For non-Pieper robotic manipulators that lack closed-form analytical solutions, inverse kinematics (IK) is typically solved using numerical or optimization-based methods. However, conventional Particle Swarm Optimization (PSO) algorithms often suffer from premature convergence, unstable performance near singular configurations, and limited trajectory smoothness. To address these challenges, this paper proposes an improved PSO framework that integrates a nonlinear inertia weight strategy with Jacobian pseudo-inverse guidance. The nonlinear inertia weight employs a two-phase adaptation mechanism, enhancing global exploration in the early iterations and improving local exploitation later, thus avoiding stagnation. The Jacobian guidance introduces gradient-based directional information, which accelerates convergence and improves robustness under singular conditions. Furthermore, a quaternion-based pose error formulation combined with a joint continuity penalty ensures smooth trajectory tracking and avoids orientation singularities. Experimental results on benchmark functions and two representative non-Pieper manipulators demonstrate that the proposed method achieves superior convergence accuracy, improved stability, and better trajectory continuity compared with multiple PSO variants. The results confirm the effectiveness and generality of the proposed framework for solving IK problems of non-Pieper robots.
Yang et al. (Sat,) studied this question.