Dynamics of rimless wheel robots during collision

Rimless wheel robots are ground robots with high mobility on a variety of uneven terrains. Rimless wheels have no rims or tires but only spokes, and rimless wheel robots move along with collisions of spokes with the ground. Their equations of collision have been derived from a conservation law of angular momentum only for the simplest type of rimless wheel robots. It is uncertain when the conservation law is satisfied or violated, and what happens in the violated case. Complete equations of collision are unknown even for the simplest type of rimless wheel robots. This paper considers three types of rimless wheel robots including the simplest type and provides complete equations of collision for each type of rimless wheel robots. In addition, this paper describes properties of the dynamics during collision. Some of them reveal relationships between the dynamics of the three types of rimless wheel robots. Another shows a relationship between the dynamics of rimless wheels and circular wheels. They also clarify when the conservation law of angular momentum is satisfied or violated, and what happens in each case.