Trajectory planning using oscillatory chirp functions applied to bipedal locomotion

This work presents a method for planning sinusoidal trajectories for an actuated joint, so that the oscillation frequency follows linear profiles, like trapezoidal ones, defined by the user or by a high level planner. The planning method adds a cubic polynomial function for the last segment of the trajectory in order to reach a desired final position of the joint. We apply this planning method to an underactuated bipedal mechanism which gait is generated by the oscillatory movement of its tail. Using linear frequency profiles allow us to modify the speed of the mechanism and to study the efficiency of the system at different speed values.