Dynamic leader-follower algorithms in mobile multi-agent networks

In this paper, we consider a Linear Time-Varying (LTV) model to describe the dynamics of a leader-follower algorithms with mobile agents. We first develop regularity conditions on the LTV system matrices, according to a random motion of the agents and the underlying communication protocol. We then study the convergence of all agents to the state of the leader, and show that this requires the underlying LTV system to be asymptotically stable. We introduce the notion of slices as non-overlapping partitions of the LTV system matrices, and relate the convergence of the multi-agent network to the length of these slices. Finally, we demonstrate the convergence and steady-state of a dynamic leader-follower network through simulations.

[1]  Usman A. Khan,et al.  Asymptotic stability of stochastic LTV systems with applications to distributed dynamic fusion , 2014, ArXiv.

[2]  Dongbing Gu,et al.  Leader–Follower Flocking: Algorithms and Experiments , 2009, IEEE Transactions on Control Systems Technology.

[3]  Camillo J. Taylor,et al.  A vision-based formation control framework , 2002, IEEE Trans. Robotics Autom..

[4]  Stephen P. Boyd,et al.  Randomized gossip algorithms , 2006, IEEE Transactions on Information Theory.

[5]  Dimos V. Dimarogonas,et al.  Leader-follower cooperative attitude control of multiple rigid bodies , 2008, 2008 American Control Conference.

[6]  A. Cicone.  A note on the Joint Spectral Radius , 2015, 1502.01506.

[7]  John N. Tsitsiklis,et al.  The Lyapunov exponent and joint spectral radius of pairs of matrices are hard—when not impossible—to compute and to approximate , 1997, Math. Control. Signals Syst..

[8]  Vijay Kumar,et al.  Leader-to-formation stability , 2004, IEEE Transactions on Robotics and Automation.

[9]  Guangming Xie,et al.  Controllability of a Leader–Follower Dynamic Network With Switching Topology , 2008, IEEE Transactions on Automatic Control.

[10]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[11]  George J. Pappas,et al.  Flocking in Fixed and Switching Networks , 2007, IEEE Transactions on Automatic Control.

[12]  Soummya Kar,et al.  DILAND: An Algorithm for Distributed Sensor Localization With Noisy Distance Measurements , 2009, IEEE Transactions on Signal Processing.

[13]  Wei Ren,et al.  Information consensus in multivehicle cooperative control , 2007, IEEE Control Systems.

[14]  Jiangping Hu,et al.  Tracking control for multi-agent consensus with an active leader and variable topology , 2006, Autom..

[15]  Soummya Kar,et al.  Distributed Sensor Localization in Random Environments Using Minimal Number of Anchor Nodes , 2008, IEEE Transactions on Signal Processing.

[16]  Daizhan Cheng,et al.  Leader-following consensus of multi-agent systems under fixed and switching topologies , 2010, Syst. Control. Lett..