Time-varying Stabilizing Control for a Hopping Robot Model during the Flight Phase

This article presents a time-varying feedback stabilizing control law for a hopping robot model during the flight phase which is an example of nonholonomic control system. The strategy is based on Lyapunov second method. This approach does not necessitate the conversion of the system model into a "chained form", and thus does not rely on any special transformation techniques. The method is general and can be applied to a sub-class of nonholonomic systems having only Lie brackets of depth one or two in their controllability Lie algebras.