Stability analysis of the Acrobot walking with observed geometry

Abstract This paper aims to extend of the previously developed analytical design for the Acrobot walking. The corresponding state feedback controller is completed in this paper by an observer to estimate some states of the Acrobot. Both the controller and the observer are based on the partial exact feedback linearization of order 3. The feedback controller and the observer are extended for the tracking of the cyclic walking-like trajectory in order to demonstrate the cyclic Acrobot walking. The cyclic walking-like trajectory starts continuous phase from certain initial conditions, that at the end of the step makes an impact and after the impact it reaches the same initial conditions as at the beginning of the step. This cyclic motion of the Acrobot enable us to prove the stability of the feedback tracking with the observer numericaly by the method of Poincare mappings. This numerical proof of the stability is supported by numerical simulations showing practically unlimited number of steps of the stable Acrobot walking.

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