Efficient dynamic collision detection using expanded geometry models

Collision detection for articulated robots along possible 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 simple formula for estimating the distance between two positions of a link within a kinematic chain. In the case of straight lines in connguration space, an eecient approximation algorithm is introduced. It calculates the next step in joint space to be close to the maximum possible length. The presented scheme allows the effort required for model{based path planning with line graphs in c{space to be reduced by at least a factor of 4 in the case of six degrees of freedom, compared to a typically used 'classical' method.