Abstract
We present an approach to analytically construct a robotic team, i.e., team members and deployment order, that achieves a specific task with quantified probability of success. We assume that each robot is Markovian, and that robots interact with each other via communication only. Our approach is based on probabilistic model checking (PMC). We first construct a set of Discrete Time Markov Chains (DTMCs) that each capture a specific “projection” of the behavior of an individual robot. Next, given a specific team, we construct the DTMC for its behavior by combining the projection DTMCs appropriately. Finally, we use PMC to evaluate the performance of the team. This procedure is repeated for multiple teams, the best one is selected. In practice, the projection DTMCs are constructed by observing the behavior of individual robots a finite number of times, which introduces an error in our results. We present an approach – based on sampling using the Dirichlet distribution – to quantify this error. We prove the correctness of our approach formally, and also validate it empirically on a mine detection task by a team of communicating Kilobots.
This material is based upon work funded and supported by the Department of Defense under Contract No. FA8721-05-C-0003 with Carnegie Mellon University for the operation of the Software Engineering Institute, a federally funded research and development center. This material has been approved for public release and unlimited distribution. DM-0001326.
This is a preview of subscription content, log in via an institution to check access.
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
V-REP: Virtual robot experimentation platform (2014)
Chen, T., Diciolla, M., Kwiatkowska, M.Z., Mereacre, A.: Quantitative Verification of Implantable Cardiac Pacemakers. In: Proceedings of the 33rd Real-Time Systems Symposium (RTSS 2012), San Juan, PR, USA, pp. 263–272. IEEE Computer Society (December 2012)
Devroye, L.: Non-Uniform Random Variate Generation. Springer, New York (1986)
Ghorbal, K., Duggirala, P.S., Kahlon, V., Ivančić, F., Gupta, A.: Efficient probabilistic model checking of systems with ranged probabilities. In: Finkel, A., Leroux, J., Potapov, I. (eds.) RP 2012. LNCS, vol. 7550, pp. 107–120. Springer, Heidelberg (2012)
Hansson, H., Jonsson, B.: A Logic for Reasoning about Time and Reliability. Formal Aspects of Computing (FACJ) 6(5), 512–535 (1994)
Heath, J., Kwiatkowska, M.Z., Norman, G., Parker, D., Tymchyshyn, O.: Probabilistic model checking of complex biological pathways. Theoretical Computer Science (TCS) 391(3), 239–257 (2008)
Huang, J.: Maximum likelihood estimation of dirichlet distribution parameters. Technical report, Robotics Institute, Carnegie Mellon University (2005)
Konur, S., Dixon, C., Fisher, M.: Analysing robot swarm behaviour via probabilistic model checking. In: Robotics and Autonomous Systems (2011)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: Verification of Probabilistic Real-Time Systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011)
Kwiatkowska, M.Z., Norman, G., Sproston, J.: Probabilistic Model Checking of Deadline Properties in the IEEE 1394 FireWire Root Contention Protocol. Formal Aspects of Computing (FACJ) 14(3), 295–318 (2003)
Rubenstein, M., Ahler, C., Nagpal, R.: Kilobot: A low cost scalable robot system for collective behaviors. In: IEEE Intl. Conf on Robotics and Automation (ICRA), p. 6 (2012)
Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, Available as Technical Report MIT/LCS/TR-676 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Chaki, S., Giampapa, J., Kyle, D., Lehoczky, J. (2014). Optimizing Robotic Team Performance with Probabilistic Model Checking. In: Brugali, D., Broenink, J.F., Kroeger, T., MacDonald, B.A. (eds) Simulation, Modeling, and Programming for Autonomous Robots. SIMPAR 2014. Lecture Notes in Computer Science(), vol 8810. Springer, Cham. https://doi.org/10.1007/978-3-319-11900-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-11900-7_12
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11899-4
Online ISBN: 978-3-319-11900-7
eBook Packages: Computer ScienceComputer Science (R0)