Convergence and consistency analysis for extended Kalman filter based SLAM

This paper investigates the convergence properties and consistency of Extended Kalman Filter (EKF) based simultaneous localization and mapping (SLAM) algorithms. Proofs of convergence are provided for the nonlinear two-dimensional SLAM problem with point landmarks observed using a range-and- bearing sensor. It is shown that the robot orientation uncertainty at the instant when landmarks are first observed has a significant effect on the limit and/or the lower bound of the uncertainties of the landmark position estimates. This paper also provides some insights to the inconsistencies of EKF based SLAM that have been recently observed. The fundamental cause of EKF SLAM inconsistency for two basic scenarios are clearly stated and associated theoretical proofs are provided. © 2007 IEEE

Convergence and Consistency Analysis for A 3D Invariant-EKF SLAM

In this paper, we investigate the convergence and consistency properties of an Invariant-Extended Kalman Filter (RI-EKF) based Simultaneous Localization and Mapping (SLAM) algorithm. Basic convergence properties of this algorithm are proven. These proofs do not require the restrictive assumption that the Jacobians of the motion and observation models need to be evaluated at the ground truth. It is also shown that the output of RI-EKF is invariant under any stochastic rigid body transformation in contrast to $\mathbb{SO}(3)$ based EKF SLAM algorithm ($\mathbb{SO}(3)$-EKF) that is only invariant under deterministic rigid body transformation. Implications of these invariance properties on the consistency of the estimator are also discussed. Monte Carlo simulation results demonstrate that RI-EKF outperforms $\mathbb{SO}(3)$-EKF, Robocentric-EKF and the "First Estimates Jacobian" EKF, for 3D point feature based SLAM

Autonomous navigation with constrained consistency for C-Ranger

Autonomous underwater vehicles (AUVs) have become the most widely used tools for undertaking complex exploration tasks in marine environments. Their synthetic ability to carry out localization autonomously and build an environmental map concurrently, in other words, simultaneous localization and mapping (SLAM), are considered to be pivotal requirements for AUVs to have truly autonomous navigation. However, the consistency problem of the SLAM system has been greatly ignored during the past decades. In this paper, a consistency constrained extended Kalman filter (EKF) SLAM algorithm, applying the idea of local consistency, is proposed and applied to the autonomous navigation of the C-Ranger AUV, which is developed as our experimental platform. The concept of local consistency (LC) is introduced after an explicit theoretical derivation of the EKF-SLAM system. Then, we present a locally consistency-constrained EKF-SLAM design, LC-EKF, in which the landmark estimates used for linearization are fixed at the beginning of each local time period, rather than evaluated at the latest landmark estimates. Finally, our proposed LC-EKF algorithm is experimentally verified, both in simulations and sea trials. The experimental results show that the LC-EKF performs well with regard to consistency, accuracy and computational efficiency

AUV SLAM and experiments using a mechanical scanning forward-looking sonar

Navigation technology is one of the most important challenges in the applications of autonomous underwater vehicles (AUVs) which navigate in the complex undersea environment. The ability of localizing a robot and accurately mapping its surroundings simultaneously, namely the simultaneous localization and mapping (SLAM) problem, is a key prerequisite of truly autonomous robots. In this paper, a modified-FastSLAM algorithm is proposed and used in the navigation for our C-Ranger research platform, an open-frame AUV. A mechanical scanning imaging sonar is chosen as the active sensor for the AUV. The modified-FastSLAM implements the update relying on the on-board sensors of C-Ranger. On the other hand, the algorithm employs the data association which combines the single particle maximum likelihood method with modified negative evidence method, and uses the rank-based resampling to overcome the particle depletion problem. In order to verify the feasibility of the proposed methods, both simulation experiments and sea trials for C-Ranger are conducted. The experimental results show the modified-FastSLAM employed for the navigation of the C-Ranger AUV is much more effective and accurate compared with the traditional methods