Proximity Queries between Convex Objects: an Interior Point Approach for Implicit Surfaces

— This paper presents an interior point approach to exact distance computation between convex objects represented as intersections of implicit surfaces. Exact distance computation algorithms are particularly important for applications involving objects that make intermittent contact, such as in dynamic simulations and in haptic interactions. They can also be used in the narrow phase of hierarchical collision detection. In contrast to geometric approaches developed for polyhedral objects, we formulate the distance computation problem as a convex optimization problem; this optimization formulation has been previously described for polyhedral objects. We demonstrate that for general convex objects represented as implicit surfaces, interior point approaches are globally convergent, and fast in practice. Further, they provide polynomial-time guarantees for implicit surface objects when the implicit surfaces have selfconcordant barrier functions. We use a primal-dual interior point algorit...

• Type: Conference
• Year: 2006
• Where: ICRA
• Authors: Nilanjan Chakraborty, Jufeng Peng, Srinivas Akella, John Mitchell
• Keywords: Distance Computation, Exact Distance Computation, ICRA 2006, Implicit Surfaces, Robotics