SLIDING BIFURCATIONS OF RECTILINEAR MOTION OF A THREE-PHASE VIBRATION-DRIVEN SYSTEM SUBJECT TO COULOMB DRY FRICTION

In recent years, mobile robots' locomotion becomes diversified assisted by the continuous development of technologies in designing them. Inspired from bionics, earthworms' peristalsis becomes an object that quite a few robot designers want their robots to imitate. To this end, vibration-driven system has been put forward and researched by scholars. In this paper, the stick-slip motion of a one-module vibration-driven system moving on isotropic rough surface is studied. In consideration of the discontinuity caused by dry friction, the system considered here is of Filippov type. Based on sliding bifurcation theory in Filippov system, different types of stick-slip motions are studied. According to the values of driving parameters, 4 situations with different sliding regions can be seen. By analyzing these situations one by one, 6 kinds of motions can be achieved. By combining these motions, 4 different stick-slip motion types are finally concluded and conditions for judging occurrence of them are also derived analytically from the view point of sliding bifurcation. In the bifurcation conditions, there are 3 bifurcation parameters which can be changed in drawing bifurcation graphs. Assisted by these bifurcation graphs, detailed analysis is given about how stick-slip motion types change from one to another when parameters change and physical explanations from the perspective of bifurcation theory are also given. At last, the original differential motion equation is solved in a numerical way and one can see that 4 different stick-slip motion types derived numerically correspond with the former analytical results, which verifies the correctness of the bifurcation analysis in this paper well.