Equations of collision of rimless wheel robots

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. Existing equations of collision for rimless wheel robots have been formulated only when a loss-of-contact assumption is satisfied. It is uncertain when the loss-of-contact assumption is satisfied or violated, and what happens in the violated case. This paper considers three types of rimless wheel robots, and provides complete equations of collision for each type of rimless wheel robots. The equations of collision clarify a loss-of-contact condition for each type of rimless wheel robots. They also clarify when each loss-of-contact condition is satisfied or violated, and what happens in each case.