Abstract: Lévy walks are random walks in which the walker moves
continuously and with a constant velocity between the reorientation events. The
durations of these displacements and correspondingly their lengths are power-law
distributed. Lévy walks were shown to be a very successful model to describe a
variety of anomalous diffusion dispersal phenomena in physics, biology and
ecology. In the context of search, Lévy walks were suggested as an optimal
strategy for finding rare renewable targets and that boosted the research in
Lévy foraging strategies in living organisms. The trend was inherited in
robotics, where Lévy algorithms were implemented in robots performing various
search tasks.

However, one important aspect intrinsically present in most living systems but
also in robotics – the existence of home range – was not considered before in
the context of random search. The fact that a bird needs to return to its nest
and a robot to its charging station seems obvious, but the implementation of
such processes on the model level is a highly non-trivial task. In this talk, we
will introduce the concept of Lévy walk bridges – Lévy walk trajectories
returning to the origin after a fixed time. We will show how to tackle the
challenge of the efficient bridge generation and how the Lévy walk bridges
operate during search. We will discuss what further intriguing problems open up
in relation to the introduced concept.