Sustainable Acrobot Walking Based on the Swing Phase Exponentially Stable Tracking

Abstract

The Acrobot is the simplest walking like underactuated system which at the same time comprises all typical difficulties of the underactuated walking. In particular, efficient algorithms for the Acrobot walking may be generalized to more general walking like configurations through their special decomposition. The main contribution of this paper is to design the algorithm how to compute a cyclic walking like trajectory which is crucial to have the hybrid exponentially stable multi step tracking of this trajectory later on. Notice, that such a design is not an easy task as the walking trajectory initial conditions are changed along the single step into different end conditions and these should be subsequently mapped by the impact map into the same initial condition for the second step. For this sake we use the special partial linearized coordinates to demonstrate their advantage for the design of the cyclic walking trajectory. Such a trajectory is then used to demonstrate the sustainable walking based on the swing phase exponentially stable tracking via computer simulations.