Accelerated Computation of Linear Complementarity Problem in Dexterous Robotic Grasping via Newton-Subgradient Non-Smooth Multi-Step Greedy Kaczmarz Method

Real-time computational capability for simultaneous grasping force and displacement determination constitutes a critical enabler for stable and reliable grasping performance in dexterous robotic grasping. To accelerate the computational efficiency of LCP in the dexterous grasping problem, as well as to ensure the stability and reproducibility of the algorithm’s output, the NSNMGK method, which incorporates sequential projection iterations across all greedy-selected active constraint rows within each NSNGRK framework iteration cycle, is developed. In each NSNMGK iteration, sequential projection operations are systematically applied to all active constraint rows, satisfying the greedy criterion. This processing strategy ensures the full utilization of qualifying constraints within the greedy subset through a same generalized Jacobian evaluation per iteration cycle. The methodology effectively mitigates inherent limitations of conventional randomized row selection, including unpredictable iteration counts and computational overhead from repeated Jacobian updates, while maintaining deterministic convergence behavior. The method’s convergence theory is rigorously established, with benchmark analyses demonstrating marked improvements in computational efficiency over the NSNGRK framework. Experimental validation in dexterous robotic grasping scenarios further confirms enhanced convergence rates through reduced iteration counts and shortened computational durations relative to existing approaches.