Mathematical modeling of trajectory motion control of a three-wheeled mobile robot

Purpose of reseach. Improving the efficiency of the trajectory movement of three-wheeled robots by developing control system algorithms and selecting parameters based on mathematical modeling of robot movement along waypoints that characterize the required trajectory. Development of methods for planning the trajectories of a threewheeled mobile robot based on the Pure Pursuit algorithm. Development of a mathematical model of the device that allows to obtain a numerical solution for the controlled movement of the robot along the waypoints. Analysis of the simulation results in order to establish the applicability of the proposed solutions for the tasks of controlling a twosection wheeled robot for landscape work.

Methods. he Pure Pursuit algorithm is used as a basis for the development of a control system for the trajectory movement of the robot, which allows forming the trajectories of the robot along waypoints with specified motion parameters. Methods of theoretical mechanics, robot mechanics, numerical integration, control theory, electrical engineering and electromechanics were used in the development of the mathematical model. When creating software products, Matlab/Simulink mathematical packages were used.

Results. As a result of the conducted research, the main regularities of the influence of the Lookahead Distance parameter of the Pure Pursuit trajectory algorithm on the nature of the controlled robot movement were discovered and confirmed. It is shown that the choice of the value of this parameter should be justified by the control tasks and working conditions of the robot. The developed mathematical model made it possible to obtain time diagrams for the parameters of the robot's movement, to establish the accuracy of the proposed algorithms.

Conclusion. It is established in the work that the Pure Pursuit algorithm proposed in the work can be used to implement trajectory control of wheeled mobile robots. The method does not require high performance of the computing system and provides satisfactory qualitative and quantitative characteristics of motion control.

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