Discrete Event Dynamic Systems

, Volume 24, Issue 4, pp 417–445 | Cite as

A Petri net based approach for multi-robot path planning

  • Marius Kloetzer
  • Cristian Mahulea


This paper presents a procedure for creating a probabilistic finite-state model for mobile robots and for finding a sequence of controllers ensuring the highest probability for reaching some desired regions. The approach starts by using results for controlling affine systems in simpliceal partitions, and then it creates a finite-state representation with history-based probabilities on transitions. This representation is embedded into a Petri Net model with probabilistic costs on transitions, and a highest probability path to reach a set of target regions is found. An online supervising procedure updates the paths whenever a robot deviates from the intended trajectory. The proposed probabilistic framework may prove suitable for controlling mobile robots based on more complex specifications.


Discrete event systems Abstractions Mobile robots Hybrid systems Algorithms 



The authors thank the anonymous reviewers for their useful comments and suggestions. This work has been partially supported at the Technical University of Iasi by the CNCS-UEFISCDI grant PN-II-RU PD 333/2010 and at University of Zaragoza by the CICYT—FEDER grant DPI2010-20413.


  1. Belta C, Habets LCGJM (2004) Constructing decidable hybrid systems with velocity bounds. In: 43rd IEEE conference on decision and control. Paradise Island, Bahamas, pp 467–472Google Scholar
  2. Choset H, Lynch KM, Hutchinson S, Kantor G, Burgard W, Kavraki LE, Thrun S (2005) Principles of robot motion: theory, algorithms, and implementations. MIT Press, BostonGoogle Scholar
  3. Cgal Community (2011) Cgal, Computational Geometry Algorithms Library.
  4. Costelha H, Lima P (2012) Robot task plan representation by Petri nets: modelling, identification, analysis and execution. Journal of Autonomous Robots 33(4)337–360Google Scholar
  5. Cowlagi RV, Tsiotras P (2010) Kinematic feasibility guarantees in geometric path planning using history-based transition costs over cell decompositions. In: American control conference (ACC), pp 5388–5393Google Scholar
  6. Cowlagi RV, Tsiotras P (2012) Hierarchical motion planning with dynamical feasibility guarantees for mobile robotic vehicles. IEEE Trans Robot 28(2):379–395CrossRefGoogle Scholar
  7. Ding J, Li E, Huang H, Tomlin CJ (2011) Reachability-based synthesis of feedback policies for motion planning under bounded disturbances. In: IEEE international conference on robotics and automation (ICRA), pp 2160–2165Google Scholar
  8. Ding XC, Smith SL, Belta C, Rus D (2011) LTL control in uncertain environments with probabilistic satisfaction guarantees. In: 18th IFAC world congress. Milan, ItalyGoogle Scholar
  9. Fainekos GE, Kress-Gazit H, Pappas GJ (2005) Hybrid controllers for path planning: a temporal logic approach. In: Proceedings of the 44th IEEE conference on decision and control, pp 4885–4890Google Scholar
  10. Fukuda K (2011) CDD/CDD+ package.
  11. Gerkey B, Mataric M (2004) A formal analysis and taxonomy of task allocation in multi-robot systems. Int J Rob Res 23(9):939–954CrossRefGoogle Scholar
  12. Habets LCGJM, Collins PJ, van Schuppen JH (2006) Reachability and control synthesis for piecewise-affine hybrid systems on simplices. IEEE Trans Autom Contr 51:938–948CrossRefGoogle Scholar
  13. Habets LCGJM, van Schuppen JH (2004) A control problem for affine dynamical systems on a full-dimensional polytope. Automatica 40:21–35CrossRefMATHGoogle Scholar
  14. Hoffman AJ, Kruskal JB (1956) Integral boundary points of convex polyhedra. In: Kuhn HW, Tucker AW (eds) Linear inequalities and related systems. Annals of mathematics studies, vol 38. Princeton University Press, pp 223–246Google Scholar
  15. Jensen K (1994) Coloured Petri nets: basic concepts, analysis methods, and practical use. In: EATCS monographs on theoretical computer science. SpringerGoogle Scholar
  16. Johnson B, Kress-Gazit H (2011) Probabilistic analysis of correctness of high-level robot behavior with sensor error. In: Robotics: science and systems. Los Angeles, CAGoogle Scholar
  17. Karmarkar N (1984) A new polynomial-time algorithm for linear programming. In: Proceedings of the 16th annual ACM symposium on theory of computing, STOC ’84. New York, NY, USA, pp 302–311Google Scholar
  18. Kim G, Chung W (2007) Navigation behavior selection using generalized stochastic Petri nets for a service robot. IEEE Trans Syst Man Cybern, Part C Appl Rev 37(4):494–503CrossRefGoogle Scholar
  19. King J, Pretty R, Gosine R (2003) Coordinated execution of tasks in a multiagent environment. IEEE Trans Syst Man Cybern, Part A, Syst Humans 33(5):615–619CrossRefGoogle Scholar
  20. Kloetzer M, Belta C (2010) Automatic deployment of distributed teams of robots from temporal logic motion specifications. IEEE Trans Robot 26(1):48–61CrossRefGoogle Scholar
  21. Kloetzer M, Mahulea C, Belta C, Silva M (2010) An automated framework for formal verification of timed continuous Petri nets. IEEE Trans Ind Informat 6(3):460–471CrossRefGoogle Scholar
  22. Kloetzer M, Mahulea C, Pastravanu O (2011) A probabilistic abstraction approach for planning and controlling mobile robots. In: IEEE Conf. on emerging technologies and factory automation (ETFA). Toulouse, France, pp 1–8Google Scholar
  23. Kloetzer M, Mahulea C, Pastravanu O (2011) Software tool for probabilistic abstraction for planning and controling mobile robots.
  24. Konur S, Dixon C, Fisher M (2012) Analysing robot swarm behaviour via probabilistic model checking. Robot Auton Syst 60(2):199–213CrossRefGoogle Scholar
  25. Lahijanian M, Belta C, Andersson S (2009) A probabilistic approach for control of a stochastic system from LTL specifications. In: IEEE conf. on decision and control. Shanghai, China, pp 2236–2241Google Scholar
  26. LaValle SM (2006) Planning algorithms. Cambridge.
  27. Little I, Thiébaux S (2007) Probabilistic planning vs replanning. In: ICAPS workshop on IPC: past, present and futureGoogle Scholar
  28. Liu W, Winfield AFT, Sa J (2007) Modelling swarm robotic systems: a case study in collective foraging. In: Towards autonomous robotic systems (TAROS), pp 25–32Google Scholar
  29. Mahulea C, Kloetzer M (2012) A probabilistic abstraction approach for planning and controlling mobile robots. In: IEEE Conf. on emerging technologies and factory automation (ETFA). Krakow, PolandGoogle Scholar
  30. Makhorin A (2007) GLPK-GNU linear programming kit.
  31. Murata T (1989) Petri nets: properties, analysis and applications. Proc IEEE 77(4):541–580CrossRefGoogle Scholar
  32. Quottrup MM, Bak T, Izadi-Zamanabadi R (2004) Multi-robot motion planning: a timed automata approach. In: IEEE conf. on robotics and automation. New Orleans, LA, pp 4417–4422Google Scholar
  33. Rippel E, Bar-Gill A, Shimkin N (2005) Fast graph-search algorithms for general-aviation flight trajectory generation. J Guid Control Dyn 28(4):801–811CrossRefGoogle Scholar
  34. Shewchuk JR (1996) Triangle: engineering a 2D quality mesh generator and delaunay triangulator. In: Lin MC, Manocha D (eds) Applied computational geometry: towards geometric engineering (Lecture Notes in Computer Science), vol 1148. Springer, pp 203–222. From the First ACM Workshop on Applied Computational GeometryGoogle Scholar
  35. Silva M (1993) Introducing Petri nets. In: Practice of Petri nets in manufacturing. Chapman & Hall, pp 1–62Google Scholar
  36. Silva M, Teruel E, Colom JM (1998) Linear algebraic and linear programming techniques for the analysis of net systems. In: Rozenberg G, Reisig W (eds) Lectures in Petri nets. I: basic models (Lecture Notes in Computer Science), vol 1491. Springer, pp 309–373Google Scholar
  37. The MathWorks (2010) MATLAB® 2010b. Natick, MAGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Automatic Control and Applied InformaticsTechnical University “Gheorghe Asachi” of IasiIasiRomania
  2. 2.Aragón Institute of Engineering Research (I3A)University of ZaragozaZaragozaSpain

Personalised recommendations