Dimos V. Dimarogonas

This paper presents a decentralized feedback control strategy that drives a system of multiple nonholonomic kinematic unicycles to agreement, maintaining at the same time the connectivity properties of the initially formed communication graph. The communication graph is created based on the initial relative distances between the team members. The proposed control law guarantees that if the communication graph is initially connected, then it remains connected throughout the closed loop system evolution. This is achieved via a control design that renders the set of edges of the initially formed communication graph positively invariant for the trajectories of the closed loop system. The proposed nonholonomic control law is discontinuous and time-invariant and tools from nonsmooth stability theory and matrix theory are used to check the stability of the overall system. The convergence properties are verified through computer simulations.

The Decentralized Navigation Functions' (DNF) based methodology, established in our previous work (D.V. Dimarogonas, M.M. Zavlanos, S.G. Loizou and K.J. Kyriakopoulos, “Decentralized motion control of multiple holonomic agents under input constraints”, in 42nd IEEE Conf. Deci. Cont., 2003, pp. 3390–3395 and S.G. Loizou, D.V. Dimarogonas and K.J. Kyriakopoulos, “Decentralized feedback stabilization of multiple nonholonomic agents”, in 2004 IEEE Int. Conf. on Robotics and Autom., 2004, pp. 3012–3017) on multi-agent systems with kinematic models of motion, is extended to the case where dynamic models of motion for both holonomic and nonholonomic agents must be treated. The proposed control scheme guarantees collision avoidance and global convergence of the multi-agent team to the desired goal configuration. The volume of each agent is taken into account and non-point models are considered. The satisfaction of the imposed system specifications under the proposed control scheme are verified and depicted through non-trivial computer simulations.

In this paper, a leader based containment control strategy for multiple unicycle agents is introduced. Similar results for the single integrator case examined in Ferrari-Trecate (2006) are derived based on the theory of partial difference equations on graphs established in Bensounssan and Menaldi (2005). The leaders converge to a desired formation based on a control law that is independent of the followers' states. Once the leaders have reached the desired formation, the followers converge to the convex hull of the leaders final positions. When the desired leader formation is infeasible, then (as was shown in Dimarogonas and Kyriakopoulos (2006)) the leaders converge to a configuration where they share the same velocities and orientations. We show in this paper that in such a situation, the followers converge to the same velocities and orientations as the leaders, with the same control law that was used for the followers in the initial containment control problem. The theoretical results are verified through computer simulations

This paper contains two main contributions: (i) a provably correct distributed control strategy for collision avoidance and convergence of multiple holonomic agents to a desired feasible formation configuration and (ii) a connection between formation infeasibility and flocking behavior in holonomic kinematic multi-agent systems. In particular, it is shown that when inter-agent formation objectives cannot occur simultaneously in the state-space then, under certain assumptions, the agents velocity vectors and orientations converge to a common value at steady state, under the same control strategy that would lead to a feasible formation. Convergence guarantees are provided in both cases using tools from algebraic graph theory and Lyapunov analysis