Optimal switching strategies for navigation in stochastic settings.

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.