Sliding mode control gain optimization for a robot arm manipulator using an improved stochastic framework

We present an optimization-control framework for trajectory tracking of a 3-DoF manipulator, where an improved Stochastic Paint Optimizer (SPO-CL1) automatically tunes the gains of a sliding mode controller. Designed to address robotic challenges such as nonlinearities, couplings, and disturbances, the approach aims to achieve high tracking accuracy, rapid convergence, reduced chattering, and limited actuation effort, while remaining simple and robust to parameter variations. SPO-CL1 integrates three structure-aware enhancements into the original SPO architecture: chaotic initialization via the Chebyshev map to diversify the initial population, Opposition-Based Learning applied after the clustering phase to accelerate convergence, and periodic Lévy flight perturbations targeting the best solution to escape local optima. The SMC gains are automatically tuned by minimizing the Integrated Squared Error cost function J = ∫₀ᵀ eᵀ(t)e(t)dt. Two phases of validation were conducted. First, SPO-CL1 is benchmarked against eleven algorithms including recent hybrid variants (IGWO, EWOA, MHHO, HSMA) on the CEC-2022 suite, achieving the best Friedman rank of 1.83 and statistically significant superiority confirmed by Wilcoxon rank-sum tests (α = 0.05). Second, a path planning experiment on a Lemniscate of Bernoulli trajectory demonstrates that SPO-CL1 achieves the lowest ISE of 1.51 × 10⁻⁴ with near-zero inter-run variance, the fastest tracking error convergence, and the tightest end-effector trajectory among all twelve compared algorithms. These results confirm that SPO-CL1 is a competitive and reliable approach for automatic SMC gain tuning in complex robotic applications.