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    points  between  the  robot  and the ground, and  it
    contributes to the mobility on  the  slope or  soft  terrain.
    The other merit is adaptability for  steps. Front passive
    wheel  is relatively small, and  its adaptability  is  limited.
    By  using leg function, the  robot  can move over higher
    steps.
    Here,  we  consider a gait  for  front legs. First  we
    assume the robot moves straight, and we consider the leg
    motion in  the  horizontal plane.  The  leg  moving
    trajectory is  seen  as a dotted  line  in  Fig.6. We define
    forward end point of the trajectory as 0, and the backward
    end as 1.  The robot is also assumed to maintain static
    stability during locomotion. Therefore, the  robot must
    always  have more than three contact points  with  the
    ground.  This means that duty factor  p  (fraction  of  a
    locomotion cycle that each leg spends in contact with  the
    ground) must be between 0.5 and  1.0.  Considering  the
    symmetry  of walking, phase difference between front two
    legs q3  is set to 0.5.  In order to continue steady walking,
    it is assumed that each leg repeats forward and backward
    motion.  Now we set a reference position of  leg motion.
    For  the left leg,  we  select  forward end point  of  the
    trajectory as a reference position. In the case  of  the
    right leg, reference position is automatically calculated
    from duty factor p and phase difference q3,  and its value is
    1/(2p).  After front two legs are positioned at their reference positions, each leg is drived along the trajectory.
    Of  course, leg motion must  be  synchronized  to the
    driving of the rear wheels.
    In  order  to
    simplify  the  problem,  we  assume that  turning  center  is
    constant  during  a leg motion cycle that starts from  the
    reference position.  By  this assumption, a transfer from
    straight movement to turning, or from turning to turning
    with different curvature  is  always done at  the  reference
    position.  Now we define s  as robot moving distance in a
    leg motion cycle.  This  means that robot  body  turns
    against the turning center by  s/r in the coordinate system
    fixed  to the  ground.  On  the  other hand, a leg turns
    against  the turning center by pdr in reverse direction in
    the body coordinate system.  Turning  radiuses  of  front
    two legs, r, and r2,  are calculated by  following equations.
    Next,  turning  gait  is  considered. where,  f  is half of y-coordinate difference of two reference
    positions,  and  d  and  e  are  x-coordinates  of  the  left
    reference position  and the right  reference position,
    respectively. Wheel driving distances  during the  leg
    motion cycle, w3 and w4 are expressed as follows. w
    leg, and rear is wheel locomotion. Although a relatively
    large wheel  is used, principally a wheel cannot  climb a
    step  whose  height  is  larger than half  of  the  wheel’s
    diameter. When  the  robot encounters a  large  step, a
    step mode is utilized. Locomotion algorithm in  the step
    mode is  shown in Fig.7. After  the  robot  stand in  front
    of  a step (a), front  wheel  is moved on  the step  by  leg
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