Control of a Class of Underactuated Systems by Successive Submanifold Stabilization

Many control design methods for underactuated systems require solving a partial differential equation, which can be complex with many degrees of freedom. In order to reduce the complexity, it is proposed decompose dynamics into several subsystems. The problem then reduces successive stabilization individual subsystems, i.e., each step submanifold reduced dimension. this way, are only practicable lower dimensional applied overall dynamical system. To ensure that subsystems stabilized independently, transformed by change coordinates form block-diagonal inertia metric. For unactuated part kinetic symmetries utilized, whereas actuated null space projectors employed decouple respect optimal or PD-like feedback. stability analysis semidefinite Lyapunov functions employed. procedure demonstrated manipulator on an elastic base and validated in simulation.