Most running robots and running models use linear leg springs. Non-linear leg springs have the potential to improve the performance of running robots and models, but it is not clear to what extent. In this paper, the effect of non-linear leg springs on disturbance rejection behavior is investigated. The optimal leg stiffness profile is determined by optimizing the gait sensitivity norm, a measure for disturbance rejection. The results of this optimization show that the optimal leg stiffness profile is strongly non-linear, and that the disturbance rejection is a factor of seven better than it would be with the optimal linear leg stiffness. The cause for this great improvement is that non-linear leg springs allow stable limit cycles that are much further away from the fall modes.
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