Motion Planning and Trajectory Tracking of Underactuated Three-link Robots

A new method for motion planning and trajectory tracking of underactuated three-link planar robots with a passive rotational third joint is proposed. One fundamental feather is to use the switching of partly stable controllers (PACs) in order to fulfill the control objective. The dynamic model of this kind of underactuated robot system is built based on Lagrange method. Different objective functions are given for motion planning and trajectory tracking. The genetic algorithm (GA) is utilized to get the optimum control actions for a given time-frame with the available set of elemental controllers. Penalty method is utilized when there are constraints and then the constrained optimizations change to be unconstrained ones. Because the proposed method does not make any hypothesis about the degree of freedom, it can be used without modification for arms with a large number of degree of freedom. At last numerical simulations are carried out to illuminate the validity of the proposed method.