cient Dynamic Collision Detection using Expanded Geometry Models

Collision detection for articulated robots along pos sible trajectories is a basic requirement for path and motion planning systems We present an approach using static collision tests at selected locations merely to check complete trajectories This is done by using slightly expanded geometry models We develop a sim ple formula for estimating the distance between two po sitions of a link within a kinematic chain In the case of straight lines in con guration space an e cient ap proximation algorithm is introduced It calculates the next step in joint space to be close to the maximum possible length The presented scheme allows the ef fort required for model based path planning with line graphs in c space to be reduced by at least a factor of in the case of six degrees of freedom compared to a typically used classical method