ANDERSON, B.D.*; FULL, R.J.; GARCIA, M.: A Spring-Mass Model of Centipede Locomotion

The laterally undulating Arizona centipede, Scolopendra heros, uses a metachronal gait in which all legs on the concave side of the bent body touch the ground at a single point. Each leg of the wave of legs traveling through this point is not on the ground for a long enough period to aid in understanding centipede locomotor dynamics. However, as a wave of legs travels through this one point of ground contact, the individual legs combine to generate ground reaction forces (GRFs) and mechanical energies (MEs) of the center of mass that are similar to a spring. This is analogous to the spring-like behavior of all legs in contact with the ground at a time, or the “virtual leg,” in symmetrical gaits. We model each wave of centipede legs as a “virtual wave-spring.” Centipedes have several points of leg contact, or virtual wave-springs, on the ground generating force at any given time. Therefore, we modeled centipede whole-body locomotor dynamics as the sum of several virtual wave-springs. The period of each virtual wave-spring and the lag between successive virtual wave-springs were altered to model different kinematic conditions. Our model predicts that only under unobserved kinematic conditions would centipedes demonstrate whole-body dynamics of a rolling wheel, as predicted by Gray (1953), or have whole-body GRF and ME patterns that complete a full cycle in a typically�defined stride period. The model predicts that under most conditions, the whole-body GRF and ME patterns will complete a full cycle in the period it takes for a wave of legs to complete its contact with the ground and the next wave of legs to be set on the ground. The period of time a wave of centipede legs is on the ground is analogous to the stride period in symmetrical gaits.