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SLAM: Simultaneous Localization and Mapping: Part I. Chang Young Kim. These slides are based on: Probabilistic Robotics , S. Thrun, W. Burgard, D. Fox, MIT Press, 2005 and Zane Goodwin’s Slide from the previous class . Many images are also taken from Probabilistic Robotics .

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## SLAM: Simultaneous Localization and Mapping: Part I

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**SLAM: Simultaneous Localization and Mapping: Part I**Chang Young Kim These slides are based on: Probabilistic Robotics, S. Thrun, W. Burgard, D. Fox, MIT Press, 2005 and Zane Goodwin’s Slide from the previous class Many images are also taken from Probabilistic Robotics. http://www.probabilistic-robotics.com**Overview**• Introduction • Basics: Bayes filters • SLAM • Formulation • EKF-SLAM • FastSLAM**Motivation**Exit < Adapted from "American Maze" by Dale Wilkins>**What is SLAM?**A robot is exploring an unknown, static environment. Given: • The robot’s controls • Observations of nearby features Estimate: • Map of features • Path of the robot**Why is SLAM a hard problem?**SLAM: robot path and map are both unknown**Indoors**Undersea Underground Space SLAM Applications**Overview**• Introduction • Basics: Bayes filters • SLAM • Formulation • EKF-SLAM • FastSLAM**Terminology**• Robot State (or pose):xt =[ x, y, θ] • Position and heading • x1:t = {x1, …, xt} • Robot Controls:ut • Robot motion and manipulation • u1:t = {u1,..., ut} • Sensor Measurements:zt • Range scans, images, etc. • z1:t = {z1,..., zt} • Landmark or Map: • Landmarks or Map**Terminology**• Observation model: or • The probability of a measurement zt given that the robot is at position xt and map m. • Motion Model: • The posterior probability that action ut carries the robot from xt-1 to xt.**(**( ) ) b b l l e e x x t t Terminology • Belief: • Posterior probability • Conditioned on available data • Prediction: • Estimate before measurement data**Bayes Filter**• Prediction • Update**Overview**• Introduction • Basics:Bayes filters • SLAM • Formulation • EKF-SLAM • FastSLAM**m1**Landmark 1 z1 z3 observations . . . x1 x2 x3 xt x0 Robot poses u1 ut-1 u1 u0 controls z2 zt m2 Landmark 2 SLAM • No Map Available and No Pose Info**SLAM algorithm**• Prediction • Update**SLAM**• The observation model makes the dependence between observations and robot locations. • The joint posterior cannot be partitioned because there is dependence between observations and robot locations.**SLAM**• Correlations between landmark estimates increase monotonically as more and more observations are made. • Thus, this dependency is solved by two different methods: • Data association using a correlation matrix (EKF-SLAM). • Rao-Blackwelized Particles Filter (FastSLAM)**EKF-SLAM**• Extended Kalman Filter approximates the posterior as a Gaussian • Mean (state vector) contains robot location and map points • Covariance Matrix estimates uncertainties and relationships between each element in state vector**EKF Algorithm**Algorithm EKF( mt-1,St-1, ut, zt): Prediction: Correction: Returnmt,St 20**EKF-SLAM**Map Correlation matrix**EKF-SLAM**Map Correlation matrix**EKF-SLAM**Map Correlation matrix**FastSLAM**• EKF-SLAM Drawbacks • EKF-SLAM employs linearized models of nonlinear motion and observation models and so inherits many caveats. • Computational effort is demand because computation grows quadratically with the number of landmarks. • Better Solution : FastSLAM using a particle filter • The particle filter represents nonlinear process model and non-Gaussian pose distribution for the robot pose estimation • Rao-Blackwellized method reduces computation (*FastSLAM still linearizes the observation model i.e., EKF)**FastSLAM**• However, • Xt is trajectory rather than the single pose xt. • The trajectory Xt is represented by particles Xt(i) • Represented by factorizing called Rao-Blackwellized Filter. • Solution • by a particle filter • by EKF.**Particle Filters**Weighted samples After resampling • Represent belief by random samples • Estimation of non-Gaussian, nonlinear processes • Sampling Importance Resampling (SIR) principle • Draw the new generation of particles • Assign an importance weight to each particle • Resampling**draw xit-1from Bel(xt-1)**draw xitfrom p(xt | xit-1,ut-1) Importance factor for xit: Particle Filter Algorithm**Particle Filters**Importance Sampling Robot Motion**x, y, **Landmark 1 Landmark 2 Landmark M … FastSLAM • Rao-Blackwellized particle filtering based on landmarks [Montemerlo et al., 2002] • Each landmark is represented by a 2x2 Extended Kalman Filter (EKF) • Each particle therefore has to maintain M EKFs Particle #1 x, y, Landmark 1 Landmark 2 Landmark M … Particle #2 x, y, Landmark 1 Landmark 2 Landmark M … … Particle N**FastSLAM – Action Update**Landmark #1 Filter Particle #1 Landmark #2 Filter Particle #2 Particle #3**FastSLAM – Sensor Update**Landmark #1 Filter Particle #1 Landmark #2 Filter Particle #2 Particle #3**Weight = 0.8**Weight = 0.4 Weight = 0.1 FastSLAM – Sensor Update Particle #1 Particle #2 Particle #3**Issues will be addressed in Part II**• Computation • Convergence • Data Association**Summary**• SLAM Is Hard • SLAM problem and the essential methods for solving it. • Key implementations and demonstrations of the methods.

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