# Dynamics Capabilities of a Mono-wheel in Emergency Maneuvers

Thierry Serre, Claire Naude, Ebrahim Riahi, Bastien Canu, Fanny Vincent, Lucas Herbin

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Thierry Serre, Claire Naude, Ebrahim Riahi, Bastien Canu, Fanny Vincent, et al.. Dynamics Capabilities of a Mono-wheel in Emergency Maneuvers. FAST-zero'25, Sep 2025, Arles, France. hal-05359196

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# Dynamics Capabilities of a Mono-wheel in Emergency Maneuvers

Thierry Serre, Claire Naude, Ebrahim Riahi, Bastien Canu, Fanny Vincent, Lucas Herbin
Laboratoire Mécanismes d'Accidents, Université Gustave Eiffel

Contact address: 304 Chemin de la Croix blanche, Salon-de-Provence, 13300, France

Phone: +33 4 90 56 86 53

Corresponding author's e-mail: thierry.serre@univ-eiffel.fr

**ABSTRACT:** Mono-wheels are new individual vehicles used by people to make their personal displacements. It is a one-wheel self-stabilized vehicle, and the user stands on this wheel using two pedals. The objective of this work is to determine the dynamic capabilities of a mono-wheel during emergency maneuvers from experimental tests performed on a track with an experienced pilot. For the longitudinal maneuvers, hard braking maneuvers were performed, and for the lateral maneuvers, avoidance maneuvers were done. Data acquisition relies on mobile phones (IMUs) fixed on the vehicle and on the user's chest. The average braking deceleration is 3 m/s² which corresponds to a stopping distance of around 6 meters. Laterally, the mono-wheel is more strained in yaw rotation than the pilot and shows capabilities to change direction quickly. While this kind of vehicle shows low braking performance, it appears more skilled at performing avoidance maneuvers.

**Keywords:** Mono-wheel, vehicle dynamics, emergency maneuver

## 1. Introduction

In recent years, new individual vehicles have been used by people to make their displacements. These vehicles can include e-scooters, gyroscopes, hoverboards... and mono-wheels [1]. The latter vehicle consists of one electric wheel that is able to self-stabilize, and the user stands on this wheel using two pedals. The main mechanical principle of the functioning of such a system has been described by several authors [2]. The main control movements for the users are located on the foot. The users have to lean their body forward (resp. backward) to accelerate (resp. brake), and have to rotate their ankles to turn (Figure 1). The speed limit of these kinds of vehicles is in most countries 25 km/h, but it can go faster if the vehicle's limits are removed. The interaction of mono-wheel users with others vehicles (cars, two-wheelers...) represents new interactions that can generate new types of accidents. Indeed, this kind of machine allows the user to circulate in dense urban areas by weaving in and out of traffic jams, using the pavement or the cyclist lane, etc. But because a monowheel is a small engine located only on the foot, a monowheel user can be considered by a four-wheel driver as a pedestrian... while their maximal speed is about 25 km/h! And since a mono-wheel user is a vulnerable user, accidents involving such users could produce physical injuries. Reciprocally, from the monowheel user's point of view, what should be the dynamic capabilities of a monowheel in case of an accident? And what are these capabilities regarding the other users on the road and their

abilities to avoid accidents? Do they allow for a safe behavior for mono-wheel users? No study has yet analyzed the behavior of this vehicle during an emergency maneuver. So, the main objective of this work is to determine the dynamics capabilities of a mono-wheel in terms of acceleration or rotational speed during emergency maneuvers like hard braking or avoidance maneuvers. This work aims to highlight the characteristics of a mono-wheel usage in order to identify skills to manipulate such a vehicle but also issues in terms of road safety.

## 2. Material and Methods

This work is based on experimental tests performed on a track with an experienced pilot. This study is focused on a mono-wheel Inmotion V5F, with a 550W power engine. This mono-wheel has an automatic braking system that limits the maximum speed to 25 km/h. As soon as it reaches 25 km/h, an audio signal "Please slow down" indicates to the driver that the system will brake slightly. The pilot who performed the experimental tests was an expert user, so the results of this research can be considered as a threshold of the dynamic capabilities achievable.

Data acquisition relies on Samsung S8 mobile phones fixed vertically on the vehicle and on the sternum of the user with a harness. The mobile phones are used as IMUs and record accelerations, angular velocities, and magnetic fields with a 50 Hz frequency, and the GPS position at 1 Hz. Videos were also recorded using the two
<figure><img src="image_3.png" /></figure>

smartphone cameras, external cameras fixed on the track, and by drone. The orientation and location of the smartphones are represented in Figure 1. To ensure signal quality, the accelerometer and gyrometer data are processed using a 1st-order Butterworth low-pass filter. In order to obtain, more particularly, the yaw angle and the roll angle, angular speeds were integrated.

<figure><img src="image_4.png" /><figcaption>Fig. 1 - Mono-wheel and instrumentation</figcaption></figure>

The tests have been configurated to reproduce emergency maneuvers in longitudinal and in lateral demands. The test procedures follow the guidelines and standard procedures commonly used to characterize vehicle dynamics during braking and obstacle avoidance maneuvers, in accordance with DIN 79010 [3].

For the longitudinal maneuver, it consists for the pilot to reach a constant speed of about 20-25 km/h and suddenly perform hard braking. The objective of the braking test is to evaluate the braking performance of the vehicle and to determine the distance required to bring it to a complete stop from a given speed, particularly at the maximum speed. The test is conducted in a straight line over a distance of 50 meters. The driver is required to accelerate to a maximal speed of 25 km/h and maintain it with stability and consistency after crossing a threshold. Subsequently, the driver must apply the maximum braking force until the vehicle stops within a designated zone. This experimental campaign was conducted on a test track on a dry road surface with a good friction coefficient.

In order to evaluate the mono-wheel capacity to execute rapid directional changes, a series of avoidance maneuvers were conducted. It consists of performing left and right avoidance maneuvers at a maximal speed of 25 km/h, with the protocol configuration described in Figure 2. These maneuvers simulate various obstacles such as an open door along the roadway, as described and studied by Johnson et al. [4]. This test is also inspired by the new motorcycle driving test in Europe [5]. Three cones are positioned along the designated path at distances of 2 meters and 3 meters, both to the right and to the left, to represent the obstacle. The tests are conducted in four configurations: right avoidance at 2 m and 3 m, left avoidance at 2 m and 3 m. The rider must attain a maximal target speed of 25 km/h, prior to entering the cone-shaped zone.

Each test is repeated three times by the same pilot to ensure the reproducibility and reliability of the results. Thresholds are positioned on the path in order to identify

passage points where the mono-wheel pass through and to overlay the three tests.

<figure><img src="image_5.png" /><figcaption>Fig. 2 - Left avoidance maneuver protocol</figcaption></figure>

### 3. Results

#### Braking performance

To evaluate the braking performance, we analyzed in particular the deceleration level, the pitch characteristics, and the stopping distance during stabilized braking. Figure 3 shows the GPS speed, the longitudinal accelerations, and the pitch angular speed acquired on the mono-wheel and on the pilot's chest for the three tests.

<figure><img src="image_6.png" /><figcaption>Fig. 3 - GPS speed, Longitudinal acceleration and Pitch speed for the mono-wheel and the pilot's chest during braking tests</figcaption></figure>

Table 1 gives the values observed on the mono-wheel and on the pilot for all emergency braking tests. From a global point of view, it can be observed that the average braking deceleration is about 3 m/s². This corresponds to a stopping distance between 5 to 7 meters.

<table><caption>Table 1 - Longitudinal deceleration, stopping distance and pitch speed during braking tests</caption><thead><tr><th rowspan="2">Test number</th><th colspan="3">Mono-wheel</th><th colspan="3">Pilot</th></tr><tr><th>1</th><th>2</th><th>3</th><th>1</th><th>2</th><th>3</th></tr></thead><tbody><tr><td>Maximal GPS speed (km/h)</td><td>22.6</td><td>20.2</td><td>21.8</td><td>22.9</td><td>22.1</td><td>21.7</td></tr><tr><td>Average deceleration per test (m/s²)</td><td>-2.6</td><td>-2.8</td><td>-3</td><td>-3</td><td>-2.8</td><td>-3.5</td></tr><tr><td>Global mean deceleration (m/s²)</td><td></td><td>-2.8</td><td></td><td></td><td>-3.1</td><td></td></tr><tr><td>Stopping distance (m)</td><td>7.6</td><td>5.6</td><td>6.1</td><td>6.7</td><td>6.7</td><td>5.2</td></tr><tr><td>Maximal pitch speed (°/s)</td><td>6.0</td><td>23.0</td><td>14.0</td><td>60.0</td><td>50.0</td><td>77.0</td></tr><tr><td>Mean pitch speed (°/s)</td><td></td><td>14.3</td><td></td><td></td><td>62.3</td><td></td></tr></tbody></table>
<figure><img src="image_7.png" /></figure>

These values tend to show that the braking performance of a monowheel is low compared to other vehicles like cars, motorbikes, bikes, or e-scooters [6]. Indeed, it is admitted that a classical car or motorbike can perform an emergency braking with a 8 m/s² deceleration, while common bikes and e-scooters reach maximal deceleration of 6 m/s² and 4m/s², respectively. But these small values for the mono-wheel also show the limit of the braking capabilities for such a system, which needs to be improved for better road safety. Consequently, the stopping distance can also be considered too long regarding the usage of these vehicles. For example, if a monowheel follows a car which realized suddenly an emergency braking, the mono-wheel users will probably impact the car from behind due to its inferior braking performance compared to the car. Moreover, considering that mono-wheel users are often in interaction with other vulnerable users such as pedestrians, cyclists, or e-scooter users, which can generate close-proximity confrontations, it is important to require good braking performance in order to perform rapid emergency maneuvers due to the uncertain displacement of the other users. For instance, a stopping distance of 6 m could be considered as too long to stop the mono-wheel in case of a pedestrian crossing. Finally, braking tests have been performed in this experimental campaign on a dry surface with a good friction surface. So, results on the deceleration rate represent favorable conditions for braking. But mono-wheel could be confronted in the street to other type of surface with lower friction rates (like concrete or rain for example). Therefore, braking performance could become very low and critical in case of emergency maneuver.

Concerning the difference of the dynamic behavior between the mono-wheel itself and the pilot, it can be observed that, in braking situations, the pilot is subjected to highest pitch demand than the mono-wheel. Indeed, it is recorded an average pitch angular speed of 60°/s for the pilot's chest, while the mono-wheel reached a maximal pitch speed of 23°/s. This observation shows that the mono-wheel stays globally stabilized during the braking, but the pilot has to lean quickly backward.

## Avoidance maneuver performance

Among all the measurements (accelerations and angular speeds), two rotations are particularly interesting to characterize the abilities of a mono-wheel in lateral demands: yaw and roll. Therefore, the yaw and roll angular velocities and their corresponding angles were particularly analyzed to assess the performance of the mono-wheel in avoidance maneuvers.

The avoidance maneuvers performed in this experimental campaign represent a risky situation corresponding to an open door along the roadway. From a qualitative point of view, performing this kind of maneuver appears to be quite easy, which tends to show the facility in operating a sudden direction change with a mono-wheel. Analysis of the drone videos confirms this

observation, as it shows that the mono-wheel user can perform the avoidance of the obstacle and quickly return (just after the obstacle) to a straight trajectory (see Figure 4). While other individual vehicles like e-scooters or bicycles need more lateral and longitudinal distance to return to the path because their radii of curvature are larger [6]. This is due to the fact that a mono-wheel has only one contact point between the tire and the road, compared to two-wheeled or four-wheeled vehicles. Therefore, the radius of curvature to turn can be smaller than that of these multi-wheeled vehicles.

<figure><img src="image_8.png" /><figcaption>Fig. 4 – Video capture by drone and frontal view of the avoidance test</figcaption></figure>

The abilities to perform such tests also show that a mono-wheel user needs short distances (at least 2 meters) to realize an emergency avoidance maneuver. Consequently, a mono-wheel has more skills to weave in and out in dense areas on the road among cars or on the pavement among pedestrians, for example.

Figures 5 and 6 give, respectively, the curves of the roll speed and the yaw speed recorded on the monowheel for the three tests in the 4 conditions: 2 m/3 m avoidance and left/right avoidance.

<figure><img src="image_9.png" /><figcaption>Fig. 5 - Roll speed (°/s) for the mono-wheel for the three tests in the 4 conditions: left/right and 2 m/3 m avoidance</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 6 - Yaw speed (°/s) for the mono-wheel for the three tests in the 4 conditions: left/right and 2 m/3 m avoidance</figcaption></figure>

From a global point of view, the 2 m avoidance tests generate obviously higher values than the 3 m avoidance. In particular, in the left configuration, the 2 m avoidance tests have roll speed and yaw speed (both around 100°/s) twice as important as those for the 3 m avoidance (about
<figure><img src="image_11.png" /></figure>

50°/s). These differences are less significant in the right avoidance configuration and could be due to the pilot's better abilities to perform right avoidance maneuvers than left ones.

Compared to other vehicles like cars, motorcycles, e-scooters, and bikes, these large yaw and roll speeds appear to be bigger and show the aptitude of a mono-wheel user to change direction quickly.

Figure 7 provides the values recorded on the mono-wheel (blue) and on the pilot's chest (red) for the yaw and roll speeds alongside the corresponding yaw and roll angles calculated by integration of the angular speed curves.

<figure><img src="image_12.png" /><figcaption>Fig. 7 - Yaw speed (°/s), Yaw angle (°), Roll speed (°/s), and Roll angle (°) for the mono-wheel (blue) and the pilot sternum (red) for a 2 m and 3 m left avoidance test.</figcaption></figure>

It is observed that the mono-wheel is more strained in yaw rotation than the pilot. Yaw speed can reach more than 100°/s on the mono-wheel for a 2 m avoidance while it is less than 50°/s for the pilot. Corresponding values are observed in the yaw angle, where 40° can be reached by the mono-wheel compared to 10° for the pilot. The same remarks can be observed in the roll rotation, where roll speed of about 100°/s can be reached while the pilot has a roll speed less than 50°/s. In terms of roll angle, integrated roll speeds give an angle of approximately 20° for the mono-wheel, respectively 10° for the pilot. These values are confirmed by a video analysis (see Figure 4) where a roll angle of 18° can be measured for the mono-wheel in the images, while a 10° is observed on the pilot trunk. In fact, this difference in values can be attributed to the rotation of the feet and knees rotations to turn the mono-wheel. This result shows that, firstly, a mono-wheel user can change direction quite quickly. Secondly, a change of direction is more "observable" on the mono-wheel than on the pilot, that is to say, more noticeable on the feet than on the upper part of the user. These findings could be linked to the difficulties for other users to understand and interpret the intended direction of a mono-wheel user. Consequently, it appears important to teach mono-wheel users to show their change of direction with their arms, for example (as it is the case with bicycles), in order to clearly indicate their intended direction.

## 4. Conclusion

This research provides initial insights into the dynamic behavior of the mono-wheel during emergency braking and obstacle avoidance. It allows us to characterize the capabilities of a mono-wheel user to react in the face of an emergency maneuver. While this kind of vehicle shows low braking performance compared to other vehicles, it appears more skilled at performing avoidance maneuvers. Thus, during an emergency situation, mono-wheel users will probably choose to perform an avoidance maneuver instead of braking. This work highlights also the ability skill of a monowheel to weave in and out of traffic (on road or pavement) and provides some recommendations to avoid accidents. In particular, it appears important for mono-wheel users to clearly show their intended direction in order to be well identified by other vehicles and avoid bad interactions which can generate accidents.

Since this research is based on only one mono-wheel vehicle and one pilot, it could be interesting in the future to test other mono-wheels with a variable sample of pilots. Based on the same instrumentation, some researches are already progressing to observe the behavior of more than 30 mono-wheel users in naturalistic driving studies.

## References

(1) Zagorskas, J., Burinskienė, M. 2019. Challenges Caused by Increased Use of E-Powered Personal Mobility Vehicles in European Cities. Sustainability, 12(1), 273.

(2) Cieslak P., Buratowski T, Uhl T., Giergiel M., 2011, The mono-wheel robot with dynamics stabilization. in Robotics and autonomous Systems 59 (2011) 611-619

(3) https://www.normadoc.com/media/preview_pdf/DE30084316.pdf (2020)

(4) Johnson, M., Newstead, S., Oxley, J., Charlton, J., 2013. Cyclists and open vehicle doors: Crash characteristics and risk factors. Safety Science, vol. 59, p. 135-140, nov. 2013, doi: 10.1016/j.ssci.2013.04.010.

(5) JORF n° 0015 du 18 janvier 2013 - Légifrance. 2013. Accessed on August 18, 2025. Available at https://www.legifrance.gouv.fr/jorf/jo/2013/01/18/01015

(6) Naude, C., Riahi, E., Canu, B., Herbin, L., Vincent,
<figure><img src="image_13.png" /></figure>

F., Serre, T., 2023. Braking and acceleration capabilities of e-bicycles, e-scooters and e-monowheels. 31st Annual Congress of the European Association for Accident Research EVU, 05-07 Oct 2023. Limasol, Cyprus