Probabilistic analysis of some navigation strategies in a dynamic environment

The problem of efficient path planning for a point robot in a partially known dynamic environment is considered. The static known part of the environment consists of point shelters distributed in planar terrain, and the dynamic, unknown part is abstracted in the form of alarms that cause the robot to leave its current (preplanned) path and divert to the nearest shelter. We give a probabilistic analysis of the expected times for the dynamic paths generated when the alarms follow a Poisson distribution with parameter λ. A case study with three shelters serves to illustrate the dependence of the expected travel times on λ for two alternate static paths. Two different strategies are presented for the general case of n shelters and shown to be superior for different ranges of values of the alarm rate λ (very low and very high values, respectively). We also discuss some ways of generalizing the approach and possible applications