Constructing a map of locally optimal paths for a controlled moving object in a threat environment

In some path planning problems for controlled objects, the main criterion is to reduce the integral risk of detection when moving in a threat environment with a given map of potential threats. In this paper, we construct all locally optimal paths in a 2D threat environment. The environment is represented by a fixed number of detectors whose positions are known to an evasive object. This object and the detectors are material points. The original problem is formalized as an optimal control problem and reduced to a boundary value problem based on Pontryagin's maximum principle. The boundary value problem is solved numerically by the shooting method. The case of point-to-point transition of the evasive object with and without the path length constraint is studied, and the results of numerical simulation are provided. A parametric analysis of the problem is carried out.