M. Pivovarov

Dynamics and Control of a Two-Module Mobile Robot on a Rough Surface

A two-module (two-body) locomotion system moving along a straight line on a rough horizontal plane is considered. The motion of the system is excited by a periodic change in the distance between the bodies. Friction between the bodies and the plane obeys Coulomb’s law. The conditions for the system to be able to start moving from a state of rest and the steady-state motion are studied. The friction force acting on the system is assumed to be small as compared with the excitation force, and the method of averaging is applied to the equation of motion of the system’s center of mass. On the basis of the averaged equation, necessary and sufficient conditions subject to which the system can start moving from a state of rest in a dry friction environment are obtained. The excitation law that implies a piecewise quadratic time history of the distance between the bodies is considered. For this excitation law, the system can start moving from a state of rest if the bodies have different masses and the times of increase and decrease of the distance between them do not coincide. Closed-form expressions for the steady-state velocity of the system’s center of mass are obtained and investigated as a function of the parameters of the system and the excitation law. The maximum magnitudes of the steady-state velocities and the respective values of the parameters are found. An experimental prototype of the robot under consideration was built. The experimental results demonstrate qualitative agreement with the theoretical predictions.

Dynamics and control of a two-degree-of-freedom vibration-driven system

Abstract A rectilinear motion of a system of two bodies connected by a spring on a rough horizontal plane is studied. The coefficient of friction between the bodies and the plane is assumed to be small. The motion of the system is excited by two identical unbalance rotors based on the respective bodies. Major attention is given to the steady-state velocity-periodic motion. A nearly-resonant excitation mode, for which the angular velocities of the rotor are close to the natural frequency of the system, is considered. It is shown that control of the steady-state motion can be provided by changing the phase shift between the rotations of the rotors and the sign of the resonant detuning measured by the difference between the angular velocity of the rotors and the natural frequency of the system. By varying the phase shift one can control the magnitude of the average velocity and varying the detuning enables one to change the direction of the motion.