3 rd Off Earth Mining Forum AUTONOMOUS SPACECRAFT NAVIGATION NEAR AN ASTEROID Arunkumar Rathinam, PhD candidate, ACSER, UNSW Sydney Slide 0
Navigation near an asteroid Major factors – size – irregular shape – weak gravitational force – non-gravitational perturbations Navigation in previous asteroid exploration missions – radiometric tracking (two-way Doppler, two-way range, Delta-DOR) – in combination with on-board optical data (based on landmark locations) Slide 1
Future Deep Space Missions list of Mars missions launching in 2020: – NASA’s Mars 2020 rover, ESA’s ExoMars 2020 rover, China’s orbiter/lander, UAE’s Hope orbiter, India’s Mars Orbiter Mission-2, SpaceX - Red Dragon Mars lander Other missions possibly using DSN in 2020: – NASA’s Odyssey orbiter, MAVEN orbiter and MRO, ESA’s Mars Express orbiter and TGO, India’s MOM, New Horizon, Voyager, OSIRIS- REx, Hayabusa-2 Spacecraft autonomy is a priority http://spacenews.com/mars-looming-traffic-jam/ Slide 2
Mission design • Asteroid characterisation phase (3-6 months) – by global mapping and observation – hovering around a home position (10~20 km above surface) – Position determinations based on radio, star-based nav. Techniques » Multiple descent operations - to determine the asteroid gravity by LIDAR and two-way Doppler measurements – Estimate unknown parameters the spin-axis orientation, rotation period – Generate shape model of the asteroid, with a core set of surface landmarks – Transition from star-based to landmark-based optical navigation - next phase Slide 3
Shape model for Navigation • From the images of asteroid – generate Maplet - small scale 3D high resolution maps – Stereophotoclinometry – Each maplet was centered on a landmark • Shape reconstruction – Limb profile to generate geometric shape Shape model of asteroid Itokawa – – assemble maplets on reconstructed shape Hayabusa mission • landmark table – helps identification and tracking of landmarks Slide 4
Challenges in Autonomous Navigation (1) • Navigation and mapping - mutually dependent problems • Optical navigation – poor illumination of asteroid surface – Stereo cameras and laser range finders won’t work at higher altitude (~20km) – need for robust image processing and data association • Dynamics – lack of accurate a priori knowledge of dynamic parameters – require good dynamic model » asteroid’s rigid body dynamics » Spacecraft’s motion (hover home pos. / establish stable orbit / manoeuvre control) Slide 5
Challenges in Autonomous Navigation (2) • Close proximity navigation – High accuracy demands – major perturbations » non-gravitational forces from solar radiation pressure » pressure exerted by re-emitted IR radiation from the spacecraft and the asteroid • Controlled manoeuvre – small delta-V (e.g. TAG, delta-V’s range between 1 ~ 20 cm/sec) • To reduce uncertainties – frequent orbit determinations and ephemeris updates – BUT, adds burden on the navigation teams Slide 6
Simultaneous Localization and Mapping (SLAM) • Estimate the robot’s pose and the map of the environment at the same time • No need for any a priori knowledge of environment • SLAM is chicken-egg problem – map is needed for localization – pose estimate is needed for mapping In probabilistic form : � � � , � | � �:� , � �:� , � � • – observation model � � � | � � , � – motion model � � � | � ��� , � � [Durrant ‐ Whyte and Bailey ‘06 ] Slide 7
SLAM Framework Sensors front-end back-end estimate feature extraction Map Data association Estimation -short-term (feature matching) Long-term (loop closure) integrate multiple sensor data Images – ONC, Attitude - star sensors, Position - radiometric ranging, Inertial - maneuver using thrusters, LIDAR/Laser altimeter, Point cloud data from Flash LIDAR Slide 8
SLAM approach • Filtering approach – EKF SLAM approach » robot pose and the environment feature positions in one state vector » quadratic nature of the map with increasing number of landmarks – Particle filter » maintains multiple map hypotheses, each conditioned on a stochastically sampled trajectory through the environment. » computationally intensive • Optimisation approach – Graph SLAM – states are represented as graph nodes Slide 9
SLAM - Factor graph – Factor graph is a bipartite graph with two types of node: variable node and factor node – Variable nodes (blue) constitutes the estimated state (x k and l i ) – Factor nodes (green) represents the joint probability distribution between the states f �, � Gaussian probability distribution b/w random variables – a & b; error between the variables must be minimized – Factors encode all the information entering the system – Graph captures the way this information is propagated to the hidden states Slide 10
Graph SLAM for asteroid navigation Factor graph representation of variables (spacecraft and asteroid state, landmark position), factors (measurement and motion) Slide 11
Preliminary experiment Experiment setup in MATLAB – asteroid’s diameter approx. 500 m – with 200 distinct features randomly distributed landmarks – rotational period : 8hr – the spacecraft orbiting at 600 m from the center – entire simulation covers a duration of about 120 key frames – revisit the landmarks between 2 ∼ 3 times Simulated Asteroid model with landmarks Slide 12
Summary – Future work » Estimate the other dynamics parameters in the process of state estimate » Develop the framework with integrating other sensor data » Want to achieve long term robustness Reconstructed model with landmarks and spacecraft positions Slide 13
THANKS Slide 14
de Santayana, R. Pardo, and M. Lauer. "Optical measurements for rosetta navigation near the comet." Proceedings of the 25th International Symposium on Space Flight Dynamics (ISSFD), Munich . 2015. Cadena, Cesar, et al. "Past, present, and future of simultaneous localization and mapping: Toward the robust-perception age." IEEE Transactions on Robotics 32.6 (2016): 1309- 1332. Slide 15
Motion model Asteroid’s dynamics model X � = � � q� � 1 2 W � � � � � Spacecraft motion model � � �J �� � � J ω � Q �� ω � � = � � � � 0 �� � � � � � 0 �� � �� �� � � �� � � �� � � � 0 q� � 1 2 W � � � � � �� � �� � � � � Q �� � � �J �� � � J � � � Q �� ω ω � �� Slide 16
Factor graph - formulation �� � � � � � � ��� , � � � � � � � � � �, � � Robot motion �� � � � � � � �� , � �� � � � � � � � �, � � Landmark measurements � � � � � � � � � ��� , � � ∝ ��� � � � � � � � � ��� , � � � � � � � � � � ��� , � � Factors � � � � � � � � � �� , � �� ∝ ��� � � � � � � � � �� , � �� � � � � � � � � �� , � �� � � � � � �� , � � � � � � � � � � �� , � � � � � � � Robot motion Errors � � � � � , � � � � � � � � � , � � � � � � Landmark measurements � � � ��� � � � � � � � � � � Slide 17
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