Orbital Elements,” Journal of Guidance, Control, andDynamics (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: SystemDesign and Flight Results,” Journal of Guidance, Control, and Dynamics, accessedSeptember 13, 2013. doi: 10.2514/1.59236.
∠
MAP development
Gaias, G., D’Amico, S., Ardaens, J. -S., “Generalized Multi-Impulsive Maneuvers forOptimum Spacecraft Rendezvous,”International Conference on SpacecraftFormation Flying Missions & Technologies (SFFMT), Munich, Germany, 2013.
Slide 31Toulouse > 2013/10/31
Onboard Maneuver Planning for the AVANTI experimentwithin the DLR FireBird mission
∠
AVANTI experiment
∠
MAP Concept
∠
Guidance Solution
∠
Control Solution
∠
Example
∠
Conclusions