Research Papers

Trading Safety Versus Performance: Rapid Deployment of Robotic Swarms With Robust Performance Constraints

[+] Author and Article Information
Yin-Lam Chow

Institute for Computational and
Mathematical Engineering,
Stanford University,
Stanford, CA 94305
e-mail: ychow@stanford.edu

Marco Pavone

Department of Aeronautics and Astronautics,
Stanford University,
Stanford, CA 94305
e-mail: pavone@stanford.edu

Brian M. Sadler

Army Research Laboratory,
Adelphi, MD 20783
e-mail: brian.m.sadler6.civ@mail.mil

Stefano Carpin

School of Engineering,
University of California,
Merced, CA 95343
e-mail: scarpin@ucmerced.edu

Such mass distribution not only exists, but can be explicitly computed.

Prx0π[Xt=x] is the probability that Xt=x given the initial state x0X' and the policy π.

More in general, there exist more than one linear programming formulation that can be used, and methods based on Lagrange multipliers have been introduced as well. However, they will not be considered in this paper.

The number of vertices indeed depends on the value of Γ. In the extreme case where Γ = 0 the uncertainty set U has only one vertex.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 1, 2014; final manuscript received June 7, 2014; published online October 21, 2014. Assoc. Editor: Dejan Milutinovic.

J. Dyn. Sys., Meas., Control 137(3), 031005 (Oct 21, 2014) (11 pages) Paper No: DS-14-1057; doi: 10.1115/1.4028117 History: Received February 01, 2014; Revised June 07, 2014

In this paper, we consider a stochastic deployment problem, where a robotic swarm is tasked with the objective of positioning at least one robot at each of a set of pre-assigned targets while meeting a temporal deadline. Travel times and failure rates are stochastic but related, inasmuch as failure rates increase with speed. To maximize chances of success while meeting the deadline, a control strategy has therefore to balance safety and performance. Our approach is to cast the problem within the theory of constrained Markov decision processes (CMDPs), whereby we seek to compute policies that maximize the probability of successful deployment while ensuring that the expected duration of the task is bounded by a given deadline. To account for uncertainties in the problem parameters, we consider a robust formulation and we propose efficient solution algorithms, which are of independent interest. Numerical experiments confirming our theoretical results are presented and discussed.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Bonabeau, E., Dorigo, M., and Theraulaz, G., 1999, Swarm Intelligence: From Natural to Artificial Systems, Oxford University, New York, Vol. 4.
Bullo, F., Cortés, J., and Martínez, S., 2009, Distributed Control of Robotic Networks, Princeton University Press, Princeton, NJ.
Pavlic, T., and Passino, K., 2009, “Foraging Theory for Autonomous Vehicle Speed Choice,” Eng. Appl. Artif. Intell., 22(3), pp. 482–489. [CrossRef]
Cortes, J., Martinez, S., Karatas, T., and Bullo, F., 2004, “Coverage Control for Mobile Sensing Networks,” IEEE Trans. Rob. Autom., 20(2), pp. 243–255. [CrossRef]
Schwager, M., McLurkin, J., and Rus, D., 2006, “Distributed Coverage Control With Sensory Feedback for Networked Robots,” Proceedings of the Robotics: Science and Systems Conference, pp. 49–56.
Morlok, R., and Gini, M., 2004, “Dispersing Robots in an Unknown Environment,” Proceedings of the International Symposium on Distributed Autonomous Robotic Systems, Springer, Tokyo, pp. 253–262.
Pearce, J., Rybski, P., Stoeter, S., and Papanilolopoulos, N., 2003, “Dispersion Behaviors for a Team of Multiple Miniature Robots,” Proceedings of the IEEE International Conference on Robotics and Automation, Taiwan, pp. 1158–1163.
Purohit, A., Zhang, P., Sadler, B., and Carpin, S., 2014, “Deployment of Swarms of Micro-Aerial Vehicles: From Theory to Practice,” Proceedings of the IEEE International Conference on Robotics and Automation Hong Kong, pp. 5408–5413.
Pavone, M., Arsie, A., Frazzoli, E., and Bullo, F., 2011, “Distributed Algorithms for Environment Partitioning in Mobile Robotic Networks,” Hong Kong, IEEE Trans. Autom. Control, 56(8), pp. 1834–1848. [CrossRef]
Carpin, S., Chung, T., and Sadler, B., 2013, “Theoretical Foundations of High-Speed Robot Team Deployment,” Proceedings of the IEEE International Conference on Robotics and Automation, Karlsruhe, Germany, pp. 2025–2032.
Kloetzer, M., and Belta, C., 2007, “Temporal Logic Planning and Control of Robotic Swarms by Hierarchical Abstractions,” IEEE Trans. Rob., 23(2), pp. 320–330. [CrossRef]
Ding, X., Kloetzer, M., Chen, Y., and Belta, C., 2011, “Automatic Deployment of Robotic Teams,” IEEE Rob. Autom. Mag., 18(3), pp. 75–86. [CrossRef]
Batalin, M., and Sukhatme, G., 2007, “The Design and Analysis of an Efficient Local Algorithm for Coverage and Exploration Based on Sensor Network Deployment,” IEEE Trans. Rob., 23(4), pp. 661–675. [CrossRef]
Fink, J., Ribeiro, A., and Kumar, V., 2013, “Robust Control of Mobility and Communications in Autonomous Robot Teams,” IEEE Access, 1, pp. 290–309. [CrossRef]
Matignon, L., Jeanpierre, L., and Mouaddib, A., 2012, “Coordinated Multi-Robot Exploration Under Communication Constraints Using Decentralized Markov Decision Processes,” Proceedings of the AAAI Conference on Artificial Intelligence, Toronto, Canada, pp. 2017–2023.
Ding, X., Pinto, A., and Surana, A., 2013, “Strategic Planning Under Uncertainties Via Constrained Markov Decision Processes,” Proceedings of the IEEE International Conference on Robotics and Automation, Karlsruhe, Germany,, pp. 4568–4575.
Napp, N., and Klavins, E., 2011, “A Compositional Framework for Programming Stochastically Interacting Robots,” Int. J. Rob. Res., 30(6), pp. 713–729. [CrossRef]
Altman, E., 1996, “Constrained Markov Decision Processes With Total Cost Criteria: Occupation Measures and Primal LP,” Math. Methods Oper. Res., 43(1), pp. 45–72. [CrossRef]
Bertsekas, D., 2005, Dynamic Programming and Optimal Control, Athena Scientific, Belmont, MA, Vol. 1–2.
Puterman, M., 1994, Markov Decision Processes – Discrete Stochastic Dynamic Programming, Wiley-Interscience, Hoboken, NJ.
Altman, E., 1999, Constrained Markov Decision Processes (Stochastic Modeling), Chapman & Hall/CRC, Boca Raton, FL.
Ben-Tal, A., El Ghaoui, L., and Nemirovski, A., 2009, Robust Optimization, Princeton University, Princeton, NJ.
Bertsimas, D., and Sim, M., 2003, “Robust Discrete Optimization and Network Flows,” Math. Program., 98(1–3), pp. 49–71. [CrossRef]
Rausand, M., and Høyland, A., 2004, System Reliability Theory: Models, Statistical Methods, and Applications, Wiley, Hoboken, NJ, Vol. 396.
Purohit, A., and Zhang, P., 2011, “Controlled-Mobile Sensing Simulator for Indoor Fire Monitoring,” Proceedings of the Wireless Communications and Mobile Computing Conference, Istanbul, Turkey, pp. 1124–1129.
Kumar, V., and Michael, N., 2012. “Opportunities and Challenges With Autonomous Micro Aerial Vehicles,” Int. J. Rob. Res., 31(11), pp. 1279–1291. [CrossRef]
Kushleyev, A., Mellinger, D., and Kumar, V., 2012, “Towards a Swarm of Agile Micro Quadrotors,” Autonomous Robots, 35(4), pp. 287–300. [CrossRef]
Mellinger, D., Michael, N., and Kumar, V., 2012, “Trajectory Generation and Control for Precise Aggressive Maneuvers With Quadrotors,” Int. J. Rob. Res., 31(5), pp. 664–674. [CrossRef]
Nesterov, Y., Nemirovskii, A., and Ye, Y., 1994, Interior-Point Polynomial Algorithms in Convex Programming, Society for Industrial and Applied Mathematics, Philadelphia, PA, Vol. 13.
Luenberger, D., 2003, Linear and Nonlinear Programming, Kluwer Academic Press, Boston, MA.


Grahic Jump Location
Fig. 1

A sigmoidal shape for the safety function Se associated with the edges in the graph

Grahic Jump Location
Fig. 2

Given a graph G = (X, E) and a policy π, multiple stochastic paths from the deployment vertex v0 to the target vertex set T exist. Whenever a failure occurs, the state enters S (dashed arrows). States outside the box labeled M are in X.

Grahic Jump Location
Fig. 3

The map used to experimentally evaluate the deployment policies is the same as the one used in Ref. [10]. The deployment vertex is marked with a triangle, whereas goal vertices are indicated by crosses. Edges between vertices indicate that a path exists.

Grahic Jump Location
Fig. 4

Success rate as a function of the number of robots for different temporal deadlines using random uniform assignment

Grahic Jump Location
Fig. 5

Success rate as a function of the number of robots for different temporal deadlines using optimal target assignment



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In