Robust Belief-based Execution of Manipulation Programs
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Robust Belief-based Execution ofManipulation Programs
Kaijen HsiaoTomás Lozano-PérezLeslie Pack Kaelbling
MIT CSAIL
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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
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Discrete POMDP Formulation
• states• actions• observations• transition model• observation
model• reward
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Controller
SE
Environment
belief
actionsensing
POMDP Controller
• State estimation is discrete Bayesian filter• Policy maps belief states to actions
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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
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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
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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
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Online belief-space search
Continuous state space: discretize object state space
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Discretize object configuration space
workspace
configuration space
belief state
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Online belief-space search
Continuous state space: discretize object state space
Action for any belief: search forward from current belief state
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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
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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
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Use temporally extended actions
Primitive actions Entire trajectoriesReduce horizon Observations at end
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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 actionsLarge action branching factor: parameterize
small set of action types by current belief
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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
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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 actionsLarge action branching factor: parameterize
small set of action types by current beliefComputationally complex observation and
transition models: precompute models
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Precompute models
Execute WRT• with respect to estimated state e
• in world state w
Expected observation,transition
Based on geometric simulation
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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 actionsLarge action branching factor: parameterize
small set of action types by current beliefComputationally complex observation and
transition models: precompute modelsLarge observation branching factor: canonicalize
observations for each discrete state and action
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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
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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
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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
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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
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Grasping a Box
Most likely robot-relative position Where it actually is
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Initial belief state
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Summed over theta
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Tried to move down; finger hit corner
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Probability of contact observation at each location
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Updated belief
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Re-centered
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Trying again, with new belief
Back up Try again
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Final state and observation
Grasp Observation probabilities
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Updated belief state: Success!
Goal: variance < 1 cm x, 15 cm y, 6 deg theta
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What if Y coord of grasp matters?
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Need explicit information gathering
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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)
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Box experiments
Allowed variation in goal grasp: 1 cm, 1 cm, 5 degInitial uncertainty: 5 cm, 5 cm, 30 deg
0
20
40
60
80
100
open loop repeated WRT repeated WRT withinfo-grasp
Pe
rce
nt
gra
sp
ed
co
rre
ctl
y
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Cup experiments
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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)
0
20
40
60
80
100
1 3 5Uncertainty std in x,y (cm)
Per
cen
t gra
sped
co
rrec
tly
Open loop
RepeatedWRT
Increasing uncertainty
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Grasping a Brita Pitcher
Target grasp:
Put one finger through the handle and grasp
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Brita Pitcher experiments
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Brita Pitcher results
Increasing uncertainty
0
10
20
30
40
50
60
70
80
90
100
loc 1, rot 3 loc 3, rot 9 loc 5, rot 15 loc 5, rot 30
Uncertainty standard dev (cm, deg)
Pe
rce
nt
gra
sp
ed
co
rre
ctl
y
Open loop withperfect info
Repeated WRT
Hand-generatedguarded moves
Open loop withimperfect info
Repeated WRTwith info-grasps
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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)
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The End.
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Timing For Brita Pitcher
(2.16 GHz processor, 3.24 GB RAM running Python, times in seconds)
1 cm3 deg
3 cm9 deg
5 cm15 deg
5 cm30 deg
Grid size 5733 16337 14415 24025
Computing observation matrix (1 traj)
12 33 29 51
1st belief-state update
4 10 10 19
Choosing 1st info-grasp
10 9 17 30
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Number of Actions Used
1 cm 3 deg
3 cm9 deg
5 cm15 deg
5 cm 30 deg
Robust execution of target
1.9 2.5 3.3 3.5
Robust execution with info-grasps
not run 4.4 4.1 4.2
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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