When the three-dimensional position data were scaled in time using the touchdown and lift-off time of the LF tripod of the perturbed trial, we normalized the data by dividing the scaled reference data by the scaled data from the perturbed trial. Kinematic variables for each tripod were quantified as the maximum positive velocity, time to peak positive velocity, time between lift-off and touchdown (dwell time), and time between touchdown and lift-off (swing time). The maximum positive velocity of the base is the velocity of the base at touchdown. A positive value indicates that the base moved in the direction of the direction of travel. The time to peak velocity is the time from touchdown to peak velocity. The dwell time is the time between touchdown and lift-off. The swing time is the time between lift-off and touchdown. The timing of touchdown, lift-off, and touchdown is difficult to determine in the presence of phototaxis. Phototaxis is the tendency of cockroaches to respond to light (e.g., by homing to a light source) and is stronger at dusk than at dawn (105). We chose to define the time of touchdown and lift-off as the time at which the velocity of the base exceeded a certain threshold. We chose a threshold of 0.1 m s-1 for the positive velocity of the base and 0.05 m s-1 for the negative velocity. The velocity of the base at touchdown was the positive velocity at that time.
To calculate the limb movement on the perturbed side, we subtracted the mean position of the selected point on the reference leg at the time of the perturbation (m2(t)) from the mean position of the selected point on the perturbed leg at the time of the perturbation (m1(t)) for each tripod of each animal (Fig. 3B). In Fig. 4, we show data normalized using the scaled time data for the perturbed right (R) and left (L) legs of one animal in which the torso remained still throughout a trial.
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