Two robots stand at the origin of the infinite line and are tasked with searching collaboratively for an exit at an unknown location on the line. They can travel at maximum speed b and can change speed or direction at any time. The two robots can communicate with each other at any distance and at any time. The task is completed when the last robot arrives at the exit and evacuates. We study time-energy tradeoffs for the above evacuation problem. The evacuation time is the time it takes the last robot to reach the exit. The energy it takes for a robot to travel a distance x at speed s is measured as $x{s}^2$. The total and makespan evacuation energies are respectively the sum and maximum of the energy consumption of the two robots while executing the evacuation algorithm.

Assuming that the maximum speed is b, and the evacuation time is at most cd, where d is the distance of the exit from the origin and c is some positive real number, we study the problem of minimizing the total energy consumption of the robots. We prove that the problem is solvable only for $bc\ge 3$. For the case $bc=3$, we give an optimal algorithm, and give upper bounds on the energy for the case $bc>3$.

We also consider the problem of minimizing the evacuation time when the available energy is bounded by Δ. Surprisingly, when Δ is a constant, independent of the distance d of the exit from the origin, we prove that evacuation is possible in time $O(d^{3/2}\log d)$, and this is optimal up to a logarithmic factor. When Δ is linear in d, we give upper bounds on the evacuation time.

两个机器人站在无限线的原点，并负责协同搜索在该直线上一个未知位置的出口。它们可以以最大速度b行驶，并且可以随时更改速度或方向。这两个机器人可以在任何距离，任何时间相互通信。当最后一个机器人到达出口并撤离时，任务完成。我们针对上述疏散问题研究时间-能量的权衡。疏散时间是最后一个机器人到达出口所花费的时间。机器人以速度s行驶距离x所需的能量被测量为$X{s}^2$。执行疏散算法时，总和疏散能量分别为两个机器人的能耗之和和最大值。

假设最大速度为b，疏散时间最多为cd，其中d是出口到原点的距离，c是某个正实数，我们研究了使机器人的总能耗最小化的问题。我们证明该问题仅可解决$bC\ge 3$。对于这种情况$bC=3$，我们给出了一个最佳算法，并给出了案例能量的上限 $bC>3$。

当可用能量由Δ限制时，我们还考虑使疏散时间最小化的问题。令人惊讶的是，当Δ为常数时，与出口到原点的距离d无关，我们证明了及时疏散的可能性$Ø（d^{3/2}\mathrm{日志}d）$，这是对数因子的最佳选择。当d在d中为线性时，我们给出了疏散时间的上限。