Advertisement

Autonomous Robots

, Volume 37, Issue 4, pp 383–400 | Cite as

Approximate representations for multi-robot control policies that maximize mutual information

  • Benjamin CharrowEmail author
  • Vijay Kumar
  • Nathan Michael
Article

Abstract

We address the problem of controlling a small team of robots to estimate the location of a mobile target using non-linear range-only sensors. Our control law maximizes the mutual information between the team’s estimate and future measurements over a finite time horizon. Because the computations associated with such policies scale poorly with the number of robots, the time horizon associated with the policy, and typical non-parametric representations of the belief, we design approximate representations that enable real-time operation. The main contributions of this paper include the control policy, an algorithm for approximating the belief state, and an extensive study of the performance of these algorithms using simulations and real world experiments in complex, indoor environments.

Keywords

Entropy Mutual Information Mobile Robot Gaussian Mixture Model Particle Filter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We gratefully acknowledge the support of ONR Grant N00014-07-1-0829, ARL Grant W911NF-08-2-0004, and AFOSR Grant FA9550-10-1-0567. Benjamin Charrow was supported by a NDSEG fellowship from the Department of Defense.

References

  1. Binney, J., Krause, A., & Sukhatme, G. S. (2013). Optimizing waypoints for monitoring spatiotemporal phenomena. International Journal of Robotics Research, 32(8), 873–888.CrossRefGoogle Scholar
  2. Charrow, B., Kumar, V., & Michael, N. (2013). Approximate representations for multi-robot control policies that maximize mutual information. In Proceedings of Robotics: Science and Systems, Berlin, Germany.Google Scholar
  3. Charrow, B., Michael, N., & Kumar, V. (2014). Cooperative multi-robot estimation and control for radio source localization. The International Journal of Robotics Research, 33, 569–580.CrossRefGoogle Scholar
  4. Chung, T., Hollinger, G., & Isler, V. (2014). Search and pursuit-evasion in mobile robotics. Autonomous Robots, 31(4), 299–316.CrossRefGoogle Scholar
  5. Cover, T. M., & Thomas, J. A. (2004). Elements of information theory. New York: Wiley.Google Scholar
  6. Dame, A., & Marchand, E. (2011). Mutual information-based visual servoing. The IEEE Transactions on Robotics, 27(5), 958–969.CrossRefGoogle Scholar
  7. Djugash, J., & Singh, S. (2012). Motion-aided network slam with range. International Journal of Robotics Research, 31(5), 604–625.CrossRefGoogle Scholar
  8. Fannes, M. (1973). A continuity property of the entropy density for spin lattice systems. Communications in Mathematical Physics, 31(4), 291–294.MathSciNetCrossRefzbMATHGoogle Scholar
  9. Fox, D. (2003). Adapting the sample size in particle filters through KLD-sampling. International Journal of Robotics Research, 22(12), 985–1003.CrossRefGoogle Scholar
  10. Golovin, D., & Krause, A. (2011). Adaptive submodularity: Theory and applications in active learning and stochastic optimization. The Journal of Artificial Intelligence Research, 42(1), 427–486.MathSciNetzbMATHGoogle Scholar
  11. Grocholsky, B. (2002). Information-theoretic control of multiple sensor platforms. PhD thesis, Australian Centre for Field Robotics.Google Scholar
  12. Hahn, T. (2013, January). Cuba. http://www.feynarts.de/cuba/.
  13. Hoffmann, G., & Tomlin, C. (2010). Mobile sensor network control using mutual information methods and particle filters. The IEEE Transactions on Automatic Control, 55(1), 32–47. Google Scholar
  14. Hollinger, G., & Sukhatme, G. (2013). Sampling-based motion planning for robotic information gathering. In Proceedings of Robotics: Science and Systems, Berlin, Germany.Google Scholar
  15. Hollinger, G., Djugash, J., & Singh, S. (2011). Target tracking without line of sight using range from radio. Autonomous Robots, 32(1), 1–14.CrossRefGoogle Scholar
  16. Huber, M., & Hanebeck, U. (2008). Progressive gaussian mixture reduction. In International Conference on Information Fusion.Google Scholar
  17. Huber, M., Bailey, T., Durrant-Whyte, H., & Hanebeck, U. (2008, August). On entropy approximation for gaussian mixture random vectors. In Conference on Multisensor Fusion and Integration for Intelligent Systems, Seoul, Korea (pp. 181–188).Google Scholar
  18. Julian, B. J., Angermann, M., Schwager, M., & Rus, D. (2011, September). A scalable information theoretic approach to distributed robot coordination. In Proceedings of the IEEE/RSJ International Conference on Intellegent Robots and System, San Francisco, USA (pp. 5187–5194).Google Scholar
  19. Kassir, A., Fitch, R., & Sukkarieh, S. (2012, May). Decentralised information gathering with communication costs. In Proceedings of the IEEE International Conference on Robotics and Automation, Saint Paul, USA (pp. 2427–2432).Google Scholar
  20. Krause, A., & Guestrin, C. (2005). Near-optimal nonmyopic value of information in graphical models. In Conference on Uncertainty in Artificial Intelligence (pp. 324–331).Google Scholar
  21. nanoPAN 5375 Development Kit. (2013, September). http://nanotron.com/EN/pdf/Factsheet_nanoPAN_5375_Dev_Kit.pdf.
  22. Owen, D. (1980). A table of normal integrals. Communications in Statistics-Simulation and Computation, 9(4), 389–419.MathSciNetCrossRefGoogle Scholar
  23. Park, J.G., Charrow, B., Battat, J., Curtis, D., Minkov, E., Hicks, J. Teller, S., & Ledlie, J. (2010). Growing an organic indoor location system. In Proceedings of International Conference on Mobile Systems, Applications, and Services, San Francisco, CA.Google Scholar
  24. ROS. (2013, January). http://www.ros.org/wiki/.
  25. Runnals, A. (2007). Kullback–Leibler approach to gaussian mixture reduction. IEEE Transactions on Aerospace and Electronic Systems, 43(3), 989–999.CrossRefGoogle Scholar
  26. Ryan, A., & Hedrick, J. (2010). Particle filter based information-theoretic active sensing. Robotics and Autonomous Systems, 58(5), 574–584.Google Scholar
  27. Silva, J.F., Parada, P. (2011). Sufficient conditions for the convergence of the shannon differential entropy. In IEEE Information Theory Workshop, Paraty, Brazil (pp. 608–612).Google Scholar
  28. Singh, A., Krause, A., Guestrin, C., & Kaiser, W. J. (2009). Efficient informative sensing using multiple robots. The Journal of Artificial Intelligence Research, 34(1), 707–755.MathSciNetzbMATHGoogle Scholar
  29. Stump, E., Kumar, V., Grocholsky, B., & Shiroma, P. (2009). Control for localization of targets using range-only sensors. International Journal of Robotics Research, 28(6), 743.CrossRefGoogle Scholar
  30. Thrun, S., Burgard, W., & Fox, D. (2008). Probabilistic robotics. Cambridge: MIT Press.Google Scholar
  31. Vidal, R., Shakernia, O., Jin Kim, H., Shim, D., & Sastry, S. (2002). Probabilistic pursuit-evasion games: Theory, implementation, and experimental evaluation. IEEE Transactions on Robotics and Automation, 18(5), 662–669.CrossRefGoogle Scholar
  32. Whaite, P., & Ferrie, F. P. (1997). Autonomous exploration: Driven by uncertainty. The IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(3), 193–205.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.University of PennsylvaniaPhiladelphiaUSA
  2. 2.Carnegie Mellon UniversityPittsburghUSA

Personalised recommendations