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