Lukas Stegmaier

Master's Thesis

Understanding movement decisions in gait using inverse optimal control



10/2020 – 03/2020



Humans can perform tasks in many different ways. For example, to go from A to B,
they could walk, run, skip, or hop. However, humans choose to walk at a low speed
and run at a high speed very consistently. If we understand the mechanism that
chooses the way a task is performed, we can make accurate predictions of human
movements, which could aid the design of running shoes, prosthetic legs, and other
walking aids.
This mechanism is related to energy efficiency. Gait parameters, such as the step
rate, are chosen to minimize energy expenditure [1], and people even change their
movement if a different step rate is optimal [2]. However, in other movements,
such as bicycling, effort, which is related to the muscle activation, is minimized [3].
Recently, an experiment also pointed out that eort minimization might also be
the determining factor in choosing gait, instead of energy expenditure. These two
objective have not been compared before. Furthermore, other objectives, such as
stability, and cosmetics, might also be important.
Therefore, we aim to investigate what objectives are important in choosing the
movement pattern in gait. Inverse optimal control is a tool that allows us to evaluate
dierent objectives [4]. Specifically, the goal is to compare the objective of
minimizing effort to the objective of minimizing energy expenditure. A data set of
gait at different speeds and slopes is available. The goal of this project is to implement
an inverse optimal control approach to find an objective that can predict
walking at these different speeds and slopes. An existing software package for gait
simulations will be extended to allow for inverse optimal control.



[1] Zarrugh, Mohamed et al.: Optimization of energy expenditure during level walking.
European journal of applied physiology and occupational physiology, 1974.
[2] Selinger, Jessica et al.: Humans can continuously optimize energetic cost during
walking. Current Biology, 2015.
[3] Ansley, Les and Cangley, Patrick: Determinants of optimal cadence during cycling.
European journal of sport science, 2009.
[4] Clever, Debora and Mombaur, Katja: Inverse optimal control as a tool to under-
stand human movement. In Geometric and Numerical Foundations of Movements,