Rao—Blackwellized particle filters (RBPFs) are an implementation of sequential Bayesian filtering that has been successfully applied to mobile robot simultaneous localization and mapping (SLAM) and exploration. Measuring the uncertainty of the distribution estimated by a RBPF is required for tasks such as information gain-guided exploration or detecting loop closures in nested loop environments. In this paper we propose a new measure that takes the uncertainty in both the robot path and the map into account. Our approach relies on the entropy of the expected map (EM) of the RBPF, a new variable built by integrating the map hypotheses from all of the particles. Unlike previous works that use the joint entropy of the RBPF for active exploration, our proposal is better suited to detect opportunities to close loops, a key aspect to reduce the robot path uncertainty and consequently to improve the quality of the maps being built. We provide a theoretical discussion and experimental results with real data that support our claims.
Arulampalam, M., Maskell, S., Gordon, N., Clapp, T., Sci, D., Organ, T. and Adelaide, S. (2002). A tutorial on particle filters for online nonlinear/non-GaussianBayesian tracking. IEEE Transactions on Signal Processing, 50(2): 174—188.
2.
Blanco, J., Gonzalez, J. and Fernandez-Madrigal, J. (2006). The Trajectory Parameter Space (TP-Space): a new space representation for non-holonomic mobile robot reactive navigation. Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1195— 1200.
3.
Bourgault, F., Makarenko, A., Williams, S., Grocholsky, B. and Durrant-Whyte, H. (2002). Information based adaptive robotic exploration. Proceedings of IEEE International Symposium on Computational Intelligence in Robotics and Automation, Vol. 1.
4.
Burgard, W., Fox, D., and Thrun, S. (1997). Active mobile robot localization. Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI). San Mateo, CA, Morgan Kaufmann.
5.
Burgard, W., Moors, M., Fox, D., Simmons, R. and Thrun, S. (2000). Collaborative multi-robot exploration. Proceedings of the IEEE International Conference on Robotics and Automation , Vol. 1, pp. 476—481.
6.
Cover, T. and Thomas, J. (1991). Elements of Information Theory. New York, John Wiley & Sons.
7.
Dellaert, F., Fox, D., Burgard, W., and Thrun, S. (1999). Monte Carlo localization for mobile robots.Proceedings of the IEEE International Conference on Robotics and Automation , Vol. 2.
8.
Dissanayake, M., Newman, P., Clark, S., Durrant-Whyte, H. and Csorba, M. (2001). A solution to the simultaneous localization and map building (SLAM) problem. IEEE Transactions on Robotics and Automation, 17(3): 229—241.
9.
Doucet, A., de Freitas, N., Murphy, K. and Russell, S. (2000a). Rao—Blackwellised particle filtering for dynamic Bayesian networks. Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence, pp. 176—183.
10.
Doucet, A., Godsill, S. and Andrieu, C. (2000b). On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 10(3): 197—208.
11.
Elfes, A. (1989). Using occupancy grids for mobile robot perception and navigation. Computer, 22(6): 46—57.
12.
Fernandez-Madrigal, J. (2004). Assistive navigation of a robotic wheelchair using a multihierarchical model of the environment. IntegratedComputer-Aided Engineering, 11(4): 309—322.
13.
Fox, D. (2003). Adapting the sample size in particle filters through KLD-sampling. International Journal of Robotics Research, 22(12): 985—1003.
14.
Fox, D., Burgard, W. and Thrun, S. (1999). Markov localization for mobile robots in dynamic environments. Journal of Artificial Intelligence Research , 11(3):391—427.
15.
Gonzalez, J., Muñoz, A., Galindo, C., Fernandez-Madrigal, J. and Blanco, J. (2006). A description of the SENA robotic wheelchair. Proceedings of the IEEE Mediterranean Electrotechnical Conference , pp. 437—440.
16.
Grisetti, G., Stachniss, C. and Burgard, W. (2007a). Improved techniques for grid mapping with Rao—Blackwellized particle filters. IEEE Transactions on Robotics, 23: 34— 46.
17.
Grisetti, G., Tipaldi, G., Stachniss, C., Burgard, W. and Nardi, D. (2007b). Fast and accurate slam with Rao— Blackwellized particle filters. Robotics and Autonomous Systems, 55(1): 30—38.
18.
Hahnel, D., Burgard, W., Fox, D. and Thrun, S. (2003). An efficient FastSLAM algorithm for generating maps of large-scale cyclic environments from raw laser range measurements . Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Vol. 1.
19.
Intel, Inc. (1999). Intel Architecture Software Developer's Manual. Volume 2: Instruction Set Reference. Available at: http://developer.intel.com/design/pentiumii/manuals/243191.htm.
20.
Julier, S. and Uhlmann, J. (1997). A new extension of the Kalman filter to nonlinear systems. Proceedings of the International Symposium on Aerospace/Defense Sensing, Simulation and Controls, Vol. 3.
21.
Kalman, R. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1): 35— 45.
22.
Ko, J., Stewart, B., Fox, D., Konolige, K. and Limketkai, B. (2003). A practical, decision-theoretic approach to multi-robot mapping and exploration. Proceedings of the IEEE/ RSJ International Conference on Intelligent Robots and Systems, Vol. 4, pp. 3232—3238.
23.
Liu, J. (1996). Metropolized independent sampling with comparisons to rejection sampling and importance sampling. Statistics and Computing, 6(2): 113—119.
24.
Lu, F. and Milios, E. (1997). Globally consistent range scan alignment for environment mapping. Autonomous Robots, 4(4): 333—349.
25.
Montemerlo, M., Thrun, S., Koller, D. and Wegbreit, B. (2002). FastSLAM: A factored solution to the simultaneous localization and mapping problem. Proceedings of the AAAI National Conference on Artificial Intelligence, pp. 593—598.
26.
Moravec, H. (1988). Sensor fusion in certainty grids for mobile robots . AI Magazine, 9(2): 61—74.
27.
Moravec, H. and Elfes, A. (1985). High resolution maps from wide angle sonar. Proceedings of the IEEE International Conference on Robotics and Automation , Vol. 2.
28.
Porta, J. and Kröse, B. (2006). Appearance-based concurrent map building and localization . Robotics and Autonomous Systems, 54(2): 159—164.
29.
Roy, N., Burgard, W., Fox, D. and Thrun, S. (1999). Coastal navigation—mobile robot navigation with uncertainty in dynamic environments. Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems , Vol. 1.
30.
Saez, J. and Escolano, F. (2005). Entropy minimization SLAM using stereo vision . Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 36—43.
31.
Sim, R. and Roy, N. (2005). Global A-optimal robot exploration in SLAM. Proceedings of the IEEE International Conference on Robotics and Automation, pp. 661— 666.
32.
Stachniss, C. (2006). Exploration and Mapping with Mobile Robots. Ph.D. Thesis, Universität Freiburg.
33.
Stachniss, C., Grisetti, G. and Burgard, W. (2005a). Information gain-based exploration using Rao—Blackwellized particle filters. Proceedings of Robotics: Science and Systems (RSS).
34.
Stachniss, C., Grisetti, G. and Burgard, W. (2005b). Recovering particle diversity in a Rao—Blackwellized particle filter for SLAM after actively closing loops. Proceedings of the IEEE International Conference on Robotics and Automation .
35.
Stachniss, C., Hahnel, D. and Burgard, W. (2004). Exploration with active loop-closing for FastSLAM . Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Vol. 2.
36.
Thrun, S. (2003). Learning occupancy grid maps with forward sensor models. Autonomous Robots, 15(2): 111—127.
37.
Thrun, S., Burgard, W. and Fox, D. (2005). Probabilistic Robotics. Cambrideg, MA, MIT Press.
38.
Vlassis, N., Motomura, Y., and Krose, B. (1999). An information-theoretic localization criterion for robot map building. Proceedings of International Conference on Machine Learning and Applications, pp. 1—6.
39.
Yamauchi, B. (1998). Frontier-based exploration using multiple robots . Proceedings of the Second International Conference on Autonomous Agents. New York, ACM Press, pp. 47—53.
