N-axis mobile robotmotion equations derivations by considering the effects of nonlinear phenomena: slip and wheels' motor backlash

In this article, using Euler-Lagrange equations, the motion equation of an n-axis wheeled mobile robot is derived. The robot motion is limited by holonomic and non-holonomic constraints. To obtain the solution, the positions of robot wheels and the mass center of the robot platform are found in two coordinate systems. Then, based on the velocity vectors of these two points, the dynamic equations of the robot are calculated. In view of the effects of flexibility, backlash, and friction of wheels, one should not neglect these parameters when the number of axes rises. Accordingly, these non-linear parameters are taken into consideration when deriving the motion equations. Finally, the resulting equations are simulated for a 4-axis mobile platform with 4 mobile wheels and the results are compared in three different cases of surface slipping ratio. This robot can be utilized in space exploration and uncharted territories as a rescue robot.