Locomotion based on differential friction

This paper analyzes the locomotion of simple mechanisms when the inertial forces are much smaller compared to the applied forces. The induced motion of the body is entirely due to viscous friction contact with the environment. The friction coefficient depends on the body geometry, and we assume a model where it is simply a function of the sign of the velocity. In this case the kinematics and dynamics are easily solvable as a hybrid system. Moreover, scale invariance of the solution is shown. Thus only the pattern as function of time is left to be determined and/or optimized. We consider a hypothetical flapper in detail, for which the optimal control is derived. This is further illustrated on similar models mimicking locomotion found in nature.