移动机器人在日常生活中随处可见，为人们提供了方便，并且有助于减少各种安全事故的发生。同步定位与地图构建（Simultaneous Localization and Mapping，SLAM）是移动机器人关键的技术之一，本文针对移动机器人SLAM算法进行研究，主要研究内容如下：

首先，对移动机器人的 SLAM 系统进行模块化建模。建立了SLAM概率模型，便于数学处理和计算优化，针对机器人 SLAM 研究，选用笛卡尔坐标系作为坐标系模型，并构建了移动机器人的简化模型。通过建立移动机器人的运动模型来预测机器人位姿的变化。根据激光雷达传感器建立观测模型，获取观测信息。此外，采用解释树模型建立数据关联模型。最后，建立了栅格地图便于对整体建图效果的观测。

其次，针对粒子滤波算法存在粒子退化和贫化的问题，借鉴群智能优化的思想，提出一种改进的鲸鱼粒子滤波算法（IWOA-PF），该算法在初始化阶段使用反向学习，并通过修正鲸鱼算法中的螺旋方式，提高了算法前期和后期的各种寻优能力，并对优秀粒子进行柯西变异，使得粒子分布相对合理，可以有效的解决粒子滤波中存在的问题，在仿真实验中，通过与粒子滤波算法，粒子群滤波算法，鲸鱼粒子滤波算法相比较，IWOA-PF状态估计更加接近真实值，滤波精度相较于以上算法分别提升了27.4%，18.7%和8.0%，并且粒子分布较广，改善了粒子的多样性。

然后，将改进的鲸鱼粒子滤波算法应用在移动机器人SLAM中，优化FastSLAM中的路径估计，改善移动机器人位姿采样粒子的分布情况，使得粒子更接近于机器人的真实位姿，并且有效缓解了FastSLAM算法中粒子退化与贫化现象。

最后，在Matlab 2019b和ROS中进行仿真，通过与FastSLAM和鲸鱼粒子滤波SLAM算法相比较，改进的鲸鱼粒子滤波SLAM算法定位精度更高，并且建图不偏移，轮廓清晰，能够实现准确的定位与建图，满足移动机器人同步定位与建图的实际应用需求。

Mobile robots can be seen everywhere in daily life, providing convenience and helping to reduce various safety accidents. Simultaneous Localization and Mapping (SLAM) is one of the key technologies for mobile robots. This article focuses on the study of SLAM algorithms for mobile robots and the main research contents are as follows:

Firstly, modular modeling of the SLAM (Simultaneous Localization and Mapping) system for mobile robots is conducted. A probabilistic model for SLAM is established to facilitate mathematical processing and computational optimization. For the study of robot SLAM, a Cartesian coordinate system is chosen as the coordinate model, and a simplified model for mobile robots is constructed. The motion model of the mobile robot is established to predict changes in the robot's pose. An observation model is established based on the laser radar sensor to acquire observation information. Additionally, a data association model is established using an explanation tree model. Finally, a grid map is created to facilitate the observation of the overall mapping effect.

Secondly, to solve the problem of particle degradation and impoverishment in the particle filter algorithm, an improved Whale particle filter algorithm (IWOA-PF) is proposed based on the idea of swarm intelligent optimization. The algorithm uses reverse learning in the initialization stage and improves various optimization capabilities in the early and late stages by modifying the spiral mode in the whale algorithm. In addition, Cauch- mutation is performed on excellent particles to make the particle distribution relatively reasonable and effectively solve the problems existing in the particle filter. In the simulation experiment, compared with the particle filter algorithm, particle swarm filter algorithm and whale particle filter algorithm, the state estimation of IWOA-PF is closer to the real value, and the filtering accuracy is improved by 27.4% respectively compared with the above algorithms. 18.7% and 8.0%, and the particle distribution is wide, which improves the particle diversity.

Then, the improved whale particle filter algorithm is applied to mobile robot SLAM to optimize path estimation in FastSLAM. This improvement enhances the distribution of particles used for sampling the mobile robot's pose, making them closer to the true pose of the robot. It effectively alleviates particle degeneracy and impoverishment issues commonly encountered in FastSLAM algorithms..

Finally, simulation is carried out in Matlab 2019b and ROS. Compared with FastSLAM and whale particle filter SLAM algorithms, the improved whale particle filter SLAM algorithm has higher positioning accuracy, no deviation in map construction, clear outline, and can achieve accurate positioning and map construction. It can meet the practical application requirements of simultaneous positioning and mapping of mobile robots.