Maxim V. Bakanov, Aleksey V. Daneev, Victor N. Sizykh

Irkutsk State transport University

The article develops mathematical models of a three-wheeled mobile robot based on the apparatus of state variables and in operator form, on the basis of which the synthesis of its adaptive control system is carried out using the method of constructing modal PID controllers and the method of inverse problems of dynamics. The mathematical model allows, without hardware implementation of a mobile robot, to analyze the work of the created control system and, if necessary, make the necessary corrections. The mathematical model of a mobile robot consists of kinematic and dynamic models. The kinematic model is the simplest description of the behavior of a mobile robot and allows the study of its properties. The dynamic model is a more detailed description of the mobile robot and takes into account the force and moment effects produced by the actuators. In order to mathe-matically describe the mobile robot, a number of conditions are introduced, formulated as the following assump-tions: 1) the mobile robot is considered under the condition that its mechanism is rigidly connected; 2) the wheels are non-deformable and are in point contact with the surface; 3) the movement of the robot is carried out without slipping; 4) the platform is considered as a solid body on which the wheel system is fixed. The paper presents the following results of the study: developed mathematical models of a mobile robot in the state space and in operator form; the robot motion control algorithm was synthesized based on the method of inverse prob-lems of dynamics; a Simulink model of a controlled mobile robot was developed based on the modal PID control technique. The stability of the control system is ensured by introducing an external negative feedback on the an-gular velocity of the robot platform. The simulation results show that, compared with an accurate continuous mathematical model of robot control, the errors in coordinates, angular and linear velocities and moments are 5-7%, which allows us to draw a conclusion on the acceptability of the developed digital robot model, its accurate continuous analogue.

autonomous mobile robot, mathematical models in the state space and in operator form, modal PID controller, method of inverse problems of dynamics