中文摘要：

研究了移动机器人同步定位与地图构建（SLAM）过程中的轨迹规划问题．提出了一种新的目标函数，它同时考虑机器人运动对地图覆盖面积、地图不确定性、定位不确定性、导航代价等几个方面的影响．提出了一步最优和多步最优轨迹规划的概念，并分别设计了两种最优标准下的规划算法和近似计算方法．最后，通过对比仿真实验验证了所提出的方法的有效性，并指出了今后的研究方向．

英文摘要：

The trajectory planning in the Simultaneous Localization And Mapping （SLAM） problem is investigated. A novel objective function is proposed, which simultaneously considers the effect of the robot motion on the coverage area of the map, uncertainty of the map, uncertainty of the robot location, and the cost of navigation. The concepts of single step optimal trajectory planning and multi-step optimal trajectory planning are put forward, the planning algorithms under the two optimal criterions and the approximated computation methods for these algorithms are designed. Finally, contrastive simulation experiments validate the feasibility of the methods, and the future research topics are provided.