Skip to main content
SpringerLink
Log in

Partial Satisfaction of Signal Temporal Logic Specifications for Coordination of Multi-robot Systems

  • Conference paper
  • First Online:
Algorithmic Foundations of Robotics XV (WAFR 2022)

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 25))

Included in the following conference series:

Abstract

This paper introduces a partial satisfaction (PS) notion for Signal Temporal Logic (STL), finding solutions for specifications that might contain unfeasible or conflicting subformulae. We formulate the planning problem for teams of agents with robust PS of STL missions as a bi-level optimization problem. The goal is to maximize the number of subformulae satisfied with preference to larger ones that have lower depth in the syntax tree of the overall specification. The second objective is to maximize the smallest STL robustness of the feasible subformulae. First, we propose three Mixed Integer Linear Programming (MILP) methods to solve the inner level of the optimization problem, two exact and a relaxation. Then, the MILP solutions are used to find approximate solutions to the outer level optimization using a linear program. Finally, we show the performance of our methods in two multi-robot case studies: motion planning in continuous spaces, and routing for heterogeneous teams over finite graph abstractions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Lower-depth node satisfaction implies a higher percentage of specification satisfaction since every all node underneath are guaranteed to be satisfied when their parent nodes are satisfied.

  2. 2.

    A formula can have many equivalent ASTs [15] determined by the parsing methods used.

References

  1. Cai, M., Peng, H., Li, Z., Gao, H., Kan, Z.: Receding horizon control-based motion planning with partially infeasible ltl constraints. IEEE Control Syst. Lett. 5(4), 1279–1284 (2020)

    Article  MathSciNet  Google Scholar 

  2. Cai, M., Peng, H., Li, Z., Kan, Z.: Learning-based probabilistic ltl motion planning with environment and motion uncertainties. IEEE Trans. Autom. Control 66(5), 2386–2392 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cardona, G.A., Calderon, J.M.: Robot swarm navigation and victim detection using rendezvous consensus in search and rescue operations. Appl. Sci. 9(8), 1702 (2019)

    Article  Google Scholar 

  4. Choudhury, S., Gupta, J.K., Kochenderfer, M.J., Sadigh, D., Bohg, J.: Dynamic multi-robot task allocation under uncertainty and temporal constraints. Robot.: Sci. Syst. 46(1), 231–247 (2020)

    Google Scholar 

  5. Cortés, J., Egerstedt, M.: Coordinated control of multi-robot systems: a survey. SICE J. Control Meas. Syst. Integr. 10(6), 495–503 (2017)

    Article  Google Scholar 

  6. Cortes, J., Martinez, S., Karatas, T., Bullo, F.: Coverage control for mobile sensing networks. IEEE Trans. Robot. Autom. 20(2), 243–255 (2004)

    Article  Google Scholar 

  7. Davey, B.A., Priestley, H.A.: Introduction to lattices and order. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  8. Dokhanchi, A., Hoxha, B., Fainekos, G.: On-line monitoring for temporal logic robustness. In: 5th International Conference on Runtime Verification, Toronto, ON, Canada, pp. 231–246. Springer (2014)

    Google Scholar 

  9. Donzé, A., Maler, O.: Robust satisfaction of temporal logic over real-valued signals. In: International Conference on Formal Modeling and Analysis of Timed Systems, pp. 92–106. Springer (2010)

    Google Scholar 

  10. Emam, Y., Mayya, S., Notomista, G., Bohannon, A., Egerstedt, M.: Adaptive task allocation for heterogeneous multi-robot teams with evolving and unknown robot capabilities (2020). arXiv:2003.03344

  11. Emam, Y., Wilson, S., Hakenberg, M., Munz, U., Egerstedt, M.: A receding horizon scheduling approach for search & rescue scenarios. arXiv pp. arXiv-2004 (2020)

    Google Scholar 

  12. Fainekos, G.E., Pappas, G.J.: Robustness of temporal logic specifications for continuous-time signals. Theor. Comput. Sci. 410(42), 4262–4291 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Gurobi Optimization, LLC: Gurobi optimizer reference manual. https://www.gurobi.com (2021)

  14. Heemels, W., De Schutter, B., Bemporad, A.: Equivalence of hybrid dynamical models. Automatica 37(7), 1085–1091 (2001)

    Article  MATH  Google Scholar 

  15. Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to automata theory, languages, and computation. Acm Sigact. News 32(1), 60–65 (2001)

    Article  MATH  Google Scholar 

  16. Jones, A.M., Leahy, K., Vasile, C., Sadraddini, S., Serlin, Z., Tron, R., Belta, C.: Scratchs: Scalable and robust algorithms for task-based coordination from high-level specifications. In: International Symposium of Robotics Research, International Federation of Robotics Research (2019)

    Google Scholar 

  17. Kamale, D., Karyofylli, E., Vasile, C.I.: Automata-based optimal planning with relaxed specifications. In: 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE (2021)

    Google Scholar 

  18. Khalil, H.K.: Nonlinear Systems, 3rd edn. Patience Hall, Hoboken (2002)

    MATH  Google Scholar 

  19. Lacerda, B., Parker, D., Hawes, N.: Optimal policy generation for partially satisfiable co-safe ltl specifications. In: Twenty-Fourth International Joint Conference on Artificial Intelligence (2015)

    Google Scholar 

  20. Lahijanian, M., Almagor, S., Fried, D., Kavraki, L.E., Vardi, M.Y.: This time the robot settles for a cost: a quantitative approach to temporal logic planning with partial satisfaction. In: Twenty-Ninth AAAI Conference on Artificial Intelligence (2015)

    Google Scholar 

  21. Leahy, K., Jones, A., Vasile, C.I.: Fast decomposition of temporal logic specifications for heterogeneous teams. IEEE Robot. Autom. Lett. 7(2), 2297–2304 (2022)

    Google Scholar 

  22. Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Formal Techniques, Modelling and Analysis of Timed and Fault-Tolerant Systems, pp. 152–166. Springer (2004)

    Google Scholar 

  23. Notomista, G., Mayya, S., Hutchinson, S., Egerstedt, M.: An optimal task allocation strategy for heterogeneous multi-robot systems. In: 2019 18th European Control Conference (ECC), pp. 2071–2076. IEEE (2019)

    Google Scholar 

  24. Raman, V., Donzé, A., Maasoumy, M., Murray, R.M., Sangiovanni-Vincentelli, A., Seshia, S.A.: Model predictive control with signal temporal logic specifications. In: 53rd IEEE Conference on Decision and Control, pp. 81–87. IEEE (2014)

    Google Scholar 

  25. Sadraddini, S., Belta, C.: Robust temporal logic model predictive control. In: 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp. 772–779. IEEE (2015)

    Google Scholar 

  26. Schillinger, P., Bürger, M., Dimarogonas, D.V.: Simultaneous task allocation and planning for temporal logic goals in heterogeneous multi-robot systems. Inter. J. Robot. Res. 37(7), 818–838 (2018)

    Article  Google Scholar 

  27. Ulusoy, A., Smith, S.L., Ding, X.C., Belta, C., Rus, D.: Optimality and robustness in multi-robot path planning with temporal logic constraints. Int. J. Robot. Res. 32(8), 889–911 (2013)

    Article  Google Scholar 

  28. Voos, H.: Nonlinear control of a quadrotor micro-uav using feedback-linearization. In: 2009 IEEE International Conference on Mechatronics, pp. 1–6. IEEE (2009)

    Google Scholar 

  29. Wilamowsky, Y., Epstein, S., Dickman, B.: Optimization in multiple-objective linear programming problems with pre-emptive priorities. J. Oper. Res. Soc. 41(4), 351–356 (1990)

    Article  MATH  Google Scholar 

  30. Zhou, D., Schwager, M.: Vector field following for quadrotors using differential flatness. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 6567–6572 (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering and Mechanics at Lehigh University, Bethlehem, PA, 18015, USA

    Gustavo A. Cardona & Cristian-Ioan Vasile

Authors
  1. Gustavo A. Cardona
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cristian-Ioan Vasile
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gustavo A. Cardona .

Editor information

Editors and Affiliations

  1. Center for Ubiquitous Computing, University of Oulu, Oulu, Finland

    Steven M. LaValle

  2. Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA

    Jason M. O’Kane

  3. Department of Aerospace Engineering, University of Maryland, College Park, MD, USA

    Michael Otte

  4. Gates Computer Science, Stanford University, Stanford, CA, USA

    Dorsa Sadigh

  5. Department of Computer Science, University of Maryland, College Park, MD, USA

    Pratap Tokekar

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Cardona, G.A., Vasile, CI. (2023). Partial Satisfaction of Signal Temporal Logic Specifications for Coordination of Multi-robot Systems. In: LaValle, S.M., O’Kane, J.M., Otte, M., Sadigh, D., Tokekar, P. (eds) Algorithmic Foundations of Robotics XV. WAFR 2022. Springer Proceedings in Advanced Robotics, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-031-21090-7_14

Download citation

Publish with us

Policies and ethics

Search

Navigation