Single Actuator Control Analysis of a Planar 3DOF Hopping Robot

In this paper we explore the mechanism of energy transfer between the single actuated DOF of a one-legged hopping robot and the remaining unactuated DOFs, during stable running. The concept of the energy transfer mechanism is laid out, after which follows an analytical study. Using this study, an initial controller is derived for the control of a simple SLIP model with friction in the leg and hip, using a single actuator at the hip. We show that while this controller is capable of stable motion for the SLIP model, it does not lead to stable locomotion for the full realistic robot model with pitching body, leg inertia and friction in hip and leg. This indicates that the SLIP model often used for controller design may be unsuitable for this purpose. The necessary modifications are then made to the controller to achieve stable locomotion for the full model, again with a single, easy-toimplement actuator located at the hip. Finally, results are shown from applying the controller to the full model for a wide range of parameters leading to stable motions. Index Terms one-legged hopping robot, control, underactuated.