Output synchronization of systems in chained form

In this article we extend previous results for back-stepping and passivity-based design of cooperative control laws to a class of chained form systems that includes certain drift-free nonholonomic systems. We exploit the cascaded structure and feedback equivalence to passive systems to derive suitable control laws using a modified backstepping methodology. A virtual output is obtained and shared within the group in such a way that full state synchronization for the group is achieved. Given a static, strongly connected and balanced communication network we prove stability of the proposed controller. Further, an extension to higher order chained forms is shown, providing a methodology to coordinate general nonholonomic systems. The effectiveness of the method is demonstrated by synchronizing a collective of unicycles.