Eşzamanlı konum belirleme ve harita oluşturmaya Kalman filtre yaklaşımları

Yıl 2010, Cilt: 1 Sayı: 1, 13 - 20, 01.06.2010

Haydar Ankışhan Murat Efe

Öz

Eşzamanlı konum belirleme ve haritalama (EKBH) robotlar ve özerk araçlar tarafından, bilinmeyen bir
çevre içersinde mevcut yer ile birlikte çevrenin haritasını çıkarma veya verilen bir haritaya bağlı olarak
mevcut yer ve haritanın bilgi güncellemesi için kullanılan bir yöntemdir. EKBH son 20 yıldır robotlar ve
özerk araçlar için büyük önem arz eden bir problem olarak bilinmektedir. Bu problemi çözmek için Kalman
filtreleri, beklenti en büyütme ve parçacık filtreleri gibi bir takım istatistiksel teknikler uygulanmıştır. Bu
çalışmada daha önceki çalışmalardan farklı olarak karekök kokusuz (KKUKF) ve karekök merkez fark
(KKMFKF) Kalman filtreleri kullanılmaktadır. Filtrelerin vermiş oldukları kestirim sonuçları aynı harita ve
sınır işaretleri kullanılarak karıştırılarak (interlaced) genişletilmiş Kalman filtresi (GKF) ve kokusuz
Kalman filtresiyle ( UKF) hem pozisyon hem de robot başlığı açısal ortalama kare hataları hesaplanarak
karşılaştırılmıştır. Deneysel çalışmalardan görülmektedir ki, KKUKF ve KKMFKF EKBH probleminin
çözümüne bir alternatif olmaktadır. Konum ve başlık ortalama kare hataları ile işlem süreleri GKF, UKF ve
FASTSLAM II modellerinden daha düşük çıkmıştır.

Anahtar Kelimeler

Eşzamanlı konum belirleme ve harita oluşturma, Kara kök merkez fark Kalman filtresi, Kara kök kokusuz Kalman filtresi, Parçacık Filtreleri

Kalman filter approach for simultaneous localization and mapping

Öz

Simultaneous Localization and Mapping (SLAM) is
a method which is used by robot and autonomous
vehicles to build up a map within an unknown
environment or to update a map within a known
environment. SLAM has been a significant problem
for robots/autonomous vehicles for the last two
decades. Some statistical techniques such as Kalman
based filters, expectation maximization and particle
based filters have been used for solving this
problem. There are extensive research works to be
reported related to the Kalman filters to address
several aspects of the SLAM problem (Guivant and
Nebot, 2001, Davison and Murray, 2002, Bailey,
2002, Williams et al., 2000). Some several successful
applications have been realized for this problem; for
indoor applications (Bosse et al., 2002,Thrun et al.,
1998), underwater and underground applications
(Williams et al., 2001, Thrun et al., 2003), etc. These
type of approaches estimate and store robot/vehicle
pose and the feature positions within the
environment in the form of a complete state vector
and uncertainties in these estimates in the error
covariance matrices, and update state matrices. The
performances of this type of filters depend on the
correct a priori knowledge of process and
measurement noise state, parameter and covariance
matrices (Q and R, respectively). If not a good prior
knowledge, then the results will not be good and can
be significant degradation in performance.
The other approach to solve the SLAM problem is
expectation maximization (EM) algorithm. Which is
a statistical method to develop in the context of
maximum likelihood (ML) estimation is an ideal
option for map building, but not localization
(Aulinas et al., 2008). The EM algorithm is able to
build a map when robot/vehicle pose is known. EM
algorithm iterates in two steps; expectation step, and
maximization step. The main advantage of algorithm
with respect to the Kalman based filters is able to be
successful the corresponding data association
problem (Thrun et al., 2002).
The other used filters are particle filters which have
been successful determining robot/vehicle position
and orientation, but not to map building, that is,
landmark position and orientation. So there are no
any work to use particle filter for whole SLAM
problem, but there exists few works that deals with
the problem using a combination of particle filter
with other techniques, which are fast SLAM I
(Montemerlo and Thrun, 2003), and fast SLAM II
(Montemerlo et al., 2003). Those models divide
SLAM problem into a robot localization problem
and a collection of landmark estimation problem.
Fast SLAM uses particle filter to sample over
robot/vehicle paths, which is important for less
memory usage and computational time than a
standard extended Kalman or Kalman filters.
However, particle based filtering need to employ
large number of particles, if then, can be very close
to true pose of the vehicle/robot at each sampling
time instant (Frese et al., 2005).
In this study, the use of square root central
difference Kalman filter and square root unscented
Kalman filter is proposed for the SLAM problem.
Estimation results produced by the proposed
methods have been compared to that of interlaced
extended Kalman filter (IEKF) and unscented
Kalman filter in terms of both position and rms
robot/vehicle heading angle error for the same map
and landmarks. Results have revealed that square
root unscented Kalman filter and square root central
difference Kalman filter could be good alternatives
to be used to address the SLAM problem. They have
been successfully showed that in each case,
especially time update part, are able to improve
performance of SLAM problem solution and these
filters, especially SRCD Kalman filter, can provide
robust and accurate solutions. Simulation results
show that the proposed methods have produced
better heading angle, process time and position
error in comparison to the IEKF, UKF and
FASTSLAM II for the proposed scenario.

Anahtar Kelimeler

Simultaneous Localization and Mapping, Square Root Unscented Kalman Filter, Square Root Central Difference Kalman Filter, Particle Filter