Journal of Mechanical Science and Technology 23 (2009) 980~986
www.springerlink.com/content/1738-494x
DOI 10.1007/s12206-009-0325-4
Journal of
Mechanical
Science and
Technology
Stabilization of a bicycle with two-wheel steering and two-wheel
driving by driving forces at low speed
†
Chihiro Nakagawa
1
, Yoshihiro Suda
2
, Kimihiko Nakano
2
and Shoichiro Takehara
3,*
1
Department of Engineering Synthesis, University of Tokyo, 4-6-1, Komaba, Meguro, Tokyo, Japan
2
Institute of Industrial Science, University of Tokyo, 4-6-1, Komaba, Meguro, Tokyo, Japan
3
Department of Mechanical Engineering, Tokyo Metropolitan University,
1-1, Minamiosawa, Hachioji, Tokyo, Japan
(Manuscript Received December 24, 2008; Revised March 16, 2009; Accepted March 16, 2009)
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Abstract
Recently, the personal mobility vehicle (PMV), a vehicle suitable for personal use, has been developed. It moves at
low speed and is sufficiently small that it can be ridden in pedestrian space. This vehicle is expected to be a new me-
thod of transportation that is practical and environmentally friendly. As one form of PMV, the authors propose a two-
wheel vehicle with two modes: a two-wheel steering and two-wheel driving bicycle mode and a parallel two-wheel
mode. This vehicle has four electric motors, two for driving and two for steering, and one generator connected to the
pedals. In the bicycle mode, the rider rotates the pedals to generate electric power, and the motors in the wheels pro-
duce torque using the generated energy. The front and rear wheels are steered by the electric motor according to the
angle of the handle. Therefore, this bicycle is controlled by a steer-by-wire and a drive-by-wire system. In the parallel
two-wheel mode, the vehicle is stabilized according to the theory of the inverted pendulum. In this paper, we focus on
the bicycle mode and analyze its stability. Stabilizing the bicycle is not easy since the proposed vehicle has tires with
small diameters and the traveling speed is assumed to be low. It is known that the stability of bicycles is tuned by ad-
justing the bicycle parameters and changing the rear steer angle. However, since we aim to use the vehicle in a narrow
walking space at low speed, such conventional methods are not always suitable. The authors propose the stabilization
of the bicycle using driving forces and design a controller using linear-quadratic control theory. The results of the nu-
merical simulations show the proposed method is effective in stabilizing the bicycle.
Keywords: Bicycle; Personal Mobility Vehicle; Stabilization control; Vehicle dynamics
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1. Introduction
In terms of sustainable development, it has been
noted that spaces such as streets, sidewalks and facili-
ties that are important in daily life need to be recon-
structed in a practical and environmentally friendly
manner. In contemporary Japan in particular, inbound
traffic congestion in metropolitan cities decreases
transportation efficiency and deteriorates the city
environment via air pollution and noise. A new vehi-
cle that is practical and environmentally friendly is
required. Recently, a personal mobility vehicle
(PMV), which is a vehicle suitable for personal use,
has become available [1, 2]. It moves at low speed
and is sufficiently small that it can be used for travel
in pedestrian space. Considering the usage of PMVs
on streets and sidewalks and inside facilities, stability
at low speed and a pedestrian affinity for the PMV is
important. Although the PMV needs electrical power,
the amount of consumed power is far smaller than
that for a typical automobile. For a PMV, the follow-
ing features should be considered. 1) Short range
†This paper was presented at the 4th Asian Conference on Multibody
Dynamics(ACMD2008), Jeju, Korea, August 20-23, 2008.
*
Corresponding author. Tel.: +81 3 5452 6098, Fax.: +81 3 5452 6195
E-mail address: chihiro@iis.u-tokyo.ac.jp
© KSME & Springer 2009