General swing-up methodology for the vertical three-link underactuated manipulator

The underactuated mechanical systems (UMS) are a special class of nonlinear systems with fewer inputs than their degree-of-freedoms (DOF). Currently the research works of such systems mainly focus on the equilibrium point stabilization and periodic trajectory tracking problem. The problem of steering a UMS to arbitrary points in its state space is hardly studied. The existing methods for the swing-up control problem of UMS mainly deal with two DOF UMS and are difficult to be applied in high order DOF UMS. Here in this paper, the problem of swing the UMS to arbitary point is studied. We proposed a virtual constraint based algorithm to generate periodic trajectories that pass through desired point and utilized the Lyapunov based control algorithm to track the generated trajectory. The proposed methods can be applied to a class of UMS and a UMS can be steered from an initial position to the desired position by tracking the generated periodic trajectories. The proposed methods are implemented using a RRR underactuated manipulator and the simulation results demonstrated their performance and verified their effectiveness.