Efficient distance computation in configuration space

We address the problem of computing a measure of the distance between two configurations of a rigid or an articulated model. The underlying distance metric is defined as the maximum length of the displacement vectors over the vertices of the model between two configurations. Our algorithm is based on Chasles theorem from Screw theory, and we show that for a rigid model the maximum distance is realized by one of the vertices on the convex hull of the model. We use this formulation to compute the distance, and present two acceleration techniques: incremental walking on the dual space of the convex hull and culling vertices on the convex hull using a bounding volume hierarchy (BVH). Our algorithm can be easily extended to articulated models by maximizing the distance over its each link and we also present culling techniques to accelerate the computation. We highlight the performance of our algorithm on many complex models and demonstrate its applications to generalized penetration depth computation and motion planning.