Constructive tool for orbital stabilization of underactuated nonlinear systems: Virtual constraints approach

We present a constructive tool for generation and orbital stabilization of periodic solutions for underactuated nonlinear systems. Our method can be applied to any mechanical system with a number of independent actuators smaller than the number of degrees of freedom by one. The synthesized feedback control law is nonlinear and time-dependent. It is derived from a feedback structure that explicitly uses the general or full integral of the systems zero dynamics. The control law generates a periodic solution and makes it exponentially orbitally stable.