Quotient method for controlling the acrobot

— This paper describes a two-sweep control design method to stabilize the acrobot, an input-affine under-actuated system, at the upper equilibrium point. In the forward sweep, the system is successively reduced, one dimension at a time, until a two-dimensional system is obtained. At each step of the reduction process, a quotient is taken along one-dimensional integral manifolds of the input vector field. This decomposes the current manifold into classes of equivalence that constitute a quotient manifold of reduced dimension. The input to a given step becomes the representative of the previous-step equivalence class, and a new input vector field can be defined on the tangent of the quotient manifold. The representatives remain undefined throughout the forward sweep. During the backward sweep, the controller is designed recursively, starting with the twodimensional system. At each step of the recursion, a well-chosen representative of the equivalence class ahead of the current lev...

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Sudarsandhari Shibani Willson, Philippe Müllhaupt, Dominique Bonvin
• Keywords: CDC 2009, Control Systems, Forward Sweep, Quotient Manifold, Upper Equilibrium Point