基于Sigma点滤波的移动机器人同时定位与地图创建算法的研究
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摘要
摘要：移动机器人的同时定位与地图创建(SLAM)(?)司题是移动机器人学研究领域的热点问题之一,它作为机器人进行导航、避障、路径规划及执行其它任务的基础,决定着机器人能否真正实现对未知环境的自主探索。所谓同时定位与地图创建,是指移动机器人利用自身携带的传感器,从一个未知环境开始移动,构建未知环境地图的同时,确定自身在该地图中位姿的过程。该过程中涉及到了传感器信息的处理、地图表示方法的选择及SLAM算法的实现等问题,而SLAM算法的实现又是其中非常重要的一个方面。
针对SLAM问题中机器人运动模型和观测模型的非线性特性,Sigma点滤波方法被引入到SLAM算法中。论文对基于不同采样规则的Sigma点卡尔曼滤波(SPKF)——包括无迹卡尔曼滤波(UKF)和中心差分卡尔曼滤波(CDKF)的SLAM算法,从准确度、一致性和计算复杂度等方面,对其性能进行了分析比较。在此基础上提出一些改进算法,以提高SLAM算法的准确度、计算效率和鲁棒性等性能,拓展其使用范围。论文的创新性工作主要包括：
(1)提出一种基于平方根CDKF (SR-CDKF)的SLAM算法,该算法通过QR分解和Cholesky更新实现了对状态方差矩阵平方根矩阵的直接更新,提高了基于CDKF的SLAM算法的计算效率。
(2)提出一种计算复杂度降低的基于CDKF (CR-CDKF)的SLAM算法,它以CDKF的线性回归卡尔曼滤波形式为基础,通过重构预测、观测更新和地图增广过程中的状态变量和相应的方差矩阵改进上述过程中的Sigma点采样策略,使算法的计算复杂度降为O(n2)。对该算法应用压缩滤波的思想,提出一种基于压缩CDKF的SLAM算法,进一步降低计算复杂度,实现了其在大规模环境中的应用。
(3)提出一种基于优化迭代SPKF (O-ISPKF)的SLAM算法,该算法在观测更新过程中采用阻尼高斯-牛顿迭代的方法,通过引入调节参数和相应的判定条件,增强算法的稳定性,能够有效提高基于SPKF的SLAM算法的准确度。
(4)探讨了基于非线性H∞滤波的SLAM算法中滤波参数γ对估计准确度和收敛性的影响。提出一种改进的基于Sigma点H∞滤波(SPHF)的SLAM算法,它利用改进的Sigma点采样策略降低计算复杂度,且与基于SPKF的SLAM算法相比具有更好的鲁棒性。
论文通过不同环境中的仿真实验和用于评价SLAM算法的标准数据集的实验对所提出的算法分别进行了验证,实验结果表明了算法的有效性。
Mobile robot Simultaneous Localization and Mapping (SLAM) problem is one of the most active research areas in mobile robotics. As the base of navigation, obstacle avoidance, path planning and other tasks, it determines the realization of truly autonomous for mobile robot in unknown environment. SLAM is the process of building a map of an unknown environment with onboard sensors, while at the same time determining the pose of the mobile robot within this map. The process concerns several aspects including sensor techniques, map representation and algorithm realization. And the SLAM algorithm realization is one of the most important aspects.
Considering the nonlinear characteristics of the motion model and observation model in SLAM, Sigma point filter is introduced into SLAM algorithms. In this dissertation, Sigma point Kalman filter (SPKF), including unscented Kalman filter (UKF) and central difference Kalman filter (CDKF) SLAM algorithms with different sampling rules are studied. The properties including accuracy, consistency and computational complexity of these algorithms are analyzed and compared. Several improved algorithms are proposed to improve accuracy, computational efficiency, robustness respectively and to extend SLAM application domains. The innovation of this dissertation is as follows.
(1) A square root CDKF (SR-CDKF) SLAM algorithm is presented. By using QR factorization and Cholesky update to get the square root of the state covariance matrix directly, the computational efficiency is impoved.
(2) A computational complexity reduced CDKF (CR-CDKF) SLAM algorithm is proposed. It is presented in the context of the linear regression Kalman filter. An improved sampling strategy is given by reconstructing the estimated state and its covariance during prediction, observation update and map augmentation process. The computational complexity of this algorithm is reduced to O(n2). The idea of compressed filter is then used in the above algorithm and a compressed CDKF SLAM algorithm is proposed. The computational complexity is further reduced which makes it more suitable for the application in large scale environment.
(3) An optimized iterated SPKF (O-ISPKF) SLAM algorithm is proposed. The damped Gauss-Newton iteration is adopted by introducing the parameter λ and the corresponding condition during the observation update process. The proposed algorithm is proved to be stable and be able to improve the accuracy of SPKF SLAM algorithm effectively.
(4) The affections of parameter y in nolinear H∞filter SLAM algorithms to the estimated accuracy and convergence are discussed. An improved Sigma point H∞, filter (SPHF) SLAM algorithm which employs the improved sampling strategy is presented. It has lower computational complexity and better robustness than SPKF SLAM algorithm.
All of the proposed algorithms are proved to be effective through the simulation experiments of different environments and also through the experiments on the standard datasets for SLAM algorithms' evaluation.
针对SLAM问题中机器人运动模型和观测模型的非线性特性,Sigma点滤波方法被引入到SLAM算法中。论文对基于不同采样规则的Sigma点卡尔曼滤波(SPKF)——包括无迹卡尔曼滤波(UKF)和中心差分卡尔曼滤波(CDKF)的SLAM算法,从准确度、一致性和计算复杂度等方面,对其性能进行了分析比较。在此基础上提出一些改进算法,以提高SLAM算法的准确度、计算效率和鲁棒性等性能,拓展其使用范围。论文的创新性工作主要包括：
(1)提出一种基于平方根CDKF (SR-CDKF)的SLAM算法,该算法通过QR分解和Cholesky更新实现了对状态方差矩阵平方根矩阵的直接更新,提高了基于CDKF的SLAM算法的计算效率。
(2)提出一种计算复杂度降低的基于CDKF (CR-CDKF)的SLAM算法,它以CDKF的线性回归卡尔曼滤波形式为基础,通过重构预测、观测更新和地图增广过程中的状态变量和相应的方差矩阵改进上述过程中的Sigma点采样策略,使算法的计算复杂度降为O(n2)。对该算法应用压缩滤波的思想,提出一种基于压缩CDKF的SLAM算法,进一步降低计算复杂度,实现了其在大规模环境中的应用。
(3)提出一种基于优化迭代SPKF (O-ISPKF)的SLAM算法,该算法在观测更新过程中采用阻尼高斯-牛顿迭代的方法,通过引入调节参数和相应的判定条件,增强算法的稳定性,能够有效提高基于SPKF的SLAM算法的准确度。
(4)探讨了基于非线性H∞滤波的SLAM算法中滤波参数γ对估计准确度和收敛性的影响。提出一种改进的基于Sigma点H∞滤波(SPHF)的SLAM算法,它利用改进的Sigma点采样策略降低计算复杂度,且与基于SPKF的SLAM算法相比具有更好的鲁棒性。
论文通过不同环境中的仿真实验和用于评价SLAM算法的标准数据集的实验对所提出的算法分别进行了验证,实验结果表明了算法的有效性。
Mobile robot Simultaneous Localization and Mapping (SLAM) problem is one of the most active research areas in mobile robotics. As the base of navigation, obstacle avoidance, path planning and other tasks, it determines the realization of truly autonomous for mobile robot in unknown environment. SLAM is the process of building a map of an unknown environment with onboard sensors, while at the same time determining the pose of the mobile robot within this map. The process concerns several aspects including sensor techniques, map representation and algorithm realization. And the SLAM algorithm realization is one of the most important aspects.
Considering the nonlinear characteristics of the motion model and observation model in SLAM, Sigma point filter is introduced into SLAM algorithms. In this dissertation, Sigma point Kalman filter (SPKF), including unscented Kalman filter (UKF) and central difference Kalman filter (CDKF) SLAM algorithms with different sampling rules are studied. The properties including accuracy, consistency and computational complexity of these algorithms are analyzed and compared. Several improved algorithms are proposed to improve accuracy, computational efficiency, robustness respectively and to extend SLAM application domains. The innovation of this dissertation is as follows.
(1) A square root CDKF (SR-CDKF) SLAM algorithm is presented. By using QR factorization and Cholesky update to get the square root of the state covariance matrix directly, the computational efficiency is impoved.
(2) A computational complexity reduced CDKF (CR-CDKF) SLAM algorithm is proposed. It is presented in the context of the linear regression Kalman filter. An improved sampling strategy is given by reconstructing the estimated state and its covariance during prediction, observation update and map augmentation process. The computational complexity of this algorithm is reduced to O(n2). The idea of compressed filter is then used in the above algorithm and a compressed CDKF SLAM algorithm is proposed. The computational complexity is further reduced which makes it more suitable for the application in large scale environment.
(3) An optimized iterated SPKF (O-ISPKF) SLAM algorithm is proposed. The damped Gauss-Newton iteration is adopted by introducing the parameter λ and the corresponding condition during the observation update process. The proposed algorithm is proved to be stable and be able to improve the accuracy of SPKF SLAM algorithm effectively.
(4) The affections of parameter y in nolinear H∞filter SLAM algorithms to the estimated accuracy and convergence are discussed. An improved Sigma point H∞, filter (SPHF) SLAM algorithm which employs the improved sampling strategy is presented. It has lower computational complexity and better robustness than SPKF SLAM algorithm.
All of the proposed algorithms are proved to be effective through the simulation experiments of different environments and also through the experiments on the standard datasets for SLAM algorithms' evaluation.
引文
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