STRICT MATHEMATICAL SUBSTANTIATION AND MULTI-OBJECTIVE OPTIMIZATION OF PARAMETERS OF A TWO-MODULE VIBRATION-DRIVEN LOCOMOTION SYSTEM

Abstract

Problem statement. Existing research on multi-module vibration-driven robots primarily focuses on maximizing locomotion speed by assuming ideal kinematic excitation. However, the inverse dynamic effect – the influence of the platforms’ vibrations on the driving torques of the unbalanced rotors – is often neglected. This leads to significant motor overloads, torque ripples, and reduced energy efficiency in real-world autonomous applications. Purpose. This paper aims to rigorously substantiate the optimal inertial, stiffness, damping, and excitation parameters (particularly the phase shift angle) of a two-module vibration-driven system to maximize the average locomotion speed while simultaneously minimizing the dynamic torques in the exciter drives and the overall energy consumption. Methodology. The comprehensive dynamic model of the system is derived using the Euler-Lagrange equations, coupling the translational motion of the masses with the rotational dynamics of the exciters. A non-dimensional transformation is applied to ensure the scalability of the results. The multi-criteria design problem is methodologically reduced to a single-criterion optimization task using a scalarization approach based on the Cost of Transport (CoT) index. Findings. Analytical dependencies connecting the phase shift of the unbalanced rotors with the system’s velocity and reactive driving torques are established. It is mathematically proven that a phase shift that maximizes the average speed generates extremely high peak torques on the drives. Optimal compromise parameter zones are identified. Originality. For the first time, a comprehensive multi-criteria optimization incorporating root-mean-square (RMS) drive torque and Cost of Transport (CoT) is applied to the parametric synthesis of a multi-module vibration-driven robot. Practical value. The obtained energy-optimal parameter sets provide engineers with a rigorous mathematical methodology for designing energy-efficient control systems and selecting appropriate low-power actuators for mobile vibratory machines. Scopes of further investigations. Future studies will focus on implementing the derived optimal control strategies in a physical prototype and analyzing the system’s behavior under stochastic friction conditions.