Uncovering Universal Characteristics of Homing Paths using Foraging Robots

Homing–the incredible ability of animals to navigate back to their homes from unfamiliar places is surprisingly widespread and crucial for their survival. However, the physical understanding of this phenomenon is not yet developed. Here we use a light-controlled robot mimicking foraging and homing behavior to investigate this phenomenon. The robot as a forager is a self-propelled active particle programed to undergo an in-plane active Brownian (AB) motion whose velocity vector <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi mathvariant="bold">v</a:mi></a:math> undergoes rotational diffusion of magnitude <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>D</c:mi><c:mi>r</c:mi></c:msub></c:math>. During the homing phase, the robot undergoes guided motion toward a positive light gradient aided by repeated reorientations, directing it back to its home. Our key finding is an interesting optimal behavior where the mean homing time becomes independent of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>D</d:mi><d:mi>r</d:mi></d:msub></d:math> beyond a critical value posited as a signature of enhanced efficiency. We develop a first-passage-based theoretical model of homing motion, which elucidates this finding as well as accurately captures quantitative features of the homing trajectories in the form of temporal autocorrelation function of the robot's orientation. Inspired by the paradigm of stochastic resetting processes, we also perform an alternative homing motion in a computer, which integrates an AB motion with course correction resets, corroborating our experimental findings. Finally, we test our model on the publicly available data on homing pigeons and capture similar key characteristics of the homing trajectories. Together, these results offer valuable insights into the physics of homing dynamics, providing a statistical basis for its robustness across the animal kingdom. Published by the American Physical Society 2024