A Simple Stabilizing Control for Sagittal Plane Locomotion

The spring loaded inverted pendulum model has been shown to accurately model sagittal plane locomotion for a variety of legged animals and has been used as a target for control for higher dimensional robotic implementations. Tuned appropriately, the model exhibits passively stable periodic gaits using either fixed leg touch-down angle or swing-leg retraction leg touch-down protocols. In this work, we examine the performance of the model when model parameters are set to values characteristic of an insect, in particular the cockroach Blaberus discoidalis. While body motions and forces exhibited during a stride are shown to compare well with those observed experimentally, almost all of the resulting periodic gaits are unstable. We therefore develop and analyze a simple adaptive control scheme that improves periodic gait stability properties. Since it is unlikely that neural reflexes can act quickly enough during a stride to effect control, control is applied once per stance phase through appropriate choice of the leg touch-down angle. The control law developed is novel since it achieves gait stabilization solely through a judicious combination of leg lift-off and touch-down angles, instead of utilizing all of the system positions and velocities in full-state feedback control. Implementing the control law improves the stability properties of a large number of periodic gaits and enables movement between stable periodic gaits by changing a single parameter.