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群体定位未知标量场源（即最大值）的解决方案。与传统依赖梯度信息的方法不同，该群体能够确定一个上升方向，以任意精度逼近源点。该上升方向基于机器人位置处的场强测量值及其相对于质心的相对位置计算得出。我们并非聚焦于单个机器人，而是分析单位面积内的机器人密度，从而确保群体更具弹性，即：即使任务过程中部分个体丢失或偏离预定位置，群体功能仍得以维持。通过为群体形态提供充分条件（使上升方向几乎与梯度平行），我们增强了算法的鲁棒性。群体能够通过改变自身形态并利用多个上升方向的存在性来应对意外环境。最后，我们使用数百个机器人通过数值方法验证了我们的方案。大量机器人始终能计算出一个上升方向这一事实，不仅弥补了个体损失，还缓解了由执行器与传感器噪声引发的问题。