Optimal turning gait for a three-link underwater robot

High maneuverable turning gait is essential to improve the locomotion ability for the three-link underwater robot. Using the traditional method, the optimal turning gait is a numerical solution. This paper proposes a geometric method to get the optimal turning gait which is the analytical solution. Generally, the zero-contour of the orientation angle for the 3-link underwater robot is the optimal gait [6]. However for the actual robot, the boundary constraints should also be considered. The curve fitting method is used to analyze the boundary constraints. Then the optimal sinusoidal gait is derived by using the analytical geometry and the optimal boundary gait is derived by using Fourier series. By calculation, the rotational angle with optimal sinusoidal gait and the optimal boundary gait increases 21.79% and 27.74% compared to the "C" gait [10]. The numerical simulation shows posture change with the optimal sinusoidal gait and with the optimal boundary gait over one period for the 3-link underwater robot.