Research on Trajectory Tracking of Robotic Fish Based on DBO-Backstepping Control

Advancements in underwater robotic fish have generated new requirements for diverse underwater scenarios, presenting challenges in attaining efficient and precise control, particularly in the realm of classical trajectory tracking. In response to the inherently nonlinear and underactuated characteristics of underwater robot control design, this study introduces a trajectory tracking backstepping control method for the planar motion of underactuated underwater robotic systems. The method is grounded in dung beetle optimization (DBO) backstepping control. Firstly, a dynamic model of a single-node tail-actuated robotic fish is introduced, and the model is averaged. Based on the averaged model and Lyapunov functions, the design of the backstepping control scheme is derived to ensure the stability of the control system. Subsequently, the derived backstepping control is further optimized through the application of the DBO optimization algorithm, then the optimal backstepping control (OBC) approach is presented. Finally, the proposed control scheme is applied to the simulation experiments with the robotic fish. The simulation results for straight-line tracking indicate that OBC is superior to the PID method in terms of overshoot performance, reducing the average overshoot from 0.23 to 0.02. Additionally, OBC reduces the average velocity error from 0.043 m/s (backstepping control) to 0.035 m/s, which is lower than that of the PID method, with an average velocity error of 0.054 m/s. In turn tracking, the simulation results reveal that OBC reduces the average velocity error from 0.067 m/s (backstepping control) to 0.055 m/s and demonstrates better performance than the PID method, with an average velocity error of 0.066 m/s. Under various disturbance conditions, the simulations reveal that OBC exhibits superior performance when compared to other control methods.