Taming inter-distance mismatches in formation-motion control for rigid formations of second-order agents

This paper presents an analysis on the influence of distance mismatches in the standard gradient-based rigid formation control for second-order agents. It is shown that, akin to the first-order case as recently discussed in literature, these mismatches introduce two undesired group behaviors: a distorted final shape and a steady-state motion of the group formation. We show that such undesired behaviors can be eliminated by combining the standard rigid formation control law with distributed estimators. Finally, we show how the mismatches can be effectively employed as design parameters in order to control a combined translational and rotational motion of the formation.

[1]  Shaoshuai Mou,et al.  Geometrical methods for mismatched formation control , 2014, 53rd IEEE Conference on Decision and Control.

[2]  Zhiyong Sun,et al.  Rigid formation control systems modelled by double integrators: System dynamics and convergence analysis , 2015, 2015 5th Australian Control Conference (AUCC).

[3]  Vijay Kumar,et al.  Trajectory generation and control for precise aggressive maneuvers with quadrotors , 2012, Int. J. Robotics Res..

[4]  Brian D. O. Anderson,et al.  Control of Minimally Persistent Formations in the Plane , 2009, SIAM J. Control. Optim..

[5]  Juan Luis Varona,et al.  Port-Hamiltonian systems: an introductory survey , 2006 .

[6]  Zhiyong Sun,et al.  Controlling a triangular flexible formation of autonomous agents , 2017, ArXiv.

[7]  Brian D. O. Anderson,et al.  Formation control using range-only measurements , 2011, Autom..

[8]  Ming Cao,et al.  Distributed Rotational and Translational Maneuvering of Rigid Formations and Their Applications , 2016, IEEE Transactions on Robotics.

[9]  P. Olver.  Nonlinear Systems , 2013 .

[10]  Brian D. O. Anderson,et al.  Combined Flocking and Distance-Based Shape Control of Multi-Agent Formations , 2016, IEEE Transactions on Automatic Control.

[11]  Hector Jesús Garcia de Marina Peinado,et al.  Distributed formation control for autonomous robots , 2016 .

[12]  A. Schaft.  Port-Hamiltonian systems: an introductory survey , 2006 .

[13]  R. Murray,et al.  Graph rigidity and distributed formation stabilization of multi-vehicle systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[14]  Mireille E. Broucke,et al.  Stabilization of infinitesimally rigid formations of multi-robot networks , 2008, 2008 47th IEEE Conference on Decision and Control.

[15]  Vincent D. Blondel,et al.  Formation Reorganization by Primitive Operations on Directed Graphs , 2008, IEEE Transactions on Automatic Control.

[16]  Geoffrey A. Hollinger,et al.  Multi-UAV exploration with limited communication and battery , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[17]  Ming Cao,et al.  Distributed algorithm for controlling scale-free polygonal formations , 2017, ArXiv.

[18]  Guido C. H. E. de Croon,et al.  Gust disturbance alleviation with Incremental Nonlinear Dynamic Inversion , 2016, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[19]  A. Isidori.  Nonlinear Control Systems , 1985 .

[20]  Ming Cao,et al.  Distributed scaling control of rigid formations , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[21]  Hyo-Sung Ahn,et al.  A survey of multi-agent formation control , 2015, Autom..

[22]  Shin Kato,et al.  An automated truck platoon for energy saving , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[23]  Shaoshuai Mou,et al.  Undirected Rigid Formations Are Problematic , 2015, IEEE Transactions on Automatic Control.

[24]  S. Hara,et al.  Distributed formation control for target-enclosing operations based on a cyclic pursuit strategy , 2008 .

[25]  Wolfram Burgard,et al.  Collaborative multi-robot exploration , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[26]  Zhiyong Sun,et al.  Generalized controllers for rigid formation stabilization with application to event-based controller design , 2015, 2015 European Control Conference (ECC).

[27]  Hyo-Sung Ahn,et al.  Distance‐based undirected formations of single‐integrator and double‐integrator modeled agents in n‐dimensional space , 2014 .

[28]  Lebrecht Henneberg,et al.  Die graphische Statik der Starren Systeme , 1911 .

[29]  Jing Guo,et al.  Local control strategy for moving-target-enclosing under dynamically changing network topology , 2010, Syst. Control. Lett..

[30]  Shaoshuai Mou,et al.  Formation movements in minimally rigid formation control with mismatched mutual distances , 2014, 53rd IEEE Conference on Decision and Control.

[31]  John T. Wen,et al.  Cooperative Control Design - A Systematic, Passivity-Based Approach , 2011, Communications and control engineering.

[32]  J. Hendrickx,et al.  Rigid graph control architectures for autonomous formations , 2008, IEEE Control Systems.

[33]  Mireille E. Broucke,et al.  Stabilisation of infinitesimally rigid formations of multi-robot networks , 2009, Int. J. Control.

[34]  Thor I. Fossen,et al.  Marine Control Systems Guidance, Navigation, and Control of Ships, Rigs and Underwater Vehicles , 2002 .

[35]  Ming Cao,et al.  Controlling Rigid Formations of Mobile Agents Under Inconsistent Measurements , 2015, IEEE Transactions on Robotics.