We present a solution for locating the source, or maximum, of an unknown scalar field using a swarm of mobile robots. Unlike relying on the traditional gradient information, the swarm determines an ascending direction to approach the source with arbitrary precision. The ascending direction is calculated from measurements of the field strength at the robot locations and their relative positions concerning the centroid. Rather than focusing on individual robots, we focus the analysis on the density of robots per unit area to guarantee a more resilient swarm, i.e., the functionality remains even if individuals go missing or are misplaced during the mission. We reinforce the robustness of the algorithm by providing sufficient conditions for the swarm shape so that the ascending direction is almost parallel to the gradient. The swarm can respond to an unexpected environment by morphing its shape and exploiting the existence of multiple ascending directions. Finally, we validate our approach numerically with hundreds of robots. The fact that a large number of robots always calculate an ascending direction compensates for the loss of individuals and mitigates issues arising from the actuator and sensor noises.

翻译：我们提出了一种利用移动机器人集群定位未知标量场源点（即最大值）的解决方案。与传统依赖梯度信息的方法不同，该集群通过确定一个上升方向以任意精度逼近源点。上升方向根据机器人在各自位置测得的场强值及其相对于质心的相对位置计算得出。我们的分析重点不在于单个机器人，而是关注单位面积内的机器人密度，以此保证集群具备更强的弹性——即使在任务执行过程中有个体机器人丢失或错位，集群功能仍能维持。我们通过给出集群形态的充分条件来增强算法的鲁棒性，确保上升方向几乎与梯度方向平行。集群能够通过改变自身形态并利用多个上升方向的存在来应对意外环境变化。最后，我们通过数百个机器人的数值实验验证了所提方法。大量机器人持续计算上升方向这一特性，有效补偿了个体损失，并缓解了由执行器与传感器噪声引起的问题。