Calculation of Robot Multi-Fingered Grasping Force and Displacement Based on the Newton–Subgradient Non-Smooth Greedy Randomized Kaczmarz Method for Solving Linear Complementarity Problem

The calculation of grasping force and displacement is important for multi-fingered stable grasping and research on slipping damage. By linearizing the friction cone, the robot multi-fingered grasping problem can be represented as a linear complementarity problem (LCP) with a saddle-point coefficient matrix. Because the solution methods for LCP proposed in the field of numerical computation cannot be applied to this problem and the Pivot method can only be used for solving specific grasping problems, the LCP is converted into a non-smooth system of equations for solving it. By combining the Newton method with the subgradient and Kaczmarz methods, a Newton-subgradient non-smooth greedy randomized Kaczmarz (NSNGRK) method is proposed to solve this non-smooth system of equations. The convergence of the proposed method is established. Our numerical experiments indicate its feasibility and effectiveness in solving the grasping force and displacement problems of multi-fingered grasping.