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Robust Belief-Based Execution of Manipulation Programs for Goal Achievement Under Uncertainty

This work focuses on the execution of manipulation programs that utilize belief-based planning to achieve goals under uncertainty. It discusses discrete POMDP (Partially Observable Markov Decision Process) formulation, handling current states, and action selection based on observed information. The paper highlights the challenges of continuous state spaces, complex models, and how to achieve effective robot grasping in uncluttered environments. Key strategies include online belief-space search, using temporally extended actions, and parameterizing actions based on current beliefs to optimize decision-making processes.

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Robust Belief-Based Execution of Manipulation Programs for Goal Achievement Under Uncertainty

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  1. Robust Belief-based Execution ofManipulation Programs Kaijen Hsiao Tomás Lozano-Pérez Leslie Pack Kaelbling MIT CSAIL

  2. Achieving Goals under Uncertainty • Two kinds of uncertainty: • current state: • need to plan in information space • results of future actions: • search branches on outcomes as well as actions • Choice of action must be dependent on current information state

  3. Discrete POMDP Formulation • states • actions • observations • transition model • observation model • reward

  4. POMDP Controller Controller • State estimation is discrete Bayesian filter • Policy maps belief states to actions belief  SE sensing action Environment

  5. Action selection in POMDPs • Off-line optimal policy generation • Intractable for large spaces • On-line search: finite-depth expansion of belief-space tree from current belief state to select single action • Tractable in broad subclass of problems

  6. Challenges for action selection • Continuous state spaces • Requirement to select action for any belief state • Long horizon • Action branching factor • Outcome branching factor • Computationally complex observation and transition models

  7. Grasping in uncluttered environments • Points of leverage: • Robot pose is approximately observable • Robot dynamics are nearly deterministic • Bounded uncertainty over unobserved object parameters • Room to maneuver

  8. Online belief-space search • Continuous state space: discretize object state space

  9. Discretize object configuration space workspace configuration space belief state

  10. Online belief-space search • Continuous state space: discretize object state space • Action for any belief: search forward from current belief state

  11. Search forward from current belief • Low entropy belief states enable reliable grasp • Use entropy as static evaluation function at leaves • Actions can be useful for information gathering

  12. Online belief-space search • Continuous state space: discretize object state space • Action for any belief: search forward from current belief state • Long horizon: use temporally extended actions

  13. Use temporally extended actions • Primitive actions Entire trajectories • Reduce horizon Observations at end

  14. Online belief-space search • Continuous state space: discretize object state space • Action for any belief: search forward from current belief state • Long horizon: use temporally extended actions • Large action branching factor: parameterize small set of action types by current belief

  15. Parameterize actions with belief • Actions are entire world-relative trajectories • In current belief state, • execute with respect to most likely object configuration • terminate on contact or end of trajectory

  16. Online belief-space search • Continuous state space: discretize object state space • Action for any belief: search forward from current belief state • Long horizon: use temporally extended actions • Large action branching factor: parameterize small set of action types by current belief • Computationally complex observation and transition models: precompute models

  17. Precompute models • Execute WRT • with respect to estimated state e • in world state w • Expected observation,transition • Based on geometric simulation

  18. Online belief-space search • Continuous state space: discretize object state space • Action for any belief: search forward from current belief state • Long horizon: use temporally extended actions • Large action branching factor: parameterize small set of action types by current belief • Computationally complex observation and transition models: precompute models • Large observation branching factor: canonicalize observations for each discrete state and action

  19. Canonicalize observations • Any (e, w) pair with same relative transformation has same world-relative outcomes and observations • Only sample for one e with w varying within initial range of uncertainty • Cluster observations and represent each bin of object configurations by a single representative one • Only branch on canonical observations

  20. Algorithm • Off-line: • plan WRTs for grasping and info gathering • compute models • On-line: • while current belief state doesn’t satisfy goal • compute expected info gain of each WRT • execute best WRT until termination • use observation to update current belief • return to initial pose • execute final grasp trajectory

  21. Application to grasping with simulated robot arm • Initial conditions (ultimately from vision) • Object shape is roughly known (contacted vertices should be within ~1 cm of actual positions) • Object is on table and pose (x, y, rotation) is roughly known (center of mass std ~5 cm, 30 deg) • Achieve specific grasp of object

  22. Observations • Fingertips: 6-axis force/torque sensors • position • normal • Additional contact sensors: • just contact • Swept non-colliding path rules out poses that would have generated contact

  23. Grasping a Box Most likely robot-relative position Where it actually is

  24. Initial belief state

  25. Summed over theta

  26. Tried to move down; finger hit corner

  27. Probability of contact observation at each location

  28. Updated belief

  29. Re-centered

  30. Trying again, with new belief Back up Try again

  31. Final state and observation Observation probabilities Grasp

  32. Updated belief state: Success! Goal: variance < 1 cm x, 15 cm y, 6 deg theta

  33. What if Y coord of grasp matters?

  34. Need explicit information gathering

  35. Simulation Experiments • Methods tested: • Single open-loop execution of goal-achieving WRT with respect to the most likely state • Repeated execution of goal-achieving WRT with respect to the most likely state • Online selection of information-gathering and goal-achieving grasps (1-step lookahead)

  36. Box experiments • Allowed variation in goal grasp: 1 cm, 1 cm, 5 deg • Initial uncertainty: 5 cm, 5 cm, 30 deg

  37. Cup experiments

  38. Cup experiments • Goal 1 cm x, 1 cm y, rotation doesn’t matter (no info-grasps used) • Start uncertainty 30 deg theta (x,y varies) Increasing uncertainty

  39. Grasping a Brita Pitcher Target grasp: Put one finger through the handle and grasp

  40. Brita Pitcher experiments

  41. Brita Pitcher results Increasing uncertainty

  42. Other recent probabilistic approaches to manipulation • Off-line POMDP solution for grasping (Hsiao et al. 2007) • Bayesian state estimation using tactile sensors to locate object before grasping (Petrovskaya et al. 2006) • Finding a fixed trajectory that is most likely to succeed under uncertainty (Alterovitz et al. 2007, Burns and Brock 2007)

  43. The End.

  44. Timing For Brita Pitcher • (2.16 GHz processor, 3.24 GB RAM running Python, times in seconds)

  45. Number of Actions Used

  46. Creating Information-gain Trajectories • Trajectory generation • Generate endpoints, use randomized planner (such as OpenRAVE) to find nominal collision-free path • Sweep through entire workspace • Choose a small set based on information gain from start uncertainty

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