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MIT 16 412J - Particle Filters and Their Applications

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Particle Filters and Their Applications Kaijen Hsiao Jason Miller Cognitive Robotics April 11, 2005 Henry de Plinval-Salgues 12 Why Particle Filters? • Tool for tracking the state of a dynamicsystem modeled by a Bayesian network(Robot localization, SLAM, robot faultdiagnosis) • dimensional problems • Key idea: Find an approximate solutionusing a complex model rather than an exact solution using a simplified model Similar applications to Kalman Filters, but computationally tractable for large/high-Why should you be interested in particle filters? Because, like Kalman filters, they’re a great way to track the state of a dynamic system for which you have a Bayesian model. That means that if you have a model of how the system changes in time, possibly in response to inputs, and a model of what observations you should see in particular states, you can use particle filters to track your belief state. Applications that we’ve seen in class before, and that we’ll talk about today, are Robot localization, SLAM, and robot fault diagnosis. So why should you use particle filters instead of Kalman filters? Well, the main reason is that for a lot of large or high-dimensional problems, particle filters are tractable whereas Kalman filters are not. The key idea is that a lot of methods, like Kalman filters, try to make problems more tractable by using a simplified version of your full, complex model. Then they can find an exact solution using that simplified model. But sometimes that exact solution is still computationally expensive to calculate, and sometimes a simplified model just isn’t good enough. So then you need something like particle filters, which let you use the full, complex model, but just find an approximate solution instead. 23 Outline • ) • Particle Filters in SLAM (Henry) • Particle Filters in Rover Fault Diagnosis (Jason) Introduction to Particle Filters (Kaijen34 Outline • Introduction to Particle Filters – Demo! – – Quick Review of Robot Localization/Problem – Overview of Particle Filters – The Particle Filter Algorithm Step by Step • Particle Filters in SLAM • Particle Filters in Rover Fault Diagnosis Formalization of General Problem: Bayes Filters with Kalman Filters 45 Demo of Robot Localization University of Washington Robotics and State Estimation Lab http://www.cs.washington.edu/ai/Mobile_Robotics/mcl/ What you see here is a demo from the University of Washington Robotics and State Estimation Lab. This is a frozen panel of the beginning of a robot localization task. The little blue circle is our best guess as to where the robot is now. The little red dots are different hypotheses for where the robot might be—at the beginning of the task, we have no idea where the robot is, so the hypotheses cover the entire space. As we’ll see later, each hypothesis is called a ‘particle’. The lines extending from the robot are sensor measurements taken by a laser rangefinder. The reason the lines extend well past the walls on the map is because the robot isn’t actually in that location. The robot movement comes from a person driving the robot manually; there is no automatic exploration going on. 56 Demo of Robot Localization University of Washington Robotics and State Estimation Lab http://www.cs.washington.edu/ai/Mobile_Robotics/mcl/ As you watch the animated gif, the best-guess location of the robot will jump around as the most likely hypothesis changes. As the robot moves and takes measurements, it figures out that most of the hypotheses it started with are pretty unlikely, so it gets rid of those. Pretty soon, the number of hypotheses is reduced to a few clouds in the hallway; the robot is actually in the hallway, but there’s a lot of symmetry there, so it’s not sure exactly where. Then it’s down to two hypotheses, and when the robot finally enters a room and looks around, it becomes clear that its current best hypothesis was actually correct. 67 Outline • Introduction to Particle Filters – Demo! – – Quick Review of Robot Localization/Problem – Overview of Particle Filters – The Particle Filter Algorithm Step by Step • Particle Filters in SLAM • Particle Filters in Rover Fault Diagnosis Formalization of General Problem: Bayes Filters with Kalman Filters Now I will discuss the formalization of the general problem that both particle filters and Kalman filters solve, which is called Bayes Filtering. 78 • Used for estimating the state of a dynamical system from sensor measurements • Predict/update cycle • Bayes Filters Examples of Bayes Filters: – Kalman Filters – Particle Filters Bayes Filtering is the general term used to discuss the method of using a predict/update cycle to estimate the state of a dynamical system from sensor measurements. As mentioned, two types of Bayes Filters are Kalman filters and particle filters. 89 Trying to find: belief about the current state p(xt | d ) t t t t), t | x , u ) Bayes Filters cont. x state variable u inputs z observations d data (inputs and observations combined) o…tGiven: u , z , perceptual model p(z | xaction model p(xt-1 t-1XNow we introduce the variables we will be using. X is the state variable, and t is the state variable at time t. U is the inputs to your system, z is the observations made by the sensors, and d just refers to inputs and observations together. What the Bayes Filter is trying to find at any point in time is the belief about the current state, which is the probability of xt given all the data we’ve seen so far. What we are given is the inputs, the observations, the perceptual model, which is the probability that you’ll see a particular observation give n that you’re in some state at time t, and the action model, which is the probability that you’ll end up in state xt at time t, assuming that you started in state xt-1 at time t-1, and input ut-1 to your system. 910 Outline • Introduction to Particle Filters – Demo! – – Quick Review of Robot Localization/Problem – Overview of Particle Filters – The Particle Filter Algorithm Step by Step • Particle Filters in SLAM • Particle Filters in Rover Fault Diagnosis Formalization of General Problem: Bayes Filters with Kalman Filters Now I will give a quick review of robot localization and show what the problem is with doing localization with Kalman filters. 1011 Robot Localization x = (x,y,q) motion model p(xt | x , u ): t t): t-1


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