Formation Tracking Control of Heterogeneous Underactuated Planar Agents with Stable Internal Dynamics

Distributed formation tracking control of a system of heterogeneous underactuated agents on a 2-D plane is proposed based on the leader-follower approach and using the inter-agent displacements. A typical example of such an agent is an underactuated surface vessel whose planar surge-sway-yaw motion is considered, while only two independent controls are available, thus underactuated. Formation tracking control law is developed to steer certain offset points on the longitudinal axes of the agents, called hand points, to the target formation asymptotically and exponentially fast in the presence of bounded disturbances. A distinct feature of such an underactuated planar vehicle is that its lateral motion representing the non-actuated degree of freedom is unrestricted and can be unstable. Thus, a sufficient condition on the the leader's velocity and the hand points' locations for the stability of the lateral motion of the agents is provided. Simulation results of formation tracking control of underactuated surface vessels support the theoretical analysis.