| Contents |
| We present a toy mass-spring model of bio-locomotion to identify core mathematical principles for modelling e.g.~walking or crawling.
The system is invariant under the isometry group of the (2D/3D) environment. We use a combination of symmetry, dissipation, and
regularization of ground contact to prove the existence of a relative limit cycle, that is, a trajectory which is a limit cycle upon reduction by symmetry. After actuating the system and lifting a perturbed limit cycle to the original phase space, we find that the
phase shift of each period can be viewed as the step size of a locomotive gait. |
|