Control of Rigid Formations Subject to Nonholonomic Dynamics Constraints and Velocity Bounds

We propose a control framework for a network of agents, each obeying second-order Newtonian dynamics and subject to nonholonomic constraints and velocity bounds. The first control objective is that the agents move in formation as though they were part of a single rigid body. A desired behavior is specified for the formation. The second control objective is that the formation asymptotically tracks this desired behavior. Both objectives are achieved using a method to embed the constraints of rigid body motion within a simple linear error feedback. The framework is demonstrated for the representative special case of a network of agents in the plane, with unicycle dynamics and bounded linear and angular velocities. To our knowledge, the result significantly extends the best results for formation control in this case. The method is designed specifically for decentralized implementation, and is extendable to correct formation errors or to allow formation reconfiguration.