Approximated Collision Detection for Contact-Rich Dexterous Manipulation with Nonnegative Least Squares

Abstract

Collision detection between robotic hands and manipulated objects is crucial to model predictive control (MPC) for contact-rich dexterous manipulation. Based on the Gilbert-Johnson-Keerthi (GJK) algorithm and the expanding polytope algorithm (EPA), the GJK-EPA method has achieved success while requiring iterative optimizations. Recently, a signed distance function (SDF) based collision detection (C-SDF) method is used to estimate the contact information, which avoids iterations at the cost of matrix derivative operations. Inspired by this, in this paper, a simplified nonnegative least squares (NNLS) based quadratic programming (QP) algorithm is used to construct an approximated solution to the QP formulation of collision detection, for estimating collision points. Then, contact distances and Jacobians are calculated via physics computations and differentiable kinematics. Consequently, a C-NNLS method is proposed, which uses NNLS formulation to approximate the collision detection routine in the MPC while avoiding iterative optimizations and matrix derivatives. The C-NNLS method is applied to extensive simulative tasks, achieving lower average error while consuming 45.59% less time on average compared with the C-SDF method. Furthermore, the C-NNLS method is deployed on a real Allegro hand for on-palm reorientation. Results show that the C-NNLS method reduces average task time by 30.33% compared with the C-SDF method while maintaining high-quality dexterous manipulation.