Abstract:Mobile robot has become an important branch in the domain of robotics. In order to achieve its movement in some narrow and special environments, the vibration-driven system has been proposed and researched by domestic and foreign scholars. In this paper, such a vibration-driven system consisting of an external rigid box and two internal mass blocks which are driven by three-phase control on two parallel orbits is researched. And the box is always in contact with the rough ground via three rigid support elements. This kind of vibration-driven system has simple structure, good sealing performance, and relies on the friction force between the box and the rough ground to realize its directional movement. Based on the two-dimensional LuGre friction model and Lagrange equations of the second kind, the dynamic modeling method and numerical algorithm of the vibration-driven system are presented in an isotropic friction environment. The use of the two-dimensional LuGre friction model can effectively avoid the difficulty of solving the dynamic equations caused by the discontinuity of the Coulomb friction model, and can accurately reveal the stick-slip switching phenomenon during the movement of vibration-driven systems. The numerical simulation results show that the driving parameters of the internal mass blocks can be adjusted to realize rectilinear translation, rotation about a fixed-axis and general plane motion of the rigid box. And four types of stick-slip motion with different sliding regions can occur during the translation and rotation of the rigid box, such as grazing sliding, crossing sliding, switching sliding and no stick. In addition, the translational speed and rotational speed of the box body and the radius of curvature of the box centroid trajectory can be changed by adjusting the driving parameters.