A disturbance rejection measure for limit cycle walkers: The Gait Sensitivity Norm

The construction of more capable bipedal robots highly depends on the ability to measure their performance. This performance is often measured in terms of speed or energy efficiency,but these properties are secondary to the robot's ability to prevent failing given the inevitable presence of disturbances, i.e., its disturbance rejection. Existing disturbance rejection measures (zero moment point, basin of attraction, Floquet multipliers) are unsatisfactory due to conservative assumptions, long computation times, or bad correlation to actual disturbance rejection. This paper introduces a new measure called the Gait Sensitivity Norm that combines a short calculation time with good correlation to actual disturbance rejection. It is especially suitable for implementation on limit cycle walkers, a class of bipeds that currently excels in terms of energy efficiency, but still has limited disturbance rejection capabilities. The paper contains an explanation of the Gait Sensitivity Norm and a validation of its value on a simple walking model as well as on a real bipedal robot. The disturbance rejection of the simple model is studied for variations of floor slope, foot radius, and hip spring stiffness. We show that the calculation speed is as fast as the standard Floquet multiplier analysis, while the actual disturbance rejection is correctly predicted with 93% correlation on average.