Planar motion analysis and control of vibration-driven system driven by three-phase motion of two internal masses

The research on vibration-driven system with several internal masses is of great significance for creeping robots in some narrow space, while seldom scholars study the planar motion with continuously changing curvature. The planar locomotion of this system with two internal masses, driven by three-phase motion, under viscous and anisotropic friction is studied in this paper. When the period ratio of the two moving internal masses is equal to 1, the trajectory of the system is a circle. The analytical solutions of steady-state linear velocity and angular velocity of circular motion are obtained by using the averaging method. When the period ratio is not equal to 1, the trajectory of the system is a linear. The influence of relative acceleration and the period ratio of the two moving internal masses on the planar motion of the system is analyzed by using the Velocity-Verlet integration method, which is verified by the Runge-Kutta method. The planar locomotion of the system can be obtained. It follows from the above analysis results that the six types of the switching trajectory can arise by controlling the driven parameters. Finally, integrating the different switching trajectories, one can obtain any continuous-curvature paths, which has important application value for the trajectory planning of the mobile robot.