Simulation-based fast collision detection for scaled polyhedral objects in motion by exploiting analytical contact equations

Abstract

Based on the results of the study of convex object motion 1 (J. Hopcroft and G. Wilfong, "Motion of objects in contact," Int. J. Robot. Res., 4(4), 32-46 (1986)), this paper addresses the problem of exact collision detection of a pair of scaled convex polyhedra in relative motion, and determines the contact conditions of tangential contact features, arbitrary relative motion involving translation and rotation, and uniform scaling of the objects about a fixed point. We propose a new concept of the decision curve based on analytical contact equations that characterize a continuum of scaling factors (or a single scaling factor), which ensures that a pair of objects undergoing a scaling transformation will maintain the same tangential contact feature pair (or make instantaneous tangential contact feature transitions). We propose a reliable simulation-based approach to construct the decision curve by hybridizing analytical contact equations and conventional collision detection method, called the Fast Collision Detection Method (FCDM). This method can determine whether two scaled objects will make contact at specific tangential contact features (vertices, edges, or faces) under particular uniform scaling factors and after distinctive relative motion with better accuracy and less computational time than the existing collision detection methods. Finally, we demonstrate our approach for solving motion design in simple assembly/disassembly problems.

Active learning of the collision distance function for high-DOF multi-arm robot systems

“…To do so, CAD models of the robot, obstacles, and the environment together with a simulation environment are usually assumed available. Typically, the links and obstacles are approximated by boxes [11], spheres [12], capsules [13], and other simple convex shapes [14] that simplify collision calculations, and standard computational geometric algorithms for collision checking are employed. For typical low-DOF robots operating in static structured environments, these methods work well enough.…”

“…The main drawback with existing methods, and a significant one, is the explosion in data requirements as the degrees of freedom and number of obstacles increase. To illustrate the case of two seven-DOF arms operating in a shared workspace, discretizing the joint configuration space for the combined 14-DOF robot system at 10-degree intervals (which is clearly insufficient in realistic settings), and assuming a 200-degree joint range for each joint, this coarse sampling would result in more than 100 billion robot configurations (∼ 20 14 ).…”