Global Vector Field Computation for Feedback Motion Planning
Liangjun Zhang, Steven M. LaValle, Dinesh Manocha

Abstract

We present a global vector field computation algorithm in configuration spaces for smooth feedback motion planning. Our algorithm performs approximate cell decomposition in the configuration space and approximates the free space using rectanguloid cells. We compute a smooth local vector field for each cell in the free space and address the issue of the smooth composition of the local vector fields between the non-uniform adjacent cells. We show that the integral curve over the computed vector field is guaranteed to converge to the goal configuration, be collision-free, and maintain C∞ smoothness. As compared to prior approaches, our algorithm works well on non-convex robots and obstacles. We demonstrate its performance on planar robots with 2 or 3 DOFs, articulated robots composed of 3 serial links and multi-robot systems with 6 DOFs

Paper

Global Vector Field Computation for Feedback Motion Planning
Liangjun Zhang, Steven M. LaValle, Dinesh Manocha
IEEE International Conference on Robotics and Automation (ICRA), 2009
PDF, PPT(Digest), Bib

Overview


Feedback planning for a translating Gear-shaped robot with 2 degrees of freedom (DOF)

Approximate cell decomposition in the robot's configuration space

A vector field is computed in the robot's free space. All integral curves over the vector field are guaranteed to converge to the goal.

Results and Videos


L-Shape: The computed vector field can guide the
robot from any initial configuration to the goal.
3 DOFs, Video



Gear: 3 DOFs
Video



3-Link: An articulated robot with 3-revolute-joint
3 DOFs, Video




Mulit-Robot: Coordinating 3 translating planar robots
6 DOFs
Video

 Performance


Performance of our vector field computation algorithm