Gliding robotic fish, a new type of underwater robot, combines both strengths of underwater gliders and robotic fish, featuring long operation duration and high maneuverability. In this paper, we present both analytical and experimental results on a novel gliding motion, tail-enabled three-dimensional (3D) spiraling, which is well suited for sampling a water column. A dynamic model of a gliding robotic fish with a deflected tail is first established. The equations for the relative equilibria corresponding to steady-state spiraling are derived and then solved recursively using Newton's method. The region of convergence for Newton's method is examined numerically. We then establish the local asymptotic stability of the computed equilibria through Jacobian analysis and further numerically explore the basins of attraction. Experiments have been conducted on a fish-shaped miniature underwater glider with a deflected tail, where a gliding-induced 3D spiraling maneuver is confirmed. Furthermore, consistent with model predictions, experimental results have shown that the achievable turning radius of the spiraling can be as small as less than 0.4 m, demonstrating the high maneuverability.
On the robust Newton’s method with the Mann iteration and the artistic patterns from its dynamics
