Proceedings of the 5th International Symposium on Future Active Safety Technology toward Zero Accidents

(FAST-zero ’19)

September 9-11, 2019, Blacksburg, VA, USA

Vertical Stability Improvement of Bicycle for

Falling Accident Prevention by Effects of Gyroscope

Kairi Mochizuki, Yoshimi Furukawa*, Hiroshi Hasegawa**, Hiroshi Mashimo***

Department of Machinery and Control System, Shibaura Institute of Technology,

307 Fukasaku, Minuma-ku, Saitama City, Saitama, 337-5870, Japan. E-mail: mf19076@shibaura-it. ac. jp

*Co-author’s E-mail: furukawa@shibaura-it.ac.jp

**Co-author’s E-mail: h-hase@shibaura-it.ac.jp **Co-author’s E-mail: mashimoh@tk9.so-net.ne.jp

Keyword(s): Motion Control, Active safety, Motorcycle

Abstract

Two-wheels vehicles have been receiving attention to be energy saving and convenient vehicles. However, the

two-wheels vehicle are usually unstable especially at low speed, and they often fall into accidents due to external

factors e. g. strong wind, slipping and road roughness etc. Moreover, two-wheels vehicles require special driving

skills to control vehicle’s trajectory and stable attitude. Elderly people cannot easily control two-wheels vehicles as

lack of skills. Therefore, Motor-and-bicycle Anti Roll-down System (MARS) is developed to solve this problem.

The MARS can prevent falling down accident for two-wheels vehicle by using gyroscopic effects and can control

the stability of vehicle. In this paper, the experimental results are reported to verify the stability improvement of

two-wheels vehicle by using a prototype vehicle.

I. Introduction

In recent years, various self-supporting control techniques for two-wheeled vehicles have been researched and

developed. In Japan, where is abstracted that the number of bicycle accidents by elderly people is increased in step

with the aging of the population, these technologies will be a new safety assist system for two-wheels vehicles

mobility. For example, Araki et al. examined how to maintain vehicle stability by adding self-sustaining control

only when the motorcycle was stopping or running at very low speed [1]. In addition, the authors proposed the

cheaper and easier-to-use device that could prevent bicycle’s fall down accidents by the elderly using the controlled

gyroscopic effects [2-3]. The device is designed to be attached to an existing bicycle because this concept could

avoid lot more fall down accident than the concept of equipping for new bicycles could. In this paper, control

design of fall down prevention system by Gyroscopic torque is introduced and the effects of the system on roll

motion is analyzed by computer simulation, and by experiments using prototype system.

II. Configurations

A. Fall Prevention Device for Bicycle

Fig. 1 shows a photo image of the prototype equipped with the fall prevention device. Fig. 2 shows a system

configuration of the control device. The concept of the system was the “additional device” to existing bicycles, not

designed as integrated device to bicycle, in order to became widely used in amount of people. The devices differ in

the maximum torque required by the bicycle. The device generated the maximum torque required to control the roll

motion of bicycle, as the roll motion control performances generated. Since the control performance of the system

could not be predicted precisely until actually experiments would be conducted, the device was designed with a

marginal specification. When the system will be concreted as the products for the aged society in the future, the

system can be designed as lighter and more compact one.

2

Fig. 1 Prototype with Fall Prevention Device for Bicycle

mounted on the back of the bicycle [3].

Fig. 2 Configuration of a system in which the flywheel

installed in the fall prevention device generates the fall

prevention torque of the bicycle.

B. Design of a Self-Standing Control System

The prototype system and bicycle were considered as one rigid body, then the state equation was calculated from

the physical dynamics model. Equation 1 shows the state equation of the prototype. Here, the roll angle is 𝑥1[𝑟𝑎𝑑], the roll angular velocity is 𝑥2[𝑟𝑎𝑑/𝑠], and the relative yaw angle of the flywheel to bicycle is 𝑥3[rad] as a state

variable. In Equation 1, the mass of the prototype is 𝑚[𝑘𝑔], the height of the center of gravity of the prototype is

ℎ[𝑚], the inertia moment of the vehicle body in roll direction is 𝐼𝑥[𝑘𝑔 ∙ 𝑚2], the inertia moment of the flywheel is

𝐼𝐹𝑊 [𝑘𝑔 ∙ 𝑚2], the rotational speed of the flywheel is 𝜔[𝑟𝑎𝑑/𝑠], and the angular velocity of the flywheel axis in

yaw direction as control input is 𝑢[𝑟𝑎𝑑/𝑠2]. Table 1 shows each design parameter determined as from the prototype

specification.

𝑑

𝑑𝑥[

𝑥1

𝑥2

𝑥3

] = [

0 0 0𝑚𝑔ℎ

𝐼𝑥

0 1

0 0 0

] [

𝑥1

𝑥2

𝑥3

] + [0

𝐼𝐹𝑊𝜔1

] 𝑢 (1)

Table 1 Specifications of a prototype equipped with a fall prevention device on a bicycle.

Parameter name Quantity symbol Unit Value

Total weight of prototype (weight of bicycle and anti-tip device) 𝑚 𝑘𝑔 76

Center of gravity height of prototype ℎ 𝑚 0.8

Flywheel inertia moment 𝐼𝐹𝑊 𝑘𝑔 ∙ 𝑚2 0.0156

Rotation speed of flywheel ω 𝑟𝑝𝑚 3000

The self-standing control system needed to be designed so that the roll angle 𝑥1 , which was a state variable,

converged to 0 [rad] in a short time, and the values of the roll angular velocity 𝑥2 and the relative yaw angle of the

flywheel 𝑥3 did not increase. Therefore, the optimal regulator was designed on the self-standing control system, and

the controller of the state feedback gain type that realizes the regulator control was calculated. Equation 2 shows a

controller of the state feedback gain type that implements regulator control. Here, a gain for the roll angle 𝑥1 is 𝑘1,

a gain for the roll angular velocity 𝑥2 is 𝑘2, and a gain for the relative yaw angle of the flywheel 𝑥3 is 𝑘3.

𝑢 = 𝒌𝒙

= [𝑘1 𝑘2 𝑘3] [

𝑥1

𝑥2

𝑥3

] (2)

The block diagram of the control system (Fig. 3) used in performing the simulation and the self-standing experiment

was designed from the Equations 1 and 2. Reducing the weight of a lighter rider was planned for weight reduction

in practical use. Therefore, the self-standing control was performed without the rider, assuming that the weight of

the rider was included in this experimental device. In control, the control target roll angle was set to 0 [rad], which

was a freestanding state, and the yaw angular velocity of the flywheel was controlled to generate a gyro moment in

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the roll direction opposite to the vehicle falling down direction to support the vehicle. As the relative yaw angle of

the flywheel gets farther from the center during control, the gyro moment decreases. Therefore, a control for the

relative yaw angle was also added to gradually return to the center position of the flywheel. This control system

adopted PD control in which the roll angle and the roll angular velocity of the prototype detected from the inertial

sensor and the relative yaw angle of the flywheel detected from the motor encoder were used as feedback.

Fig. 3 Block diagram of self-standing control system in prototype [3].

C. Influence of regulator gain k in the self-standing control system on equipment

The influence of the regulator gain 𝒌 in Equation 2 on each state variable 𝒙 was examined. The gain value 𝑘1 was

initially set to 1000, 2000, 4000, 6000, 8000, and 10000 because it falls when the gain value 𝑘1 is 1000 or less.

Then, the influence of the gain k on the simulation result using the autonomous control system shown in Fig. 3 was

examined. The other gains were 1, and the initial roll angle is 0.1 [deg]. Fig. 4 shows the influence of the gain 𝑘1

on each state variable 𝒙. Fig. 4-a shows that the vibration of the prototype can be suppressed as the gain 𝑘1 is larger,

but the time required for the roll angle 𝑥1 to converge does not change. Further, Figs. 4-b and 4-c show that the

smaller the gain 𝑘1, the faster the convergence of the roll angular velocity 𝑥2 and the relative yaw angle of the

flywheel 𝑥3, and the more vibration can be suppressed.

a. The effect of gain 𝑘1on the roll

angle 𝑥1.

b. The effect of gain 𝑘1 on the roll

angular velocity 𝑥2 . c. The effect of gain 𝑘1 on the relative

yaw angle of the flywheel 𝑥3. Fig. 4 Simulation results of the effect of gain 𝑘1 for the roll angle 𝑥1 on each state variable 𝒙.

Next, the gain value 𝑘2 was set to 1, 5 and 10, and the influence on the simulation result using the self-standing

control system shown in Fig. 3 was examined. The gain 𝑘1 for the roll angle 𝑥1 was 10000, the gain 𝑘3 for the

relative yaw angle of the flywheel 𝑥3 was 1, and the initial roll angle was 0.1 [deg]. Fig. 5 shows the influence of

the gain 𝑘2 on each state variable 𝒙. Fig. 5 shows that the smaller the gain 𝑘2, the shorter the time required for the

convergence of the roll angle 𝑥1, the roll angular velocity 𝑥2, and the relative yaw angle of the flywheel 𝑥3, but the

frequency does not change.

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a. The effect of gain 𝑘2 on the roll

angle 𝑥1.

b. The effect of gain 𝑘2 on the roll

angular velocity 𝑥2 . c. The effect of gain 𝑘2 on the relative

yaw angle of the flywheel 𝑥3 . Fig. 5 Simulation results of the effect of gain 𝑘2 for the roll angular velocity 𝑥2 on each state variable 𝒙.

Finally, the gain value 𝑘3 was set to 1, 5 and 10, and the influence on the simulation result using the self-standing

control system shown in Fig. 3 was examined. The gain 𝑘1 for the roll angle 𝑥1 was 10000, the gain 𝑘2 for the

relative yaw angle of the flywheel 𝑥2 was 1, and the initial roll angle was 0.1[deg]. Fig. 6 shows the influence of the

gain 𝑘3 on each state variable 𝒙. Fig. 6 shows that the smaller the gain 𝑘3, the shorter the time required for the

convergence of the roll angle 𝑥1, the roll angular velocity 𝑥2, and the relative yaw angle of the flywheel 𝑥3, but the

frequency does not change.

a. The effect of gain 𝑘3 on the roll

angle 𝑥1 .

b. The effect of gain 𝑘3 on the roll

angular velocity 𝑥2.

c. The effect of gain 𝑘3 relative yaw

angle of the flywheel 𝑥3 .

Fig. 6 Simulation results of the effect of gain 𝑘3 for the relative yaw angle of the flywheel 𝑥3 on each state variable 𝒙.

III. Results and Discussion

The experiment was conducted using only the bicycle prototype without the rider, and the effect of the fall

prevention and the vehicle stabilization by the fall prevention device was confirmed. The experiment started from

an upright position and confirmed how much period the prototype could stand on its own. First, the authors waited

until the rotational speed of the flywheel reached 3000 [rpm], then started the device with the prototype upright and

started the experiment by releasing the prototype. When the prototype tilts and reaches roll angle of 8 [deg], the

experiment ends as a fall status. The fall angle 8 [deg] was an average value of angles at which three riders felt

danger and reached their feet. Based on the characteristics of the gain 𝒌 confirmed in the second chapter C, Table 2

shows the gains 𝒌 when adjusting the respective gains 𝒌 and making the actual prototype stand longer for a long

time. Fig. 7 shows the roll angle 𝑥1 during the experiment and the yaw angle 𝑥3. The prototype stood for 173

seconds, and the effect of fall prevention and vehicle stabilization by the fall prevention device was confirmed.

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Gain name Quantity

symbol

Value

Gain for the roll angle 𝑥1. 𝑘1 525.62

Gain for the roll angular

velocity 𝑥2.

𝑘2 268.57

Gain for the relative yaw angle

of the flywheel 𝑥3.

𝑘3 -10

Table 2 Gain 𝒌 when the prototype stood upright for the

longest time in the experiment.

Fig. 7 Roll angle 𝑥1 and relative yaw angle of the flywheel

𝑥3 when the prototype is upright for the longest time.

However, the device could not support the prototype as the relative yaw angle of the flywheel 𝑥3 continued to rotate and approached 90[𝑑𝑒𝑔] and the gyro moment decreased. The fall was caused by the fact that the upright angle of the vehicle and the zero point of the inertial sensor did not match, and the sensor recognizes the tilt of the prototype despite the fact that the upright angle is reached, and the flywheel continued rotating to generate a gyro moment. The device could not support the prototype, as the gyro-moment decreases as the relative yaw angle of the flywheel 𝑥3increases. Furthermore, because of the many mechanical connection elements included in the fall prevention device, uncertain errors such as the offset between the upright angle of the prototype and the zero point of the inertial sensor existed. Therefore, it was necessary to observe the state of a true prototype using a Kalman filter or a particle filter. In observation, it was confirmed from the simulation using the independent control system shown in Fig. 3 how much the uncertainty error can hold the independence of the prototype. Table 2 shows the uncertainty associated with the prototype. The simulation was stopped when the roll angle 𝑥1 of the prototype exceeded the fall angle 8 [deg] and when the yaw angle 𝑥3 of the flywheel exceeded ± 60 [deg] at which the gyro moment decreased to about 50%. The gain 𝒌 shown in Table 2 was used.

Table 2 Uncertainty error list in the fall prevention device.

Detail of errors

Vibration of prototype during self-standing experiment.

Error between the actual roll angle 𝑥1 and the roll angle 𝑥1 detected by the inertial sensor in the prototype.

Error between the actual roll angular velocity 𝑥2 and the roll angular velocity 𝑥2 detected by the inertial sensor in

the prototype.

Error between the actual relative yaw angle of the flywheel 𝑥2 and the relative yaw angle of the flywheel 𝑥2

detected by the inertial sensor in the prototype.

First, since the vibration of the prototype at the time of the self-standing experiment and the error of the actual roll angle 𝑥1 and the roll angle 𝑥1 detected by the inertial sensor affected the roll angle 𝑥1, these errors of the roll angle 𝑥1 was 𝑑1. As the error 𝑑1 of the roll angle 𝑥1 was gradually increased, as shown in Fig. 8, the simulation stopped because the relative yaw angle of the flywheel 𝑥3 reaches the limit angle when the error 𝑑1 of the roll angle 𝑥1 was 0.78 [deg].

a. Effect of the error 𝑑1 on the roll angle 𝑥1 . b. Effect of the error 𝑑1on the relative yaw angle of the

flywheel 𝑥3.

Fig. 8 Simulation result showing the effect of error 𝑑1 of the roll angle 𝑥1.

Next, an error between the actual roll angular velocity 𝑥2 and the roll angular velocity 𝑥2 detected by the inertial sensor was defined as 𝑑2. As shown in Fig. 9, as the error 𝑑2 of the roll angular velocity 𝑥2 was gradually increased,

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the simulation stopped because the flywheel deflection angle 𝑥3 reached the limit angle when the error 𝑑2 of the roll angular velocity 𝑥2 was 1.52 [deg / s].

a. Effect of the error 𝑑2 on the roll angle 𝑥1. b. Effect of the error 𝑑2on the relative yaw angle of the

flywheel 𝑥3.

Fig. 9 Simulation result showing the effect of error 𝑑2 of the roll angular velocity 𝑥2.

Finally, the error between the actual relative yaw angle of the flywheel 𝑥3 and the relative yaw angle of the flywheel 𝑥3 detected by the encoder was defined as 𝑑3. As shown Fig. 10, as the error 𝑑3 of the relative yaw angle of the flywheel 𝑥3 was gradually increased, the simulation stops because the relative yaw angle of the flywheel 𝑥3 reaches the limit angle when the error 𝑑3 of the relative yaw angle of the flywheel 𝑥3 was 40. 8 [deg].

a. Effect of the error 𝑑3 on the roll angle 𝑥1. b. Effect of the error 𝑑3on the relative yaw angle of the

flywheel 𝑥3.

Fig. 10 Simulation result showing the effect of error 𝑑3 of the relative yaw angle of the flywheel 𝑥3. From the above, it was necessary to design the filter so that the error 𝑑 between the actual state variable and the detected value falls within the determined range. IV. Conclusion

The prototype that implemented the fall prevention device on the bicycle succeeded 173 seconds of standing. As a result, it was possible to show the device overturn avoidance and running stability. In addition, the existence of uncertain errors of the equipment, which could not be understood in the simulation, was clarified. In the future, V. Acknowledgements

Authors show their application to Yasushi Nakajima from Sakae Seiki Co., Ltd. for his cooperation in conducting this research.

References

[1] Makoto Araki、 Kazushi Akimoto、Toru Takenaka、“Research on self-sustaining assist control of motorcycle in stationary state (in Japanese)”、 Society of Automotive Engineers of Japan, Inc. 、 (2018).

[2] Daisaku Senoo、Yoshimi Furukawa、Kazuaki Takeya、Hiroshi Hasegawa、Toshio Ito、“Development of Motor-and-bicycle Anti Roll-down System”、 FAST-zero 2015 Symposium、 (2015).

[3] Daisaku Senoo、Yoshimi Furukawa、Hiroshi Hasegawa、Toshio Ito、“Development of fall prevention device for motorcycle using gyroscipic effect (in Japanese)”、The Japan Society of Mechanical Engineering、(2017).