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

• Main Authors: Mathis, Frank B., Jafari, Rouhollah, Mukherjee, Ranjan
• Format: Conference Proceeding
• Language: English
• Subjects: 0) (J; 2} and j ∈ {1; 9.81 m.s; angular displacement of the k-th link; Angular velocity; angular velocity of the k-th link; angular velocity of the k-th link (rad/s); as defined in Fig.1 (rad); constants; cos θ; distance between the k-th joint and center-of-mass of the k-th link (m); E total energy of the acrobot (J); Equations; external torque required to instantaneously stop the second joint (N.m); For the nomenclature below; Force; g acceleration due to gravity; immediately after application of the impulsive torque (m/s); immediately after application of the impulsive torque (rad/s); immediately prior to application of the impulsive torque (m/s); immediately prior to application of the impulsive torque (rad/s); impulsive force acting at the center-of-mass of the k-th link (N); impulsive force acting at the shoulder joint (N); impulsive moment acting at the center-of-mass of the k-th link (N.m); Joints; k angular velocity of the k-th link; k ∈ {1; kinetic energy of the k-th link (J); length of the k-th link (m); mass moment of inertia of the k-th link about its center-of-mass (kg.m; mass of the k-th link (kg); Simulation; sin θ; Torque; total energy of the acrobot when (θ; Trajectory; velocity of the center-of-mass of the k-th link; velocity of the center-of-mass of the k-th link (m/s); whose values depend on kinematic and dynamics parameters of the acrobot; θ; π/2; τ external torque applied on the second link (N.m)
• ISSN: 0743-1619; 2378-5861
• DOI: 10.1109/ACC.2011.5991189

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.