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8/7/2019 A Study on Straight-Line Tracking Bicycle
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 1, JANUARY 2009 159
A Study on Straight-Line Tracking andPosture Control in Electric Bicycle
Yasuhito Tanaka and Toshiyuki Murakami, Member, IEEE
Abstract—The development of automatic control for driving abicycle is a challenging theme and is expected to be a human assistsystem. Previously, an acceleration-based method for stabilizingbicycle posture was proposed by the authors. In the experimentswith this controller, the posture of the bicycle might be stabilized,but it is impossible to run on the desired trajectory, because thereis no consideration with respect to a trajectory control. For thesake of expanding this system into more sophisticated equipment,a realization of the trajectory control for the bicycle is important.From the viewpoint of an assist system for human motion, a unifiedcontrol of posture and trajectory brings a sophisticated functionto a bicycle, and a high-performance bicycle is expected to be a
convenient vehicle, similar to a small car. This paper proposes twostrategies to stabilize bicycle posture and trajectory control thatrealizes a straight-line tracking: one is a lateral velocity controller,and the other is a steering function controller. The validity of theproposed approaches is evaluated by simulations and experiments.
Index Terms—Bicycle, inverted pendulum, line trackingcontrol, posture control.
I. INTRODUCTION
IN THE RECENT age of advanced information society, it is
common for one to own a mobile terminal for private use.
New technologies are developed one after another under the
growth of digital society. Digitalization also makes progressin bicycles. For example, a new bicycle headlight that detects
surrounding brightness and automatically turns on a light is
already in use. Electric bicycles that assist humans with the
pedal are also in practical use. In the near future, navigation
systems or Global Positioning System equipment may be ap-
plied to bicycles. However, bicycles have the defect of not being
able to stabilize their postures without human manipulation. In
any case, bicycles enhance human’s mobility and assist human
transportation; thus, although they are not capable of stabilizing
their postures, the production of a wide variety of sophisticated
bicycles that support, for instance, posture stabilization, pedal
driving, and navigation can be considered feasible.
The goal of this paper is to establish highly sophisticated
bicycle systems that support human motion in several aspects
and are expected to be safe vehicles, similar to small cars [20].
In this paper, as the first step, an electric bicycle system that
Manuscript received March 28, 2005; revised June 5, 2008. First publishedJuly 9, 2008; current version published December 30, 2008.
The authors are with the Department of System Design Engineering,Keio University, Yokohama 223-8522, Japan (e-mail: [email protected];[email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIE.2008.927406
stabilizes its posture and follows the desired straight line is
studied.
A strict dynamic model of a bicycle called the Sharp model
was proposed by Sharp [2], and many research works based on
this model have been reported. The Sharp model is powerful but
complicated and includes many nonlinear terms. To improve
this issue, a linearized dynamic model of a bicycle is necessary
[3], [4], [14], [15]. In the proposed approach, an acceleration
control based on a disturbance observer is employed for the
steering control [12], [16]–[19]. Moreover, an acceleration-
control-based posture control is constructed for stabilizationcontrol of the bicycle. Here, the proposed approach does not
consider any change in the person’s center of gravity (COG).
However, experiments have already been implemented when
the person is boarding the bicycle, and it is proven that the
proposed posture control is experimentally effective although
some COG change is present [11]. In this paper, the posture
controller is expanded by adding a trajectory controller as a
forward controller. In the proposed approach, first, a lateral
velocity controller is discussed. In this method, the lateral
deviation of the bicycle is utilized to generate the command of
the camber angle. The controller structure is simple and brings
easy implementation. Second, a steering function controller is
proposed. In this method, the controller is constructed basedon the trajectory parameters, i.e., the direction angle of the
bicycle and the curvature of the bicycle trajectory. Then,
the physical meaning of each feedback gain becomes clear.
The steering function controller has a similar structure as a
proportional–integral–derivative (PID) controller, and the gain
adjustment is easy because of the clear physical meaning of
the feedback gains. This is one of the remarkable points of the
proposed controller.
In this paper, a simplified dynamics model of a bicycle is
introduced in Section II. Section III shows the control algo-
rithms that stabilize bicycle posture and realize straight-line
tracking. The validity of the proposed strategies is proven by thesimulation in Section IV. The experimental results are shown in
Section V. Finally, the conclusion is summarized in Section VI.
II. MODELING
A. Equilibrium of Bicycle Posture
In the case of driving a bicycle with constant steering angle
and constant speed, the bicycle runs on a circular orbit. It
is known that the intensity of centrifugal force applied to a
running bicycle is determined by the radius of the circular orbit
and the bicycle velocity. Fig. 1 shows an overview of the bicycle
TANAKA AND MURAKAMI: STUDY ON STRAIGHT-LINE TRACKING AND POSTURE CONTROL IN ELECTRIC BICYCLE 167
path. This means that the steering function controller
is more robust against the road disturbance, i.e., the
side slip.
The experimental results show that the steering function con-
troller is more powerful than the lateral velocity controller in
straight-path tracking of the bicycle, keeping the stable posture
of the bicycle.In the experiments, the observer gain is selected to be large
enough to ignore the time delay compared to the camber re-
sponse of the bicycle. Of course, there are some coupling effects
between the trajectory controller and the posture controller. In
the proposed steering function controller, the controller is con-
structed based on the trajectory parameters, i.e., the direction
angle of the bicycle and the curvature of the bicycle trajectory.
Then, the physical meaning of each feedback gain becomes
clear. The steering function controller has a similar structure as
a PID controller, and the gain adjustment is easy because of the
clear physical meaning of the feedback gains. The instability
behavior does not appear in the experiment of the steering
function controller, as shown in Fig. 20. However, in the lateral
velocity control and the posture control only, the instability
behavior is observed. In the running bicycle experiment, the
bicycle roller is employed as a running road. In the bicycle
roller, the side slip of the bicycle tire that is unusual in the
general road surface arises, and it causes the side slip motion of
the bicycle. The lateral velocity control and the posture control
only are not able to compensate this side slip motion, and the
instability responses of trajectory appear in the experiments,
even if the posture control is stable.
From the simulation and experimental results, it is found that
the difference between simulations and experimental responses
appears. The effect of the tire feature and the sprocket chainstructure cause this difference. The tire feature has high non-
linearity, and it is difficult to employ the dynamic model in the
control algorithm, because the motion equation must be of high
order. In particular, the tire feature is related to the problem of
the side slip phenomenon. This consideration is more difficult.
To simplify the bicycle model, the tire feature is ignored in the
proposed approach. The introduction of the tire model is one of
our next challenges for high-performance bicycle control. Then,
it is also expected that the simulations are well concise with the
experimental responses. In the experiment, the gyro sensor is
utilized to detect the camber response. The detection period is
16 ms although the sampling ratio of the controller is 1 ms. Thismakes it difficult to set a high gain of k in the steering function
controller and causes the response delay, as shown in Figs. 13,
20, and 21. The improvement of the sensor response is also an
important issue from an alternative aspect.
VI. CONCLUSION
In this paper, a simplified dynamic model of a bicycle and
a kinetic model of the bicycle trajectory have been derived.
Moreover, an acceleration-based bicycle controller has been
proposed. First, a controller that may stabilize bicycle posture
has been introduced. Second, two strategies for the bicycle
trajectory control have been proposed. The validity of the pro-posed approaches is confirmed by simulations and experiments.
In particular, the continuous driving of the bicycle is achieved
by using the steering function controller, which is expected to
be applicable to not only the straight-line trajectory but also the
curved trajectory.
In past research, there are a few papers that show experi-
mental evaluation for the self-sustaining control of a bicycle. In
addition, the fusion strategy of the trajectory and self-sustainingcontrol has not been investigated from the viewpoint of a human
assist system. In this paper, however, the bicycle controller that
achieves both the stable posture and trajectory control has been
experimentally confirmed. This means that the feasibility and
the industrial contribution to realize the sophisticated bicycle
with human assist function are strongly expected by the pro-
posed strategy.
Because it is difficult to model the nonlinear characteristics
of the tire and the state change in the road, this paper has
not considered them in the proposed method; however, even if
they are not strictly considered in the experimental results, the
proposed method was able to achieve stabilization control. To
further achieve high accuracy about the control characteristic, it
is necessary to consider the tire characteristic. It is considered
to be a future task for this point.
ACKNOWLEDGMENT
The authors would like to thank the reviewers for their
patience and recommendations.
REFERENCES
[1] Y. Oda, M. Miyamoto, K. Uchiyama, and G. Shimizu, “Study on the
autonomous run by integrated control of bicycle,” in Proc. JSME 11thConf. Transp. Logistics Division, 2002, pp. 97–100.[2] R. S. Sharp, “The stability and control of motorcycles,” J. Mech. Eng. Sci.,
vol. 13, no. 5, pp. 316–329, 1971.[3] K. Astrom et al., “Bicycle dynamics and control: Adapted bicycles
for education and research,” IEEE Control Syst. Mag., vol. 25, no. 4,pp. 26–46, Aug. 2005.
[4] P. A. J. Ruijs and H. B. Pacejka, “Research in the lateral dynamics of motorcycles,” in Proc. 9th IAVSD Symp. Dyn. Vehicles Roads Tracks,1996, pp. 467–478.
[5] Y. Tanaka and T. Murakami, “Self sustaining bicycle robot with steeringcontroller,” in Proc. 8th IEEE Int. Workshop AMC , Mar. 25–28, 2004,pp. 193–197.
[6] Y. Tanaka and T. Murakami, “The bicycle robot driving on an optionaltrajectory,” in Proc. IEEE Int. Conf. Mechatron. Robot., Sep. 13–15, 2004,pp. 641–646.
[7] Y. J. Kanayama and F. Fahroo, “A new line tracking method for non-
holonomic vehicles,” in Proc. IEEE Int. Conf. Robot. Autom., Apr. 1997,pp. 2908–2913.
[8] Y. Ou and Y. Xu, “Stabilization and line tracking of the gyrosco-pically stabilized robot,” in Proc. IEEE ICRA, May 11–15, 2002, vol. 2,pp. 1753–1758.
[9] M. Komoda, Control Engineering. Tokyo, Japan: Asakura-Shoten,1993.
[10] H. Sakai, Tire Engineering. Tokyo, Japan: Grand Prix Publication, 1987.[11] H. Niki and T. Murakami, “An approach to self stabilization of bicycle
[12] H. Niki and T. Murakami, “An approach to stable standing motion of electric bicycle,” in Proc. CACS, Tainan, Taiwan, Nov. 18–19, 2005.CD-ROM.
[13] T. Yamaguchi, T. Shibata, and T. Murakami, “Self-sustaining approach of electric bicycle by acceleration control based backstepping,” in Proc. 33rd
IEEE IECON , Taipei, Taiwan, Nov. 5–8, 2007, pp. 2610–2624.[14] D. J. N. Limebeer and R. S. Sharp, “Bicycles, motorcycles, and models,” IEEE Control Syst. Mag., vol. 26, no. 5, pp. 34–61, Oct. 2006.
8/7/2019 A Study on Straight-Line Tracking Bicycle
168 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 1, JANUARY 2009
[15] A. L. Schwab, J. P. Meijaard, and J. M. Papadopoulos, “A multibody dy-namics benchmarkon the equations of motion of an uncontrolled bicycle,”in Proc. 5th EUROMECH Nonlinear Dyn. Conf., 2005, pp. 511–521.
[16] K. Ohnishi, M. Shibata, and T. Murakami, “Motion control for advancedmechatronics,” IEEE/ASME Trans. Mechatronics, vol. 1, no. 1, pp. 56–67,Mar. 1996.
[17] T. Murakami, F. Yu, and K. Ohnishi, “Torque sensorless control inmultidegree-of-freedom manipulator,” IEEE Trans. Ind. Electron., vol. 40,
no. 2, pp. 259–265, Apr. 1993.[18] T. Murakami, N. Oda, Y. Miyazawa, and K. Ohnishi, “A motion con-trol strategy based on equivalent mass matrix in multidegree-of-freedommanipulator,” IEEE Trans. Ind. Electron., vol. 42, no. 2, pp. 123–130,Apr. 1995.
[19] K. Matsushita and T. Murakami, “Nonholonomic equivalent disturbancebased backward motion control of tractor-trailer with virtual steering,”
IEEE Trans. Ind. Electron., vol. 55, no. 1, pp. 280–287, Jan. 2008.[20] H. Takahashi, D. Ukishima, K. Kawamoto, and K. Hirota, “A study on
predicting hazard factors for safe driving,” IEEE Trans. Ind. Electron.,vol. 54, no. 2, pp. 781–789, Apr. 2007.
[21] N. Mutoh, T. Kazama, and K. Takita, “Driving characteristics of anelectric vehicle system with independently driven front and rear wheels,”
IEEE Trans. Ind. Electron., vol. 53, no. 3, pp. 803–813, Jun. 2006.[22] N. Mutoh, Y. Hayano, H. Yahagi, and K. Takita, “Electric braking con-
trol methods for electric vehicles with independently driven front andrear wheels,” IEEE Trans. Ind. Electron., vol. 54, no. 2, pp. 1168–1176,
Apr. 2007.
Yasuhito Tanaka received the B.E. and M.E. de-grees from Keio University, Yokohama, Japan, in2003 and 2005, respectively.
He is currently with the Department of SystemDesign Engineering, Keio University. His researchinterests include robotics, intelligent bicycles, andmotion control.
Toshiyuki Murakami (M’93) received the B.E.,M.E., and Ph.D. degrees in electrical engineeringfrom Keio University, Yokohama, Japan, in 1988,1990, and 1993, respectively.
In 1993, he joined the Department of ElectricalEngineering, Keio University, where he is currentlya Professor with the Department of System DesignEngineering. From 1999 to 2000, he was a VisitingResearcher with The Institute for Power Electronicsand Electrical Drives, Aachen University of Tech-nology, Aachen, Germany. His research interests in-
clude robotics, intelligent vehicles, mobile robots, and motion control.