Online PSO-enhanced adaptive fractional-order sliding mode control for robust mobile robot trajectory tracking

This paper proposes an Online Particle Swarm Optimisation tuned Adaptive Fractional Order Sliding Mode Control (OPSO-AFSMC) framework for trajectory tracking of differential-drive mobile robots under uncertainties and disturbances. The approach integrates three layers: (i) an adaptive fractional-order sliding mode controller exploiting memory-dependent dynamics for enhanced disturbance rejection, (ii) an online PSO mechanism for real-time controller-gain optimisation, and (iii) a stability-constrained adaptation mechanism that restricts parameter updates to a Lyapunov-consistent safe set. Unlike existing PSO-based fractional sliding mode methods that primarily rely on offline tuning, the proposed framework combines online optimisation with projection, dwell-time, and gain-admissibility constraints to preserve closed-loop stability. Theoretical results establish discrete-time stability and finite-time convergence under bounded disturbances. The proposed update law also imposes a hard per-step parameter-rate limit and accepts updates only when they improve the currently applied parameters. The method is validated on two reference trajectories under five operating conditions, with ten independent runs per condition, and compared with an adaptive fractional-order sliding mode controller tuned by offline PSO. Online retuning reduces the integral absolute error by 20–26% under changed operating conditions while remaining within approximately 1% of the baseline when offline tuning remains valid. Simulation results demonstrate the practical potential of stability-constrained online adaptation for mobile-robot trajectory tracking.