Research On Simultaneous Localization And Mapping Based On Compressed Nonlinear Filtering And Graph Theory

Under no prior information available, Simultaneous Localization and Mapping(SLAM) means that a mobile platform realizes its localization utilizing on-board sensors, while simultaneously mapping the unknown environment. SLAM has been acknowledged to be the essential technique for a fully autonomous navigation system, and is an active research topic in mobile robotics, unmanned aerial vehicles(UAV) and so forth. In contrast to classical navigation systems, SLAM faces much more academic problems and challenges in practice, due to no external assistance information. The probabilistic form of SLAM reveals its critical ideas and implementation ways in theory, and induces two different popular solutions to SLAM, namely filtering and optimizing. Though a large number of methods have been proposed for the SLAM problem, substantial issues remain in SLAM implementations, mainly including high computational complexities, estimation inconsistencies, robustness and no-Euclidean parameters, which show direct affects in the real-time implementation, the reliability and the accuracy of SLAM. To address aforementioned problems, this thesis makes further researches on correspondingly critical techniques in SLAM.The detailed formulations of SLAM solutions are presented for the filtering-based and graph-based approaches, respectively. By utilizing the Markov assumption, the Bayes filter form of SLAM is derived detailedly. A general SLAM is partitioned to nonlinear motion update and measurement update. Subsequently, the EKF-based solution to the SLAM problem is established. For different application environment, SLAM models of the land vehicle and UAV are respectively presented. 2D and 3D simulation is performed to verify the possibilities. By describing the SLAM problem in graph theory, the state estimation is equivalent to the optimization of a graph structure. The model of the graph-based SLAM is then set up, with a Gauss-Newton solution.The compressed Unscented Kalman Filter(UKF) is studied for the SLAM problem. After proving the consistencies between the partial sampling and the full sampling in UKF, the model of UKF-SLAM based on the partial sampling strategy is built. In particular, the UKF obtains inferred Jacobian matrices for the propagations of cross covariance matrices. With applying the compress filter strategy, the compressed UKF is proposed, resulting in a significantly reduced computational complexity. Extensive experiments based on simulated and practical datasets are performed to validate its efficiencies and possibilities.A robust linear optimization method is studied for the graph-based SLAM. A general mathematical description is provided for the linear SLAM, where the inverse function theory is applied to circumvent Jacobian matrix inverses in the nonlinear coordinate transformation. Considering the ambiguities of loop-closures due to insufficient information, the delayed optimization is proposed to postpone the fusion of all loop-closures in the joining procedure of two submaps. The Expectation Maximization method is applied for outlier detections. Following the proof that the joining result of submaps are independent on the delayed exclusion of outliers, the Schur complement is proposed to realize the outlier exclusion fully. Simulation results confirm the robustness of the proposed method against different types of outliers, and experimental datasets with outliers are applied to validate its feasibilities in practical environment.The optimization based on the dual quaternion is studied for the graph-based SLAM in the manifold space. The dual quaternion is applied to construct the measurement error function model, which obtains a bilinear form with respect to each related vertex. By linearizing the error function around the estimation, the solution based on Gauss-Newton is provided. The properties of two different perturbation over-parameterization ways are discussed under two different noise levels. Simulated and experimental results based on 2D and 3D environment is provided to evaluate efficiencies of the proposed approach, and show that the axis-angle representation outperforms the quaternion method in terms of numerical stabilities.