The Movement Planning of Mobile Robots in Performing Search Task Based on Probability Theory

Abstract

The article is devoted to the development of searching and covering task in different areas, for example, for extinguishing fires, during search operations in the air, on the ground, etc. Two probabilistic models were created based on the characteristics of the sensors and the search zone, that is, the probability density of the target position and the conditional probability of detecting the target by the sensor under the conditions that the target is at the point of observation (depending on the distance between the sensor and the point of observation). Based on these models, the parameters and the search procedure were analyzed; more precisely, the relationship and formulas between the target detection probability, the search time and other parameters were found. The main difference of the proposed research lies in the fact that by optimizing the obtained relations and formulas it is possible to obtain an optimal distribution of time in the search process, as a result, to increase the probability of target detection. In the research process, at first, the case where the distribution probability of target position in the search area represents a discrete form (network map) is investigated, then a formula for the probability of target detection in a discrete and continuous probe is obtained. Using the method of Lagrange multipliers and dynamic programming, the optimal distribution of search time in each cell was obtained. Further, according to the result obtained, the study was expanded to a continuous distribution probability of target position in the search area, the functional probability of detecting the target of search time, probability density of target and the search trajectory (velocity) was derivated. As a result of solving this functional, for a given search time and probability density distribution of target, optimal control (trajectory and speed) was obtained. The simulation confirmed the efficiency of the proposed search method. The simulation result shows that the greater the probability density of target and the slower the agent’s movement speed, the greater the probability of target detection, for some values of the search parameters, the difference in probabilities of target detection reaches 75.3 %.