We study the problem of assigning robots with actions to track targets. The objective is to optimize the robot team's tracking quality which can be defined as the reduction in the uncertainty of the targets' states. Specifically, we consider two assignment problems given the different sensing capabilities of the robots. In the first assignment problem, a single robot is sufficient to track a target. To this end, we present a greedy algorithm (Algorithm 1) that assigns a robot with its action to each target. We prove that the greedy algorithm has a 1/2 approximation bound and runs in polynomial time. Then, we study the second assignment problem where two robots are necessary to track a target. We design another greedy algorithm (Algorithm 2) that assigns a pair of robots with their actions to each target. We prove that the greedy algorithm achieves a 1/3 approximation bound and has a polynomial running time. Moreover, we illustrate the performance of the two greedy algorithms in the ROS-Gazebo environment where the tracking patterns of one robot following one target using Algorithm 1 and two robots following one target using Algorithm 2 are clearly observed. Further, we conduct extensive comparisons to demonstrate that the two greedy algorithms perform close to their optimal counterparts and much better than their respective (1/2 and 1/3) approximation bounds.

翻译：我们研究了为机器人分配动作以跟踪目标的问题。目标是优化机器人团队的跟踪质量，该质量可定义为目标状态不确定性的降低程度。具体而言，我们根据机器人不同的感知能力考虑了两种分配问题。在第一个分配问题中，单个机器人足以跟踪一个目标。为此，我们提出了一种贪心算法（算法1），为每个目标分配一个机器人及其动作。我们证明了该贪心算法具有1/2近似比且运行时间为多项式。接着，我们研究了第二个分配问题，其中需要两个机器人来跟踪一个目标。我们设计了另一种贪心算法（算法2），为每个目标分配一对机器人及其动作。我们证明了该贪心算法达到1/3近似比且具有多项式运行时间。此外，我们在ROS-Gazebo环境中展示了两种贪心算法的性能，其中可以清晰观察到算法1中一个机器人跟随一个目标的跟踪模式，以及算法2中两个机器人跟随一个目标的跟踪模式。最后，我们通过大量对比实验证明，这两种贪心算法的性能接近其最优解，且远优于各自（1/2和1/3）的近似比界限。