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 limited scan measurements. The Translation-Affinity Scan-to-Map Alignment Metric (TAM) is proposed for reliable orientation selection at hypothesized positions and accurate final global 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 success rate, robustness under measurement uncertainty, 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即可实现机器人重定位的核心定位挑战（常发生于定位丢失或SLAM初始化时）。为此，我们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，仅通过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运行能力。所提框架将全局重定位建模为非凸优化问题，并采用多假设策略结合批处理多阶段推理与提前终止机制进行求解，在完备性与效率间取得平衡。在可通行性约束下，快速探索随机树通过渐进覆盖可达空间生成稀疏且均匀分布的可行位置假设，从根本上缩减了采样空间。假设排序通过提出的扫描平均绝对差值——一种粗粒度波束误差级度量指标进行初步筛选，该指标通过优先评估高似然候选假设以支持提前终止机制。扫描平均绝对差值的计算针对有限扫描测量数据进行了优化。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问题，本文提出平移亲和扫描-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全局位姿评估。在搭载非全景激光雷达的资源受限移动机器人上进行的真实场景实验表明，所提框架在成功率、测量不确定性下的鲁棒性及计算效率方面均表现出优越性能。