Transformed-domain predefined-time sliding mode control for actuator-constrained trajectory tracking of uncertain robotic manipulators

This paper proposes a transformed-domain predefined-time sliding-mode control method for uncertain robotic manipulators under prescribed tracking-performance constraints and actuator-oriented torque evaluation. The original tracking error is first mapped into a logarithmic prescribed-performance domain, and a predefined-time nonlinear disturbance observer is then constructed in the same transformed domain to estimate the lumped uncertainty entering the torque-control channel. An arctan-based nonsingular fast terminal sliding manifold and a continuous double-power reaching law are further combined to improve transient shaping and reduce discontinuous switching in the nominal torque command. Lyapunov analysis proves feasible-domain practical predefined-time boundedness and preservation of the original prescribed-performance boundary. Simulations on a 2-DOF manipulator with 20% model mismatch and time-varying disturbances show that the proposed method achieves lower RMSE, IAE and settling time than the nonlinear disturbance observer-based predefined-time sliding mode control (NDO-PTSMC) and the nonsingular fast terminal sliding mode control (NFTSMC). Ablation, mismatch-sweep and saturation tests further verify the roles of transformed-domain compensation, prescribed-performance transformation and arctan manifold shaping.