Constraint-Based Motion Planning Using Voronoi Diagrams

Abstract

We present a novel algorithm for planning the motion of rigid and articulated robots in complex, dynamic, 3D environments. Our approach is to reformulate the motion planning problem as a simulation of a constrained dynamical system, and guide this system using generalized Voronoi diagrams (GVDs). In our framework, each rigid robot is subject to virtual forces induced by geometric and mechanical constraints. These may include constraints to have a robot follow an estimated path computed using a GVD, constraints to link rigid objects together to represent an articulated robot, or constraints to enforce a spatial relationship between multiple collaborative robots. The resulting algorithm uses all constraint forces to move the robot along an estimated path through the environment, while avoiding collisions with obstacles and enforcing joint and positional constraints. Our algorithm works well in dynamic environments with moving obstacles and is applicable to planning scenarios where multiple robots must move simultaneously to achieve a collision free path.