Adaptive Backstepping Control for Six-Degree-of-Freedom ROV Trajectory Tracking Under Hydrodynamic Parameter Uncertainty

This paper addresses six-degree-of-freedom (6-DOF) trajectory tracking of a free-swimming remotely operated vehicle (ROV) under hydrodynamic parameter uncertainty. Four controllers are designed on a common benchmark and compared: cascaded proportional–integral–derivative (PID) control, whose tuning is simple and whose steady-state behaviour is predictable, but which couples the six channels only through the plant and therefore produces large oscillatory transients and large tracking errors; pure backstepping, which recovers accurate tracking at low computational cost, but whose constant feedback gains must be re-tuned whenever the vehicle or its operating conditions change, because the gains have no mechanism to absorb model–plant mismatch; a boundary-layer sliding-mode controller, which is robust to bounded matched disturbances but pays for this robustness with chattering-prone control activity and a residual steady-state error set by its boundary-layer thickness; and the proposed adaptive backstepping controller, which replaces the constant backstepping gains with σ-modified adaptive feedback gains on the position and velocity errors. The adaptation carries a modest sensitivity to its learning rate, and, like every adaptive scheme, it converts part of the model–plant mismatch into a transient gain-learning excursion; in exchange, it retains the backstepping transient shape while improving steady-state tracking accuracy and reducing the control effort required by the fixed-gain designs. The trade-offs are quantified on the Chin and Lau 75 kg benchmark in circular trajectory tracking, step response, and repeated runs under measurement noise, and the robustness of the ordering is examined under controller-side model error, ocean currents, and reduced thruster authority. Across the four control families, robustness to model error is bought either a priori (sliding-mode control, SMC, at the price of chattering and a boundary-layer-limited nominal accuracy) or online (adaptation, at the price of a learning-rate sensitivity and a transient gain-learning excursion); neither is free. The adaptive controller is further ported, without retuning, to C code generated by Embedded Coder running on a 168 MHz STM32F407 at a fixed 10 ms period, and it is shown to reproduce the offline behaviour closely within the CPU budget, supporting implementation-level feasibility; this hardware-in-the-loop study validates the real-time implementation, not the control law against physical vehicle dynamics.