Dynamical behavior of a mobile system with two degrees of freedom near the resonance

The design of mobile robots that can move without wheels or legs is an important engineering and technological problem. Self-propelling mechanisms consisting of a body that has contact with a rough surface and moveable internal masses are considered. Mathematical models of such systems are presented in this paper. First, a model of a vibration driven robot that moves along a rough horizontal plane with isotropic dry friction is studied. It is shown that by changing the off-resonance frequency detuning in sign, one can control the direction of motion of the system. In addition, a locomotion system which moves in an environment with anisotropic viscous friction is considered. For all models, the method of averaging to obtain an algebraic equation for the steady-state “average” velocity of the system is used. Prototypes were constructed to compare the theoretical results with experimental ones.