Viscous friction-like relationship arises from a simple Columb friction locomotion model

It is well known in thermodynamics that viscosity-like dissipation relationships appear in particle models even after only a small number of collisions was simulated. We present a minimalistic model of a robot moving inchworm-like in a Columb friction regime, which exhibits a similar effect. This model is sufficiently simple to allow the relationship between actuation force and asymptotic average speed to be solved in closed form. For the range of parameters relevant for decimeter to meter length robots, the relationship of force and speed that arises is nearly linear - suggesting that the average behavior of this locomoting system appears similar to pushing through a viscous medium, and that viscosity-like models might be more appropriate to robots than we previously assumed.