The snake is made of total 9 links and hence has 8 joints. To generate the gaits for various motions, a curve fitting algorithm is used (Refer to [1] and [2]). Let theta represent the joint angle of the links. Assume the joint angles to be zero when links are parallel. Then the joint angles in the vertical and horizontal joints can be calculated using the following equation:
A = Amplitude
w = Frequency of sine wave
t = Time
i = Link no.
Delta = phase diff. between two
consecutive links in same plane
Delta not
= phase diff. between 2 adjecent links in horizontal and vertical
plane
O = default Orientation of the robot
ver, hor = Vertical, Horizontal
GAIT

A

ω

δ

δ_{0}

O

Lateral
Undulation

A_{ver
}=60^{0}
A_{hor}=0

ω_{ver}=5π/6
s
ω_{hor}=0

δ_{ver}=2π/3
δ_{hor}=0

δ_{0}=0

O_{ver}=0
O_{hor}=0

Sidewinding

A_{ver
}=30^{0}
A_{hor}=30^{0}

ω_{ver}=5π/6
s
ω_{hor}=5π/6
s

δ_{ver}=2π/3
δ_{hor}=2π/3

δ_{0}=0

O_{ver}=0
O_{hor}=0

Rolling

A_{ver
}=60^{0}
A_{hor}=60^{0}

ω_{ver}=5π/6
s
ω_{hor}=5π/6
s

δ_{ver}=0
δ_{hor}=0

δ_{0}=30^{0}^{}

O_{ver}=0
O_{hor}=0

Corkscrew

A_{ver
}=30^{0}
A_{hor}=60^{0}

ω_{ver}=5π/12
s
ω_{hor}=5π/6
s

δ_{ver}=2π/3
δ_{hor}=2π/3

δ_{0}=0

O_{ver}=0
O_{hor}=0

[1] “Bioinspired locomotion for a modular snake robot” by Shubo Zhang and Yi Guo
[2] “Generating gaits for snake robots: annealed chain fitting and keyframe wave extraction” by Ross L. Hatton · Howie Choset
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