Thin Junction Tree Filters for Simultaneous Localization and Mapping

The Simultaneous Localization and Mapping problem is a fundamental problem in mobile robotics: while a robot navigates in an unknown environment, it must incrementally build a map of its surroundings and localize itself within that map. Traditional approaches to the problem are based upon Kalman filters, but suffer from complexity issues: first, the belief state grows quadratically in the size of the map; and second, the filtering operation can take time quadratic in the size of the map. I present a linear-space filter that maintains a tractable approximation of the belief state as a thin junction tree. The junction tree grows under measurement and motion updates and is periodically "thinned" to remain tractable. The time complexity of the filter operation is linear in the size of the map. I also present simple enhancements that permit constant-time approximate filtering.

[1]  Peter Cheeseman,et al.  On the Representation and Estimation of Spatial Uncertainty , 1986 .

[2]  T. Speed,et al.  Gaussian Markov Distributions over Finite Graphs , 1986 .

[3]  Peter C. Cheeseman,et al.  Estimating uncertain spatial relationships in robotics , 1986, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[4]  Dan Geiger,et al.  Identifying independence in bayesian networks , 1990, Networks.

[5]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[6]  S. Umeyama,et al.  Least-Squares Estimation of Transformation Parameters Between Two Point Patterns , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Ingemar J. Cox,et al.  Dynamic Map Building for an Autonomous Mobile Robot , 1992 .

[8]  Ross D. Shachter,et al.  Global Conditioning for Probabilistic Inference in Belief Networks , 1994, UAI.

[9]  Denise Draper,et al.  Clustering Without (Thinking About) Triangulation , 1995, UAI.

[10]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[11]  Patrick Hébert,et al.  Probabilistic Map Learning: Necessity and Difficulties , 1995, Reasoning with Uncertainty in Robotics.

[12]  Xavier Boyen,et al.  Tractable Inference for Complex Stochastic Processes , 1998, UAI.

[13]  David J. Spiegelhalter,et al.  Probabilistic Networks and Expert Systems , 1999, Information Science and Statistics.

[14]  Xavier Boyen,et al.  Exploiting the Architecture of Dynamic Systems , 1999, AAAI/IAAI.

[15]  Nando de Freitas,et al.  Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks , 2000, UAI.

[16]  Rudolph van der Merwe,et al.  The unscented Kalman filter for nonlinear estimation , 2000, Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373).

[17]  Steffen L. Lauritzen,et al.  Stable local computation with conditional Gaussian distributions , 2001, Stat. Comput..

[18]  Eduardo Mario Nebot,et al.  Optimization of the simultaneous localization and map-building algorithm for real-time implementation , 2001, IEEE Trans. Robotics Autom..

[19]  Michael I. Jordan,et al.  Thin Junction Trees , 2001, NIPS.

[20]  Wolfram Burgard,et al.  Robust Monte Carlo localization for mobile robots , 2001, Artif. Intell..

[21]  John J. Leonard,et al.  Robust Mapping and Localization in Indoor Environments Using Sonar Data , 2002, Int. J. Robotics Res..

[22]  Uri Lerner,et al.  Hybrid Bayesian networks for reasoning about complex systems , 2002 .

[23]  Sebastian Thrun,et al.  FastSLAM: a factored solution to the simultaneous localization and mapping problem , 2002, AAAI/IAAI.

[24]  Sebastian Thrun,et al.  Results for outdoor-SLAM using sparse extended information filters , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[25]  Sebastian Thrun,et al.  Simultaneous localization and mapping with unknown data association using FastSLAM , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[26]  Michael Bosse,et al.  An Atlas framework for scalable mapping , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[27]  Sebastian Thrun,et al.  Robotic mapping: a survey , 2003 .

[28]  P. Rousseeuw,et al.  Wiley Series in Probability and Mathematical Statistics , 2005 .