Advertisement

Coordinate-Free Control of Multirobot Formations

  • Miguel Aranda
  • Gonzalo López-Nicolás
  • Carlos Sagüés
Chapter
Part of the Advances in Industrial Control book series (AIC)

Abstract

It is undoubtedly interesting, from a practical perspective, to solve the problem of multirobot formation stabilization in a decentralized fashion, while allowing the agents to rely only on their independent onboard sensors (e.g., cameras), and avoiding the use of leader robots or global reference frames . However, a key observation that serves as motivation for the work presented in this chapter is that the available controllers satisfying these conditions generally fail to provide global stability guarantees. In this chapter, we provide novel theoretical tools to address this issue; in particular, we propose coordinate-free formation stabilization algorithms that are globally convergent. The common elements of the control methods we describe are that they rely on relative position information expressed in each robot’s independent frame, and that the absence of a shared orientation reference is dealt with by introducing locally computed rotation matrices in the control laws. Specifically, three different nonlinear formation controllers for mobile robots are presented in the chapter. First, we propose an approach relying on global information of the team, implemented in a distributed networked fashion. Then, we present a purely distributed method based on each robot using only partial information from a set of formation neighbors. We finally explore formation stabilization applied to a target enclosing task in a 3D workspace. The developments in this chapter pave the way for novel vision-based implementations of control tasks involving teams of mobile robots, which is the leitmotif of the monograph. The controllers are formally studied and their performance is illustrated with simulations.

References

  1. 1.
    Mesbahi M, Egerstedt M (2010) Graph theoretic methods in multiagent networks. Princeton University Press, PrincetonCrossRefzbMATHGoogle Scholar
  2. 2.
    Zavlanos MM, Pappas GJ (2007) Distributed formation control with permutation symmetries. In: IEEE conference on decision and control, pp 2894–2899Google Scholar
  3. 3.
    Dong W, Farrell JA (2008) Cooperative control of multiple nonholonomic mobile agents. IEEE Trans Autom Control 53(6):1434–1448MathSciNetCrossRefGoogle Scholar
  4. 4.
    Sabattini L, Secchi C, Fantuzzi C (2011) Arbitrarily shaped formations of mobile robots: artificial potential fields and coordinate transformation. Auton Robots 30(4):385–397CrossRefGoogle Scholar
  5. 5.
    Alonso-Mora J, Breitenmoser A, Rufli M, Siegwart R, Beardsley P (2012) Image and animation display with multiple mobile robots. Int J Robot Res 31(6):753–773CrossRefGoogle Scholar
  6. 6.
    Becker A, Onyuksel C, Bretl T, McLurkin J (2014) Controlling many differential-drive robots with uniform control inputs. Int J Robot Res 33(13):1626–1644CrossRefGoogle Scholar
  7. 7.
    Lin Z, Francis B, Maggiore M (2005) Necessary and sufficient graphical conditions for formation control of unicycles. IEEE Trans Autom Control 50(1):121–127MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ji M, Egerstedt M (2007) Distributed coordination control of multiagent systems while preserving connectedness. IEEE Trans Rob 23(4):693–703CrossRefGoogle Scholar
  9. 9.
    Dimarogonas DV, Kyriakopoulos KJ (2008) A connection between formation infeasibility and velocity alignment in kinematic multi-agent systems. Automatica 44(10):2648–2654MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Cortés J (2009) Global and robust formation-shape stabilization of relative sensing networks. Automatica 45(12):2754–2762MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Kan Z, Dani AP, Shea JM, Dixon WE (2012) Network connectivity preserving formation stabilization and obstacle avoidance via a decentralized controller. IEEE Trans Autom Control 57(7):1827–1832MathSciNetCrossRefGoogle Scholar
  12. 12.
    Oh KK, Ahn HS (2012) Formation control of mobile agents without an initial common sense of orientation. In: IEEE conference on decision and control, pp 1428–1432Google Scholar
  13. 13.
    Franceschelli M, Gasparri A (2014) Gossip-based centroid and common reference frame estimation in multiagent systems. IEEE Trans Rob 30(2):524–531CrossRefGoogle Scholar
  14. 14.
    Montijano E, Zhou D, Schwager M, Sagüés C (2014) Distributed formation control without a global reference frame. In: American control conference, pp 3862–3867Google Scholar
  15. 15.
    Olfati-Saber R, Murray RM (2002) Graph rigidity and distributed formation stabilization of multi-vehicle systems. In: IEEE international conference on decision and control, pp 2965–2971Google Scholar
  16. 16.
    Dimarogonas DV, Johansson KH (2009) Further results on the stability of distance-based multi-robot formations. In: American control conference, pp 2972–2977Google Scholar
  17. 17.
    Krick L, Broucke ME, Francis BA (2009) Stabilisation of infinitesimally rigid formations of multi-robot networks. Int J Control 82(3):423–439MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Guo J, Lin Z, Cao M, Yan G (2010) Adaptive control schemes for mobile robot formations with triangularised structures. IET Control Theory Appl 4(9):1817–1827CrossRefGoogle Scholar
  19. 19.
    Oh KK, Ahn HS (2011) Formation control of mobile agents based on inter-agent distance dynamics. Automatica 47(10):2306–2312MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Anderson BDO, Yu C, Fidan B, Hendrickx JM (2008) Rigid graph control architectures for autonomous formations. IEEE Control Syst Mag 28(6):48–63MathSciNetCrossRefGoogle Scholar
  21. 21.
    Anderson BDO (2011) Morse theory and formation control. In: Mediterranean conference on control & automation, pp 656–661Google Scholar
  22. 22.
    Tian YP, Wang Q (2013) Global stabilization of rigid formations in the plane. Automatica 49(5):1436–1441MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Lin Z, Wang L, Han Z, Fu M (2014) Distributed formation control of multi-agent systems using complex Laplacian. IEEE Trans Autom Control 59(7):1765–1777MathSciNetCrossRefGoogle Scholar
  24. 24.
    Gu K, Kharitonov VL, Chen J (2003) Stability of time-delay systems. Birkhäuser, BaselCrossRefzbMATHGoogle Scholar
  25. 25.
    Richard JP (2003) Time-delay systems: an overview of some recent advances and open problems. Automatica 39(10):1667–1694MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Hua C, Guan X (2008) Output feedback stabilization for time-delay nonlinear interconnected systems using neural networks. IEEE Trans Neural Netw 19(4):673–688CrossRefGoogle Scholar
  27. 27.
    Papachristodoulou A, Jadbabaie A, Münz U (2010) Effects of delay in multi-agent consensus and oscillator synchronization. IEEE Trans Autom Control 55(6):1471–1477MathSciNetCrossRefGoogle Scholar
  28. 28.
    Nedic A, Ozdaglar A (2010) Convergence rate for consensus with delays. J Global Optim 47(3):437–456MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Desai JP, Ostrowski JP, Kumar V (2001) Modeling and control of formations of nonholonomic mobile robots. IEEE Trans Robot Autom 17(6):905–908CrossRefGoogle Scholar
  30. 30.
    Moshtagh N, Michael N, Jadbabaie A, Daniilidis K (2009) Vision-based, distributed control laws for motion coordination of nonholonomic robots. IEEE Trans Rob 25(4):851–860CrossRefGoogle Scholar
  31. 31.
    López-Nicolás G, Aranda M, Mezouar Y, Sagüés C (2012) Visual control for multirobot organized rendezvous. IEEE Trans Syst Man Cybern Part B: Cybern 42(4):1155–1168Google Scholar
  32. 32.
    Antonelli G, Arrichiello F, Chiaverini S (2008) The entrapment/escorting mission. IEEE Robot Autom Mag 15(1):22–29CrossRefGoogle Scholar
  33. 33.
    Mas I, Li S, Acain J, Kitts C (2009) Entrapment/escorting and patrolling missions in multi-robot cluster space control. In: IEEE/RSJ international conference on intelligent robots and systems, pp 5855–5861Google Scholar
  34. 34.
    Lan Y, Lin Z, Cao M, Yan G (2010) A distributed reconfigurable control law for escorting and patrolling missions using teams of unicycles. In: IEEE conference on decision and control, pp 5456–5461Google Scholar
  35. 35.
    Guo J, Yan G, Lin Z (2010) Cooperative control synthesis for moving-target-enclosing with changing topologies. In: IEEE international conference on robotics and automation, pp 1468–1473Google Scholar
  36. 36.
    Franchi A, Stegagno P, Rocco MD, Oriolo G (2010) Distributed target localization and encirclement with a multi-robot system. In: IFAC symposium on intelligent autonomous vehiclesGoogle Scholar
  37. 37.
    Montijano E, Priolo A, Gasparri A, Sagüés C (2013) Distributed entrapment for multi-robot systems with uncertainties. In: IEEE conference on decision and control, pp 5403–5408Google Scholar
  38. 38.
    Marasco AJ, Givigi SN, Rabbath CA (2012) Model predictive control for the dynamic encirclement of a target. In: American control conference, pp 2004–2009Google Scholar
  39. 39.
    Kawakami H, Namerikawa T (2009) Cooperative target-capturing strategy for multi-vehicle systems with dynamic network topology. In: American control conference, pp 635–640Google Scholar
  40. 40.
    Franchi A, Stegagno P, Oriolo G (2016) Decentralized multi-robot encirclement of a 3D target with guaranteed collision avoidance. Auton Robots 40:245–265CrossRefGoogle Scholar
  41. 41.
    Olfati-Saber R, Fax JA, Murray RM (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–233CrossRefGoogle Scholar
  42. 42.
    Cortés J, Martínez S, Bullo F (2006) Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. IEEE Trans Autom Control 51(8):1289–1298MathSciNetCrossRefGoogle Scholar
  43. 43.
    Schwager M, Julian B, Angermann M, Rus D (2011) Eyes in the sky: decentralized control for the deployment of robotic camera networks. Proc IEEE 99(9):1541–1561CrossRefGoogle Scholar
  44. 44.
    McKee TA, McMorris FR (1999) Topics in intersection graph theory. Society for Industrial and Applied Mathematics (SIAM), PhiladelphiaGoogle Scholar
  45. 45.
    Gower JC, Dijksterhuis GB (2004) Procrustes problems. Oxford University Press, OxfordGoogle Scholar
  46. 46.
    Kabsch W (1976) A Solution for the Best Rotation to Relate Two Sets of Vectors. Acta Crystallogr A 32:922–923CrossRefGoogle Scholar
  47. 47.
    Kanatani K (1994) Analysis of 3-D rotation fitting. IEEE Trans Pattern Anal Mach Intell 16(5):543–549CrossRefGoogle Scholar
  48. 48.
    Freundlich C, Mordohai P, Zavlanos MM (2013) A hybrid control approach to the next-best-view problem using stereo vision. In: IEEE international conference on robotics and automation, pp 4493–4498Google Scholar
  49. 49.
    Spong MW, Hutchinson S, Vidyasagar M (2006) Robot modeling and control. Wiley, New YorkGoogle Scholar
  50. 50.
    Weiss S, Scaramuzza D, Siegwart R (2011) Monocular-SLAM based navigation for autonomous micro helicopters in GPS-denied environments. J Field Robot 28(6):854–874CrossRefGoogle Scholar
  51. 51.
    Eren T, Whiteley W, Morse AS, Belhumeur PN, Anderson BDO (2003) Sensor and network topologies of formations with direction, bearing, and angle information between agents. In: IEEE conference on decision and control, pp 3064–3069Google Scholar
  52. 52.
    Franchi A, Giordano PR (2012) Decentralized control of parallel rigid formations with direction constraints and bearing measurements. In: IEEE conference on decision and control, pp 5310–5317Google Scholar
  53. 53.
    Bishop AN, Shames I, Anderson BDO (2011) Stabilization of rigid formations with direction-only constraints. In: IEEE conference on decision and control and European control conference, pp 746–752Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Miguel Aranda
    • 1
  • Gonzalo López-Nicolás
    • 2
  • Carlos Sagüés
    • 2
  1. 1.ISPRSIGMA Clermont, Institut PascalAubièreFrance
  2. 2.Instituto de Investigación en Ingeniería de AragónUniversidad de ZaragozaZaragozaSpain

Personalised recommendations