Motion control method of planar Acrobot based on trajectory characteristics

A motion control method of planar underactuated 2R robot Acrobot (no gravity) is proposed in this paper on the basis of the trajectory characteristic analysis. Firstly, two constraint relationships of each angular velocity and angle between the two links are obtained, through the dual integral dynamic equation of the underactuated joint. Then, analysing movement characteristics by the angle relationship, it is proved that the system reachable position is limited and the trajectory is fixed when model parameters and system initial state have been determinate. Finally, according to the trajectory characteristics, a strategy based on Lyapunov function is designed to control the system moving between any two points in the reachable trajectory. The simulation results demonstrate the validity of this method.