Implicit Sampling for Path Integral Control, Monte Carlo Localization, and SLAM

Implicit sampling is a recently developed variationally enhanced sampling method that guides its samples to regions of high probability, so that each sample carries information. Implicit sampling may thus improve the performance of algorithms that rely on Monte Carlo (MC) methods. Here the applicability and usefulness of implicit sampling for improving the performance of MC methods in estimation and control is explored, and implicit sampling based algorithms for stochastic optimal control, stochastic localization, and simultaneous localization and mapping (SLAM) are presented. The algorithms are tested in numerical experiments where it is found that fewer samples are required if implicit sampling is used, and that the overall runtimes of the algorithms are reduced.

[1]  Wolfram Burgard,et al.  A Probabilistic Approach to Concurrent Mapping and Localization for Mobile Robots , 1998, Auton. Robots.

[2]  Wolfram Burgard,et al.  A Tutorial on Graph-Based SLAM , 2010, IEEE Intelligent Transportation Systems Magazine.

[3]  A. Chorin,et al.  Implicit particle filtering for models with partial noise, and an application to geomagnetic data assimilation , 2011, 1109.3664.

[4]  Wolfram Burgard,et al.  Monte Carlo localization for mobile robots , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[5]  J. Geweke,et al.  BAYESIAN INFERENCE IN ECONOMETRIC MODELS USING , 1989 .

[6]  Stefan Schaal,et al.  A Generalized Path Integral Control Approach to Reinforcement Learning , 2010, J. Mach. Learn. Res..

[7]  Robert F. Stengel,et al.  Optimal Control and Estimation , 1994 .

[8]  Peter Reynolds,et al.  Monte Carlo Methods In Ab Initio Quantum Chemistry , 1994 .

[9]  David Mautner Himmelblau,et al.  Applied Nonlinear Programming , 1972 .

[10]  Robert N. Miller,et al.  A potential implicit particle method for high-dimensional systems , 2013 .

[11]  Eric Vanden-Eijnden,et al.  DATA ASSIMILATION IN THE LOW NOISE, ACCURATE OBSERVATION REGIME WITH APPLICATION TO THE KUROSHIO CURRENT , 2012 .

[12]  Matthias Morzfeld,et al.  Conditions for successful data assimilation , 2013, 1303.2714.

[13]  Matthias Morzfeld,et al.  Implicit particle filters for data assimilation , 2010, 1005.4002.

[14]  Matthias Morzfeld,et al.  Path Integral Formulation of Stochastic Optimal Control with Generalized Costs , 2014, 1406.7869.

[15]  H. J. Moore,et al.  Overview of the Mars Pathfinder mission and assessment of landing site predictions. , 1997, Science.

[16]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

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

[18]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[19]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[20]  J. Geweke,et al.  Bayesian Inference in Econometric Models Using Monte Carlo Integration , 1989 .

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

[22]  Sebastian Thrun,et al.  FastSLAM 2.0: an improved particle filtering algorithm for simultaneous localization and mapping that provably converges , 2003, IJCAI 2003.

[23]  Sebastian Thrun,et al.  Probabilistic robotics , 2002, CACM.

[24]  E. Vanden-Eijnden,et al.  Rare Event Simulation of Small Noise Diffusions , 2012 .

[25]  Hugh F. Durrant-Whyte,et al.  Field Robots , 2001, ISRR.

[26]  W. Fleming.  Exit probabilities and optimal stochastic control , 1977 .

[27]  E. Vanden-Eijnden,et al.  Data Assimilation in the Low Noise Regime with Application to the Kuroshio , 2012, 1202.4952.

[28]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[29]  H. Kappen.  Path integrals and symmetry breaking for optimal control theory , 2005, physics/0505066.

[30]  Hugh F. Durrant-Whyte,et al.  Uncertain geometry in robotics , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[31]  A. Chorin,et al.  Implicit sampling for particle filters , 2009, Proceedings of the National Academy of Sciences.

[32]  A. Chorin,et al.  Stochastic Tools in Mathematics and Science , 2005 .

[33]  Sebastian Thrun,et al.  FastSLAM: A Scalable Method for the Simultaneous Localization and Mapping Problem in Robotics , 2007 .

[34]  H. Kappen.  Linear theory for control of nonlinear stochastic systems. , 2004, Physical review letters.

[35]  Matthias Morzfeld,et al.  A random map implementation of implicit filters , 2011, J. Comput. Phys..

[36]  A. Chorin,et al.  Implicit Particle Methods and Their Connection with Variational Data Assimilation , 2012, 1205.1830.

[37]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[38]  Manuela M. Veloso,et al.  Corrective Gradient Refinement for mobile robot localization , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[39]  H. Kappen.  An introduction to stochastic control theory, path integrals and reinforcement learning , 2007 .

[40]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[41]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

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

[43]  Hugh F. Durrant-Whyte,et al.  A solution to the simultaneous localization and map building (SLAM) problem , 2001, IEEE Trans. Robotics Autom..

[44]  Manuela M. Veloso,et al.  Localization and navigation of the CoBots over long-term deployments , 2013, Int. J. Robotics Res..

[45]  Kevin P. Murphy,et al.  Bayesian Map Learning in Dynamic Environments , 1999, NIPS.

[46]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[47]  Wolfram Burgard,et al.  A system for volumetric robotic mapping of abandoned mines , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).