Periodic stabilizing control of systems with collisions-application to walking robots

The focus of this work is to generate and realize automatically an ideal periodic gait of walking robots which depends on properties of the system and an environment. In conventional works, a robot walking are realized by a tracking control for a predetermined desired trajectory. A necessary control for walking robots is not to track a desired trajectory but to generate a suitable trajectory according to changes of the environment. In order to realize this function, two methods will be discussed in this paper. The first one is the control method to realize a suitable steady periodic motion. The method will be called ´phase synchronous control,´ which creates a stable limit cycle for the system which has an unstable one. The second one is the algorithm which is called ´desired state optimization´ and modifies the motion to an optimal one, that a criterion function is optimized. Using this algorithm, if the environment of the system is changed, an ideal motion for the environment is automatically realized. The validity of the proposed method will be examined by numerical simulations