A robust control approach to the swing up control problem for the Acrobot

nderactuated mechanical systems are those possessing fewer U actuators than degrees of freedom. Examples of such systems abound, including flexible joint and flexible link robots, space robots, mobile robots, and robot models that include ac-tuator dynamics and rigid body dynamics together. Complex intemal dynamics, nonholonomic behavior, and lack of feedback linearizability are often exhibited by such systems, making the class a rich one from a control standpoint. In this article we study a particular underactuated system known as the Acrobot: a two-degree-of-freedom planar robot with a single actuator. We consider the so-called swing up control problem using the method of partial feedback linearization. We give conditions under which the response of either degree of freedom may be globally decou-pled from the response of the other and linearized. This result can be used as a starting point to design swing up control algorithms. Analysis of the resulting zero dynamics as well as analysis of the energy of the system provides an understanding of the swing up ~~ The author is with The algorithms. Simulation results are presented showing the swing up motion resulting from partial feedback linearization designs.