Starting over without forgetting the past can benefit your search

In the past decade, the resetting of random processes has been studied extensively, being relevant to natural processes. Under resetting, a random process can reach a stationary steady state that may reduce the average time it takes to reach a target. A resetting process generally includes cycles of a period of random motion followed by a period of return to the origin. When the random process is reset, the entire system starts from the same initial conditions as in the previous cycle. Inspired by scent trails left by ants, we study the case where random motion leaves a mark on the environment. Namely, after resetting the system, the environment retains the memory of former trajectories. We implement this process using a self-propelled bristle robot moving within an arena filled with mobile obstacles. We return the bristle robot to the origin at constant time intervals. Our main finding is that even the basic interaction between an agent and its environment, that we have implemented here, benefits the search. We find that this is a result of the increased mobility of a searcher when it walks on old tracks since it is no longer hindered by the need to clear its path. The higher mobility leads to a larger range of motion at the given time window for search. This, in turn, results in a decrease in the search duration. The essential ingredients for utilizing the environment for this purpose are that the trail a searcher leaves enhances the mobility of a second search along the same trail and that the searcher performs a persistent walk along the trail.

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