One method for autonomously exploring unknown environments is to treat the environment as a scalar potential field. In this scenario, one or more robots acquire measurements of the field (e.g., radiation, temperature, or carbon dioxide concentrations) and use those measurements to guide their path as they explore. An important behavior robots may need is that of extremum seeking-that is, the ability to autonomously drive toward a region containing a maximum or a minimum of the field and reliably stay with this extremum even if its location is moving. In this paper, we describe an extremum seeking control law for three-dimensional scalar potential fields built upon a previous two-dimensional law. We derive an equilibrium trajectory, prove its local stability for the case of a radial scalar field, and characterize the stability as a function of parameters by numerically evaluating its Floquet multipliers. Additionally, we consider the case where the field is constant except for a small range around the source and allow the source to be diffusing with an unknown diffusion coefficient. We derive an approximate expected first passage time and use numerical simulations to show how to optimally select parameters so that the expected tracking time is maximized.

中文翻译：

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通过非完整极值搜索跟踪扩散三维源


自主探索未知环境的一种方法是将环境视为标量势场。在这种情况下，一个或多个机器人获取现场的测量值（例如，辐射、温度或二氧化碳浓度），并使用这些测量值来指导它们探索的路径。机器人可能需要的一个重要行为是极值搜索，即能够自主行驶到包含最大或最小场的区域，并可靠地保持在该极值处，即使其位置正在移动。在本文中，我们描述了基于先前二维定律的三维标量势场的极值寻求控制律。我们推导出平衡轨迹，证明其在径向标量场情况下的局部稳定性，并通过数值评估其 Floquet 乘数将稳定性表征为参数的函数。此外，我们考虑除了源周围的小范围外场恒定的情况，并允许源以未知的扩散系数扩散。我们得出近似的预期首次通过时间，并使用数值模拟来展示如何最佳选择参数以使预期跟踪时间最大化。