基于增量平滑的移动机器人同时定位与地图构建的研究

发布时间：2017-12-27 04:18

本文关键词：基于增量平滑的移动机器人同时定位与地图构建的研究　出处：《北京交通大学》2016年硕士论文　论文类型：学位论文

【摘要】：SLAM(Simultaneous Localization and Mapping)问题,即机器人同时定位与制图问题,它指的是机器人从一个未知环境中开始运动,在运动过程中根据自身运动模型和所携带的传感器对环境进行观测来定位,同时建立周围的环境地图的过程。其解决方法主要是基于概率估计的方法,其中主要有两类经典的算法,一类是基于卡尔曼滤波的相关算法(Extended Kalman Filter, EKF),一类是基于粒子滤波的相关算法(Particle Filter, PF)。EKF算法以递归的方式对机器人当前的位姿和所有的路标的位置的高斯密度函数进行估计。然而,EKF算法的计算复杂度增加的很快,因此很难解决具有大规模环境方面的问题。同时,滤波算法被用于解决非线性SLAM问题时总会产生不一致的问题。因此,近几年基于优化的算法应运而生,与基于滤波的方法相比,它具有效率更高、稳定性更好、通用性更强等优点,因此本文主要研究基于优化方法的SLAM问题。基于优化方法解决SLAM问题的主要思想是,把SLAM问题转化为最小二乘法问题,通过利用最优化方法对最小二乘法问题求解,计算出全局地图和机器人运动的整条轨迹,因此,优化算法也称之为平滑算法。然而,在优化的过程中需要把非线性模型进行线性化,因此不可避免的产生了线性化的误差。因此,本论文在平滑算法的基础上,提出一种改善优化算法问题的方法,使之尽可能的减小线性化误差,从而达到降低系统误差的目的。本文的主要工作如下：首先,对SLAM问题进行建模。用因子图来表示SLAM问题,进而通过详细的公式推导,把SLAM求解转化为大规模稀疏系统的非线性最小二乘法优化问题。其次,介绍最小二乘法优化求解。最小二乘法问题包括线性最小二乘法问题和非线性最小二乘法问题,然而它们的求解方法截然不同。本文重点介绍非线性最小二乘法问题的求解方法,并把此方法用于求解一个简单的SLAM例子上。再次,深入研究两种比较流行的基于优化方法的算法,即平滑式的SLAM问题,包括平滑与制图算法(Smoothing and Mapping),简称SAM,以及增量平滑与地图构建算法(incremental Smoothing and Mapping),即iSAM。前者是一种离线式的算法,其目标是在最后一次性求解出机器入的整个运动轨迹和地图。后者基于快速递增的矩阵因式分解,能够在任何时刻求得机器人的运动轨迹和当前的地图,是一种有效且实用的解决方案。最后,在增量平滑算法的基础上,基于无迹变换以及数值微分理论对算法进行了改进。并通过仿真实验将新方法和已有算法进行综合性能对比,主要包括精度性能、计算代价等方面,验证算法性能的改善。
[Abstract]:SLAM (Simultaneous Localization and Mapping), and robot localization and mapping problem, it refers to the robot start moving from an unknown environment, in the process of movement according to their motion model and carried by the sensor observes the environment positioning process while building the environment map. The solution is mainly based on the probability estimation method. There are mainly two classical algorithms, one is the Extended Kalman Filter (EKF) algorithm based on Calman filter, the other is particle filter based correlation algorithm (Particle Filter PF). The EKF algorithm estimates the Gauss density function of the robot's current position and the location of all the road signs recursively. However, the computational complexity of the EKF algorithm is increasing rapidly, so it is difficult to solve the problem with large scale environment. At the same time, the filter algorithm is used to solve the problem of nonlinear SLAM problem. Therefore, in recent years, based on the optimization algorithm came into being, compared with the filtering method, it has the advantages of higher efficiency, better stability and stronger versatility. Therefore, this paper mainly studies the SLAM problem based on optimization method. The main idea of optimization method to solve the SLAM problem based on SLAM, the problem is transformed into a least squares problem is solved by using optimization method of least squares method, calculate the global map and robot motion of the whole trajectory, so the optimization algorithm called smoothing algorithm. However, it is necessary to linearize the nonlinear model in the process of optimization, so the linearization error is unavoidable. Therefore, based on the smoothing algorithm, this paper proposes a method to improve the optimization algorithm, so as to minimize the linearization error, so as to achieve the purpose of reducing the system error. The main work of this paper is as follows: first, the SLAM problem is modeled. The SLAM problem is represented by factor graph, and then the SLAM solution is transformed to the nonlinear least squares optimization problem of large-scale sparse system by detailed formula deduction. Secondly, the least square method is introduced to optimize the solution. The least squares problems include the linear least square problem and the nonlinear least squares problem, but their solutions are very different. This paper focuses on the solution of the problem of nonlinear least square method, and uses this method to solve a simple SLAM example. Thirdly, we further study two popular algorithms based on optimization, namely the smoothing SLAM problem, including Smoothing and Mapping (SAM) and incremental Smoothing and Mapping, namely iSAM. The former is an off-line algorithm whose goal is to solve the whole motion trajectory and map of the machine at the last time. The latter is based on the fast increasing matrix factorization, and it is an effective and practical solution to get the trajectory and map of the robot at any time. Finally, on the basis of the incremental smoothing algorithm, the algorithm is improved based on the non - Trace transformation and the numerical differential theory. The performance of the new algorithm and the existing algorithm is compared through simulation experiments, including accuracy performance and computational cost, which verify the improvement of algorithm performance.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP242

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