This paper addresses the problem of trajectory planning for information gathering with a dynamic and resolution-varying sensor footprint. Ergodic planning offers a principled framework that balances exploration (visiting all areas) and exploitation (focusing on high-information regions) by planning trajectories such that the time spent in a region is proportional to the amount of information in that region. Existing ergodic planning often oversimplifies the sensing model by assuming a point sensor or a footprint with constant shape and resolution. In practice, the sensor footprint can drastically change over time as the robot moves, such as aerial robots equipped with downward-facing cameras, whose field of view depends on the orientation and altitude. To overcome this limitation, we propose a new metric that accounts for dynamic sensor footprints, analyze the theoretic local optimality conditions, and propose numerical trajectory optimization algorithms. Experimental results show that the proposed approach can simultaneously optimize both the trajectories and sensor footprints, with up to an order of magnitude better ergodicity than conventional methods. We also deploy our approach in a multi-drone system to ergodically cover an object in 3D space.

翻译：本文研究了在传感器覆盖范围动态变化且分辨率可调的情况下，用于信息采集的轨迹规划问题。遍历规划提供了一种原则性框架，通过规划轨迹使得在某一区域停留的时间与该区域的信息量成正比，从而平衡探索（覆盖所有区域）与利用（聚焦高信息区域）。现有的遍历规划方法通常过度简化感知模型，假设传感器为点传感器或具有固定形状和分辨率的覆盖范围。实际上，随着机器人运动，传感器覆盖范围可能发生剧烈变化，例如配备下视摄像头的空中机器人，其视场取决于姿态和高度。为克服这一局限，我们提出了一种考虑动态传感器覆盖范围的新度量，分析了理论局部最优性条件，并提出了数值轨迹优化算法。实验结果表明，所提方法能够同时优化轨迹和传感器覆盖范围，其遍历性比传统方法提升高达一个数量级。我们还将该方法部署于多无人机系统中，以遍历方式覆盖三维空间中的目标。