Robótica Móvil CC5316 Clase 15: Localización Semestre Primavera 2012 Profesor: Pablo Guerrero

Localización

Grados de Dificultad Conocimiento a Priori: – Localización Local – Localización Global Proceso – Raptos Disponibilidad de Mapa: – No SLAM Ambigüedad (multimodalidad): – Resoluble localmente – Resoluble globalmente

Tipos de Mapas Listas de objetos (sensores visuales) Mapas de ocupancia (sensores de rango) Mixtos

Mapas de Ocupancia The application determines Map precision The map and feature precisions must match the sensor precisions There is a clear trade-off between precision and computational complexity Similar to belief representations, there are two main types: – Continuous – Discretized

Continous line-based

Exact cell decomposition

Fixed cell decomposition

Adaptive cell decomposition

Topological decomposition

Markov Localization Can localize from any unknown position in map Recovers from ambiguous situation However, to update the probability of all positions within the whole state space requires discrete representation of space. This can require large amounts of memory and processing power.

Kalman Filter Localization Tracks the robot and is inherently precise and efficient However, if uncertainty grows too large, the KF will fail and the robot will get lost.

Particle Filter Localization Like Markov localization, Particle Filters represent the belief state with a set of possible states, and assigning a probability of being in each of the possible states. Unlike Markov localization, the set of possible states are not constructed by discretizing the configuration space. They are a randomly generated set of particles.

Problema de Matching Las observaciones ambiguas pueden corresponder a distintos objetos o partes del mapa Para cada hipótesis de estado se debe encontrar el (los) objetos más probables de producir dicha observación

Partícula A particle is an individual state estimate. A particle is defined by its: 1.State values that determine its location in the configuration space, e.g. [x y θ] 2.A probability that indicates it’s likelihood. Particle filters use many particles for representing the belief state.

Ejemplo A Particle filter uses 3 particles to represent the position of a (white) robot in a square room. If the robot has a perfect compass, each particle is described as: x[1] = [x1 y1] x[2] = [x2 y2] x[3] = [x3 y3]

Ejemplo: Pesos Each of the particles x[1], x[2], x[3] also have associated weights w[1], w[2], w[3]. In the example below, x[2] should have the highest weight if the filter is working.

Ejemplo: Inicio El robot empieza en una posición desconocida del espacio x[0]

Ejemplo: Inicialización At time step t0: We randomly pick N=3 states represented as X0 ={x0[1], x0[2], x0[3]} For simplicity, assume known heading

Ejemplo: Predicción For Time step t1: – Randomly generate new states by propagating previous states X0 with u1 X1 - ={x1[1], x1[2], x1[3]}

Entrada: Odometría Consiste en la predicción del cambio incremental de estado Puede: – Medirse (encoders) – Estimarse (velocidad, sensores de presión, etc) Se expresa como el estado predicho en referencia al estado anterior

Composición de Odometrías Una odometría puede interpretarse como una pose relativa al sistema anterior Una pose se puede expresar como una matriz homogénea

Ruido del Proceso

Ejemplo

Importance Sampling For Time step t1: Using the measurement z1, calculate the expected weights w[i] = p( z1 | x1[i] ) for each state. W1 = {w1[1], w1[2], w1[3]}

Importance Sampling For Time step t1: To calculate p( z1 | x1[i] ) we use the sensor probability distribution. Ex: a single Gaussian of mean μ1[i] that is the expected range for the particle The gaussian variance can be taken from sensor data.

Resampling For Time step t1: Resample from the temporary state distribution based on the weights w1[2] > w1[1] > w1[3] X1 ={x1[2], x1[2], x1[1]}