# Quantification of balance control strategies while cycling

François May, Laura Dubuis, Antoine Muller, Thomas Robert

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François May, Laura Dubuis, Antoine Muller, Thomas Robert. Quantification of balance control strategies while cycling. Multidisciplinary Biomechanics Journal, 2025, 50th congress of the., 10.46298/mbj.16216. hal-05191770v2

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Submitted on 23 Oct 2025

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Distributed under a Creative Commons Attribution 4.0 International License
# Quantification of balance control strategies while cycling

François May, Laura Dubuis, Antoine Muller, Thomas Robert*

Univ Eiffel, Univ Lyon 1, LBMC UMR T_9406, F-69622 Lyon, France

* Corresponding author: thomas.robert@univ-eiffel.fr

Received date: 03/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

**Keywords:** Bicycle, Inverted pendulum, Dynamic equilibrium

© 2025 The Authors
Licence CC-BY 4.0
Published by Société de Biomécanique

## 1. Introduction

Maintaining balance on a bicycle is a very complex problem that is still not well understood. Notably, the relative contribution of the control strategies, namely the steering and the regulation of the system's angular momentum through rider's movements, remains unclear. Moore et al. (2011) studied bicycle and rider's kinematics while riding on a treadmill. They highlighted that steering movements are predominant and thus concluded that steering is the main control strategy. Yet, impacts of these movements on system balance was not verified.

Maintaining balance on a bicycle or in a standing posture has some similarities, such as the Center of Mass (CoM) placed above a relatively small base of support. Hof (2007) proposed an approach to decipher the impact of different balance control strategies, in postural tasks.

This study aims to adapt this approach in order to identify the relative contribution of the steering vs. angular momentum regulation to balance on a bicycle.

## 2. Methods

### 2.1 Data acquisition

This is a retrospective analysis from data collected by Ronné et al. (2023), where 30 participants rode a cargo bicycle on a track including straight lines and turns. Each participant made 10 trials. Three Inertial Measurement Units (IMU) (on the frame, the front assembly and the rear wheel) were synchronised and recorded data at 120Hz. For this study, only the data

from the straight-line were used. The overall range of speeds for these trials is between 1 and 5 m/s. All data were filtered (band-pass between 0.05 and 3 Hz) to avoid IMU drift and noise.

### 2.2 Bicycle model

The bicycle was represented using the Carvallo-Whipple linearized model (Meijaard et al., 2007), made of 4 rigid segments (two wheels, a rear-frame and a front assembly). To compute the bicycle's movements, we used angular and gyroscopic data for each IMU.

### 2.3 Inverted Pendulum (IP) model

The IP used in this study is the same as Hof (2007), expressed in the reference frame of the bike-frame. The mass (m) is the mass of {bicycle+rider}, and the length ($l_e$) of the pendulum is its equivalent length (taking into account the inertia of the {bicycle+rider} along the longitudinal axis of the frame). We made the hypothesis that the CoM of the rider is sufficiently close to the frame that it can be considered fixed in the frame. We defined the Center of Pressure (CoP) as the intersection between the front plane of the CoM (the plane in figure 1.a.) and the line created by the contact points between the wheels and the ground. We finally computed the centrifugal acceleration ($a_{centri}$) of the frame, in this frontal plane.

### 2.4 Strategy analysis

We considered that riders use two strategies to balance on a bicycle: angular momentum regulation and steering.
Angular momentum regulation is the same action as in standing tasks (Hof 2007). Steering can be decomposed into two actions (figure 1.a): moving the CoP (depending on the trail and the steering angle), which is the same action as for standing tasks, and generating centrifugal force (depending on the speed of the bicycle, steer angle and its derivatives).

We computed the moments equilibrium on the $\vec{x}_B$ axis, with respect to CoM, the vertical projection of the CoM on the ground, and rearranged it, as in (Hof 2007), to express the contribution of the strategies to the system balance:

$$y_{aCoM} = y_{steer} + y_{body} \quad (1)$$

With $y_{aCoM} = a_{CoM}l_e/g$ corresponding to the lateral acceleration, estimated from measurements, and $y_{steer} = a_{centr}l_e/g - (y_{CoP} - y_{CoM})$ corresponding to steering, estimated from measurements and Carvallo-Whipple equations, and $y_{body} = H/mg$ corresponding to the angular momentum regulation, estimated using equation 1. $a_{CoM}$ is the lateral acceleration of the CoM (the controlled variable), $y_{CoP}$ and $y_{CoM}$ the lateral position of the CoP and CoM, and $\dot{H}$ is the angular momentum time derivative. The relative contribution of each strategy was then estimated in % of the total contribution according to Hof (2007).

<figure><img src="image_2.png" /><figcaption>Figure 1. a. CoP and CoM position in the frontal plane, the bicycle is moving toward us, leaning and turning right. The dashed grey line represents the IP. b. Relative contributions of the two strategies as a function of the bicycle speed for every trial, R² = 0.16 and p < 0.05 for both regressions.</figcaption></figure>

## 3. Results and discussion

The overall results are presented in the figure 1.b. First, we can observe that for every speeds, the steering strategy

is more used than the angular momentum regulation, which is consistent with the results presented by Moore et al. (2011). Then, the higher the speed, the more dominant the steering strategy is.

This can be explained by the fact that on a bicycle with no speed, the CoP displacement in the frame remains very limited with regard to the centrifugal acceleration generated. This latter increases with the speed of the bicycle, which explains the increase of its impact with speed. This approach relied on several hypotheses, notably the fact that the CoM remains fixed within the bicycle frame, that should be further investigated. Moreover, the use of IMUs for measuring bicycle's movements may limit the accuracy of angle measurements.

## 4. Conclusions

This study presents a new approach for analyzing balance on a bicycle using a simple IP model, extending an approach used for balance analysis while standing. It allowed quantifying the impact of both control strategies available while cycling and confirming the wide spread hypothesis that steering control is the dominant strategy. It also highlighted the increased impact of steering with speed. This approach could be further used to investigate the influence of the bicycle design or rider's expertise.

## Conflict of Interest Statement

The authors declare no conflict of interest during this study.

## Contributor Roles

FM: Methodology, Conceptualization, Writing original draft; LD: Validation, Supervision, review & editing;

AM: Validation, Supervision, review & editing; TR: Methodology, Conceptualization, review & editing.

## References

Hof, A. L. (2007). The equations of motion for a standing human reveal three mechanisms for balance. *Journal of Biomechanics*, 40(2), 451–457.

Meijaard, J. P., Papadopoulos, J. M., Ruina, A., & Schwab, A. L. (2007). Linearized dynamics equations for the balance and steer of a bicycle: A benchmark and review. *Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, 463(2084), 1955–1982. https://doi.org/10.1098/rspa.2007.1857
Moore, J. K., Kooijman, J. D. G., Schwab, A. L., & Hubbard, M. (2011). «Rider Motion Identification during Normal Bicycling by Means of Principal Component Analysis». *Multibody System Dynamics*, 25(2), 225–244. https://doi.org/10.1007/s11044-010-9225-8

Ronné, J., Dubuis, L., & Robert, T. (2023). Assessment of bicycle experimental objective handling quality indicators. *The Evolving Scholar - BMD 2023, 5th Edition*. https://doi.org/10.59490/6504c0e90df003ee2fc2a2e0