Open-loop stable control of periodic multibody systems

We investigate the open-loop stability of periodic mechanical systems with state discontinuities and multiple phases of motion. Examples for such systems are walking and running motions in robotics and biomechanics. In this paper, we focus an an ostrich-like running robot that consists of a trunk and two legs and has very small feet. It is capable of open-loop stable periodic running motions without any feedback even though it has no statically stable standing position. Running as opposed to walking involves flight phases which makes stability a particularly difficult issue. The concept of open-loop stability implies that the actuators receive purely periodic torque or force inputs that are never altered by any feedback in order to prevent the robot from falling. The choice of model parameter values and actuator inputs leading to stable motions is a difficult task that could only be accomplished using newly developed stability optimization methods.