Sliding control approach to underactuated multibody systems

A robust control algorithm is proposed for stabilization and tracking control of underactuated multibody mechanical systems governed by nonlinear equations of motion. Sliding, or variable structure, control is a simple but robust nonlinear control approach that is capable of handling both disturbances and parameter uncertainties. We formulate the sliding control approach for general underactuated multibody systems, and define first order sliding surfaces, one per actuated degrees of freedom, as a linear combination of the tracking position and velocity errors of both actuated and unactuated coordinates. The controllers are then determined based on a Lyapunov function construction. The Lyapunov stability analysis, along with the bounds defined for parameter uncertainties and disturbances, guarantee that all system trajectories reach and remain on the sliding surfaces. The sliding surfaces are proved to be asymptotically or marginally stable, depending on the presence or absence of potential energy terms in the equations of motion. A 3-dimensional multibody model of a complex satellite system is presented and its equations of motion are derived. The proposed sliding control approach is developed for the satellite system and applied to maneuver the satellite using its appendages when it has lost all three rotational degrees of freedom.