Directed Formation Control of n Planar Agents with Distance and Area Constraints

In this paper, we take a first step towards generalizing a recently proposed method for dealing with the problem of convergence to incorrect equilibrium points of distance-based formation controllers. Specifically, we introduce a distance and area-based scheme for the formation control of n-agent systems in two dimensions using directed graphs and the single-integrator model. We show that under certain conditions on the edge lengths of the triangulated desired formation, the control ensures almost-global convergence to the correct formation.

[1]  W. Beyer.  CRC Standard Mathematical Tables and Formulae , 1991 .

[2]  Vincent D. Blondel,et al.  Three and higher dimensional autonomous formations: Rigidity, persistence and structural persistence , 2007, Autom..

[3]  Kazunori Sakurama,et al.  Formation shape control with distance and area constraints , 2017, IFAC J. Syst. Control..

[4]  Ivan Izmestiev.  INFINITESIMAL RIGIDITY OF FRAMEWORKS AND SURFACES , 2009 .

[5]  H. Marquez.  Nonlinear Control Systems: Analysis and Design , 2003, IEEE Transactions on Automatic Control.

[6]  B. Anderson,et al.  Directed graphs for the analysis of rigidity and persistence in autonomous agent systems , 2007 .

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

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

[9]  Daniel Lazard,et al.  Quantifier Elimination: Optimal Solution for Two Classical Examples , 1988, J. Symb. Comput..

[10]  L. Clark Lay.  An Elementary Theory of Equations. , 1971 .

[11]  B. Jackson.  Notes on the Rigidity of Graphs , 2007 .

[12]  Zhiyong Sun,et al.  Rigid formation control of double-integrator systems , 2017, Int. J. Control.

[13]  B. Roth,et al.  The rigidity of graphs, II , 1979 .

[14]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.

[15]  Kazunori Sakurama.  Distributed Control of networked multi-agent systems for formation with freedom of special Euclidean group , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[16]  Eduardo Gamaliel Hernández-Martínez,et al.  Distance-based Formation Control Using Angular Information Between Robots , 2016, J. Intell. Robotic Syst..

[17]  Sergey Bereg,et al.  Certifying and constructing minimally rigid graphs in the plane , 2005, SCG.

[18]  Tyler H. Summers,et al.  Control of Minimally Persistent Leader-Remote-Follower and Coleader Formations in the Plane , 2011, IEEE Transactions on Automatic Control.

[19]  E. L. Rees,et al.  Graphical Discussion of the Roots of a Quartic Equation , 1922 .

[20]  Eduardo Gamaliel Hernández-Martínez,et al.  Adaptive control of distance-based spatial formations with planar and volume restrictions , 2016, 2016 IEEE Conference on Control Applications (CCA).

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

[22]  Florian Dörfler,et al.  Geometric Analysis of the Formation Problem for Autonomous Robots , 2010, IEEE Transactions on Automatic Control.

[23]  Calin Belta,et al.  Translational and Rotational Invariance in Networked Dynamical Systems , 2018, IEEE Transactions on Control of Network Systems.