IEEE Robotics & Automation Magazine - March 2016 - 59

3

1

4

Reference Path

2

px (m)

py (m)

2

0

py (m)

6
Path of CM of Robot

0
-2

-1
-4

-2

0
2
px (m)

4

-4

6

0

20

(a)

50
i (°)

0
-50

80

0.25
0.2
0.15

z0 (°)

i
iref

yt (m/s)

100

40
60
Time (s)
(b)

3
2.5
2
1.5
1
0.5
0
- 0.5
-1

0.1
0.05

-100
0

20

40
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Time (s)
(d)

0

80

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Time (s)
(e)

80

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0

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Time (s)
(c)

80

0

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Time (s)
(f)

80

Path of CM of Robot
Reference Path

py (m)

2
1
0
-1

-4 −2

0 2 4
px (m)

px (m)

3

6

8
6
4
2
0
-2
-4
-6
0

py (m)

Figure 18. The simulation results for straight-line path following for a snake robot with n = 9 links initially headed along the desired
path, and with the initial distance from the CM being p y = 1.89 m for lateral undulation with gait parameters a = 35c, ~ = 120c/s
and d = 40c: (a) the path of the CM, (b) the position along the path p x, (c) the cross-track error p y, (d) the heading angle i, (e) the
forward velocity yrt , and (f) the joint angle offset z 0 .

50
100
Time (s)

-50
- 100
0

50

100

50

150

0.15
0.1
0.05
0

0

50

100

150

(c)

z0 (°)

i (°)

0

0

Time (s)

0.2
yt (m/s)

i
iref

50

150

(b)

(a)
100

3
2.5
2
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-0.5
-1

100

150

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5
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-5
- 10
- 15
- 20

0

50

100

Time (s)

Time (s)

Time (s)

(d)

(e)

(f)

150

Figure 19. The simulation results for straight-line path following for a snake robot with n = 9 links initially headed along the desired
path, and with the initial distance from the CM being p y = 2.75 m for eel-like motion with gait parameters a = 40c, ~ = 120c/s and
d = 40c: (a) the path of the CM, (b) the position along the path p y, (c) the cross-track error p y, (d) the heading angle i, (e) the
forward velocity yrt , and (f) the joint angle offset z 0 .

was chosen as D = 0.9 similar to the experimental trials.
The initial values of all states of the robot were set to zero except for the initial position of the CM, which was selected as
p CM (0) = [- 3.58, 1.89] and p CM (0) = [- 4.20, 2.75] for
lateral undulation and eel-like motion, respectively, i.e., the
same as the initial values of the experiments presented in
Figures 10 and 12. The simulation results are shown in Figures 18 and 19. In addition, Figures 20 and 21 present the

comparison results for the cross-track error and the heading
between the simulated and the physical robot.
The results shown in Figures 18-21 indicate that the qualitative behavior of the simulated system is similar to the behavior of the physical robot. In particular, from Figures
10(a), 12(a) and Figures 18(a), 19(a) it can be seen that the
physical snake and the simulated snake followed almost the
same path for both lateral undulation and eel-like motion
march 2016

*

IEEE ROBOTICS & AUTOMATION MAGAZINE

*

59



Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - March 2016

IEEE Robotics & Automation Magazine - March 2016 - Cover1
IEEE Robotics & Automation Magazine - March 2016 - Cover2
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IEEE Robotics & Automation Magazine - March 2016 - Cover3
IEEE Robotics & Automation Magazine - March 2016 - Cover4
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https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2022
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https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2022
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https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2021
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https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2021
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https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2020
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https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2020
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https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2019
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2019
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2019
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https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2018
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2018
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2018
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2018
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2017
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2017
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2017
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2017
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2016
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2016
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2016
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2016
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2015
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2015
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2015
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2015
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2014
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2014
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2014
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2014
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2013
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2013
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2013
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2013
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2012
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2012
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2012
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2012
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2011
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2011
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2011
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2011
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2010
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2010
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