First-exit model predictive control of fast discontinuous dynamics: Application to ball bouncing

We extend model-predictive control so as to make it applicable to robotic tasks such as legged locomotion, hand manipulation and ball bouncing. The online optimal control problem is defined in a first-exit rather than the usual finite-horizon setting. The exit manifold corresponds to changes in contact state. In this way the need for online optimization through dynamic discontinuities is avoided. Instead the effects of discontinuities are incorporated in a final cost which is tuned offline. The new method is demonstrated on the task of 3D ball bouncing. Even though our robot is mechanically limited, it bounces one ball robustly and recovers from a wide range of disturbances, and can also bounce two balls with the same paddle. This is possible due to intelligent responses computed online, without relying on pre-existing plans.