Abstract
In this paper, we consider the automated planning of optimal paths for a robotic team satisfying a high level mission specification. Each robot in the team is modeled as a weighted transition system where the weights have associated deviation values that capture the non-determinism in the traveling times of the robot during its deployment. The mission is given as a Linear Temporal Logic (LTL) formula over a set of propositions satisfied at the regions of the environment. Additionally, we have an optimizing proposition capturing some particular task that must be repeatedly completed by the team. The goal is to minimize the maximum time between successive satisfying instances of the optimizing proposition while guaranteeing that the mission is satisfied even under non-deterministic traveling times. After computing a set of optimal satisfying paths for the members of the team, we also compute a set of synchronization sequences for each robot to ensure that the LTL formula is never violated during deployment. We implement and experimentally evaluate our method considering a persistent monitoring task in a road network environment.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press (2008)
Bianco, A., Alfaro, L.D.: Model Checking of Probabilistic and Nondeterministic Systems. In: Thiagarajan, P.S. (ed.) FSTTCS 1995. LNCS, vol. 1026, pp. 499–513. Springer, Heidelberg (1995)
Clarke, E.M., Peled, D., Grumberg, O.: Model checking. MIT Press (1999)
Ding, X.C., Smith, S.L., Belta, C., Rus, D.: MDP Optimal Control under Temporal Logic Constraints. In: IEEE Conf. on Decision and Control, Orlando, FL, pp. 532–538 (2011)
Emerson, E.A.: Temporal and Modal Logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science: Formal Models and Semantics, pp. 995–1072. North-Holland Pub. Co./MIT Press (1990)
Hopcroft, J., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison Wesley (2007)
Karaman, S., Frazzoli, E.: Complex Mission Optimization for Multiple-UAVs using Linear Temporal Logic. In: American Control Conference, Seattle, WA, pp. 2003–2009 (2008)
Karaman, S., Frazzoli, E.: Vehicle Routing Problem with Metric Temporal Logic Specifications. In: IEEE Conf. on Decision and Control, Cancún, México, pp. 3953–3958 (2008)
Kloetzer, M., Belta, C.: Automatic Deployment of Distributed Teams of Robots from Temporal Logic Specifications. IEEE Transactions on Robotics 26(1), 48–61 (2010)
Kress-Gazit, H., Fainekos, G., Pappas, G.J.: Where’s Waldo? Sensor-Based Temporal Logic Motion Planning. In: IEEE Intl. Conf. on Robotics and Automation, pp. 3116–3121 (2007)
Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic Symbolic Model Checking with PRISM: A Hybrid Approach. International Journal on Software Tools for Technology Transfer, 52–66 (2002)
Kloetzer, M., Belta, C.: Dealing with Non-Determinism in Symbolic Control. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 287–300. Springer, Heidelberg (2008)
Smith, S.L., Tůmová, J., Belta, C., Rus, D.: Optimal Path Planning for Surveillance with Temporal Logic Constraints. Intl. Journal of Robotics Research 30(14), 1695–1708 (2011)
Tabuada, P., Pappas, G.J.: Linear Time Logic Control of Discrete-Time Linear Systems. IEEE Transactions on Automatic Control 51(12), 1862–1877 (2006)
Thomas, W.: Infinite Games and Verification. In: Intl. Conf. on Computer Aided Verification, pp. 58–64 (2002)
Toth, P., Vigo, D. (eds.): The Vehicle Routing Problem. Monographs on Discrete Mathematics and Applications. SIAM (2001)
Tumova, J., Yordanov, B., Belta, C., Cerna, I., Barnat, J.: A Symbolic Approach to Controlling Piecewise Affine Systems. In: IEEE Conf. on Decision and Control, Atlanta, GA, pp. 4230–4235 (2010)
Ulusoy, A., Smith, S.L., Belta, C.: Optimal Multi-Robot Path Planning with LTL Constraints: Guaranteeing Correctness Through Synchronization (2012), http://arxiv.org/abs/1207.2415
Ulusoy, A., Smith, S.L., Ding, X.C., Belta, C.: Robust Multi-Robot Optimal Path Planning with Temporal Logic Constraints. In: IEEE Intl. Conf. on Robotics and Automation, St. Paul, MN, USA, pp. 4693–4698 (2012)
Ulusoy, A., Smith, S.L., Ding, X.C., Belta, C., Rus, D.: Optimal Multi-Robot Path Planning with Temporal Logic Constraints. In: IEEE/RSJ Intl. Conf. on Intelligent Robots & Systems, San Francisco, CA, USA, pp. 3087–3092 (2011)
Wongpiromsarn, T., Topcu, U., Murray, R.M.: Receding Horizon Control for Temporal Logic Specifications. In: Hybrid Systems: Computation and Control, Stockholm, Sweden, pp. 101–110 (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ulusoy, A., Smith, S.L., Belta, C. (2014). Optimal Multi-Robot Path Planning with LTL Constraints: Guaranteeing Correctness through Synchronization. In: Ani Hsieh, M., Chirikjian, G. (eds) Distributed Autonomous Robotic Systems. Springer Tracts in Advanced Robotics, vol 104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55146-8_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-55146-8_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-55145-1
Online ISBN: 978-3-642-55146-8
eBook Packages: EngineeringEngineering (R0)