GVF-MPC Depth Control Framework Motivated by Restoring-Moment Mechanism Analysis for Bionic Robotic Fish

Abstract

Longitudinal oscillations are commonly observed in depth control of low-speed underwater platforms such as bio-inspired robotic fish. To investigate this issue, this letter conducts a quantitative analysis of the vertical-plane dynamics. It reveals the speed-dependent coupling between the depth and pitch channels as the swimming speed decreases, and clarifies the underdamped mechanism induced by restoring-moment dominance. A critical speed condition for the onset of low-speed oscillations is also derived. Based on the dynamic analysis, a hierarchical GVF–MPC depth control framework is proposed, which structurally decouples geometric guidance from dynamic execution. The guidance layer employs a guiding vector field (GVF) to generate naturally smooth attitude references from geometric information, with reduced sensitivity to model degradation and pitch disturbances. The inner loop applies model predictive control (MPC) to track the guidance commands while explicitly accounting for dynamic constraints, balancing convergence speed and control-input smoothness to improve stability and safety under low-speed conditions. Simulation and experiments are conducted to evaluate the effectiveness and robustness of the proposed method. Simulations consider sinusoidal and V-shaped depth path and compare the proposed approach with LOS, PID, and SMC based controllers. Experiments are performed in still water and under simulated Sea-State 1 disturbances to assess steady state accuracy, disturbance recovery, and overall robustness.