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

This paper investigates depth and heading control for 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 through a first-order backstepping step and augmented with proportional damping. Both controllers employ an identical allocation-aware anti-windup mechanism, which is a leaky back-calculation driven by the allocation shortfall Δτ 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 parameter-mismatch/tight-actuation condition (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. The results highlight that (i) allocation-driven anti-windup is essential when limits are active and (ii) modest backstepping shaping of the sliding surface markedly improves disturbance rejection and robustness without increasing control activity.