navigation among movable obstacles

the problem of navigation among movable obstacles (namo) is to find a collision free path for a robot while the robot is able to manipulate and transfer some objects (if possible or needed) to clear its path toward the goal. namo is a np-complete problem and is in a class of motion planning problems that have dynamic environments. in this domain, an optimal plan for the robot can be defined with respect to many different criteria such as length of the transit and transfer paths, number of manipulated obstacles, total number of displacements of all the objects and time. in this article, we have tried to design an algorithm capable of solving a wide variety of namo problems, using concepts like, visibility graph and penetration depth. using the recursive function to solve some existing problems in the literature shows significant reduction in number of transferred movable obstacles as well as total number of displacements of all the objects.