Optimal control strategy for high jump based on complementarity modeling

This paper proposes an optimal control strategy for a jumping robot system based on the complementarity modeling. We consider a variable constraint jumping system consisting of a robot part and an environment (catapult) part. Such a system can be efficiently modeled as a complementarity system, in the sense that the discontinuous phenomena such as collision or separation are handled in a unified framework. First, we give a simple criterion to judge the contact/taking-off condition based on the complementarity modeling. Next, we formulate an optimal control problem to maximize the peak height in a jump and give a numerical solution; due to the pre-specified input limitation, the resulting control is of bang-bang type. Finally, the optimal controller is analytically reconsidered and is implemented as a switching state feedback law