Backstepping–Sliding Mode With Anti-Windup for Autonomous Underwater Vehicle Heave and Yaw Control Under Thruster Limits

This paper investigates depth and heading control of an underactuated autonomous underwater vehicle (AUV) subject to hard thruster limits and allocation constraints. A classical sliding-mode controller with boundary layer (SMC-sat) is compared against a backstepping sliding-mode variant (BS-SMC-sat), in which the sliding surface is shaped via a first-order backstepping step and augmented with proportional damping. Both controllers employ an identical allocation-aware anti-windup mechanism, implemented as a leaky back-calculation driven by the allocation shortfall △τ returned by the thruster allocator. The BlueROV2 (Heavy) heave–yaw slice is used as a realistic benchmark with smooth multi-step reference commands. Three operating scenarios are examined: nominal, matched-step disturbances, and a combined parameter-mismatch/tight-actuation stress test (reduced thruster ceilings and perturbed inertial/damping offsets). Under nominal conditions, both controllers achieve comparable tracking performance with negligible control effort and a saturation duty of <3%. Under disturbances, BS-SMC-sat reduces depth RMSE by ≈66% and heading RMSE by ≈65% relative to SMC-sat, while cutting yaw effort by ≈10%. Under parameter mismatch and tighter actuation, BS-SMC-sat remains robust, lowering RMSE by ≈31% (depth) and ≈72% (heading) with effort essentially unchanged. These results demonstrate that allocation-driven anti-windup is essential when limits are active, and modest backstepping shaping of the sliding surface markedly improves disturbance rejection and robustness without increasing control activity.