A Novel Optimization-Based Pruning Strategy for Concave Minimum Distance Problems
Juan A. Carretero, Raja Uppuluri · 2004
The simulation of multibody dynamical systems often requires the determination of the separation or interference distance between two moving objects. That is the case of robotic systems where it is often required to perform such distance queries at a very high speed. Some algorithms obtain the exact separation or interference distance while sacrificing computational speed, whereas other algorithms give fast results by sacrificing precision. In this paper, a novel two-stage optimization-based strategy is proposed to allow fast and precise distance calculations. In the first stage, a novel pruning strategy is used in order to obtain features that are closest to the other object and vice-versa. In the second stage, the set of closest features are used in a more common local optimization technique in order to solve a simple constrained optimization problem. The set of surfaces obtained through the pruning method is only a small subset of those describing the entire objects. As a result, the solution time needed to find the exact distance using the local optimization method in the second stage is drastically reduced. Numerical examples showing the algorithm’s capabilities are included