Optimal turning gait for undulatory locomotion

This paper addresses the optimal turning gait of a robotic locomotion system traveling in a curved path. The optimal gait problem is formulated as a minimization of a desired cost function subject to constraints in average tangential and rotational velocities, using a bilinear rectifier model that describes the locomotion of a link-chain system in the body frame. A global solution is found by showing that the problem reduces to two minimization problems, where one solves for the constant offset of the shape variables resulting in turning, and the other solves for the harmonic gait through generalized eigenvalue computation. A case study of a chain of links is provided, which shows the optimal solution resulting in undulatory locomotion traveling the desired curved path.