angles-only autonomous rendezvous navigation to a space ... · motivation: distributed space...

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Angles-Only Autonomous Rendezvous Navigation to a Space Resident Object

Josh Sullivan PhD. Candidate, Space Rendezvous Laboratory PI: Dr. Simone D’Amico

Dr. D’Amico, S. > A Vision for Distributed Space Systems > 02/10/2012

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people.stanford.edu/damicos

Contents

 Research motivation  Problem description  Previous work on the topic  Research goals  Technical details §  Observability assessment §  Navigation filter design  Conclusions and way forward

Tango S/C

Vega

First image taken during ARGON April 23, 2012 (DLR)


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Motivation: Distributed Space Systems  Navigation approach which only makes use of camera-based measurements.  Is an enabling technology for many distributed space systems applications.

Autonomous Rendezvous

Novel Science Missions

General Space

Situational Awareness


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Motivation: Metrology Systems

LIDAR

Vision-‐Based

Laser-‐Ranging

Radio-‐Frequency GNSS


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Problem Description

 Reconstruct relative translational motion state from a set of camera-based measurements. §  No range information available. §  Measurements are two angles from

single sensor.  Devise guidance and navigation architecture for rendezvous that considers: §  Choice of state representation §  Observability constraints §  Navigation conditions §  Orbit geometry

Radial, R

Cross-track, N

Along-track, T

Chief

Deputy/Target


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Existing Rendezvous Techniques

Δv Δv Δv

Δv

Radial, or

Along-track, ot Chief Deputy

Δv

Chief

Deputy

Δv

Δv

V-Bar

R-Bar

Along-track, ot

Radial, or


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Existing Rendezvous Techniques

E/I-Vector Separation

 Uses size and orientation of relative eccentricity and inclination vectors.

 Design of passively safe relative trajectories based on minimum R-N separation.

SAFE UNSAFE


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Existing Work on Angles-Only Navigation Theory Development  Lacking a unified connection between state, observability constraints,

measurement model formulation, and navigation conditions  General result: Angles-only navigation problem is inherently unobservable as currently formulated.

 Proposed remedies: §  Orbit/attitude maneuvers to change

line-of-sight trend §  Binocular vision §  Offset camera from S/C CG

Angles-Only Navigation

Performance

Trajectory Planning

(Guidance)

Resulting Trajectory


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ARGON (PRISMA) Ground-in-the-

loop: image processing,

navigation, and maneuver planning

AVANTI (FireBIRD) Autonomous

guidance, navigation, and

maneuver planning

mSTAR (CEAA) Fully

autonomous vision-based

rendezvous with ejected nano-sat

Existing Work on Angles-Only Navigation Representative Missions


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Short-Term Research Goals

Dynamics State

Measurement Modeling

Observability Constraints

Navigation Conditions

Orbit Geometry

Navigation Architecture


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Long-Term Research Goals

mSTAR (CEAA) mDOT (SLAB)

High-fidelity validation in SLAB multi-

sensor testbed


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Dynamics State: Relative Orbital Elements

 Relative Orbital Elements (ROE)

Rel. Semi-Major Axis

Rel. Eccentricity Vector

Rel. Inclination Vector

Rel. Mean Arg. of Latitude

 Straightforward inclusion of perturbations (geopotential, differential drag, control)  Insight into relative orbit geometry  Unobservable state has been shown to decouple


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Observability Assessment

 Goal: determine how well state can be reconstructed from measurements.  Ingredients: dynamics and measurement model §  State Transition Matrix (STM) §  Measurement Sensitivity Matrix (MSM)  Criteria: Observability Matrix (OM) and Observability Gramian (OG) §  Rank of OM: first indication of observability. §  Condition Number of OG: sensitivity of reconstructed state

Observability Matrix Observability Gramian


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Observability: Variable Simulation Parameters  Simulation varies navigation conditions and orbit geometry for each state representation and choice of measurement model formulation.  Returns conditioning characteristics at each iteration.

Parameter Nominal Value

Navigation Procedure Duration 1 day

Measurement Density 30 measurements/orbit

Relative Orbit Drift Rate 0.50 km/orbit

Radial Oscillation Amplitude 4 km

Cross-Track Oscillation Amplitude 4 km

Mean Along-Track Separation 10 km

Eccentricity/Inclination Angle 0 radians


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Nominal Relative Orbit Trajectory


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Observability: Example Simulation Output


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Navigation Filter Design  EKF with ROE state and nonlinear measurement model  Gaussian white noise with σ = 40” added to azimuth and elevation measurements  State initialization error on the order of 0.5 km

Blue: Est. Error Red: 1-σ Green: 3-σ


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Navigation Filter Design  EKF with rectilinear state  Gaussian white noise with σ = 40” added to azimuth and elevation measurements  No state initialization error


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Navigation Filter Improvement  Estimation error is largely influenced by initialization and not measurement error.  Improvement: deterministic batch initial orbit determination algorithm that initializes the EKF with a more favorable accuracy.

Batch Estimation

Sequential Estimation


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Navigation Filter Improvement  Preliminary algorithm returns initialization error on the order of 30m.  Idea: use batch algorithm to sequentially re-initialize for improved observability.  Run sequential estimation while batch is building.

Blue: Est. Error Red: 1-σ Green: 3-σ


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Ways Forward

 Introduce sequential re-initialization of EKF with orbit determination algorithm- similar to using maneuvers to improve observability.  Improve ROE state transition matrix for more applications.  Consideration of maneuvers to further improve observability.  Validate in SLAB high-fidelity spacecraft simulation software.  Embedding algorithms and testing with hardware-in-the-loop.


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Thank you for your time!

Questions?


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Backup


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 Curvilinear State §  Hill-Clohessy-Wiltshire (HCW) model for

relative curvilinear position and velocity

§  Approximates curvature of relative orbit with arc segments.

 Rectilinear State §  Hill-Clohessy-Wiltshire (HCW) model for

relative rectilinear position and velocity §  Approximates curvature of relative orbit

with straight line segments.

State Comparison: Rectilinear and Curvilinear


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State Comparison: Integration Constants


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Observability: Measurement Model  Line-of-sight unit vector from reference spacecraft camera frame to target.  Described by two angles: azimuth and elevation.

Azimuth is angle from boresight to LOS

projection on x-z plane

Elevation is angle from x-z plane to

LOS vector

Measurements can be modeled from state knowledge

Actual VBS line-of-sight trend during PRISMA mission

Image Credit: DLR


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Measurement Models: Rectilinear State

 Measurement Sensitivity Matrix (MSM): sensitivity of measurement with respect to the state of interest.

Measurements are only position-dependent

Sensitivity of measurements w.r.t relative position in camera frame

Absolute attitude of camera

Mapping from vehicle RTN to absolute attitude

Proposed attitude of the camera is a permutation of the RTN frame


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Measurement Models: ROE State

 Built off of Rectilinear MSM by adding one additional mapping to the new state representation.  Mapping comes from solution of HCW equations, represented in terms of the Relative Orbital Elements

Mapping between rectilinear position and

ROE state

Mapping measurement sensitivity in rectilinear

representation to sensitivity in ROE

Rectilinear Portion


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Observability: Example Simulation Output


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Initial Orbit Determination

 Built from batch of LOS measurements.  Leverages the planar assumption: the observed orbit LOS vectors must lie in a plane because the target orbit forms a plane.  Determined position vectors are not independent.

angles-only autonomous rendezvous navigation to a space ... · motivation: distributed space...

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