Consider a sensor that reports whether or not an event has occurred somewhere along a path, but that has no conception of where along the path that event has occurred. We name this type of sensor a path-based sensor and describe the recursive Bayesian update that can be used to calculate posterior beliefs about the presence of a sensor triggering phenomenon given a path-based sensor observation. We show how the Bayesian update can be leveraged to calculate the expected Shannon information that will be gained along a particular path. We formalize two iterative information-gathering problems that result from this scenario and present path-planning algorithms to solve them. These include: 1) gathering information about the path-based sensor triggering phenomena and 2) assuming the path-based sensor triggering event is “robot destruction,” simultaneously gather information about: 1) hazards using a path-based sensor and 2) information about another environmental phenomenon using a standard sensor, such as the locations of search and rescue targets with a camera. We evaluate our methods using Monte Carlo simulations and observe that they outperform other techniques with respect to the new problems that we consider. Note to Practitioners—This work is motivated by the problem of searching for robot-destroying hazards that are otherwise invisible to the robots. That is, we can observe whether or not a robot survives a path, but, if a robot is destroyed, then we have no idea where, along the path, its destruction has occurred. A mathematically equivalent problem happens in any scenario, in which an agent is equipped with an event sensor that can only be set/triggered once, but that requires postprocessing to figure out if the sensor has been triggered or not. For example, postprocessing is needed if the determination of whether or not a biological specimen was obtained requires a manual laboratory inspection. We also consider an extension of the hazard detection problem, in which we simultaneously collect information about search-and-rescue victims using a “victim sensor,” such as a camera. In this problem, hazards indirectly affect information gathered about victims because new information about victims is lost whenever a robot is destroyed. We provide algorithms to solve these types of problems. The algorithms work even in cases with noise such that false positives and false negatives are possible. This work is useful in any application where observations take the form of a cumulative “yes” or “no” along a path.

中文翻译：

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基于路径的传感器：作为传感器的路径、贝叶斯更新和香农信息收集


考虑一个传感器，它报告事件是否在路径上的某个地方发生，但不知道事件在路径上的何处发生。我们将这种类型的传感器命名为基于路径的传感器，并描述了递归贝叶斯更新，该更新可用于计算关于给定基于路径的传感器观察的传感器触发现象的存在的后验信念。我们展示了如何利用贝叶斯更新来计算沿着特定路径获得的预期香农信息。我们形式化了这种情况下产生的两个迭代信息收集问题，并提出了路径规划算法来解决它们。其中包括：1) 收集有关基于路径的传感器触发现象的信息，2) 假设基于路径的传感器触发事件​​是“机器人破坏”，同时收集以下信息：1) 使用基于路径的传感器的危险和 2) 信息使用标准传感器了解另一种环境现象，例如使用摄像头确定搜索和救援目标的位置。我们使用蒙特卡罗模拟评估我们的方法，并观察到它们在我们考虑的新问题方面优于其他技术。从业者须知——这项工作的动机是寻找机器人无法看到的破坏机器人的危险。也就是说，我们可以观察机器人是否在一条路径中幸存下来，但是，如果机器人被摧毁，那么我们不知道它的破坏发生在路径的哪个位置。在任何场景中都会发生数学上等效的问题，其中代理配备了只能设置/触发一次的事件传感器，但这需要后处理来确定传感器是否已被触发。 例如，如果确定是否获得生物样本需要人工实验室检查，则需要后处理。我们还考虑危险检测问题的扩展，其中我们使用“受害者传感器”（例如摄像机）同时收集有关搜救受害者的信息。在这个问题中，危险间接影响收集到的有关受害者的信息，因为每当机器人被摧毁时，有关受害者的新信息就会丢失。我们提供算法来解决这些类型的问题。即使在有噪声的情况下，算法也能工作，从而可能出现误报和漏报。这项工作在任何以沿路径累积“是”或“否”形式进行观察的应用中都很有用。