Impulse Control for Planar Spring-Mass Running

In this paper, we present a novel control strategy for running which is robust to disturbances, and makes excellent use of passive dynamics for energy economy. Our strategy combines two ideas: an existing flight phase policy, and a novel stance phase impulse control policy. The state-of-the-art flight phase policy commands a leg angle trajectory that results in a consistent horizontal center-of-mass velocity from hop to hop when running over uneven terrain, thus maintaining a steady gait and avoiding falls. Our novel stance phase control policy rejects ground disturbances by matching the actuated model's toe impulse profile to that of a passive spring-mass system hopping on flat rigid ground. This combined strategy is self-stable for changes in ground impedance or ground height, and thus does not require a ground model. Our strategy is promising for robotics applications, because there is a clear distinction between the passive dynamic behavior of the model and the active controller, it does not require sensing of the environment, and it is based on a sound theoretical background that is compatible with existing high-level controllers for ideal spring-mass models.