Collision Handling with Variable-Step Integrators

Abstract

This paper deals with collision handling of many convex shapes in offline simulations of Modelica-like object-oriented models,unsing variable-step Integrators with error control. Hereby, it is assumed that collisions appear only from time to time and/or that path planning algorithm shall utilize the provided information for collision avoidance. If a collision occurs, the collision force is computed with a spring/damper force element depending on the Penetration depth. Improvements to existing algorithms and methods are proposed: The Minikowski Protal Refinement (MPR) algorithm is enhanced so that not only Penetration depths but also closet distances between convex shapes are computed and that Special collision situations are treated properly. The broad and narrow phases of collision detection algorithms are enhanced as well, so that zero-crossing functions can be provided for the Integrator in order to Trigger Events when contact starts and Ends.