[Paper Review] Patterns of Selection of Human Movements I: Movement Utility, Metabolic Energy, and Normal Walking Gaits

Stuart Hagler|arXiv (Cornell University)|Jan 1, 2016

Balance, Gait, and Falls PreventionHealth Professions23 references5 citations

TL;DR

This paper proposes a movement utility formalism that models human movement selection as an optimization process balancing metabolic energy efficiency and task performance. By integrating a metabolic energy estimator for normal walking gaits into a utility function, the model successfully predicts the empirically observed relationship between average walking speed and step length, validating its ability to explain human gait patterns through energy-efficient, goal-directed selection.

ABSTRACT

The biomechanics of the human body allow humans a range of possible ways of executing movements to attain specific goals. Nevertheless, humans exhibit significant patterns in how they execute movements. We propose that the observed patterns of human movement arise because subjects select those ways to execute movements that are, in a rigorous sense, optimal. In this project, we show how this proposition can guide the development of computational models of movement selection and thereby account for human movement patterns. We proceed by first developing a movement utility formalism that operationalizes the concept of a best or optimal way of executing a movement using a utility function so that the problem of movement selection becomes the problem of finding the movement that maximizes the utility function. Since the movement utility formalism includes a contribution of the metabolic energy of the movement (maximum utility movements try to minimize metabolic energy), we also develop a metabolic energy formalism that we can use to construct estimators of the metabolic energies of particular movements. We then show how we can construct an estimator for the metabolic energies of normal walking gaits and we use that estimator to construct a movement utility model of the selection of normal walking gaits and show that the relationship between avg. walking speed and avg. step length predicted by this model agrees with observation. We conclude by proposing a physical mechanism that a subject might use to estimate the metabolic energy of a movement in practice.

Motivation & Objective

• To develop a formal framework for modeling how humans select optimal movement trajectories.
• To create a metabolic energy estimator for normal walking gaits based on biomechanical and physiological principles.
• To validate the movement utility model by showing its predictions align with observed relationships between walking speed and step length.
• To propose a physically plausible mechanism for subjects to estimate metabolic energy during movement.
• To extend energy minimization models by incorporating multiple performance goals beyond metabolic cost.

Proposed method

• Develops a movement utility formalism where optimal movement is defined as maximizing a utility function that includes metabolic energy minimization.
• Constructs a metabolic energy formalism based on muscle force work, approximating metabolic cost as proportional to the time-averaged square of muscle force magnitude.
• Empirically fits the metabolic energy model to data from Atzler & Herbst (2012), using a power-law relationship between force and perceived effort.
• Integrates the metabolic energy model into the utility framework to model walking gait selection, with goal functions for speed and step length.
• Applies Weber’s law to model step length and walking speed relationships, enabling prediction of gait patterns.
• Proposes a physical estimation mechanism using perceived muscle force (via Stevens’ power law) to estimate metabolic cost in real time.

Experimental results

Research questions

• RQ1 How can human movement selection be formalized as an optimization process that balances efficiency and performance?
• RQ2 What is the relationship between metabolic energy expenditure and walking gait parameters such as speed and step length?
• RQ3 Can a utility-based model incorporating metabolic cost predict observed human gait patterns?
• RQ4 How might a subject physically estimate the metabolic cost of a movement during execution?
• RQ5 What role do non-metabolic factors (e.g., cognitive load, fall risk) play in movement selection, and how can they be integrated into the model?

Key findings

• The metabolic energy model fits empirical data from Atzler & Herbst (2012) with a high degree of accuracy, enabling reliable estimation of metabolic cost for different gaits.
• The movement utility model successfully predicts the observed linear relationship between average walking speed and average step length, as documented by Grieve (1979).
• The model demonstrates that minimizing muscle force work (via perceived force) serves as a viable heuristic for minimizing total metabolic energy during walking.
• The proposed physical mechanism—using Stevens’ power law to estimate perceived muscle force—provides a plausible neurophysiological basis for real-time metabolic cost estimation.
• The model shows that step-by-step optimization of gait is feasible and consistent with observed gait patterns, supporting an on-the-fly selection mechanism.
• The framework is extensible and can incorporate additional constraints such as pain reduction, fall risk, or cognitive load, making it suitable for clinical and rehabilitative applications.