final presentation - École polytechnique fédérale de lausanne · 2019-02-22 · final...
TRANSCRIPT
![Page 1: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/1.jpg)
Final Presentation
CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots
Author:
Rui Vasconcelos
Supervisors:
Simon Hauser
Florin Dzeladini
Prof. Auke Ijspeert
Prof. Paulo Oliveira1
![Page 2: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/2.jpg)
Is there a general approach to control
arbitrary modular robots?
Control Problem
2
![Page 3: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/3.jpg)
Is there a general approach to control
arbitrary modular robots?
Simplifications:
1. 8 degrees of freedom
2. Symmetric configuration
3. Central body
Control Problem
quadrupedal
3
![Page 4: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/4.jpg)
Bioinspiration
[Ijspeert A.]
4
![Page 5: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/5.jpg)
Methods
![Page 6: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/6.jpg)
Base Morphology
Simulation Hardware
Simplifications:
1. Planar Limbs
2. Specialized foot
𝐵𝑤𝑔 = 1.4 Kg 𝐵𝑤𝑔 = 2 Kg
6
![Page 7: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/7.jpg)
Base Morphology
Simulation
𝜗
𝜗𝑟𝑒𝑓𝜗
𝜏
(𝑥, 𝑦, 𝑧) (Φ, Θ,Ψ)
(𝐹𝑥, 𝐹𝑦 , 𝐹𝑧)
7
![Page 8: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/8.jpg)
Base Morphology
Hardware18V18V12V
RS-485
TTL
8
![Page 9: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/9.jpg)
Base Morphology
Current Hardware
IMU
3D force
Joint ReferenceJoint Position
New
9
![Page 10: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/10.jpg)
Step Trajectory
𝜃𝑚𝑎𝑥
𝑝2
𝑝1𝑝3
𝑙2
ℎ𝑠𝑡
𝑙1
ℎ𝑠𝑤
𝜃𝑚𝑎𝑥
𝑝1𝑝4𝑝3
𝑙2
𝑙1Parameters:
1. 𝜃𝑚𝑎𝑥
2. ℎ𝑠𝑡
3. ℎ𝑠𝑤
Swing phaseStance phase
10
![Page 11: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/11.jpg)
𝑝1
𝑝2
𝑝4
𝑝3
𝜙𝑡 𝜙𝑖
Control Approaches
𝑖 = 1 𝑖 = 2
𝑖 = 4 𝑖 = 3
Open Loop CPG Tegotae
Parameters:
1. 𝑓
2. 𝑑𝑓
3. 𝜓𝑖𝑗 = −𝜓𝑗𝑖
Parameters:
1. 𝑓
2. 𝜎
𝑖 = 1 𝑖 = 2
𝑖 = 4 𝑖 = 3
11
![Page 12: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/12.jpg)
𝑝1
𝑝2
𝑝4
𝑝3
𝜙𝑡 𝜙𝑖
Control Approaches
Open Loop CPG Tegotae
Binary Tegotae
Parameters:
1. 𝑓
2. 𝑑𝑓
3. 𝜓𝑖𝑗 = −𝜓𝑗𝑖
𝑖 = 1 𝑖 = 2
𝑖 = 4 𝑖 = 3
12
![Page 13: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/13.jpg)
Goals
![Page 14: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/14.jpg)
Thesis Goals
Open Loop CPG Tegotae
1. Trajectory
2. Duty factor
Energy
Speed
Stability
Steady State
1. Trajectory
2. Effect of 𝜎
3. Scaled byfrequency?
4. Binary Tegotae?Convergence
14
![Page 15: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/15.jpg)
Results
![Page 16: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/16.jpg)
𝑝1
𝑝2
𝑝4
𝑝3
𝜙𝑡 𝜙𝑖
Control Approaches
Open Loop CPG Tegotae
Binary Tegotae
Parameters:
1. 𝑓
2. 𝑑𝑓
3. 𝜓𝑖𝑗 = −𝜓𝑗𝑖
𝑖 = 1 𝑖 = 2
𝑖 = 4 𝑖 = 3
16
![Page 17: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/17.jpg)
Subject to:
Particle Swarm Optimization
Open Loop CPG
> ℎ𝑚𝑖𝑛
Maximize:
Validation on hardware
17
![Page 18: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/18.jpg)
Subject to:
Particle Swarm Optimization
Open Loop CPG
Maximize:
18
![Page 19: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/19.jpg)
Particle Swarm Optimization
Open Loop CPG
𝑣𝑑 [𝑚 ∙ 𝑠−1]
0.25 0.5 0.75 1
Trot
BL
Maximize:
19
![Page 20: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/20.jpg)
Particle Swarm Optimization
Open Loop CPG
𝑣𝑑 [𝑚 ∙ 𝑠−1]
0.25 0.5 0.75 1
Trot
Rotary Gallop
BL
Maximize:
20
![Page 21: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/21.jpg)
Particle Swarm Optimization
Open Loop CPG
𝑣𝑑 [𝑚 ∙ 𝑠−1]
0.25 0.5 0.75 1
Trot
Rotary Gallop
Bound
BL
Maximize:
21
![Page 22: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/22.jpg)
Maximize:
Particle Swarm Optimization
Open Loop CPG
Imposed Trot
𝑣𝑑 [𝑚 ∙ 𝑠−1]
0.25 0.5 0.75 1
Trot
Rotary Gallop
Bound
BL
Trot
𝑓 = 0.25 𝐻𝑧 , 𝜃𝑚𝑎𝑥 = 0.3 𝑟𝑎𝑑 , ℎ𝑠𝑤 = 15 𝑚𝑚, ℎ𝑠𝑡 = 0𝑚𝑚
Validation on hardware
22
0Validated on hardware
≥ 0.5
![Page 23: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/23.jpg)
Steady State Systematic Search: Trajectories
Open Loop CPG
𝑓 = 0.25 𝐻𝑧
Simulation
23
![Page 24: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/24.jpg)
Open Loop CPG
Steady State Systematic Search: Trajectories
Hardware
𝑓 = 0.25 𝐻𝑧𝑑𝑓 = 0.5
24
![Page 25: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/25.jpg)
𝑝1
𝑝2
𝑝4
𝑝3
𝜙𝑡 𝜙𝑖
Control Approaches
Open Loop CPG Tegotae
Binary Tegotae
Parameters:
1. 𝑓
2. 𝑑𝑓
3. 𝜓𝑖𝑗 = −𝜓𝑗𝑖
𝑖 = 1 𝑖 = 2
𝑖 = 4 𝑖 = 3
1. Convergence
2. Steady State 25
![Page 26: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/26.jpg)
1. Convergence
TegotaeTrot
𝜙0 = [0,0,0,0]
𝝈 = 𝟎. 𝟐𝟓
Hardware
𝑓 = 0.25 𝐻𝑧 , 𝜃𝑚𝑎𝑥 = 0.3 𝑟𝑎𝑑 , ℎ𝑠𝑤 = 15 𝑚𝑚, ℎ𝑠𝑡 = 0𝑚𝑚26
![Page 27: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/27.jpg)
1. Convergence
Binary Tegotae
𝝈𝒃 = 𝟎. 𝟔
27
![Page 28: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/28.jpg)
1. Convergence
Binary Tegotae
28
![Page 29: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/29.jpg)
Tegotae
2. Steady State
29
Simulation 1. Trajectory
2. Effect of 𝜎
![Page 30: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/30.jpg)
Tegotae
2. Steady State
30
Simulation
3. Scaled byfrequency?
1. Trajectory
2. Effect of 𝜎
![Page 31: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/31.jpg)
Tegotae
2. Steady State
31
Simulation
3. Scaled byfrequency?
1. Trajectory
2. Effect of 𝜎
Best15
Speed
Best 15 EnergyEfficiency
![Page 32: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/32.jpg)
Tegotae
𝑓 = 0.25 𝐻𝑧 , 𝜃𝑚𝑎𝑥 = 0.3 𝑟𝑎𝑑 , ℎ𝑠𝑤 = 15 𝑚𝑚, ℎ𝑠𝑡 = 0𝑚𝑚
2. Steady State
Hardware
32
![Page 33: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/33.jpg)
TegotaeHardware
𝝈 = 𝟎 𝝈 = 𝟎. 𝟑
2. Steady State
33
![Page 34: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/34.jpg)
Tegotae
2. Steady State
Step cycle
𝝈 = 𝟎 𝝈 = 𝟎. 𝟑
Hardware
34
![Page 35: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/35.jpg)
Tegotae
2. Steady State
𝝈 = 𝟎 𝝈 = 𝟎. 𝟑
Hardware
35
![Page 36: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/36.jpg)
Tegotae
2. Steady State
Hardware
36
𝝈 = 𝟎. 𝟓 𝝈 = 𝟏
![Page 37: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/37.jpg)
2. Steady State
Binary Tegotae
37
𝝈𝒃 = 𝟎. 𝟔 𝝈𝒃 = 𝟎. 𝟔
![Page 38: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/38.jpg)
Conclusions
![Page 39: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/39.jpg)
Conclusions
Open Loop CPG Tegotae
Binary Tegotae
1. Slower convergence
2. Less efficient steady state
39
Simulation VS Hardware
Particle Swarm Optimizations:
𝑣𝑑 [𝑚 ∙ 𝑠−1]0.25 0.5 0.75 1
Trot
Rotary Gallop
Bound
BL
ℎ𝑠𝑡 = 0
Systematic Search:
Convergence:𝜎Steady state:
𝜎 Fast + Efficient
𝜎 Stable
𝜎(𝑡)
Trot
ℎ𝑠𝑤 ∈ 10,20 𝑚𝑚
𝜃𝑚𝑎𝑥 Fast + Efficient
H:
𝜃𝑚𝑎𝑥 Slow + Efficient
S:
![Page 40: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/40.jpg)
Future Work
1. More experiments!
2. Rough Terrain
40
Tegotae
3. Compliance
4. Mophology changes Crawling?
![Page 41: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/41.jpg)
Ground Reaction Force [N]
41
Future Work
Tegotae1. More experiments!
2. Rough Terrain
3. Compliance
4. Mophology changes
![Page 42: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/42.jpg)
Acknowledgements
42
![Page 43: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/43.jpg)
Final Presentation
CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots
Author:
Rui Vasconcelos
Supervisors:
Simon Hauser
Florin Dzeladini
Prof. Auke Ijspeert
Prof. Paulo Oliveira43
![Page 44: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/44.jpg)
Appendix: Cat Gallop
44
![Page 45: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/45.jpg)
Appendix: Validation on ℎ𝑠𝑡 ≠ 0
Validation on hardware
𝒉𝒔𝒕 = 𝟓𝒎𝒎
45
![Page 46: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/46.jpg)
Appendix: Statistics on CLSS
46
![Page 47: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/47.jpg)
Appendix: Simulation VS Hardware
47
![Page 48: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/48.jpg)
Appendix: Open Loop Systematic Search
48
![Page 49: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/49.jpg)
Appendix: Open Loop Systematic Search
49
![Page 50: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/50.jpg)
Appendix: D-S run
Open Loop CPG
𝑣𝑑 [𝑚 ∙ 𝑠−1]
0.25 0.5 0.75 1
Trot
Rotary Gallop
D-S run
50
![Page 51: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/51.jpg)
Appendix: 0.75 Hz Binary Convergence
51
![Page 52: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/52.jpg)
Appendix: Robot version 1
52
![Page 53: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/53.jpg)
Appendix: Hardware Limitations
53
![Page 54: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/54.jpg)
Appendix: PSO Results
54
![Page 55: Final Presentation - École Polytechnique Fédérale de Lausanne · 2019-02-22 · Final Presentation CPG and Tegotae based Locomotion Control of Quadrupedal Modular Robots Author:](https://reader034.vdocuments.site/reader034/viewer/2022050405/5f82278cbe57b07b872af584/html5/thumbnails/55.jpg)
Appendix: PSO Results
55