Abstract
A new control concept for a class of simple underactuated mechanical system, the so-called Acrobot, is presented here. Despite being seemingly simple system, the acrobot comprises many important difficulties when controlling the most challenging underactuated system - the walking robot. This paper presents the exponential stabilization of the acrobot from the wide range of initial positions, much wider than typical local results in the current literature. Moreover, contrary to standard control methods available for stabilization of such systems, the control presented herein provides a large domain of attraction and avoids any switching scheme. This result is achieved thanks to special transformation of the system combined with certain robust stabilization technique. The proposed control is then compared with other approaches based on different transformations and presented in earlier publications. Besides theoretical proofs, our approach is supported by numerical simulations.
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