Mori Francesco, Mahadevan L
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, UK.
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.
J R Soc Interface. 2025 Jun;22(227):20240677. doi: 10.1098/rsif.2024.0677. Epub 2025 Jun 18.
When navigating complex environments, animals often combine multiple strategies to mitigate the effects of external disturbances. These modalities often correspond to different sources of information, leading to speed - accuracy trade-offs. Inspired by the intermittent reorientation strategy seen in the behaviour of the dung beetle, we consider the problem of the navigation strategy of a correlated random walker moving in two dimensions. We assume that the heading of the walker can be reoriented to the preferred direction by paying a fixed cost as it tries to maximize its total displacement in a fixed direction. Using optimal control theory, we derive analytically and confirm numerically the strategy that maximizes the walker's speed, and show that the average time between reorientations scales inversely with the magnitude of the environmental noise. We then extend our framework to describe execution errors and sensory acquisition noise. As a result, we provide a range of testable predictions and suggest new experimental directions. Our approach may be amenable to other navigation problems involving multiple sensory modalities that require switching between egocentric and geocentric strategies.
在复杂环境中导航时，动物常常会结合多种策略来减轻外部干扰的影响。这些模式通常对应于不同的信息来源，从而导致速度与准确性之间的权衡。受蜣螂行为中间歇性重新定向策略的启发，我们考虑二维空间中相关随机游走者的导航策略问题。我们假设，游走者在试图使自身在固定方向上的总位移最大化时，可以通过付出固定代价将行进方向重新定向到首选方向。利用最优控制理论，我们进行了分析推导并通过数值方法予以证实，得出了使游走者速度最大化的策略，并表明重新定向之间的平均时间与环境噪声的大小成反比。然后，我们扩展了框架以描述执行误差和感官获取噪声。由此，我们提供了一系列可检验的预测，并提出了新的实验方向。我们的方法可能适用于其他涉及多种感官模式的导航问题，这些问题需要在以自我为中心和以地球为中心的策略之间进行切换。
