1. David Hsu, Robert Kindel, Jean- Claude Latombe, Stephen Rock Presented by: Haomiao Huang Vijay Pradeep Randomized Kinodynamic Motion Planning with Moving Obstacles

2. Planner Overview - Account for robot’s kinematics & dynamics - Use a forward dynamics model - Plan in state x time space -Avoid moving obstacles Robot Obstacle Planner Overview

3. Straight Line Segments 1) Randomly Generate New Milestone 2) Try to connect the milestone to existing milestones Traditional PRM

4. Planner Overview 1) Choose an existing milestone 2) Generate a new milestone using a random control input t=1 t=2 t=1 t=3 t=2 Goal Region Current State Terminate When Milestone reaches Goal Region Control Sampling PRM

5. Planner Overview Goal Region Sampling Strategy 1 1 1 2 1 1 1 1 2 Weighted sampling approximates ideal sampling

6. Planner Overview Goal Region Terminate When Milestone in first tree is “close enough” to milestone in second tree Forward & Backward Integration

7. 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

8. Planner Overview Car Like Robots

9. Planner Overview Running Times Histogram Run Times, Collision Checks, Milestones, And Propagations Car Like Robots

10. Planner Overview Double Integrator Dynamics, Moving Obstacles x y ARL Air-Cusion Robot

11. Planner Overview x y t Moving Obstacles

12. Planner Overview “Real-Time” Planning – Escape Trajectories Goal Safe Region Not always possible to find solution to goal in allotted computation time Robot

13. Planner Overview “Real Time” Planning – Time delays Computing the trajectory also takes time Robot Δt plan =0.4 sec Instantaneous planning Propagating dynamics by Δt plan

14. Planner Overview Actual Obstacle Trajectory “Real Time” Planning – On-the-fly Replanning Robot Estimated Obstacle Trajectory Planned Trajectory

15. Planner Overview Path Planning with Moving Obstacles

16. 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