The optimal control of a UAV searching for a target moving, with known constant speed, on a road network and heading toward one of many goal locations is considered. To aid the UAV, some roads in the network are instrumented with unattended ground sensors (UGSs) that detect the target’s motion and record the time it passes by the UGS. When the UAV flies over an UGS location, this time stamped information, if available, is communicated to it. At time 0, the target enters the road network and selects a path leading to one of the exit nodes. The UAV also arrives at the same entry UGS after some delay and is thus informed about the presence of the target in the network. The UAV has no on-board sensing capability and so, capture entails the UAV and target being colocated at an UGS location. If this happens, the UGS is triggered and this information is instantaneously relayed to the UAV, thereby enabling capture. On the other hand, if the target reaches an exit node without being captured, he is deemed to have escaped. We transform the road network, which is restricted to a directed acyclic graph, into a time tree whose node is a tuple comprising the UGS location and evader arrival time at that location. For a given initial delay, we present a recursive forward search method that computes the minimum capture time UAV pursuit policy, under worst-case target action. The recursion scales poorly in the problem parameters, i.e., number of nodes in the time tree and number of evader paths. We present a novel branch and bound technique and a pre-processing step that is experimentally shown to reduce the computational burden by at least two orders of magnitude. We illustrate the applicability of the proposed pruning methods, which result in no loss in optimality, on a realistic example road network.

中文翻译：

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无人机在地面传感器协助下以图形方式搜索正在移动的地面目标

考虑了无人机的最佳控制，该无人机以已知的恒定速度搜索目标网络，并朝许多目标位置之一前进。为了帮助无人机，网络中的某些道路都装有无人值守的地面传感器（UGS），用于检测目标的运动并记录目标经过UGS的时间。当UAV飞越UGS位置时，会将此时间戳信息（如果可用）传达给它。在时间0，目标进入道路网络并选择通向出口节点之一的路径。在一段时间延迟后，UAV也会到达相同的条目UGS，因此会被告知网络中存在目标。无人机不具备机载传感功能，因此捕获需要将无人机和目标共同放置在UGS位置。如果发生这种情况 UGS被触发，并且该信息被立即中继到UAV，从而实现捕获。另一方面，如果目标没有被捕获就到达出口节点，则认为他已逃脱。我们将道路网络（仅限于有向无环图）转换为时间树，其节点是一个元组，包括UGS位置和逃避者到达该位置的时间。对于给定的初始延迟，我们提出了一种递归前向搜索方法，该方法计算在最坏情况下的目标动作下的最小捕获时间无人机追踪策略。递归在问题参数（即时间树中的节点数和规避者路径的数）方面的伸缩性很差。我们提出了一种新颖的分支定界技术和一个预处理步骤，该步骤在实验上显示出可以将计算负担减少至少两个数量级。我们在实际的示例道路网络上说明了所提出的修剪方法的适用性，该修剪方法不会导致最优性损失。