A Multi-Objective Hybrid PSO-DLS Optimization Framework for Redundant Inverse Kinematics of Anthropomorphic Upper-Limb Manipulators

The inverse kinematics (IK) of anthropomorphic (humanoid) upper-limb manipulators presents two main challenges: the inherent non-uniqueness of solutions and inter-frame discontinuities near singularities or joint limits. Under real-time constraints, the trade-off among end-effector accuracy, near-singularity robustness, and motion smoothness becomes critical. To address these challenges, this paper proposes an on-demand global-local hybrid solver that minimizes end-effector position error, incorporates a manipulability-based robustness term, and penalizes inter-frame joint changes under a unified cost function. The solver combines Damped Least Squares (DLS) for efficient local refinement with gated Particle Swarm Optimization (PSO), which is activated only when increasing frame difficulty is indicated by rising error, declining manipulability, or emerging feasibility risks. At the trajectory level, smoothness and feasibility are maintained through previous-frame initialization, early stopping, and joint-limit projection. Under a unified metric suite, the proposed method is systematically compared with Always PSO-DLS, DLS-only, Classical Jacobian Pseudoinverse, and Quadratic Programming-based IK baselines. The results show that the proposed method achieves a favorable balance among tracking accuracy, continuity, robustness, and computational cost: it preserves behavior close to Always PSO-DLS while substantially reducing computation, improves difficult-frame stability and reliability relative to purely local refinement, and maintains low runtime on low-complexity frames by avoiding the fixed overhead of always-on global search. Ablation and sensitivity analyses further support the effectiveness and stability of the on-demand mechanism and its key parameter settings. Overall, the proposed framework provides a promising IK core for rehabilitation robots, upper-limb exoskeletons, and anthropomorphic manipulators in continuous tracking tasks with real-time requirements.