This paper addresses the Kidnapped Robot Problem (KRP), a core localization challenge of relocalizing a robot in a known map without prior pose estimate when localization loss or at SLAM initialization. For this purpose, a passive 2-D global relocalization framework is proposed. It estimates the global pose efficiently and reliably from a single LiDAR scan and an occupancy grid map while the robot remains stationary, thereby enhancing the long-term autonomy of mobile robots. The proposed framework casts global relocalization as a non-convex problem and solves it via the multi-hypothesis scheme with batched multi-stage inference and early termination, balancing completeness and efficiency. The Rapidly-exploring Random Tree (RRT), under traversability constraints, asymptotically covers the reachable space to generate sparse, uniformly distributed feasible positional hypotheses, fundamentally reducing the sampling space. The hypotheses are preliminarily ordered by the proposed Scan Mean Absolute Difference (SMAD), a coarse beam-error level metric that facilitates the early termination by prioritizing high-likelihood candidates. The SMAD computation is optimized for non-panoramic scans. The Translation-Affinity Scan-to-Map Alignment Metric (TAM) is proposed for reliable orientation selection at hypothesized positions and accurate final pose evaluation to mitigate degradation in conventional likelihood-field metrics under translational uncertainty induced by sparse hypotheses, as well as non-panoramic LiDAR scan and environmental changes. Real-world experiments on a resource-constrained mobile robot with non-panoramic LiDAR scans show that the proposed framework achieves competitive performance in both global relocalization success rate and computational efficiency.

翻译：本文针对机器人绑架问题——一种在已知地图中无需先验位姿估计进行机器人重定位的核心挑战（常发生于定位丢失或SLAM初始化时），提出了一种被动式二维全局重定位框架。该框架在机器人保持静止状态下，仅利用单帧激光雷达扫描数据与占据栅格地图即可高效可靠地估计全局位姿，从而提升移动机器人的长期自主能力。所提框架将全局重定位建模为非凸优化问题，并通过多假设方案结合批量多阶段推理与早期终止策略进行求解，以权衡完备性与计算效率。在可通行性约束下，快速探索随机树渐进覆盖可达空间以生成稀疏、均匀分布的可行位置假设，从根本上缩减了采样空间。假设集通过本文提出的扫描平均绝对差值进行初步排序，该粗粒度波束误差级度量通过优先评估高似然候选假设来促进早期终止，并针对非全景扫描进行了计算优化。为缓解传统似然场度量在稀疏假设导致的平移不确定性、非全景激光雷达扫描及环境变化下的性能退化，本文进一步提出平移亲和扫描-地图对齐度量，用于在假设位置实现可靠的方向选择及精确的最终位姿评估。在搭载非全景激光雷达的资源受限移动机器人上的真实场景实验表明，所提框架在全局重定位成功率和计算效率方面均展现出竞争优势。