Study of underactuated mechanisms in the presence of holonomic constraints: the constrained Acrobot

Underactuated mechanical systems are mechanical systems with fewer actuators than degrees-of-freedom. Examples of underactuated mechanisms of engineering importance are mobile robots, wheeled vehicles and space robotics. One such example of interest is the Acrobot. In this paper the Acrobot is modified so as to impose holonomic constraints on the system. The problem of formulating the equations of motions of the system along with the holonomic constraints using traditional methods is then addressed. An alternate method is then used to incorporate the holonomic constraints. This is followed by design of a control law for the swing up of the constrained Acrobot.