Partial exact linearization design for the Acrobot walking

A new control concept for a class of simple underactuated mechanical system, the so-called acrobot, is presented here. Despite being seemingly a simple system, the acrobot comprises many important difficulties when controlling the most challenging underactuated system - the walking robot. This paper presents the design of the asymptotical tracking of the prescribed trajectory generated by a suitable open-loop input of the acrobot. Such a design is based on the partial exact linearization of the third order combined with a certain robust stabilization technique. The proposed control is then demonstrated by the exponential tracking of the walking-like trajectory of the acrobot. Besides theoretical proofs, our approach is supported by numerical simulations and illustrated by acrobot movement animations.