Robotic systems, particularly in demanding environments like narrow corridors or disaster zones, often grapple with imperfect state estimation. Addressing this challenge requires a trajectory plan that not only navigates these restrictive spaces but also manages the inherent uncertainty of the system. We present a novel approach for graph-based belief space planning via the use of an efficient covariance control algorithm. By adaptively steering state statistics via output state feedback, we efficiently craft a belief roadmap characterized by nodes with controlled uncertainty and edges representing collision-free mean trajectories. The roadmap's structured design then paves the way for precise path searches that balance control costs and uncertainty considerations. Our numerical experiments affirm the efficacy and advantage of our method in different motion planning tasks. Our open-source implementation can be found at https://github.com/hzyu17/VIMP/tree/BRM.

翻译：机器人系统，特别是在狭窄走廊或灾害区域等严苛环境中，常面临状态估计不完善的问题。应对这一挑战需要制定既能穿越这些受限空间、又能管理系统内在不确定性的轨迹规划。我们提出一种基于图的高效信念空间规划新方法，利用高效的协方差控制算法。通过输出状态反馈自适应地调控状态统计量，我们高效构建了一个信念道路图，其节点具有可控的不确定性，边则代表无碰撞的平均轨迹。该道路图的结构化设计为精确路径搜索奠定了基础，能够平衡控制代价与不确定性考量。数值实验验证了该方法在不同运动规划任务中的有效性和优越性。我们的开源实现可访问 https://github.com/hzyu17/VIMP/tree/BRM。