Adding Inertia and Mass to Test Stability Predictions in Rapid Running Insects
A spring-mass model for the horizontal plane dynamics of sprawled running animals (Lateral Leg Spring Model) predicts that added inertia reduces stability and increases the time required to recover from a perturbation.
To empirically test this model, we perturbed cockroaches while running across a platform inserted into a track. Cockroaches (Blaberus discoidalis; N=9, 2.17 g mass, 2.18 g*cm2 moment of inertia) ran along the surface of the platform at 31±6 cm/sec with a stride frequency of 12.5±1.7 Hz. We accelerated the platform (10 cm x 25 cm) laterally at 0.6±0.1 g in a 0.1 sec interval providing a 50±3 cm/sec velocity change from the impulse. We affixed one of three backpacks on the cockroach to change its inertia distribution and mass. We used a computer vision-based tracking of body roll, pitch, yaw, leg position, and velocity on the translating platform. The control backpack increased the animal's mass by 36% and moment of inertia by 25%; the mass backpack increased mass by 84% and moment of inertia by 26%; the inertia backpack increased mass by 93% and moment of inertia by 865%.
Animals equipped with the inertia backpack were not less stable than controls, thereby rejecting the prediction of the horizontal plane Lateral Leg Spring Model. Animals running with the mass backpack were least stable, showing greater body angular changes than other conditions. Larger angular body exercisions of the animals with mass backpacks were delayed by approximately one to two steps. Consistent with this delay was a lag in the change of lateral foot placement relative to the body axis along with its recovery to the pre-perturbation values. Results suggest that a three dimensional model is necessary even in sprawled- posture animals to test hypotheses of self-stabilization, and the role of both mechanical and neural feedback.
