Robot Localization With Particles Filter Using Gpu

Robot Localization with Particles Filter Using GPU
Olmer Garcia Mechanical Computational Department UNICAMP
Abstract
The article present the description of the nal project of the course IM434. The particle lters, also known as a sequential Monte Carlo method (SMC), is a sophisticated model estimation technique based on simulation. This project implement a particles lter for localization(know the position) of a simulated Ackerman car robot which use a simplied kinematic model with input the linear displacement and the steer angle with some Gaussian noise. The car has integrated a simulated GPS and a compass which has Gaussian noise. The program described here was designed in a client server architecture, where the client is a web program(HTML5+JS+AJAX) responsible for the task ofvisualization, and in the server is implemented the particle lter algorithm using CUDA and Thrust libraries with the idea to reduce the time of calculus of the particle lter.

1 Mathematical Background
The mathematical background is divided in two sections the car robot model and the particles lter algorithm.

1.1 Car Robot model
The car robot model is described by the kinematic simpliedmodel of a Ackerman car in the plane xy which can be described by gure 1. The position of the vehicle can be described by three variables x, y and θ know like the state vector of the car x. In a discrete time the state equation can be aproximated to     xk−1 + d · cos(θk−1 ) xk  yk  =  yk−1 + d · sin(θk−1 )  d θk θk−1 + L · tan(ψ) where , L is the distance between a tires of the car , dis a input composed by the distance plus a Gaussian noise N (0, distnoise ), ψ is a input composed by steer angle plus a Gaussian noise N (0, steeringnoise ).

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1 Mathematical Background

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Fig. 1:

bicycle model for the ackerman car

by

The GPS and the compass result are the measure vector y which is described

 xk + N (0, gpsnoise )  yk + N (0, gpsnoise ) yk =  θk + N (0,compassnoise ) 

1.2 Particles lter algorithm
The mathematical algorithm is described in the next step 1. Generate the state xp for P particles using uniform random distribution   U (xmin , xmax ) xp =  U (ymin , ymax )  U (0, 2π) 2. Obtain xk and yk
p 3. For each particle p, obtain xp ,yk and probability P (xp |yk ) = wp . In this k k problem , assuming that the sensor has error with anormal distribution N (0, σ) and the sensor measures independent is just the product of each sensor i. N sensor

wp =

where σi is the standard deviation of each sensor. 4. Re sampling the particles. Here many algorithm exist , which can be classied in multinomial , residual , stratied and systematic re-sampling [2]. This part of the algorithm is not trivial to paralyze and dierent approachhave been studied [3, 1]. In this project the residual method

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1 √ 1 e2 2πσi

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p y −yki ki σi 2

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