Efficient swing-up of the acrobot using continuous torque and impulsive braking

An efficient swing-up algorithm for the acrobot is proposed. The algorithm is based on using a combination of continuous torque and impulsive braking torque. The continuous torque is derived from a positive definite Lyapunov-like function, proposed earlier in the literature. The impulsive braking torques are applied at specific instants of time which result in discrete jumps in certain states of the system and a discrete reduction in the value of the Lyapunov-like function. We prove asymptotic stability of the closed-loop impulsive dynamical system and use simulation results to show that the proposed algorithm is more efficient than the algorithms using only continuous torques derived from the same Lyapunov-like function.