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A little damping goes a long way: code and data


Heim, Steve; Millard, Matthew; Le Mouel, Charlotte; Badri-Spröwitz, Alexander (2020), A little damping goes a long way: code and data, Dryad, Dataset,


It is currently unclear if damping plays a functional role in legged locomotion, and simple models often do not include damping terms. We present a new model with a damping term that is isolated from other parameters: that is, the damping term can be adjusted without retuning other model parameters for nominal motion. We systematically compare how increased damping affects stability in the face of unexpected ground-height perturbations. Unlike most studies, we focus on task-level stability: that is, instead of observing whether trajectories converge back towards a nominal limit-cycle, we quantify the ability to avoid falls using a recently developed mathematical measure. This measure allows trajectories to be compared quantitatively instead of only being separated into a binary classification of “stable” or “unstable”. Our simulation study shows that increased damping contributes significantly to task-level stability; however, this benefit quickly plateaus after only a small amount of damping. These results suggest that the low intrinsic damping values observed experimentally may have stability benefits, and are not simply minimized for energetic reasons. All Python code and data needed to generate our results are available open-source.


This is a simulation study of the effect of damping in a simple model of running, with large amounts of data generated by simulation. Both the simulation-generated data used in the paper, as well as the code to generate the data is provided. Code to process and visualize the data is also provided.

Usage Notes

A readme and guide is included in the zip file.

This codebase is also hosted online at If you wish to use the tools for new studies, we recommend using this, as it will be kept more up to date, including potential bugfixes and new features.


Max-Planck-Gesellschaft, Award: Group Leader

Deutsche Forschungsgemeinschaft, Award: MI 2109/1-1

Deutscher Akademischer Austauschdienst, Award: 57381410