Backstepping control of gliding robotic fish for pitch and 3D trajectory tracking

Underwater gliders are known for their energy-efficiency and long-duration operations, with demonstrated applications in ocean exploration, fish tracking, and environmental sampling. Many applications such as exploring a large area of underwater ruins would benefit from accurate trajectory tracking. Trajectory tracking is particularly challenging for underwater gliders due to their under-actuated, highly nonlinear dynamics. Taking gliding robotic fish as an example, a backstepping-based controller is proposed to track the desired pitch angle and reference position in the 3D space. In particular, under-actuation is addressed by exploiting the coupled dynamics and introducing a modified error term that combines pitch and horizontal position tracking errors. Two-time-scale analysis of singularly perturbed systems is used to establish the convergence of all tracking errors to a neighborhood around zero. The effectiveness of the proposed control scheme is demonstrated via simulation and experimental results, and its advantages are shown via comparison with a PID controller and a baseline backstepping controller that does not use the modified error. This paper is accompanied by a video available at: https://youtu.be/D8Vej3weeGc.