An interval partitioning algorithm for constraint satisfaction problems

Abstract

We propose an efficient interval partitioning algorithm to solve the continuous constraint satisfaction problem (CSP). The method comprises a new dynamic tree search management system that also invokes local search in selected subintervals. This approach is compared with two classical tree search techniques and three other interval methods. We study some challenging kinematics problems for testing the algorithm. The goal in solving kinematics problems is to identify all real solutions of the system of equations defining the problem. In other words, it is desired to find all object positions and orientations that satisfy a coupled non-linear system of equations. The kinematics benchmarks used here arise in industrial applications.