GFM-Planner: Perception-Aware Trajectory Planning with Geometric Feature Metric

Like humans who rely on landmarks for orientation, autonomous robots depend on feature-rich environments for accurate localization. In this paper, we propose the GFM-Planner, a perception-aware trajectory planning framework based on the geometric feature metric, which enhances LiDAR localization accuracy by guiding the robot to avoid degraded areas. First, we derive the Geometric Feature Metric (GFM) from the fundamental LiDAR localization problem. Next, we design a 2D grid-based Metric Encoding Map (MEM) to efficiently store GFM values across the environment. A constant-time decoding algorithm is further proposed to retrieve GFM values for arbitrary poses from the MEM. Finally, we develop a perception-aware trajectory planning algorithm that improves LiDAR localization capabilities by guiding the robot in selecting trajectories through feature-rich areas. Both simulation and real-world experiments demonstrate that our approach enables the robot to actively select trajectories that significantly enhance LiDAR localization accuracy.