Rough Sets Meta-Heuristic Schema for Inverse Kinematics and Path Planning of Surgical Robotic Arms

Surgical robots require sub-millimeter accuracy and reliable inverse kinematics across anatomies. Population-based metaheuristics address this, but static parameters may limit achieving the needed precision for clinical use. This study introduces the Rough Sets Meta-Heuristic Schema (RSMS) for dynamic, context-aware control. RSMS categorizes agents (Elite, Boundary, Poor) via Rough Set discretization based on fitness and distribution, allocating resources accordingly without problem-specific heuristics. To demonstrate the approach’s effectiveness, RSMS was implemented within Particle Swarm Optimization and evaluated as a surgical robotics inverse kinematics solver and path planner. In simulations using three surgical problems, RS-PSO allowed upgrading of the performance of the standard PSO in terms of consistent convergence and success in tight search spaces. Statistical tests confirmed these improvements. Using a 7-DOF KUKA LBR iiwa robot and surgical benchmarks of landmark acquisition, spiral trajectory tracking, and constrained path, RS-PSO achieved success rates of 100%, 67%, and 100%, respectively, meeting surgical requirements. The results demonstrate clinical gains in accuracy, consistency, and reproducibility for minimally invasive surgery. These findings support the practical advantages of RS-PSO and, more importantly, show that the RS-MH framework can be used as a general, reusable tool to improve the robustness, precision, and reproducibility of many swarm-based meta-heuristics for surgical robotics and other applications.