Control Strategy for Optimal High Jump Based on Complementarity Modeling

摘要

In this paper, we propose an optimal high jump control strategy for a jumping robot system, based on complementarity modeling approach. The jumping robot system is composed of a simple jumper part, an environment (trampoline) part and some hooks to limit the robot length. It is essentially a hybrid system, due to variable mechanical constraints, such as collision with trampoline, and length limitations. At first, we provide an efficient model of the system as a complementarity-slackness, which enables us to handle discontinuous phenomena of hybrid systems, i.e., discontinuous change of dynamics and leap of solution, in a unified and mathematically sound framework. Then we formulate the high jump problem as a maximizing problem of the peak height of the robot's center of gravity in a given time interval. The optimal control is derived numerically by performing a dynamic programming algorithm, and its validity is verified with computer simulations. The advantage of this modeling approach is that we need not to deal with the awkward variable constraints when we formulate control problem, since they are all considered in the model itself.