Interactive Generalized Penetration Depth Computation for Rigid and Articulated Models Using Object Norm

摘要

We present a novel, real-time algorithm to accurately approximate the generalized penetration depth (PD_g) between two overlapping rigid or articulated models. Given the high complexity of computing PD_g, our algorithm approximates PD_g based on iterative, constrained optimization on the contact space, defined by the overlapping objects. The main ingredient of our algorithm is a novel and general formulation of distance metric, the object norm, in a configuration space for articulated models, and a compact closed-form solution for it. Then, we perform constrained optimization, by linearizing the contact constraint, and minimizing the object norm under such a constraint. In practice, our algorithm can compute locally optimal PD_g for rigid or articulated models consisting of tens of thousands of triangles in tens of milliseconds. We also suggest three applications using PD_g computation: retraction-based motion planning, physically-based animation, and data-driven grasping.