Multi-Agent Coordination by Decentralized Estimation and Control

We describe a framework for the design of collective behaviors for groups of identical mobile agents. The approach is based on decentralized simultaneous estimation and control, where each agent communicates with neighbors and estimates the global performance properties of the swarm needed to make a local control decision. Challenges of the approach include designing a control law with desired convergence properties, assuming each agent has perfect global knowledge; designing an estimator that allows each agent to make correct estimates of the global properties needed to implement the controller; and possibly modifying the controller to recover desired convergence properties when using the estimates of global performance. We apply this framework to the problem of controlling the moment statistics describing the location and shape of a swarm. We derive conditions which guarantee that the formation statistics are driven to desired values, even in the presence of a changing network topology.

[1]  R. Hardt,et al.  Topological properties of subanalytic sets , 1975 .

[2]  Peng Yang,et al.  A General Stability Condition for Multi-Agent Coordination by Coupled Estimation and Control , 2007, 2007 American Control Conference.

[3]  H. Bruyninckx,et al.  Active Sensing for Robotics – A Survey , 2002 .

[4]  Xiaoming Hu,et al.  A control Lyapunov function approach to multiagent coordination , 2002, IEEE Trans. Robotics Autom..

[5]  Shaun M. Fallat,et al.  Extremizing algebraic connectivity subject to graph theoretic constraints , 1998 .

[6]  Peng Yang,et al.  Stability and Convergence Properties of Dynamic Average Consensus Estimators , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[7]  S.I. Roumeliotis,et al.  Optimal motion strategies for range-only distributed target tracking , 2006, 2006 American Control Conference.

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

[9]  Steven V. Viscido,et al.  Self-Organized Fish Schools: An Examination of Emergent Properties , 2002, The Biological Bulletin.

[10]  Mireille E. Broucke,et al.  Formations of vehicles in cyclic pursuit , 2004, IEEE Transactions on Automatic Control.

[11]  Randy A. Freeman,et al.  Distributed Cooperative Active Sensing Using Consensus Filters , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[12]  Naomi Ehrich Leonard,et al.  Virtual leaders, artificial potentials and coordinated control of groups , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[13]  Calin Belta,et al.  Abstraction and control for Groups of robots , 2004, IEEE Transactions on Robotics.

[14]  Richard M. Murray,et al.  DYNAMIC CONSENSUS FOR MOBILE NETWORKS , 2005 .

[15]  Richard M. Murray,et al.  DISTRIBUTED SENSOR FUSION USING DYNAMIC CONSENSUS , 2005 .

[16]  J. Cortés.  Characterizing robust coordination algorithms via proximity graphs and set-valued maps , 2006, 2006 American Control Conference.

[17]  Jie Lin,et al.  The multi-agent rendezvous problem , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

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

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

[20]  Vijay Kumar,et al.  Modeling and control of formations of nonholonomic mobile robots , 2001, IEEE Trans. Robotics Autom..

[21]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[22]  Randal W. Beard,et al.  Decentralized Scheme for Spacecraft Formation Flying via the Virtual Structure Approach , 2004 .

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

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

[25]  Amit Kumar,et al.  Formation Stabilization of Multiple Agents Using Decentralized Navigation Functions , 2005, Robotics: Science and Systems.

[26]  Matthew D. Lieberman,et al.  Birds of a feather , 1994, Nature Structural Biology.

[27]  Mehran Mesbahi,et al.  Formation flying control of multiple spacecraft via graphs , 2001 .

[28]  E. Bierstone,et al.  Semianalytic and subanalytic sets , 1988 .

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

[30]  M. Spong,et al.  Stable flocking of multiple inertial agents on balanced graphs , 2006, 2006 American Control Conference.

[31]  P. S. Krishnaprasad,et al.  Equilibria and steering laws for planar formations , 2004, Syst. Control. Lett..

[32]  R. Hardt.  Stratification of real analytic mappings and images , 1975 .

[33]  Maurizio Porfiri,et al.  Environmental tracking and formation control of a platoon of autonomous vehicles subject to limited communication , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[34]  Randy A. Freeman,et al.  Robust Nonlinear Control Design , 1996 .

[35]  Marie-Françoise Roy,et al.  Real algebraic geometry , 1992 .

[36]  I. Couzin,et al.  Collective memory and spatial sorting in animal groups. , 2002, Journal of theoretical biology.

[37]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[38]  Sonia Martínez,et al.  Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions , 2006, IEEE Transactions on Automatic Control.

[39]  Nader Motee,et al.  Distributed receding horizon control of spatially invariant systems , 2006, 2006 American Control Conference.

[40]  Juergen Kurths,et al.  Weighted networks are more synchronizable: how and why , 2005 .

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

[42]  Randal W. Beard,et al.  A decentralized approach to formation maneuvers , 2003, IEEE Trans. Robotics Autom..

[43]  Randy A. Freeman,et al.  Decentralized Environmental Modeling by Mobile Sensor Networks , 2008, IEEE Transactions on Robotics.

[44]  F. Bullo,et al.  Analysis and design tools for distributed motion coordination , 2005, Proceedings of the 2005, American Control Conference, 2005..

[45]  Craig W. Reynolds.  Flocks, herds, and schools: a distributed behavioral model , 1998 .

[46]  F. Bullo,et al.  Robust rendezvous for mobile autonomous agents via proximity graphs in d dimensions , .

[47]  Randy A. Freeman,et al.  Optimal information propagation in sensor networks , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[48]  R. Olfati-Saber.  Ultrafast consensus in small-world networks , 2005, Proceedings of the 2005, American Control Conference, 2005..

[49]  Tucker R. Balch,et al.  Behavior-based formation control for multirobot teams , 1998, IEEE Trans. Robotics Autom..

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

[51]  Wei Ren,et al.  Consensus based formation control strategies for multi-vehicle systems , 2006, 2006 American Control Conference.

[52]  K. V. Ramachandra,et al.  Kalman Filtering Techniques for Radar Tracking , 2000 .

[53]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.