Instrumentation & Measurement Magazine 25-9 - 32

occurs when the feet reach the highest position, occurs between
the second and third stages. The speed then increases in
the stance phase, which is also the speed of motion, from zero
to the target speed. Due to the fact that the foot is lifted off and
lowered to the substrate during these two actions, they are important
in the motion control of robots.
It has also been discovered for a single leg that before contacting
the substrate, the swing feet reach the same speed as the
stance feet along the moving direction, while it maintains the
moving speed for a short time before leaving the ground at the
end of the stance phase, reducing interference with the contact
substrate. This is an excellent source of ideas for robot foot trajectory
planning.
Fig. 4b shows the proposed robot foot trajectory inspired
by the experimental results. The solid black line represents
the up-down modelled curve, and the colorful line is the modelled
curve in a moving direction. In the first half motion cycle,
the foot swings. The two short red curves are at the beginning
and end of the swing phase, respectively, and their speeds are
consistent with those in the stance phase. Cubic Bezier curves
and trigonometric functions may be used in practice for the
switching period (green curves) to avoid a sudden change in
the curve.
For a robot to move smoothly and steadily, the transition
between the rearmost to the frontmost position is crucial. It is
not typical for there to be a sudden change in acceleration or
speed when moving. According to the experimental result, the
cosine trigonometric function is suggested because of its continuous
and smooth kinematic and dynamic characteristics.
Thus, the fitting function is developed as:
f  22
x
where d0 and d1
 

d d dd1 01
T
 
cos t sh
(1)
represent the starting and final positions of the
transition stages; T is the time of transition; sh is the time shift.
It is used for trajectory planning along the up-down direction
and the position transition along the moving direction.
Robot Modeling and Locomotion Control
After simplifying the motion mechanism of the gecko in Fig.
2c, the gecko-mimic sprawling robot model can be provided,
as shown in Fig. 5a. The robot has a total of 12 degrees of freedom
(DoF), with three of them on each leg based on the DOF
distribution of a gecko's leg, which is identical with the gecko.
After specific structure design, the model is imported into
Dynamic Analysis software for motion simulation before
Fig. 5. The gecko-mimic robot. (a) Motion mechanism of the robot, used with permission from [24] ©2017 Springer; (b) Simulation model; (c) Simulation results of
foot trajectories relative to the hip joint; (d) Robot experiment.
32
IEEE Instrumentation & Measurement Magazine
December 2022
Instrumentation & Measurement Magazine 25-9

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