The task of planning the trajectory of a mobile robot is considered in the following formulation: it is necessary to choose the optimal trajectory of the robot's movement over hilly terrain from one point to another among the many available paths. The developed algorithm for planning the optimal trajectory of movement of mobile objects allows minimizing energy costs when moving over hilly terrain. The optimal trajectory is determined from the condition of minimum of the functional of the rolling friction forces work. To find the optimal trajectory on which the friction forces work is minimal, is used the dynamic programming method. The proposed algorithm for planning the optimal trajectory can be used to reduce energy consumption in the process of moving over hilly terrain not only autonomous robotic systems, but also other vehicles.

Keywords: planning algorithms, rolling friction force operation, dynamic programming, optimization according to the selected criterion