A Probabilistic Functional-Based Trajectory Planning Method in an Environment with Obstacles and Hazardous Areas

This paper considers the problem of motion planning in an environment with polygonal stationary obstacles and threat sources with limited areas of action. This problem is relevant, for example, when planning motion during fires, in environments with chemical and radioactive contamination. This paper proposes a method that maximizes the probability of successful evasion from threat sources for fixed starting and ending points. This method is based on characteristic probability functions that allow one to consider a wide class of threat sources whose area of action is specified by an arbitrary polygonal figure. The method allows one to iteratively correct the initial trajectory of motion in a given neighborhood until a given value of the probability of successful evasion is achieved. In this paper, a previously known method of nonsmooth optimization of the probability of successful evasion from disturbance sources is reduced to a smooth optimization problem. For this purpose, continuous approximations are introduced for the membership functions of threat areas and their partial derivatives. The proposed method is based on a closed representation of the probability of successful passage of a piecewise linear trajectory located in the field of action of disturbance sources with specified characteristic probability functions. The optimization problem is solved numerically by the gradient method under restrictions on the maximum distance of the target trajectory from the initial trajectory and a specified admissible probability of successful passage. A comparative analysis of the computational efficiency of the proposed algorithm is carried out, showing the feasibility of its scaling and extension to complex conflict areas of movement.