Approximated Collision Detection for Contact-Rich Dexterous Manipulation with Nonnegative Least Squares
Weibing Li, Jiajun Luo, Lei Yang, Yehui Li, Kai Huang
AI summary
Problem
Efficient and accurate collision detection is critical for model predictive control in contact-rich dexterous manipulation, yet existing methods struggle with either slow iterative optimization or expensive matrix derivative calculations.
Approach
The authors propose C-NNLS, which replaces iterative solvers with a simplified nonnegative least squares formulation and hyperparameterized projections to explicitly approximate collision points, distances, and Jacobians.
Key results
- Lower average orientation error than GJK-EPA and C-SDF in simulation
- 45.59% reduction in average computational time compared to C-SDF
- 30.33% faster real-world task completion on a physical Allegro hand
- 100% success rate across all simulated reorientation tasks
Why it matters
Provides a fast, reliable collision detection alternative for real-time MPC, advancing the development of contact-rich robotic manipulation systems.
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.