Eşzamanlı konum belirleme ve harita oluşturmaya Kalman filtre yaklaşımları

Abstract

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.

Keywords

• 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

Abstract

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.

Keywords

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