Coordinated control of networked mechanical systems with unstable dynamics

In this paper we present a coordinating control law for a network of mechanical systems with unstable dynamics. The control law is derived using the Method of Controlled Lagrangians together with potential shaping designed to couple the mechanical systems. The coupled system is Lagrangian with symmetry, and energy methods are used to prove stability and coordinated behavior. The class of mechanical systems we consider includes the planar inverted pendulum on a cart as well as the spherical inverted pendulum on a 2D cart. For these examples, the control law stabilizes each inverted pendulum and coordinates the relative motion of the carts.