This paper addresses the Kidnapped Robot Problem (KRP), a core localization challenge of relocalizing a robot in a known map without prior pose estimate upon 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：本文针对绑架机器人问题（KRP）——即在定位丢失或SLAM初始化时，机器人需在已知地图中无初始位姿估计的情况下重定位的核心挑战——提出了一种被动式二维全局重定位框架。该框架利用单帧LiDAR扫描和占据栅格地图，在机器人保持静止状态下高效可靠地估计全局位姿，从而增强移动机器人的长期自主性。所提框架将全局重定位建模为非凸优化问题，并通过多假设策略结合批量多阶段推断与提前终止机制求解，兼顾完备性与效率。在可通行性约束下，快速探索随机树（RRT）渐进覆盖可达空间，生成稀疏且均匀分布的可行位置假设，从根本上缩减采样空间。为假设排序提出扫描平均绝对差（SMAD）——一种粗粒度波束误差度量，通过优先处理高似然候选实现提前终止。SMAD计算针对有限扫描测量进行了优化。进一步提出平移亲和性扫描-地图对齐度量（TAM），用于假设位置处的可靠朝向选择和最终全局位姿的精确评估，以缓解稀疏假设导致的平移不确定性、非全景LiDAR扫描及环境变化对传统似然场度量的退化影响。在配备非全景LiDAR的资源受限移动机器人上的实景实验表明，所提框架在成功率、测量不确定度下的鲁棒性及计算效率方面均具有竞争力。