The paper considers an algorithm for gradient motion on a surface that simulates a scene with target objects and obstacles. To implement the gradient descent algorithm, the principles of functionalvoxel modeling are used, which allow organizing a region of gradient characteristics for a given scene space. The mathematical apparatus of R-functions is chosen as a tool for describing a scene with obstacles. Approaches for obtaining the inverse expression of the R-function, i.e. removing an object from the scene to solve problems of dynamic rearrangement of obstacles and goals, are investigated. A functional-voxel approach to solving the procedure for the inverse expression of an R-function without loss of the sign of the function value is shown, which does not allow performing an algebraic expression of an R-function directly. The result of the inverse decomposition into objects is demonstrated by the example of the application of the R-intersection function. The principle of functional-voxel modeling of the area of the intersection law of two specific objects is implemented, which allows solving the direct and inverse problem of R-functional modeling.

Gradient descent, functional-voxel modeling, R-functional modeling, obstacle course search, inverse R-function

Tolok A.V.,  ,  orcid.org/0000-0002-7257-9029,  V.A. Trapeznikov Institute of Control Science of Russian Academy of Sciences

Petukhov P.A.,  ,  orcid.org/0000-0002-2333-3524,  Moscow State University of Technology 'STANKIN'