Final Presentation CPG and Tegotae based Locomotion Control of - PowerPoint PPT Presentation

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 Oliveira 1

Control Problem Is there a general approach to control arbitrary modular robots? 2

Control Problem Is there a general approach to control quadrupedal arbitrary modular robots? Simplifications: 1. 8 degrees of freedom 2. Symmetric configuration 3. Central body 3

Bioinspiration [Ijspeert A.] 4

Methods

Base Morphology Simulation Hardware 𝐶 𝑥𝑕 = 2 Kg 𝐶 𝑥𝑕 = 1.4 Kg Simplifications: 1. Planar Limbs 2. Specialized foot 6

Base Morphology Simulation (𝑦, 𝑧, 𝑨) (Φ, Θ, Ψ) 𝜘 𝑠𝑓𝑔 𝜘 𝜘 𝜐 (𝐺 𝑦 , 𝐺 𝑧 , 𝐺 𝑨 ) 7

Base Morphology Hardware 18V 18V 12V RS-485 TTL 8

Base Morphology Joint Reference Hardware Joint Position Current New IMU 3D force 9

Step Trajectory Stance phase Swing phase Parameters: 𝜄 𝑛𝑏𝑦 𝜄 𝑛𝑏𝑦 𝑚 1 𝑚 1 1. 𝜄 𝑛𝑏𝑦 𝑚 2 2. ℎ 𝑡𝑢 𝑚 2 3. ℎ 𝑡𝑥 𝑞 3 𝑞 3 𝑞 1 𝑞 1 𝑞 4 𝑞 2 ℎ 𝑡𝑥 ℎ 𝑡𝑢 10

Control Approaches Open Loop CPG Tegotae 𝑞 4 𝑗 = 2 𝑗 = 1 𝑗 = 2 𝑗 = 1 𝑞 3 𝑞 1 𝜚 𝑢 𝜚 𝑗 𝑞 2 Parameters: Parameters : 1. 𝑔 𝑗 = 4 𝑗 = 3 𝑗 = 4 𝑗 = 3 1. 𝑔 2. 𝑒𝑔 2. 𝜏 3. 𝜔 𝑗𝑘 = −𝜔 𝑘𝑗 11

Control Approaches Open Loop CPG Tegotae 𝑞 4 Binary Tegotae 𝑗 = 2 𝑗 = 1 𝑞 3 𝑞 1 𝜚 𝑢 𝜚 𝑗 𝑞 2 Parameters: 1. 𝑔 𝑗 = 4 𝑗 = 3 2. 𝑒𝑔 3. 𝜔 𝑗𝑘 = −𝜔 𝑘𝑗 12

Goals

Thesis Goals Open Loop CPG Tegotae 1. Trajectory 1. Trajectory 2. Effect of 𝜏 2. Duty factor 3. Scaled by Steady frequency? State Energy 4. Binary Tegotae? Speed Convergence Stability 14

Results

Control Approaches Open Loop CPG Tegotae 𝑞 4 Binary Tegotae 𝑗 = 2 𝑗 = 1 𝑞 3 𝑞 1 𝜚 𝑢 𝜚 𝑗 𝑞 2 Parameters: 1. 𝑔 𝑗 = 4 𝑗 = 3 2. 𝑒𝑔 3. 𝜔 𝑗𝑘 = −𝜔 𝑘𝑗 16

Particle Swarm Optimization Open Loop CPG Maximize : > ℎ 𝑛𝑗𝑜 Subject to: Validation on hardware 17

Particle Swarm Optimization Open Loop CPG Maximize : Subject to: 18

Particle Swarm Optimization Open Loop CPG Maximize Trot 𝑤 𝑒 [𝑛 ∙ 𝑡 −1 ] : 0.25 0.5 0.75 1 BL 19

Particle Swarm Optimization Open Loop CPG Rotary Gallop Maximize Trot 𝑤 𝑒 [𝑛 ∙ 𝑡 −1 ] : 0.25 0.5 0.75 1 BL 20

Particle Swarm Optimization Bound Open Loop CPG Rotary Gallop Maximize Trot 𝑤 𝑒 [𝑛 ∙ 𝑡 −1 ] : 0.25 0.5 0.75 1 BL 21

Particle Swarm Optimization Bound Open Loop CPG Rotary Gallop Maximize Validated on hardware Trot 𝑤 𝑒 [𝑛 ∙ 𝑡 −1 ] Trot 0 : 0.25 0.5 0.75 1 ≥ 0.5 BL Imposed Trot Validation on hardware 𝑔 = 0.25 𝐼𝑨 , 𝜄 𝑛𝑏𝑦 = 0.3 𝑠𝑏𝑒 , ℎ 𝑡𝑥 = 15 𝑛𝑛, ℎ 𝑡𝑢 = 0 𝑛𝑛 22

Steady State Systematic Search: Trajectories Open Loop CPG Simulation 𝑔 = 0.25 𝐼𝑨 23

Steady State Systematic Search: Trajectories Open Loop CPG Hardware 𝑔 = 0.25 𝐼𝑨 𝑒𝑔 = 0.5 24

Control Approaches Open Loop CPG Tegotae 𝑞 4 Binary Tegotae 𝑗 = 2 𝑗 = 1 𝑞 3 𝑞 1 𝜚 𝑢 𝜚 𝑗 𝑞 2 Parameters: 1. 𝑔 𝑗 = 4 𝑗 = 3 2. 𝑒𝑔 1. Convergence 3. 𝜔 𝑗𝑘 = −𝜔 𝑘𝑗 2. Steady State 25

1. Convergence Tegotae Trot 𝝉 = 𝟏. 𝟑𝟔 Hardware 𝜚 0 = [0,0,0,0] 26 𝑔 = 0.25 𝐼𝑨 , 𝜄 𝑛𝑏𝑦 = 0.3 𝑠𝑏𝑒 , ℎ 𝑡𝑥 = 15 𝑛𝑛, ℎ 𝑡𝑢 = 0 𝑛𝑛

1. Convergence Binary Tegotae 𝝉 𝒄 = 𝟏. 𝟕 27

1. Convergence Binary Tegotae 28

2. Steady State Tegotae 1. Trajectory Simulation 2. Effect of 𝜏 29

2. Steady State Tegotae 1. Trajectory Simulation 2. Effect of 𝜏 3. Scaled by frequency? 30

2. Steady State Tegotae 1. Trajectory Simulation 2. Effect of 𝜏 3. Scaled by frequency? Best Best 15 Energy 15 Efficiency Speed 31

2. Steady State Tegotae Hardware 𝑔 = 0.25 𝐼𝑨 , 𝜄 𝑛𝑏𝑦 = 0.3 𝑠𝑏𝑒 , ℎ 𝑡𝑥 = 15 𝑛𝑛, ℎ 𝑡𝑢 = 0 𝑛𝑛 32

2. Steady State Tegotae Hardware 𝝉 = 𝟏 𝝉 = 𝟏. 𝟒 33

2. Steady State Tegotae Hardware 𝝉 = 𝟏 𝝉 = 𝟏. 𝟒 Step cycle 34

2. Steady State Tegotae Hardware 𝝉 = 𝟏 𝝉 = 𝟏. 𝟒 35

2. Steady State Tegotae Hardware 𝝉 = 𝟏. 𝟔 𝝉 = 𝟐 36

2. Steady State Binary Tegotae 𝝉 𝒄 = 𝟏. 𝟕 𝝉 𝒄 = 𝟏. 𝟕 37

Conclusions

Conclusions Open Loop CPG Tegotae 𝜏(𝑢) Convergence: 𝜏 Particle Swarm Optimizations: Trot Bound Steady 𝜏 Fast + Efficient 𝜏 Rotary Gallop state: Stable ℎ 𝑡𝑢 = 0 Trot 𝑤 𝑒 [𝑛 ∙ 𝑡 −1 ] 0.25 0.5 0.75 1 BL Binary Tegotae Systematic Search: ℎ 𝑡𝑥 ∈ 10,20 𝑛𝑛 1. Slower convergence 𝜄 𝑛𝑏𝑦 Fast + H: 2. Less efficient steady state Efficient 𝜄 𝑛𝑏𝑦 Slow + S: Simulation VS Hardware Efficient 39

Future Work Tegotae 1. More experiments! 2. Rough Terrain 3. Compliance Crawling? 4. Mophology changes 40

Future Work Tegotae 1. More experiments! 2. Rough Terrain 3. Compliance Ground Reaction Force [N] 4. Mophology changes 41

Acknowledgements 42

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 Oliveira 43

Appendix: Cat Gallop 44

Appendix: Validation on ℎ 𝑡𝑢 ≠ 0 𝒊 𝒕𝒖 = 𝟔 𝒏𝒏 Validation on hardware 45

Appendix: Statistics on CLSS 46

Appendix: Simulation VS Hardware 47

Appendix: Open Loop Systematic Search 48

Appendix: Open Loop Systematic Search 49

Appendix: D-S run Open Loop CPG D-S run Rotary Gallop Trot 𝑤 𝑒 [𝑛 ∙ 𝑡 −1 ] 0.25 0.5 0.75 1 50

Appendix: 0.75 Hz Binary Convergence 51

Appendix: Robot version 1 52

Appendix: Hardware Limitations 53

Appendix: PSO Results 54

Appendix: PSO Results 55