vertical stability improvement of bicycle for falling ... program... · adopted pd control in which...
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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: [email protected]
**Co-author’s E-mail: [email protected] **Co-author’s E-mail: [email protected]
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.
4
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.
5
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).