Kernel design for coordination of autonomous, time-varying multi-agent configurations

The coordination of agents in an autonomous system can greatly increase its ability to perform missions in a wide array of applications including distributed computing, coordination of mobile autonomous agents, and cooperative sensing. To expand the functionality of these systems to a wider array of applications, a need exists for coordinated control algorithms driving the system of nodes or agents to any prescribed state configuration in both time and space using only information passed between communicating agents. Using tools from graph theory, this paper derives a graph transformation method that maps the kernel of a graph's Laplacian matrix to any desired state configuration vector while retaining inter-agent communication characteristics of the graph. Using the transformation, this paper derives a theoretically-justified, decentralized control algorithm driving kinematic agents to any relative time-varying state configuration. Theoretical results are illustrated with numerical examples including load distribution in a computing network and surveillance of a moving target with kinematic agents.

[1]  Wenwu Yu,et al.  An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination , 2012, IEEE Transactions on Industrial Informatics.

[2]  Dusan M. Stipanovic,et al.  Formation Control and Collision Avoidance for Multi-agent Non-holonomic Systems: Theory and Experiments , 2008, Int. J. Robotics Res..

[3]  Derek A. Paley,et al.  Stabilization of Collective Motion in a Time-Invariant Flowfield , 2009 .

[4]  Lionel Lapierre,et al.  Distributed Control of Coordinated Path Tracking for Networked Nonholonomic Mobile Vehicles , 2013, IEEE Transactions on Industrial Informatics.

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

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

[7]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[8]  Jiangping Hu,et al.  Distributed tracking control of leader-follower multi-agent systems under noisy measurement , 2011, Autom..

[9]  Wei Ren,et al.  Multi-vehicle consensus with a time-varying reference state , 2007, Syst. Control. Lett..

[10]  Vijay Kumar,et al.  Decentralized formation control with variable shapes for aerial robots , 2012, 2012 IEEE International Conference on Robotics and Automation.

[11]  Emilio Frazzoli,et al.  Decentralized Policies for Geometric Pattern Formation and Path Coverage , 2007 .

[12]  J. A. Fax,et al.  Graph Laplacians and Stabilization of Vehicle Formations , 2002 .

[13]  Naomi Ehrich Leonard,et al.  Collective Motion of Self-Propelled Particles: Stabilizing Symmetric Formations on Closed Curves , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[14]  Dusan M. Stipanovic,et al.  Trajectory tracking with collision avoidance for nonholonomic vehicles with acceleration constraints and limited sensing , 2014, Int. J. Robotics Res..

[15]  Gianluca Antonelli,et al.  Decentralized time-varying formation control for multi-robot systems , 2014, Int. J. Robotics Res..

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

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

[18]  Sunil Surve,et al.  Consensus Based Dynamic Load Balancing for a Network of Heterogeneous Workstations , 2011 .