A Stackelberg-game approach for tracking problems of flexible robots

摘要

We give a tracking algorithm for flexible robots, which is based on Stackelberg equilibria of linear quadratic differential games. For the modelling of the plant we take the Hamiltionian approach to describe the motion of the undamped system. The Hamiltonian energy-functional will be treated as “cost” for one of the players, whereas the other player receives higher costs if the elastic beam does not exactly follow the pre-described trajectory. The aim, that each player tries to find a control strategy, that minimizes costs leads to a noncooperative differential game. As it will be discussed, a Stackelberg equilibrium yields the desired optimal control function. The calculated results will be verified and compared to experimental results.