Analytical forecasting of the optimal trajectory of mobile robot

Abstract

The purpose of the research, the results of which are presented in the article, is the analytical synthesis of the law of control of a wheeled mobile robot while it moves along a trajectory specified by reference points on the surface in an inertial coordinate system. The analysis of the existing various approaches to the formation of a given trajectory of movement of a mobile robot, based on a different mathematical formulation of the problem, is carried out. To achieve this goal, the trajectory of motion is considered to consist of separate intervals, at each of which the control optimization problem is solved. The optimization criterion in general form and its representation in the form of a minimized quadratic quality functional, convenient for analytical synthesis of control, are substantiated. As components of the functional, the parameters of the deviation of the trajectory of the mobile robot from the given points in space are considered, as well as the predicted parameters of the velocity vector and the controlling normal acceleration of the mobile robot mass center. In this case, at each given point in space, the trajectory direction to the next point is taken into account, which ensures the optimal curvature of the trajectory at a given flight speed of the aircraft. As a result of analytical synthesis, mathematical dependences were obtained to determine the control acceleration, which allow in the robot control system to obtain a given optimal control law in the form of the rotation angle of the velocity vector, which ultimately ensures the minimum energy consumption by the mobile robot for various conditions of its use. The validity of the proposed theoretical provisions is confirmed by an illustrative example, in which, for a simplified mathematical formulation of the problem, the optimal laws of changing the direction of the velocity vector and the parameters of the trajectory of a mobile robot are calculated by means of computer modeling. The illustrations show the trajectories of the robot through various given points in space and the law of changing the direction of the velocity vector.