Lévy robotics

Two the most common tasks for autonomous mobile robots is to explore the environment and locate a target. %In the last case, the objective is either to find a target in the shortest time possible or, alternatively, to find %as many targets as possible for a given amount of time. Targets could range from sources of chemical contamination to people needing assistance in a disaster area. From the very beginning, the quest for most efficient search algorithms was strongly influenced by behavioral science and ecology, where researchers try to figure out the strategies used by leaving beings, from bacteria to mammals. Since then, bio-inspired random search algorithms remain one the most important directions in autonomous robotics. Recently a new wave arrived bringing a specific type of random walks as a universal search strategy exploited by immune cells, insects, mussels, albatrosses, sharks, deers, and a dozen of other animals including humans. These \textit{L\'{e}vy} walks combine two key features, the ability of walkers to spread anomalously fast while moving with a finite velocity. The latter is especially valuable in the context of robotics because it respects the reality autonomous robots live in. There is already an impressive body of publications on L\'{e}vy robotics; yet research in this field is unfolding further, constantly bringing new results, ideas, hypothesis and speculations. In this mini-review we survey the current state of the field, list latest advances, discuss the prevailing trends, and outline further perspectives.