Vertical-Plane Locomotion Control of a High-Speed Robotic Tuna via NMPC

The development of bionic underwater robots has brought new vitality to ocean exploration. Motion control is crucial for the stability of underwater robots due to significant differences in flow field characteristics at various swimming speeds. This study focuses on vertical-plane motion and proposes a model predictive control method to achieve integrated control of depth position and pitch attitude for bionic robotic fish. First, based on a robotic tuna system, high-maneuverability vertical-plane motion configuration elements are analyzed and summarized, laying the foundation for motion stability and controllability. Second, through hydrodynamic sampling in aquatic environments, a system model covering the range of swimming speeds is established. Regarding the control method, the proposed motion planning approach converts the desired motion sequence into an equivalent “pitch-depth” trajectory curve. A nonlinear model predictive controller (NMPC) is then designed to track the trajectory curve, ultimately achieving the desired vertical-plane motion. Experimental results validate that the proposed method not only ensures control accuracy under both low and high-speed conditions, but also enables the execution of complex motion sequence control. This study provides a fresh perspective on the motion instability analysis of robotic fish at high swimming speed and a novel control framework for regulating continuous posture sequences in the vertical plane. Note to Practitioners—The motivation of this paper is to address the challenges associated with stable motion and control of robotic fish in the vertical plane, given the variability of flow field characteristics at different swimming speeds. Existing methods for controlling pitch attitude and depth in bionic underwater robots are typically designed for stable flow conditions encountered during low-speed swimming. However, the instability and agility of high-speed robotic fish movements have not been adequately considered. Additionally, the coupling between pitch attitude and depth poses challenges for joint control of their combined states. This paper proposes a configuration analysis and control methodology to achieve desired vertical-plane locomotion for robotic fish. Specifically, using a robotic tuna as the research subject, a configuration analysis method for high-maneuverability motion in the vertical plane is presented, providing a foundation for ensuring motion stability and controllability. To accurately evaluate the motion of robotic fish under varying flow speeds, a system model for vertical plane motion is constructed based on hydrodynamic data collected from aquatic environments. A motion planning approach is proposed to convert desired vertical plane motion sequences into controllable “pitch-depth” trajectory curves, and a nonlinear model predictive controller is designed to track these trajectories. Configuration simulations and control experiments validate the effectiveness of the proposed method. Hopefully, our proposed methods can provide valuable insights and support for high-maneuverability motion control and continuous posture sequences tracking of bionic underwater robots in the vertical plane.