Stabilization laws for collective motion in three dimensions

This paper proposes a framework for the design of control laws that stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Under the assumption of all-to-all communication, the derived control laws only require relative orientations and positions. We extend the obtained results in the presence of limited communication topologies by equipping each agent with a consensus estimator.

[1]  Peng Yang,et al.  Distributed estimation and control of swarm formation statistics , 2006, 2006 American Control Conference.

[2]  L. Moreau,et al.  Stability of continuous-time distributed consensus algorithms , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[3]  J.N. Tsitsiklis,et al.  Convergence in Multiagent Coordination, Consensus, and Flocking , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[4]  Sonia Martínez,et al.  Coverage control for mobile sensing networks , 2002, IEEE Transactions on Robotics and Automation.

[5]  R. Sepulchre,et al.  Collective optimization over average quantities , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[6]  R. Olfati-Saber,et al.  Distributed Kalman Filter with Embedded Consensus Filters , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[7]  Naomi Ehrich Leonard,et al.  Stabilization of Planar Collective Motion: All-to-All Communication , 2007, IEEE Transactions on Automatic Control.

[8]  Naomi Ehrich Leonard,et al.  Stabilization of Planar Collective Motion With Limited Communication , 2008, IEEE Transactions on Automatic Control.

[9]  J. Willems Lyapunov Functions for Diagonally Dominant Systems , 1975 .

[10]  Hal L. Smith,et al.  Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions , 1995 .

[11]  Naomi Ehrich Leonard,et al.  Collective Motion, Sensor Networks, and Ocean Sampling The goal is design and control of optimum trajectories for mobile sensor networks, like a fleet of self-directed underwater gliders that move with ocean currents and sample dynamic ocean variables. , 2007 .

[12]  Alain Sarlette,et al.  Synchronization and balancing on the N-torus , 2007, Syst. Control. Lett..

[13]  Richard M. Murray,et al.  INFORMATION FLOW AND COOPERATIVE CONTROL OF VEHICLE FORMATIONS , 2002 .

[14]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[15]  E. W. Justh,et al.  Natural frames and interacting particles in three dimensions , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[16]  Naomi Ehrich Leonard,et al.  Stabilization of collective motion in three dimensions: A consensus approach , 2007, 2007 46th IEEE Conference on Decision and Control.

[17]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.