Interference Distance Calculation for Two Objects Bounded by Quadratic Surfaces

Abstract

Abstract We describe an algorithm for determining the interference or penetration distance between two moving objects. The objects are assumed to be specified by quadratic and/or linear constraints and thus, encompass a wide variety of objects encountered in robotics and multibody dynamics applications. The interference distance problem is formulated as a constrained optimization problem where we maximize the shrinkage of both objects, while maintaining a non-empty intersection volume between them. The key to the present algorithm is a nonlinear transformation which allows a closed-form description of the shrunk bodies. The resultant nonlinear programming problem is solved using an existing optimization scheme which is based on a recursive quadratic programming technique. The paper concludes with a numerical example demonstrating the validity and the computational efficiency of the proposed solution.