Improved particle swarm optimization enables robust trajectory tracking of nonlinear robotic manipulators under external disturbances

Robust trajectory tracking of nonlinear robotic manipulators under uncertainty requires controllers whose gains are both theoretically grounded in stability analysis and systematically tuned. Classical controllers such as PID are highly sensitive to gain tuning, whereas conventional sliding mode control suffers from chattering and robustness smoothness trade-offs. Moreover, standard particle swarm optimization (PSO) algorithms are prone to premature convergence and entrapment in local minima, limiting their effectiveness in complex nonlinear systems. This paper proposes an improved particle swarm optimization (IPSO) framework for tuning a fractional-order nonsingular fast terminal sliding mode controller (FONFTSMC) applied to a two-link robotic manipulator. Unlike conventional PSO, IPSO integrates four enhancements: chaos-based logistic map initialization, adaptive mutation, dynamic inertia-weight scheduling, and stagnation-triggered particle reseeding, collectively mitigating premature convergence and improving search diversity. The proposed framework optimally determines the gain parameters [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], and rigorously establishes closed-loop finite-time stability through Lyapunov analysis under bounded disturbances. Benchmarked against PSO-tuned FONFTSMC across four integral performance indices (ISE, IAE, ITAE, and ITSE), IPSO achieves reductions of approximately [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], respectively, yielding smoother control effort, faster sliding-surface convergence, and improved disturbance rejection under structured time-varying step perturbations. These results establish the IPSO-FONFTSMC framework as a practically effective and theoretically sound solution for high-precision robotic manipulator control in the presence of uncertainty and external disturbances.