Incremental Non-Gaussian Inference for SLAM Using Normalizing Flows

—This paper presents normalizing flows for incre- mental smoothing and mapping (NF-iSAM), a novel algorithm for inferring the full posterior distribution in SLAM problems with nonlinear measurement models and non-Gaussian factors. NF-iSAM exploits the expressive power of neural networks, and trains normalizing flows to model and sample the full posterior. By leveraging the Bayes tree, NF-iSAM enables efficient incre- mental updates similar to iSAM2, albeit in the more challenging non-Gaussian setting. We demonstrate the advantages of NF- iSAM over state-of-the-art point and distribution estimation algorithms using range-only SLAM problems with data association ambiguity. NF-iSAM presents superior accuracy in describing the posterior beliefs of continuous variables (e.g., position) and discrete variables (e.g., data association).

[1]  J. Leonard,et al.  Nested Sampling for Non-Gaussian Inference in SLAM Factor Graphs , 2021, IEEE Robotics and Automation Letters.

[2]  Ricardo Baptista,et al.  Coupling Techniques for Nonlinear Ensemble Filtering , 2019, SIAM Review.

[3]  John J. Leonard,et al.  A Multi-Hypothesis Approach to Pose Ambiguity in Object-Based SLAM , 2021, 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[4]  John J. Leonard,et al.  Consensus-Informed Optimization Over Mixtures for Ambiguity-Aware Object SLAM , 2021, 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[5]  Kieran A. Murphy,et al.  Implicit-PDF: Non-Parametric Representation of Probability Distributions on the Rotation Manifold , 2021, ICML.

[6]  Jonathan P. How,et al.  NF-iSAM: Incremental Smoothing and Mapping via Normalizing Flows , 2021, 2021 IEEE International Conference on Robotics and Automation (ICRA).

[7]  John J. Leonard,et al.  Advances in Inference and Representation for Simultaneous Localization and Mapping , 2021, Annu. Rev. Control. Robotics Auton. Syst..

[8]  S. Lange,et al.  Advancing Mixture Models for Least Squares Optimization , 2021, IEEE Robotics and Automation Letters.

[9]  Ivan Kobyzev,et al.  Normalizing Flows: An Introduction and Review of Current Methods , 2020, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Eric Nalisnick,et al.  Normalizing Flows for Probabilistic Modeling and Inference , 2019, J. Mach. Learn. Res..

[11]  Timothy Bretl,et al.  PoseRBPF: A Rao–Blackwellized Particle Filter for 6-D Object Pose Tracking , 2019, IEEE Transactions on Robotics.

[12]  John J. Leonard,et al.  On Reference Solutions to Non-Gaussian SLAM Factor Graphs , 2021, ArXiv.

[13]  John Leonard,et al.  Characterizing Marginalization and Incremental Operations on the Bayes Tree , 2021, WAFR.

[14]  J. Leonard,et al.  Towards Real-Time Non-Gaussian SLAM for Underdetermined Navigation , 2020, 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[15]  Ricardo Baptista,et al.  An adaptive transport framework for joint and conditional density estimation , 2020, ArXiv.

[16]  Brendan Englot,et al.  Variational Filtering with Copula Models for SLAM , 2020, 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[17]  Gurtej Kanwar,et al.  Normalizing Flows on Tori and Spheres , 2020, ICML.

[18]  David Baxter,et al.  Probabilistic Data Association via Mixture Models for Robust Semantic SLAM , 2019, 2020 IEEE International Conference on Robotics and Automation (ICRA).

[19]  J. Speagle.  dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and evidences , 2019, Monthly Notices of the Royal Astronomical Society.

[20]  Natalia Gimelshein,et al.  PyTorch: An Imperative Style, High-Performance Deep Learning Library , 2019, NeurIPS.

[21]  John Leonard,et al.  Non-parametric Mixed-Manifold Products using Multiscale Kernel Densities , 2019, 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[22]  Michael S. Brown,et al.  Noise Flow: Noise Modeling With Conditional Normalizing Flows , 2019, 2019 IEEE/CVF International Conference on Computer Vision (ICCV).

[23]  Iain Murray,et al.  Neural Spline Flows , 2019, NeurIPS.

[24]  R Devon Hjelm,et al.  Leveraging exploration in off-policy algorithms via normalizing flows , 2019, CoRL.

[25]  Yaoliang Yu,et al.  Sum-of-Squares Polynomial Flow , 2019, ICML.

[26]  Michael Kaess,et al.  MH-iSAM2: Multi-hypothesis iSAM using Bayes Tree and Hypo-tree , 2019, 2019 International Conference on Robotics and Automation (ICRA).

[27]  2019 International Conference on Robotics and Automation (ICRA) , 2019 .

[28]  Dehann Fourie,et al.  Multimodal Semantic SLAM with Probabilistic Data Association , 2019, 2019 International Conference on Robotics and Automation (ICRA).

[29]  Kee-Eung Kim,et al.  Imitation Learning via Kernel Mean Embedding , 2018, AAAI.

[30]  Youssef M. Marzouk,et al.  Inference via Low-Dimensional Couplings , 2017, J. Mach. Learn. Res..

[31]  Y. Marzouk,et al.  Transport Map Accelerated Markov Chain Monte Carlo , 2014, SIAM/ASA J. Uncertain. Quantification.

[32]  Frank Dellaert,et al.  Factor Graphs for Robot Perception , 2017, Found. Trends Robotics.

[33]  Dehann Fourie,et al.  Multi-modal and inertial sensor solutions for navigation-type factor graphs , 2017 .

[34]  Sean L. Bowman,et al.  Probabilistic data association for semantic SLAM , 2017, 2017 IEEE International Conference on Robotics and Automation (ICRA).

[35]  Gerhard Neumann,et al.  The Kernel Kalman Rule - Efficient Nonparametric Inference with Recursive Least Squares , 2017, AAAI.

[36]  Lei Xu,et al.  Input Convex Neural Networks : Supplementary Material , 2017 .

[37]  I. Reid,et al.  Past, Present, and Future of Simultaneous Localization and Mapping: Toward the Robust-Perception Age , 2016, IEEE Transactions on Robotics.

[38]  John J. Leonard,et al.  A nonparametric belief solution to the Bayes tree , 2016, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[39]  John Salvatier,et al.  Probabilistic programming in Python using PyMC3 , 2016, PeerJ Comput. Sci..

[40]  Todd P. Coleman,et al.  A scalable framework to transform samples from one continuous distribution to another , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[41]  Shakir Mohamed,et al.  Variational Inference with Normalizing Flows , 2015, ICML.

[42]  Sergey Ioffe,et al.  Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift , 2015, ICML.

[43]  Kenji Fukumizu,et al.  Monte Carlo Filtering Using Kernel Embedding of Distributions , 2014, AAAI.

[44]  Sebastian Tschiatschek,et al.  Introduction to Probabilistic Graphical Models , 2014 .

[45]  Rui Ma,et al.  Efficient Bayesian inference methods via convex optimization and optimal transport , 2013, 2013 IEEE International Symposium on Information Theory.

[46]  Marcus Obst,et al.  Switchable constraints and incremental smoothing for online mitigation of non-line-of-sight and multipath effects , 2013, 2013 IEEE Intelligent Vehicles Symposium (IV).

[47]  K. Fukumizu,et al.  Kernel Embeddings of Conditional Distributions: A Unified Kernel Framework for Nonparametric Inference in Graphical Models , 2013, IEEE Signal Processing Magazine.

[48]  Fabio Tozeto Ramos,et al.  Multi-modal estimation with kernel embeddings for learning motion models , 2013, 2013 IEEE International Conference on Robotics and Automation.

[49]  John J. Leonard,et al.  Robust incremental online inference over sparse factor graphs: Beyond the Gaussian case , 2013, 2013 IEEE International Conference on Robotics and Automation.

[50]  Nicolas Bonnotte,et al.  From Knothe's Rearrangement to Brenier's Optimal Transport Map , 2012, SIAM J. Math. Anal..

[51]  Gian Diego Tipaldi,et al.  Dynamic Covariance Scaling for Robust Map Optimization Pratik , 2013 .

[52]  Le Song,et al.  Kernel Bayes' rule: Bayesian inference with positive definite kernels , 2013, J. Mach. Learn. Res..

[53]  Edwin Olson,et al.  Inference on networks of mixtures for robust robot mapping , 2013, Int. J. Robotics Res..

[54]  Gal Elidan,et al.  Nonparanormal Belief Propagation (NPNBP) , 2012, NIPS.

[55]  F. Dellaert.  Factor Graphs and GTSAM: A Hands-on Introduction , 2012 .

[56]  Gregory S. Chirikjian,et al.  The Banana Distribution is Gaussian: A Localization Study with Exponential Coordinates , 2012, Robotics: Science and Systems.

[57]  Bernhard Schölkopf,et al.  A Kernel Two-Sample Test , 2012, J. Mach. Learn. Res..

[58]  Frank Dellaert,et al.  iSAM2: Incremental smoothing and mapping using the Bayes tree , 2012, Int. J. Robotics Res..

[59]  Larry A. Wasserman,et al.  Sparse Nonparametric Graphical Models , 2012, ArXiv.

[60]  Youssef M. Marzouk,et al.  Bayesian inference with optimal maps , 2011, J. Comput. Phys..

[61]  Le Song,et al.  Kernel Belief Propagation , 2011, AISTATS.

[62]  Frank Dellaert,et al.  The Bayes Tree: An Algorithmic Foundation for Probabilistic Robot Mapping , 2010, WAFR.

[63]  András György,et al.  A Markov-Chain Monte Carlo Approach to Simultaneous Localization and Mapping , 2010, AISTATS.

[64]  Stephan Roth,et al.  Navigating with ranging radios: Five data sets with ground truth , 2009, J. Field Robotics.

[65]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[66]  Guillaume Carlier,et al.  From Knothe's Transport to Brenier's Map and a Continuation Method for Optimal Transport , 2008, SIAM J. Math. Anal..

[67]  Frank Dellaert,et al.  iSAM: Incremental Smoothing and Mapping , 2008, IEEE Transactions on Robotics.

[68]  C. Villani.  Optimal Transport: Old and New , 2008 .

[69]  Javier González,et al.  A pure probabilistic approach to range-only SLAM , 2008, 2008 IEEE International Conference on Robotics and Automation.

[70]  Le Song,et al.  A Hilbert Space Embedding for Distributions , 2007, Discovery Science.

[71]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[72]  Frank Dellaert,et al.  iSAM: Fast Incremental Smoothing and Mapping with Efficient Data Association , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[73]  Frank Dellaert,et al.  Square Root SAM: Simultaneous Localization and Mapping via Square Root Information Smoothing , 2006, Int. J. Robotics Res..

[74]  J. Skilling.  Nested sampling for general Bayesian computation , 2006 .

[75]  Hugh F. Durrant-Whyte,et al.  Simultaneous localization and mapping: part I , 2006, IEEE Robotics & Automation Magazine.

[76]  Frank Dellaert,et al.  A Markov Chain Monte Carlo Approach to Closing the Loop in SLAM , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[77]  Anthony Widjaja,et al.  Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond , 2003, IEEE Transactions on Neural Networks.

[78]  V. Bogachev,et al.  Triangular transformations of measures , 2005 .

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

[80]  William T. Freeman,et al.  Nonparametric belief propagation , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

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

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

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

[84]  P. Heggernes,et al.  Finding Good Column Orderings for Sparse QR Factorization , 1996 .

[85]  Lutz Prechelt,et al.  Early Stopping-But When? , 1996, Neural Networks: Tricks of the Trade.

[86]  Prakash P. Shenoy,et al.  Probability propagation , 1990, Annals of Mathematics and Artificial Intelligence.

[87]  Robert E. Tarjan,et al.  Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs , 1984, SIAM J. Comput..