基于压缩非线性滤波与图论的同时定位与构图方法研究

发布时间：2018-03-17 12:43

本文选题：自主导航　切入点：同时定位与构图　出处：《国防科学技术大学》2015年博士论文　论文类型：学位论文

【摘要】：同时定位与构图(SLAM)是指在没有任何先验信息的前提下,移动平台利用自身传感器观测信息实现定位的同时完成环境地图的构建,被认为是实现真正完全自主导航的重要手段,已成为智能机器人和无人机等领域的研究热点之一。由于没有外界辅助信息,相对于经典导航系统,SLAM在理论与工程实现中面临更多问题和挑战。SLAM的概率形式从理论上揭示了其技术内涵和实现方式,并导出了SLAM两种不同的求解形式:滤波和优化。虽然多种方法相继被应用于SLAM问题的求解,然而计算复杂性、估计不一致性、鲁棒性和非欧几里德参数化仍是SLAM应用中较为突出的问题,对其实时性、可靠性和准确性有着直接影响。本文针对上述问题对SLAM相关关键技术展开深入研究。建立了SLAM问题求解的滤波模型和图论优化模型。根据马尔科夫假设,推导了SLAM问题的贝叶斯滤波形式。将一般性SLAM问题分解为非线性的运动更新和测量更新,建立了SLAM问题求解的扩展卡尔曼滤波(EKF)模型。针对不同应用环境,分别建立地面车辆和无人机应用系统模型,仿真验证SLAM在2D和3D环境中可行性。利用图论描述SLAM问题,将状态估计转化为图结构优化,建立了图论SLAM问题数学模型。基于Gauss-Newton方法,给出问题求解具体形式。研究了面向SLAM的压缩无迹卡尔曼滤波(UKF)方法。基于全采样和部分采样UKF一致性的证明,建立了基于部分采样的UKF-SLAM问题求解模型,并推导了UKF的等效雅克比矩阵计算形式。结合压缩滤波思想,提出了基于压缩UKF的SLAM问题求解方法,进一步提高了UKF在SLAM问题求解中的计算效率。通过仿真实验和地面跑车实验数据处理分析,结果证明了非线性滤波方法UKF在SLAM问题中实时应用的可行性。研究了鲁棒线性SLAM优化方法。阐述了基于广义最小二乘法的L-SLAM一般性数学描述形式,利用逆函数理论避免非线性坐标变换中雅克比矩阵求逆问题。提出了延迟最优化策略,解决子图联合过程中信息不足时野值探测问题。引入期望最大值方法实现野值探测。分析了野值延迟剔除对子图联合结果间的影响,进而提出Schur补方法实现野值信息的完全剔除。仿真结果证明了鲁棒线性SLAM优化方法对不同类型野值的鲁棒性,利用包含野值的真实实验数据验证算法实际环境适用性。研究了基于单位对偶四元数的图论SLAM优化方法。依据对偶四元数乘法特性,建立了基于单位对偶四元数的测量误差函数模型,实现测量误差函数对相关节点的双线性形式和雅克比矩阵计算的简化;推导了基于单位对偶四元数的误差函数Gauss-Newton求解模型;探索了在不同噪声水平下,基于四元数和轴-角的扰动过参数化方法对优化结果影响;实验结果验证了算法计算效率,并表明大噪声情况下轴-角过参数化方法具有更好的数值稳定性。
[Abstract]:Simultaneous location and composition (slam) means that, without any prior information, the mobile platform uses its sensor observation information to locate and complete the construction of the environmental map, which is considered to be an important means to realize the truly autonomous navigation. It has become one of the research hotspots in the fields of intelligent robots and unmanned aerial vehicles. Compared with the classical navigation system, slam faces more problems and challenges in theory and engineering implementation. The probability form of SLAM reveals its technical connotation and realization mode theoretically. Two different solutions for SLAM are derived: filtering and optimization. Although many methods have been applied to the SLAM problem successively, the computational complexity and estimation are inconsistent. Robustness and non-Euclidean parameterization are still outstanding problems in SLAM applications. The reliability and accuracy have a direct effect. In this paper, the key technologies related to SLAM are studied deeply, and the filtering model and graph theory optimization model for solving SLAM problem are established. The Bayesian filtering form of the SLAM problem is derived. The general SLAM problem is decomposed into nonlinear motion updating and measurement updating, and the extended Kalman filter (EKF) model for solving the SLAM problem is established. The application system models of ground vehicle and UAV are established, and the feasibility of SLAM in 2D and 3D environments is verified by simulation. The SLAM problem is described by graph theory, and the state estimation is transformed into graph structure optimization. The mathematical model of graph theory SLAM problem is established. Based on the Gauss-Newton method, the concrete form of solving the problem is given. The SLAM oriented compressed unscented Kalman filter (UKF) method is studied. Based on the proof of the consistency of full sampling and partial sampling UKF, The UKF-SLAM problem solving model based on partial sampling is established, and the equivalent Jacobian matrix calculation form of UKF is deduced. Combined with the idea of compression filtering, a SLAM problem solving method based on compressed UKF is proposed. The computational efficiency of UKF in solving SLAM problem is further improved. The data processing and analysis of simulation experiment and ground sports car experiment are carried out. The results show that the nonlinear filtering method UKF can be applied to the SLAM problem in real time. The robust linear SLAM optimization method is studied. The general mathematical description of L-SLAM based on the generalized least square method is presented. The inverse function theory is used to avoid the Jacobian matrix inverse problem in nonlinear coordinate transformation. In order to solve the problem of outliers detection in the process of subgraph association with insufficient information, the expected maximum value method is introduced to detect outliers. The influence of outlier delay elimination on the joint results of subgraphs is analyzed. Furthermore, the Schur complement method is proposed to eliminate outliers completely. The simulation results show that the robust linear SLAM optimization method is robust to different types of outliers. Using real experimental data including outliers to verify the applicability of the algorithm, a graph theory SLAM optimization method based on unit dual quaternion is studied. The measurement error function model based on the unit dual quaternion is established to realize the bilinear form of the measurement error function to the correlation node and the simplified calculation of the Jacobian matrix, and the Gauss-Newton solution model of the error function based on the unit dual quaternion is derived. Under different noise levels, the influence of perturbation overparameterization method based on quaternion and axis-angle on the optimization results is explored, and the computational efficiency of the algorithm is verified by the experimental results. It is shown that the axial-angle overparameterization method has better numerical stability in the case of large noise.
【学位授予单位】：国防科学技术大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TN713;O157.5

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