Modeling the Dynamics of a Heavy-Duty Mobile Robot Based on Gauss's Principle of Least Constraint

This paper presents a novel approach to model the dynamics of a heavy-duty mobile robot using Gauss’s principle of least constraint. Unlike traditional Lagrangian methods, which often lead to complex systems of differential and algebraic equations, Gauss's principle simplifies the dynamic equations by reducing the problem to an algebraic form. This method efficiently determines the accelerations of the robot, which is crucial for real-time control and optimization. The mobile robot in question features a universal platform with four wheels and two DC servomotors, driving the rear wheels. We account for both static and dynamic characteristics of the motors and introduce a methodology for modeling the forces and moments of friction on the wheels. The derived equations of motion are solved using adaptive Runge-Kutta-Fehlberg integration methods. This approach provides a powerful tool for analyzing and controlling the robot’s dynamics, offering significant advantages for large-scale industrial and transportation applications. The results are validated through simulations using high-performance computing techniques.