Onboard Maneuver Planning for the Autonomous Vision ...homepages.laas.fr/clouembe/WSrdv/gaias.pdf · G. Gaias, DLR/GSOC/Space Flight Technology Department ... Toulouse > 2013/10/31.

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








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


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


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


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


Contents








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


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


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


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


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


Contents








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)


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)


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


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


Contents








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


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


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


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


Contents








Safety concept: ROE movement due to local control

Out-of-plane control In-plane control

optimal / sub-optimal


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


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

]


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


aδa [m

]

0 2 4 6 8 10 12 14 16 18 202000

4000

6000

8000

10000

12000


aδλ [m

]


Contents








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


∠

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.


Onboard Maneuver Planning for the AVANTI experimentwithin the DLR FireBird mission

∠

AVANTI experiment

∠

MAP Concept

∠

Guidance Solution

∠

Control Solution

∠

Example

∠

Conclusions

[email protected]

Onboard Maneuver Planning for the Autonomous Vision ...homepages.laas.fr/clouembe/WSrdv/gaias.pdf · G. Gaias, DLR/GSOC/Space Flight Technology Department ... Toulouse > 2013/10/31.

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