We introduce an information measure, termed clarity, motivated by information entropy, and show that it has intuitive properties relevant to dynamic coverage control and informative path planning. Clarity defines the quality of the information we have about a variable of interest in an environment on a scale of [0, 1], and has useful properties for control and planning such as: (I) clarity lower bounds the expected estimation error of any estimator, and (II) given noisy measurements, clarity monotonically approaches a level q_infty < 1. We establish a connection between coverage controllers and information theory via clarity, suggesting a coverage model that is physically consistent with how information is acquired. Next, we define the notion of perceivability of an environment under a given robotic (or more generally, sensing and control) system, i.e., whether the system has sufficient sensing and actuation capabilities to gather desired information. We show that perceivability relates to the reachability of an augmented system, and derive the corresponding Hamilton-Jacobi-Bellman equations to determine perceivability. In simulations, we demonstrate how clarity is a useful concept for planning trajectories, how perceivability can be determined using reachability analysis, and how a Control Barrier Function (CBF) based controller can dramatically reduce the computational burden.

翻译：我们提出了一种名为“清晰度”的信息度量，该度量源于信息熵，并证明了其在动态覆盖控制及信息路径规划中具有直观的适用性质。清晰度以[0,1]区间内的数值定义了环境中感兴趣变量所拥有信息的质量，并具备对控制与规划有用的性质：（I）清晰度界定了任意估计器期望估计误差的下界；（II）在存在噪声测量数据的情况下，清晰度单调趋近于一个小于1的水平q_infty。我们通过清晰度建立了覆盖控制器与信息论之间的关联，提出了与信息获取物理过程一致的覆盖模型。进一步，我们定义了给定机器人系统（更广义而言，传感与控制系统）下环境的“可感知性”概念，即系统是否具备足够传感与执行能力以获取期望信息。研究表明，可感知性与增广系统的可达性相关，并推导了相应的Hamilton-Jacobi-Bellman方程以确定可感知性。通过仿真，我们展示了清晰度在轨迹规划中的实用价值，论证了如何通过可达性分析确定可感知性，并说明了基于控制屏障函数（CBF）的控制器可显著降低计算负担。