Solving the problem of finding a point equidistant from objects in 3D space

This article proposes a problem statement and its solution for finding a point equidistant from objects in three-dimensional space. The article considers an approach to determining the possible trajectory of a given object in an assumed threedimensional space R³, in which there are static 3D objects that impede the movement of the given object. A computer vision system is used for spatial positioning. To determine the point of displacement of the object's trajectory in space, a solution to the problem of searching for optimal trajectories on planes that do not intersect or touch the boundaries is proposed. The article discusses an algorithm for solving this problem and provides examples of determining optimal trajectories in a curved surface using the method of multicriterial interpolation of curves, with a given discretization step. The generation of a data set for a curved surface (point cloud) is described. Examples of searching for the hovering point of an object in the absence of its contact with external boundaries are given. An example of searching for an equidistant point in space with simple-shaped objects is given on a test data set, and recommendations are given for their use in robotic systems.