Sideways walking: preferred is slow, slow is optimal, and optimal is expensive

This webpage supports the following article about people walking sideways. If you need more information about this article that is not available on this page, please contact Manoj Srinivasan.

Webpage remains under construction until the article's publication.


Sideways walking: preferred is slow, slow is optimal, and optimal is expensive
Biology Letters, 10 (1), 20131006, 2014.

Authors: Matthew L. Handford and Manoj Srinivasan

Single PDF containing both the Main article + Supplementary Information.

Abstract: When humans wish to move sideways, they almost never walk sideways, except for a step or two. Instead, they usually turn and walk facing forward. Here, we show that the experimentally measured metabolic cost of walking sideways, per unit distance, is over three times as expensive than forward walking. We explain this high metabolic cost with a simple mathematical model; sideways walking is expensive because it involves repeated starting and stopping. When walking sideways, our subjects preferred a low natural speed, averaging 0.575 m/s (0.123 s.d.). Even with no prior practice, this preferred sideways walking speed is close to the empirical metabolically optimal speed, averaging 0.610 m/s (0.064 s.d.). Individual subjects were within 2.4% of their optimal metabolic cost. Thus, we argue that sideways walking is avoided because it is expensive and slow, and it is slow because the optimal speed is low, not because humans cannot move sideways fast.

Significance: The article shows the extent to which humans are energy optimal in a weird unnatural movement, with which they are not very familiar. Further, sideways walking is kinematically simpler than forward walking: the knee does not bend sideways, and the ankle can push-off only a little sideways. This simplicity may make sideways walking more amenable to modeling and analysis than forward walking.

Sideways walking, Figure 1, showing the main
            experimental results, showing how expensive sideways walking
            is and how close to optimal, people are.


Animations of sideways walking compared with forward walking, both based on inverted pendulum walking.



De-identified human subject data, all in a single file: SidewaysData_HandfordSrinivasan.txt

Software (MATLAB programs)

We provide the key MATLAB programs that help establish the main results in the article. To be practical, we do not provide all the programs that were used for the creation the various figures. But the adventurous reader should be able to modify the programs herein to obtain all our results. If you choose to substantially extend this code, we will probably not be able provide detailed support.

Compressed folder containing the programs:

This folder are two folders containing MATLAB programs:
-- Sub-folder "Sideways_vs_Forward_noLegSwingCost" contains calculations of metabolic cost with fixed step length and no leg swing cost. Helps create Fig 2b and Fig S2.
-- Sub-folder "WalkingOptimizationWithLegSwingCost" contains calculations with leg swing cost, without step length constraints. An optimization calculation is performed, using MATLAB's fmincon, so this required the optimization toolbox. Helps create Fig 2c and Figs S3 and S4.

MS and MH were both partly supported by NSF grants 1254842 and 1300655.