ABSTRACT
Underactuated mechanical systems are those have fewer actuators than degrees of
freedom. They arise in applications, such as space robots, mobile robots, flexible
robots, walking and gymnastic robots, such as the Acrobot. The swing-up control
problem is studied for the Acrobot system; as one of the most important benchmark
problem of the underactuated mechanical systems. The dynamic model based on
Lagrange formulation is present. Then, the design of the swing up control provided.
The design methodology is based on applying partial feedback linearization in a first
stage to linearized the unactuate degree of freedom pushing the Acrobot as near as
possible to its equilibrium point. Then, switch to a balancing controller linear
quadratic regulator (LQR), which forces the Acrobot to reach its equilibrium upward
position.