New Approach of the Variable Fractional-Order Model of a Robot Arm

Abstract

This paper proposes a simple mathematical model based on the variable fractional-order difference equation of a robot arm. The model of the described arm does not consider the impact of the movement of the mobile platform, it was assumed that all degrees of freedom would be taken away from it. The implementation of the task was divided into two stages. First, a mechanical model was developed. In order to estimate the torques of nodal propulsion motors, a description of the components of the Lagrange equation for the considered system, i.e., energy, power, and external interactions, and derivation of the equations of motion of the tested manipulator based on the Lagrange equation was made. An additional criterion was also considered in the selection of drives in the kinematic nodes of the links, which was to set the manipulator in a vertical position at a specific time. Processing the measured data of a robot arm, model parameters were selected, and the order function was chosen. The second stage was a simulation, whose results were compared with the collected data.

Keywords

• fractional calculus
• fractional order
• robot arm
• fractional variable difference
• pulse width modulation