David Hsu, Robert Kindel, Jean-Claude Latombe, Stephen Rock
Presented by:Haomiao HuangVijay Pradeep
Randomized Kinodynamic Motion Planning with Moving
Obstacles
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
Planner Overview
Straight Line
Segments
1) Randomly Generate New Milestone2) Try to connect the milestone to existing milestones
Traditional PRM
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
Planner Overview
Goal Region
Sampling Strategy
1
1
1
2 1
1
1
1
2
Weighted sampling approximates ideal sampling
Planner Overview
Goal Region
Terminate When Milestone in first tree is “close enough” to milestone in second tree
Forward & Backward Integration
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
Planner Overview
Car Like Robots
Planner OverviewRunning Times HistogramRun Times, Collision Checks,
Milestones, And Propagations
Car Like Robots
Planner Overview
Double Integrator Dynamics, Moving Obstacles
x
y
ARL Air-Cusion Robot
Planner Overview
x
y
t
Moving Obstacles
Planner Overview
“Real-Time” Planning – Escape Trajectories
Goal
Safe Region
Not always possible to find solution to goal in allotted computation time
Robot
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
Planner Overview
Actual Obstacle Trajectory
“Real Time” Planning – On-the-fly Replanning
Robot Estimated Obstacle Trajectory
PlannedTrajectory
Planner Overview
Path Planning with Moving Obstacles
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