Abstract—A novel approach to estimate localizability for
mobile robots is presented based on probabilistic grid map
(PGM). Firstly, a static localizability matrix is proposed for
off-line estimation over the priori PGM. Then a dynamic
localizability matrix is proposed to deal with unexpected
dynamic changes. These matrices describe both localizability
index and localizability direction quantitatively. The validity of
the proposed method is demonstrated by experiments in
different typical environments. Furthermore, two typical
localization-related applications, including active global
localization and pose tracking, are presented for illustrating the
effectiveness of the proposed localizability estimation method.
I. INTRODUCTION
In the field of mobile robotics, reliable localization
performance is an essential issue for many typical tasks such
as navigation [1] and exploration [2]. In terms of different
applications, localization problem can be classified into
global localization and pose tracking. The former one is to
determine robot pose in absence of initial location estimation
[3]. Because of the initial uncertainty, location estimation
often falls into a multi-hypothesis distribution and can’t
disambiguate similar poses [4]. Special landmarks [5] and
additional sensors [3] are often used to deal with this problem,
but high cost and non-applicability in complex environments
limit their applications. The latter one is to maintain a fast and
precise track of robot pose during the whole task-while [6].
Although several algorithms based on Extended Kalman Filter
[7] and Particle Filter [8] have great performance in
localization, pose tracking performance can still be greatly
decreased because of several dynamic changes of
environment such as dynamic obstacles [9] and crowds [10].
In order to solve these problems, researchers pay more and
more attention to estimating localizability of mobile robots [1,
2]. Through analyzing localizability of mobile robots in
different situations and finding in which situation robot has
the best localization performance, researchers can find
strategies to improve current localization algorithms. In [3,
11], authors estimate localizability of every possible pose of
mobile robot and select optimal actions during global
localization process, so that the hypotheses set is best
disambiguated. Authors in [2] implement an entropy-based
localizability estimation algorithm that evaluates every
candidate location in path-planning. The presented method
Zhe Liu, Weidong Chen (corresponding author), Yong Wang, and
Jingchuan Wang are all with the Department of Automation, Shanghai Jiao
Tong University, and Key Laboratory of System Control and Information
Processing, Ministry of Education of China, Shanghai 200240, China, and
State Key Laboratory of Robotics and System (HIT), Harbin 150001, China
( e-mail: {liuzhesjtu, wdchen, duijue, & jchwang}@ sjtu.edu.cn).
can maintain a precise track of robot pose during exploration.
Both works have improved localization performance. So
localizability estimation is a promising means to deal with the
current localization problems of mobile robots.
According to the different forms of map description,
recent researches of localizability estimation are mainly
divided into two categories. One is localizability estimation
based on probabilistic grid map (PGM) [1], which
demonstrates localizability through entropy of localization
probability distribution. Entropy is a one-dimensional
variable, which can only demonstrate overall performance of
localizability and can’t reflect directional properties of
localizability. However, localizability of a robot in a certain
pose may be inconsistent in different directions. And the
requirement of omni-directional sensors also limits this
category’s applications. The other category is localizability
estimation under geometric map, which demonstrates
structure of map (line and arc) through analytical formulas
explicitly [12, 13]. In order to estimate localizability of robot
equipped with laser range finder (LRF) in geometric map,
work in [12] calculates expected laser data and slope of
scanned environmental surfaces to get the Fisher information
matrix (FIM). This matrix can reflect directional properties of
localizability but it doesn’t take the influence of the
uncertainty of map information into consideration [14, 15].
And the analytical expression of map structure is also difficult
to get, so this method only remains in the simulation stage.
Based on the above analysis, this paper proposes a novel
approach to estimate localizability of mobile robots using
PGM. A localizability matrix is proposed and this matrix
describes both index and directional properties of
localizability quantitatively. We compare the proposed
method with classical localization algorithm and introduce
two typical applications in terms of the localizability matrix.
The experimental results demonstrate the validity of our
proposed method.
II. LOCALIZABILITY ESTIMATION
In [12], in order to estimate localizability of mobile
robots and point out the worst direction of localizability index,
FIM of localization is defined as a function of expected laser
data [12]:
T
2
1
()
n
iE iE
i
laser
rr
IP
PP
where
is the pose of robot,
is the expected distance
scanned by the
LRF ray and
is the variance of noise.
Localizability Estimation for Mobile Robots based on Probabilistic
Grid Map and its Applications to Localization
Zhe Liu, Weidong Chen, Yong Wang, Jingchuan Wang
2012 IEEE International Conference on
Multisensor Fusion and Integration for Intelligent Systems (MFI)
September 13-15, 2012. Hamburg, Germany
978-1-4673-2511-0/12/$31.00 ©2012 IEEE 46