Path planning for robotic teams based on LTL specifications and Petri net models

  • Marius KloetzerEmail author
  • Cristian Mahulea
Part of the following topical collections:
  1. Smart Manufacturing -A New DES Frontier


This research proposes an automatic strategy for planning a team of identical robots evolving in a known environment. The robots should satisfy a global task for the whole team, given in terms of a Linear Temporal Logic (LTL) formula over predefined regions of interest. A Robot Motion Petri Net (RMPN) system is used for modeling the evolution of the robotic team in the environment, bringing the advantage of a fixed topology versus the number of robots, with respect to methods based on synchronous automaton products. The algorithmic method iterates the selection of an accepted run that satisfies the specification and the search for RMPN sequences of reachable markings that can produce desired observations. A Büchi automaton witnesses the advancement towards formula fulfillment, and at the core of our methods are three Mixed Integer Linear Programming (MILP) formulations that yield firing sequences and markings of RMPN model. The cost functions of these formulations reduce the number of robot synchronizations and induce collision avoidance. Simulation examples support the computational feasibility of the proposed method.


Path planning Petri nets Linear temporal logic Optimization 



The first author acknowledges the support of Ministry of Research and Innovation (Romania) under CNCS-UEFISCDI grant PN-III-P1-1.1-TE-2016-0737. The second author acknowledges the support of the Aragonese Government (Spain) under grant T94 DisCo group, and of University of Zaragoza under grant JIUZ-2018-TEC-10.


  1. Aragues R, Shi G, Dimarogonas D, Sagues C, Johansson K (2012) Distributed algebraic connectivity estimation for adaptive event-triggered consensus. In: American Control Conference (ACC), pp 32–37Google Scholar
  2. Baier C, Katoen JP (2008) Principles of Model Checking. MIT PressGoogle Scholar
  3. Belta C, Bicchi A, Egerstedt M, Frazzoli E, Klavins E, Pappas GJ (2007) Symbolic planning and control of robot motion. IEEE Robot Autom Mag 14 (1):61–71CrossRefGoogle Scholar
  4. 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, BostonzbMATHGoogle Scholar
  5. Clarke EMM, Peled D, Grumberg O (1999) Model Checking. MIT PressGoogle Scholar
  6. Costelha H, Lima P (2012) Robot task plan representation by Petri nets: modelling, identification, analysis and execution. Auton Robot 33(4):337–360CrossRefGoogle Scholar
  7. Dallal E, Colombo A, Del Vecchio D, Lafortune S (2017) Supervisory control for collision avoidance in vehicular networks using discrete event abstractions. Discrete Event Dynamic Systems 27(1):1–44MathSciNetCrossRefGoogle Scholar
  8. DeCastro J, Ehlers R, Runggers M, Balkan A, Kress-Gazit H (2016) Automated generation of dynamics-based runtime certificates for high-level control. Discrete Event Dynamic Systems 27(2):371—405MathSciNetzbMATHGoogle Scholar
  9. Ding X, Smith SL, Belta C, Rus D (2014) Optimal control of Markov decision processes with linear temporal logic constraints. IEEE Trans Autom Control 59(5):1244–1257MathSciNetCrossRefGoogle Scholar
  10. Ding XC, Kloetzer M, Chen Y, Belta C (2011) Automatic deployment of robotic teams. IEEE Robot Autom Mag 18(3):75–86CrossRefGoogle Scholar
  11. Duret-Lutz A, Lewkowicz A, Fauchille A, Michaud T, Renault E, Xu L (2016) Spot 2.0 - a framework for LTL and ω-automata manipulation. In: Proc of ATVA’16, LNCS 9938, pp 122–129Google Scholar
  12. Esparza J, Heljanko K (2001) Implementing LTL model checking with net unfoldings. In: Proc of the 8th International SPIN Workshop on Model Checking of Software, pp 37–56CrossRefGoogle Scholar
  13. Fainekos GE, Girard A, Kress-Gazit H, Pappas GJ (2009) Temporal logic motion planning for dynamic robots. Automatica 45(2):343–352MathSciNetCrossRefGoogle Scholar
  14. Franceschelli M, Giua A, Pisano A (2014) Finite-time consensus on the median value by discontinuous control. In: American Control Conference (ACC), pp 946–951Google Scholar
  15. Franceschelli M, Rosa D, Seatzu C, Bullo F (2013) Gossip algorithms for heterogeneous multi-vehicle routing problems. Nonlinear Analysis:, Hybrid Systems 10 (1):156–174MathSciNetzbMATHGoogle Scholar
  16. Garrido S, Moreno L, Gomez J, Lima P (2013) General path planning methodology for leader-follower robot formations. Int J of Advanced Robotic Systems 10(64):1–10Google Scholar
  17. Gastin P, Oddoux D (2001) Fast LTL to büchi automata translation. In: Proc of the 13th Conference on Computer Aided Verification (CAV), LNCS 2102, pp 53–65CrossRefGoogle Scholar
  18. Guo M, Dimarogonas DV (2015) Multi-agent plan reconfiguration under local LTL specifications. The International Journal of Robotics Research 34(2):218–235CrossRefGoogle Scholar
  19. Holzmann G (2004) The Spin Model Checker, Primer and Reference Manual. Addison, ReadingGoogle Scholar
  20. Kloetzer M, Ding XC, Belta C (2011) Multi-robot deployment from LTL specifications with reduced communication. In: IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp 4867–4872Google Scholar
  21. Kloetzer M, Mahulea C (2014) A Petri net based approach for multi-robot path planning. Discrete Event Dynamic Systems:, Theory and Applications 24(4):417–445MathSciNetCrossRefGoogle Scholar
  22. Kloetzer M, Mahulea C (2015) LTL-Based planning in environments with probabilistic observations. IEEE Trans Autom Sci Eng 12(4):1407–1420CrossRefGoogle Scholar
  23. Kloetzer M, Mahulea C (2016) Multi-robot path planning for syntactically co-safe LTL specifications. In: 13Th International Workshop on Discrete Event Systems (WODES), pp 452–458Google Scholar
  24. Kloetzer M, Mahulea C, Colom JM (2013) Petri net approach for deadlock prevention in robot planning. In: IEEE 18Th Conf on Emerging Technologies Factory Automation (ETFA), Cagliari, ItalyGoogle Scholar
  25. Lacerda B, Lima P (2011) Designing petri net supervisors from LTL specifications. In: Proc. of Robotics: Science and SystemsGoogle Scholar
  26. LaValle SM (2006) Planning algorithms. CambridgeGoogle Scholar
  27. Li Z, Wu N, Zhou M (2012) Deadlock control of automated manufacturing systems based on Petri nets - a literature review. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 42(4):437–462CrossRefGoogle Scholar
  28. Lin L, Stefanescu A, Su R (2016) On distributed and parameterized supervisor synthesis problems. IEEE Trans Autom Control 61(3):777–782MathSciNetCrossRefGoogle Scholar
  29. Ma H, Koenig S (2017) AI Buzzwords explained: Multi-Agent path finding (MAPF). AI Matters 3(3):15–19CrossRefGoogle Scholar
  30. Ma H, Hoenig W, Cohen L, Uras T, Xu H, Kumar S, Ayanian N, Koenig S (2017) Overview: a hierarchical framework for plan generation and execution in multirobot systems. IEEE Intell Syst 32(6):6–12CrossRefGoogle Scholar
  31. Mahulea C, Kloetzer M (2018) Robot planning based on Boolean specifications using Petri net models. IEEE Trans Autom Control 63(7):2218–2225MathSciNetCrossRefGoogle Scholar
  32. Mahulea C, Kloetzer M (2014) Planning mobile robots with Boolean-based specifications. In: 53Rd IEEE Conference on Decision and Control (CDC), Los Angeles, USAGoogle Scholar
  33. Makhorin A (2012) GNU linear programming kit.
  34. Murata T (1989) Petri nets: Properties, analysis and applications. Proc IEEE 77(4):541–580CrossRefGoogle Scholar
  35. Parrilla L, Mahulea C, Kloetzer M (2017) RMTool:, recent enhancements. IFAC-PapersOnLine 50(1):5824–5830CrossRefGoogle Scholar
  36. Robla-Gómez S, Becerra VM, Llata JR, González-Sarabia E, Torre-Ferrero C, Pérez-Oria J (2017) Working together: a review on safe human-robot collaboration in industrial environments. IEEE Access 5(26):754–26,773Google Scholar
  37. Roszkowska E, Reveliotis S (2013) A distributed protocol for motion coordination in free-range vehicular systems. Automatica 49:1639–1653MathSciNetCrossRefGoogle Scholar
  38. Schillinger P, Bürger M, Dimarogonas D (2018) Simultaneous task allocation and planning for temporal logic goals in heterogeneous multi-robot systems. Int J Robot Res 37(7):818–838CrossRefGoogle Scholar
  39. Sharon G, Stern R, Felner A, Sturtevant N (2015) Conflict-based search for optimal multi-agent pathfinding. Artif Intell 219:40–66MathSciNetCrossRefGoogle Scholar
  40. Sharon G, Stern R, Goldenberg M (2013) Felner a: the increasing cost tree search for optimal multi-agent pathfinding. Artif Intell 195:470–495CrossRefGoogle Scholar
  41. Sheridan TB (2016) Human robot interaction: Status and challenges. Hum Factors 58(4):525–532CrossRefGoogle Scholar
  42. Silva M, Teruel E, Colom JM (1998) Linear algebraic and linear programming techniques for the analysis of P/T net systems. Lecture on Petri Nets I:, Basic Models 1491:309–373CrossRefGoogle Scholar
  43. Theorin A, Bengtsson K, Provost J, Lieder M, Johnsson C, Lundholm T, Lennartson B (2017) An event-driven manufacturing information system architecture for industry 4.0. Int J Prod Res 55(5):1297–1311CrossRefGoogle Scholar
  44. Tumova J, Dimarogonas D (2016) Multi-agent planning under local LTL specifications and event-based synchronization. Automatica 70:239–248MathSciNetCrossRefGoogle Scholar
  45. Ulusoy A, Smith S, Ding X, Belta C (2012) Robust multi-robot optimal path planning with temporal logic constraints. In: 2012 IEEE Conference on Robotics and Automation (ICRA), pp 4693–4698Google Scholar
  46. Ware S, Su R (2016) Incremental scheduling of discrete event systems. In: 13Th International Workshop on Discrete Event Systems (WODES), pp 147–152Google Scholar
  47. Wolper P, Vardi M, Sistla A, et al. (1983) Reasoning about infinite computation paths, E.N.. In: Proceedings of the 24th IEEE Symposium on Foundations of Computer Science. AZ, Tucson, pp 185–194Google Scholar
  48. Yen JY (1971) Finding the k shortest loopless paths in a network. Manag Sci 17 (11):712–716MathSciNetCrossRefGoogle Scholar
  49. Zhou Y, Hu H, Liu Y, Lin S, Dingm Z (2018) A distributed approach to robust control of multi-robot systems. Automatica 98:1–13MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

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

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