Motion planning and feedback stabilization of periodic orbits for an acrobot

This paper discusses the problem of generating by feedback stable periodic motions for an Acrobot - the 2 - link pendulum with only one control input applied to the second link. The suggested control law is derived from a new control method proposed recently by the 1st and 3rd authors, and it has a feedback structure that explicitly uses the full integral of the resulting zero dynamics. Such control law yields exponentially locally orbitally stable nontrivial periodic motions for the closed-loop system. The idea is applied for generating human-like behaviour for 3-link underactuated pendulum, see Fig 1, having actuated only the 2nd and 3rd links. Under the assumption that the 3rd link does not have a relative motion, the built system is equivalent to the Acrobot. Computer simulations display preliminary results, while the experimental work is in progress.