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David Hsu, Robert Kindel, Jean-Claude Latombe, Stephen Rock
Presented by:Haomiao HuangVijay Pradeep
Randomized Kinodynamic Motion Planning with Moving
Obstacles
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Planner Overview
- Account for robot’s kinematics & dynamics
- Use a forward dynamics model
- Plan in state x time space
-Avoid moving obstaclesRobot
Obstacle
Planner Overview
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Planner Overview
Straight Line
Segments
1) Randomly Generate New Milestone2) Try to connect the milestone to existing milestones
Traditional PRM
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Planner Overview
1) Choose an existing milestone2) Generate a new milestone using a random control input
t=1t=2
t=1
t=1
t=3
t=3
t=2
t=2
Goal Region
Current State
Terminate When Milestone reaches Goal Region
Control Sampling PRM
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Planner Overview
Goal Region
Sampling Strategy
1
1
1
2 1
1
1
1
2
Weighted sampling approximates ideal sampling
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Planner Overview
Goal Region
Terminate When Milestone in first tree is “close enough” to milestone in second tree
Forward & Backward Integration
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Planner Overview
Probabilistic Completeness & Exponential Convergence
- Volume of reachable set exponentially bounded by number of lookout points
- Probability of lookout points increases exponentially with number of milestones
- Probability of finding a solution increases exponentially with number of milestones
Expansiveness: Visibility Becomes Reachability
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Planner Overview
Car Like Robots
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Planner OverviewRunning Times HistogramRun Times, Collision Checks,
Milestones, And Propagations
Car Like Robots
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Planner Overview
Double Integrator Dynamics, Moving Obstacles
x
y
ARL Air-Cusion Robot
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Planner Overview
x
y
t
Moving Obstacles
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Planner Overview
“Real-Time” Planning – Escape Trajectories
Goal
Safe Region
Not always possible to find solution to goal in allotted computation time
Robot
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Planner Overview
“Real Time” Planning – Time delays
Computing the trajectory also takes time
Robot
RobotRobot
Δtplan=0.4 sec
Instantaneous planning
Propagating dynamics by Δtplan
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Planner Overview
Actual Obstacle Trajectory
“Real Time” Planning – On-the-fly Replanning
Robot Estimated Obstacle Trajectory
PlannedTrajectory
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Planner Overview
Path Planning with Moving Obstacles
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Planner Overview
Conclusions
• Kinodynamic constraints can be dealt with through input sampling
• Expansiveness can be generalized to kinodynamic configuration spaces through reachability
• Moving obstacles can be efficiently dealt with
• “Real-Time” Planning is tricky to do well• Issues:
– Narrow Passages?– Long tail of running time