Optimal turning gait for mechanical rectifier systems with three dimensional motion

This paper presents a method for finding the optimal turning gait of a robotic locomotor, which rectifies periodic motion of the mechanical body into sustained propulsive force through interactions with the environment. First, equations of motion for a general rectifier traveling in three dimensional space are developed in body coordinates, and accelerations are shown to be independent of body orientation. A simplified model is then developed to capture the essential dynamics, assuming small body deformation. An optimal gait problem is formulated for the simplified model as the minimization of a quadratic cost function, subject to constraints on average nominal locomotion speed and angular velocity. It is shown that the problem can be separated to two tractable optimization problems; one for the shape offset resulting in turning, and the other for the periodic movement resulting in locomotion along a fixed direction. The effectiveness of the method is demonstrated by a case study of a simple locomotor swimming in water.