使用鲁棒扩展H∞滤波的移动机器人定位

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Mobile robot localization using

robust extended H

‘

filtering

Fuwen Yang

, Zidong Wang

, Stanislao Lauria

, and Xiaohui Liu

School of Information Science and Engineering, East China University of Science and Technology, Shanghai, People’s

Republic of China

Department of Information Systems and Computing, Brunel University, Uxbridge, UK

The manuscript was received on 14 April 2009 and was accepted after revision for publication on 3 August 2009.

DOI: 10.1243/09596518JSCE791

Abstract: In this paper, a novel methodology is provided for accurate localization of a mobile

robot using autonomous navigation based on internal and external sensors. A new robust

extended H

‘

filter is developed to deal with the non-linear kinematic model of the robot and

the non-linear distance measurements, together with process and measurement noises. The

proposed filter relies on a two-step prediction–correction structure, which is similar to a

Kalman filter. Simulations are provided to demonstrate the effectiveness of the proposed

method.

Keywords: autonomous m obile robot, localization, robust extended H

‘

filtering, navigation

1 INTRODUCTION

Localization is one of the fundamental problems for

autonomous navigation of mobile robots. The

knowledge about the position and orientation of a

robot is useful in different tasks, such as office

delivery and obstacle avoidance, for example. In the

past, a variety of approaches for mobile robot

localization have been developed. They mainly differ

in the techniques used to represent the belief of the

robot about its current position, and in the type of

sensor information that is used for localization. For

the robot to be really autonomous, only on-board

sensors must be used to perform localization. This

prevents the robot from using direct configuration

measurements, and calls for suitable numerical

processing of the data provided by the sensor

equipment. The on-board sensors allow two differ-

ent kinds of localization: relative and absolute. The

former is realized through the data provided by

sensors measuring the dynamics of variables inter-

nal to the vehicle. One of the common methods used

to estimate the current position is dead reckoning

using internal sensors [1, 2], such as optical incre-

mental encoders, which are fixed to the axis of the

driving wheels or to the steering axis of the vehicle.

At each sampling instant the position is estimated on

the basis of the encoder increments along the

sampling interval. A drawback of this method is that

the errors of each measure are cumulative. The error

in dead reckoning increases as the robot travels. This

heavily degrades the position and orientation esti-

mates of the vehicle, especially for long and winding

trajectories [3].

Absolute loc alization is performed by processing

the data provided by a proper set of sensors

measuring some parameters of the environment in

which the vehicle is operating. External sensor

devices, such as a laser scanner or sonar, are

generally used for this purpose. They are fixed to

the vehicle and measure the distance with respect to

parts of the known environment [2, 4]. They are also

widely utilized for the guidance of autonomous

vehicles for obstacle avoidance in unknown envir-

onments [5, 6]. The main drawback of absolute

measures is their dependence on the characteristics

of the environment. Possible changes to environ-

mental parameters may give rise to an erroneous

interpretation of the measurements provided by the

localization algorithm.

*Corresponding author: Department of Information Systems and

Computing, Brunel University, Uxbridge, Middlesex UB8 3PH,

UK.

email: Zidong.Wang@brunel.ac.uk

1067

JSCE791 Proc. IMechE Vol. 223 Part I: J. Systems and Control Engineering

In order to obtain an accurate localization for a

mobile robot, an efficient method is to fuse together

relative and absolute measurements using sensors of

different natures. For this purpose, the localization

problem has been extensively studied in the robotics

literature (see, for instance, references [7–11], and the

references therein). The mainstream approach for

robot localization is Bayesian estimation, which is

based on stochastic assumptions about the process

and measurement errors, and is aimed at construct-

ing the posterior density of the current robot state,

conditioned on all available measurements. In parti-

cular, when the process and measurement error

processes are assumed Gaussian, the Bayesian ap-

proach results in the classical extended Kalman

filtering (EKF) framework (see references [12–14]).

However, in robotics applications, the distribution of

the sensor and process noise is generally multimodal

and imprecisely known, and the non-linearities of the

system may seriously degrade the EKF performance.

These limitations have been recognized in the

literature, and several schemes have been proposed

to overcome them. Notably, an adaptive EKF ap-

proach for online estimation of the noise statistics has

been proposed in references [9], [10], and [15], and

joint Bayesian hypothesis testing and Kalman filtering

have been proposed in reference [16]. A probabilistic

confidence set approach has been presented in

reference [11], which is optimal over a certain class

of noise distributions. A Monte Carlo approach,

where the noise density is represented by means of

a set of randomly drawn samples, is proposed in

reference [17]. The key idea of particle-filter-based

methods is to approximate the densities through

samples (particles) according to the posterior dis-

tribution over robot poses [17]. The particle repre-

sentation therefore, can provide universal density

approximators without the assumption of Gaussian

distribution and can adapt to the available computa-

tional resources by controlling the number of sam-

ples. The Markov-chain-Monte-Carlo-based method

provides a posterior distribution estimation over

robot poses [18]. Piecewise constant functions are

used instead of Gaussians to approximate the

distribution. However, the computation of the piece-

wise constant representation is very demanding.

In this paper, an alternative to an adaptive EKF

approach, called the robust extended H

‘

filtering

method, is proposed. It combines the data provided

by internal and external sensors to estimate the

robot’s position. The advantage of the robust ex-

tended H

‘

filtering technique is that it can consider

non-linear systems with unknown process noises and

measurement noises. It is suitable for use on the

kinematic model of the robot and data obtained from

sensors. The techniques proposed here are superior

to the EKF techniques proposed in the literature [19],

for the estimation of robot localization by considering

the linearization error and non-Gaussian noises in

process and measurement. The main novelty of the

proposed robust extended H

‘

filtering technique is its

ability to tolerably estimate robot localization in an

unknown environment. The computation of the

robust extended H

‘

filtering method is similar to the

EKF. It can be implemented online.

The remainder of this paper is organized as

follows. In section 2, the kinematics of the mobile

robot are described and the scheme of absolute

measurements is provided. A novel robust extended

‘

filtering algorithm is developed in section 3 for

handling non-linear processes and measurements,

and unknown noises. In section 4 a numerical

simulation is provided to demon strate the effective -

ness of the proposed algorithm. Some concluding

remarks are provided in section 5.

Notation

The notation X > Y (respectively, X . Y) where X and

Y are symmetric matrices, means that X 2 Y is positive

semi-definite (respectively, positive definite). The

superscript T stands for matrix transposition. By

, we denote the product f

. It is denoted that

Gramian matrix R

5 ^x, x&, where ^x, x& stands for the

inner product of x,i.e.^x, x& 5 xx

, and x is a vector.

2 KINEMATICS OF THE MOBILE ROBOT AND

THE ABSOLUTE MEASUREMENT

Consider a unicycle-like mobile robot with two

driving wheels, mounted on the left and right-hand

sides of the robot, with their common axis passing

through the centre of the robot (see Fig. 1). Localiza-

tion of this mobile robot in a two-dimensional space

requires knowledge of the coordinates of the mid-

point between the two driving wheels and of the

angle between the main axis of the robot and the

direction. The kinema tic model of the unicycle robot

is described by the following equations

xxtðÞ~vtðÞcos h tðÞ

yytðÞ~vtðÞsin h tðÞ

hh tðÞ~v tðÞ

ð1Þ

where

1068 Fuwen Yang, Zidong Wang, Stanislao Lauria, and Xiaohui Liu

Proc. IMechE Vol. 223 Part I: J. Systems and Control Engineering JSCE791

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