A rewinding approach to motion planning for acrobot based on virtual friction

Based on the concept of kinematical controllability, we can decouple the trajectory planning of an acrobot into two steps: finding a path in a configuration space and time-scaling it. In this paper, we apply this concept and plan the swing-up motion of an acrobot based on its falling-down motion. First, the initial state of the acrobot is set to the unstable upright equilibrium position, and the movement from this state to the stable downward equilibrium position is produced by introducing an artificial damping torque. A method to obtaining an optimal damping torque is presented. Then, the reference trajectory for the swing-up motion is taken to be the reverse of the falling-down motion. The validity of this method is demonstrated through simulations.