In this paper, we propose an optimization based SLAM approach to simultaneously optimize the robot trajectory and the occupancy map using 2D laser scans (and odometry) information. The key novelty is that the robot poses and the occupancy map are optimized together, which is significantly different from existing occupancy mapping strategies where the robot poses need to be obtained first before the map can be estimated. In our formulation, the map is represented as a continuous occupancy map where each 2D point in the environment has a corresponding evidence value. The Occupancy-SLAM problem is formulated as an optimization problem where the variables include all the robot poses and the occupancy values at the selected discrete grid cell nodes. We propose a variation of Gauss-Newton method to solve this new formulated problem, obtaining the optimized occupancy map and robot trajectory together with their uncertainties. Our algorithm is an offline approach since it is based on batch optimization and the number of variables involved is large. Evaluations using simulations and publicly available practical 2D laser datasets demonstrate that the proposed approach can estimate the maps and robot trajectories more accurately than the state-of-the-art techniques, when a relatively accurate initial guess is provided to our algorithm. The video shows the convergence process of the proposed Occupancy-SLAM and comparison of results to Cartographer can be found at \url{https://youtu.be/4oLyVEUC4iY}.

翻译：本文提出一种基于优化的SLAM方法，利用二维激光扫描（及里程计）信息同时优化机器人轨迹与占据地图。关键创新在于将机器人位姿与占据地图联合优化，这与现有占据地图构建策略（需先获取机器人位姿再估计地图）存在根本性差异。在我们的公式化表述中，地图被表示为连续占据地图，环境中每个二维点均具有对应的证据值。Occupancy-SLAM问题被构建为优化问题，其变量涵盖所有机器人位姿及选定离散网格节点处的占据值。我们提出一种高斯-牛顿法的变体来求解该新问题，从而获得优化后的占据地图、机器人轨迹及其不确定性。由于该方法基于批处理优化且涉及变量数量庞大，属于离线算法。基于仿真与公开实际二维激光数据集的评估表明：在提供较精确初始估计的条件下，所提方法能够比现有最优技术更准确地估计地图与机器人轨迹。视频展示了所提Occupancy-SLAM的收敛过程，与Cartographer的对比结果可参见网址\url{https://youtu.be/4oLyVEUC4iY}。