Optimization of mobile robot movement on a plane with finite number of repeller sources

The paper considers the problem of planning a mobile robot movement in a conflict environment, which is characterized by the presence of areas that impede the robot to complete the tasks. The main results of path planning in the conflict environment are considered. Special attention is paid to the approaches based on the risk functions and probabilistic methods. The conflict areas, which are formed by point sources that create in the general case asymmetric fields of a continuous type, are observed. A probabilistic description of such fields is proposed, examples of which are the probability of detection or defeat of a mobile robot. As a field description, the concept of characteristic probability function of the source is introduced; which allows us to optimize the movement of the robot in the conflict environment. The connection between the characteristic probability function of the source and the risk function, which can be used to formulate and solve simplified optimization problems, is demonstrated. The algorithm for mobile robot path planning that ensures the given probability of passing the conflict environment is being developed. An upper bound for the probability of the given environment passing under fixed boundary conditions is obtained. A procedure for optimizing the robot path in the conflict environment is proposed, which is characterized by higher computational efficiency achieved by avoiding the search for an exact optimal solution to a suboptimal one. A procedure is proposed for optimizing the robot path in the conflict environment, which is characterized by higher computational efficiency achieved by avoiding the search for an exact optimal solution to a suboptimal one. The proposed algorithms are implemented in the form of a software simulator for a group of ground-based robots and are studied by numerical simulation methods.