On a Problem of Programming the Movement of a Mobile Robot

The paper is devoted to the problem of controlling the movement of an unmanned mobile device along a programmable trajectory. To solve this problem, we consider the issues of mathematical modeling of kinematic properties and control of dynamics of systems with program constraints. We propose a construction of systems of differential equations that can be used for setting equations of non-stationary differential constraints. The problem of constructing dynamic equations based on the integral variational principle is considered. To solve the problem of constraint stabilization, the equations of program constraints are introduced into consideration. The application of the described modeling methods is demonstrated by the example of the problem of controlling the movement of a mobile robot with the circumvent of mobile obstacles. In the course of the solution, the kinematics equations of the system are constructed and expressed in the form of equations of non-stationary differential constraints. A model of system dynamics with program constraints is constructed. Expressions of the control forces acting on the system are defined in order to satisfy the constraint equations imposed on the system. The results of solving this problem illustrate the effectiveness of the described methods. The methods proposed in this paper are applicable to solving trajectory problems, problems of controlling the movement of electromechanical and robotic systems.