Residual-activated smooth sliding-mode control for actuator-limited quadrotor UAV attitude–altitude tracking

Residual tracking errors may persist in actuator-limited quadrotors after the main transient has decayed, particularly when motor lag, dead-zone behavior, thrust saturation, rotor drag, and partial motor-effectiveness loss weaken corrective action near the sliding surface. This study develops a friction-mode residual reaching law (FRMRL) for robust attitude–altitude control of a quadrotor UAV. The law retains the smoothness of a bounded sliding-mode reaching function and adds a residual-activated term that becomes effective when the sliding variable remains nonzero while the corresponding angular or vertical rate is small. It therefore strengthens the reaching action in the low-rate residual regime without increasing switching authority across the full operating range. The controller is formulated for a cascaded quadrotor architecture in which the directly actuated attitude–altitude channels are modeled as matched-input second-order subsystems subject to lumped perturbations and actuator nonlinearities. Lyapunov analysis establishes uniform ultimate boundedness under bounded perturbations and asymptotic convergence in the nominal case; it also shows a stronger local descent rate than the smooth reaching baseline in the residual regime. FRMRL is evaluated against PID, constant-rate SMC, exponential-reaching-law SMC, adaptive SMC, and a gain-matched smooth-reaching-law ablation baseline across six scenarios: nominal tracking, matched disturbances, wind-like disturbances, parameter uncertainty, actuator saturation with dead-zone, and partial motor-effectiveness loss. FRMRL achieves the lowest study-specific journal-oriented quality score in all six scenarios. Its mean score is 13.2%, 19.7%, 49.9%, and 78.4% lower than the corresponding mean scores for ERL-SMC, ASMC, CRL-SMC, and PID, respectively. Across the six scenarios, FRMRL also yields a mean total IAE of 15.5468 and a mean peak-to-peak control ripple of 0.3783. The gain-matched ablation indicates that residual activation, rather than differences in baseline gains, accounts for the improvement in residual-error suppression and control smoothness.