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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

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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

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Is there a general approach to control arbitrary modular robots?

Control Problem

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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

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Bioinspiration

[Ijspeert A.]

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Methods

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Base Morphology

Simulation Hardware

Simplifications: 1. Planar Limbs 2. Specialized foot

𝐢π‘₯𝑕 = 1.4 Kg 𝐢π‘₯𝑕 = 2 Kg

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Base Morphology

Simulation

𝜘 πœ˜π‘ π‘“π‘” 𝜘 𝜐 (𝑦, 𝑧, 𝑨) (Ξ¦, Θ, Ξ¨) (𝐺

𝑦, 𝐺 𝑧, 𝐺 𝑨)

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Base Morphology

Hardware

18V 18V 12V RS-485 TTL

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Base Morphology

Current

Hardware

IMU 3D force Joint Reference Joint Position New

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Step Trajectory

πœ„π‘›π‘π‘¦ π‘ž2 π‘ž1 π‘ž3 π‘š2 β„Žπ‘‘π‘’ π‘š1 β„Žπ‘‘π‘₯ πœ„π‘›π‘π‘¦ π‘ž1 π‘ž4 π‘ž3 π‘š2 π‘š1

Parameters: 1. πœ„π‘›π‘π‘¦ 2. β„Žπ‘‘π‘’ 3. β„Žπ‘‘π‘₯

Swing phase Stance phase

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π‘ž1 π‘ž2 π‘ž4 π‘ž3

πœšπ‘’ πœšπ‘—

Control Approaches

𝑗 = 1 𝑗 = 2 𝑗 = 4 𝑗 = 3

Open Loop CPG Tegotae

Parameters: 1. 𝑔 2. 𝑒𝑔 3. πœ”π‘—π‘˜ = βˆ’πœ”π‘˜π‘— Parameters : 1. 𝑔 2. 𝜏

𝑗 = 1 𝑗 = 2 𝑗 = 4 𝑗 = 3

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π‘ž1 π‘ž2 π‘ž4 π‘ž3

πœšπ‘’ πœšπ‘—

Control Approaches

Open Loop CPG Tegotae Binary Tegotae

Parameters: 1. 𝑔 2. 𝑒𝑔 3. πœ”π‘—π‘˜ = βˆ’πœ”π‘˜π‘—

𝑗 = 1 𝑗 = 2 𝑗 = 4 𝑗 = 3

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Goals

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Thesis Goals

Open Loop CPG Tegotae

  • 1. Trajectory
  • 2. Duty factor

Energy Speed Stability Steady State

  • 1. Trajectory
  • 2. Effect of 𝜏
  • 3. Scaled by

frequency?

  • 4. Binary Tegotae?

Convergence

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Results

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π‘ž1 π‘ž2 π‘ž4 π‘ž3

πœšπ‘’ πœšπ‘—

Control Approaches

Open Loop CPG Tegotae Binary Tegotae

Parameters: 1. 𝑔 2. 𝑒𝑔 3. πœ”π‘—π‘˜ = βˆ’πœ”π‘˜π‘—

𝑗 = 1 𝑗 = 2 𝑗 = 4 𝑗 = 3

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Subject to:

Particle Swarm Optimization

Open Loop CPG

> β„Žπ‘›π‘—π‘œ

Maximize :

Validation on hardware

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Subject to:

Particle Swarm Optimization

Open Loop CPG

Maximize :

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Particle Swarm Optimization

Open Loop CPG

𝑀𝑒 [𝑛 βˆ™ π‘‘βˆ’1] 0.25 0.5 0.75 1 Trot BL Maximize :

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Particle Swarm Optimization

Open Loop CPG

𝑀𝑒 [𝑛 βˆ™ π‘‘βˆ’1] 0.25 0.5 0.75 1 Trot Rotary Gallop BL Maximize :

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Particle Swarm Optimization

Open Loop CPG

𝑀𝑒 [𝑛 βˆ™ π‘‘βˆ’1] 0.25 0.5 0.75 1 Trot Rotary Gallop Bound BL Maximize :

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Maximize :

Particle Swarm Optimization

Open Loop CPG

Imposed Trot

𝑀𝑒 [𝑛 βˆ™ π‘‘βˆ’1] 0.25 0.5 0.75 1 Trot Rotary Gallop Bound BL

Trot

𝑔 = 0.25 𝐼𝑨 , πœ„π‘›π‘π‘¦ = 0.3 𝑠𝑏𝑒 , β„Žπ‘‘π‘₯ = 15 𝑛𝑛, β„Žπ‘‘π‘’ = 0 𝑛𝑛

Validation on hardware

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Validated on hardware β‰₯ 0.5

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Steady State Systematic Search: Trajectories

Open Loop CPG

𝑔 = 0.25 𝐼𝑨

Simulation

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Open Loop CPG

Steady State Systematic Search: Trajectories

Hardware

𝑔 = 0.25 𝐼𝑨 𝑒𝑔 = 0.5

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π‘ž1 π‘ž2 π‘ž4 π‘ž3

πœšπ‘’ πœšπ‘—

Control Approaches

Open Loop CPG Tegotae Binary Tegotae

Parameters: 1. 𝑔 2. 𝑒𝑔 3. πœ”π‘—π‘˜ = βˆ’πœ”π‘˜π‘—

𝑗 = 1 𝑗 = 2 𝑗 = 4 𝑗 = 3

  • 1. Convergence
  • 2. Steady State

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  • 1. Convergence

Tegotae

Trot 𝜚0 = [0,0,0,0]

𝝉 = 𝟏. πŸ‘πŸ”

Hardware

𝑔 = 0.25 𝐼𝑨 , πœ„π‘›π‘π‘¦ = 0.3 𝑠𝑏𝑒 , β„Žπ‘‘π‘₯ = 15 𝑛𝑛, β„Žπ‘‘π‘’ = 0 𝑛𝑛 26

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  • 1. Convergence

Binary Tegotae

𝝉𝒄 = 𝟏. πŸ•

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  • 1. Convergence

Binary Tegotae

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Tegotae

  • 2. Steady State

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Simulation

  • 1. Trajectory
  • 2. Effect of 𝜏
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Tegotae

  • 2. Steady State

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Simulation

3. Scaled by frequency?

  • 1. Trajectory
  • 2. Effect of 𝜏
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Tegotae

  • 2. Steady State

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Simulation

3. Scaled by frequency?

  • 1. Trajectory
  • 2. Effect of 𝜏

Best 15 Speed Best 15 Energy Efficiency

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Tegotae

𝑔 = 0.25 𝐼𝑨 , πœ„π‘›π‘π‘¦ = 0.3 𝑠𝑏𝑒 , β„Žπ‘‘π‘₯ = 15 𝑛𝑛, β„Žπ‘‘π‘’ = 0 𝑛𝑛

  • 2. Steady State

Hardware

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Tegotae

Hardware 𝝉 = 𝟏 𝝉 = 𝟏. πŸ’

  • 2. Steady State

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Tegotae

  • 2. Steady State

Step cycle

𝝉 = 𝟏 𝝉 = 𝟏. πŸ’ Hardware

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Tegotae

  • 2. Steady State

𝝉 = 𝟏 𝝉 = 𝟏. πŸ’ Hardware

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Tegotae

  • 2. Steady State

Hardware

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𝝉 = 𝟏. πŸ” 𝝉 = 𝟐

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  • 2. Steady State

Binary Tegotae

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𝝉𝒄 = 𝟏. πŸ• 𝝉𝒄 = 𝟏. πŸ•

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Conclusions

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Conclusions

Open Loop CPG Tegotae Binary Tegotae

1. Slower convergence 2. Less efficient steady state

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Simulation VS Hardware

Particle Swarm Optimizations:

𝑀𝑒 [𝑛 βˆ™ π‘‘βˆ’1] 0.25 0.5 0.75 1 Trot Rotary Gallop Bound BL β„Žπ‘‘π‘’ = 0

Systematic Search: Convergence:𝜏 Steady state: 𝜏 Fast + Efficient

𝜏

Stable

𝜏(𝑒)

Trot β„Žπ‘‘π‘₯ ∈ 10,20 𝑛𝑛

πœ„π‘›π‘π‘¦

Fast + Efficient H:

πœ„π‘›π‘π‘¦

Slow + Efficient S:

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Future Work

1. More experiments! 2. Rough Terrain

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Tegotae

3. Compliance 4. Mophology changes

Crawling?

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Ground Reaction Force [N]

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Future Work

Tegotae

1. More experiments! 2. Rough Terrain 3. Compliance 4. Mophology changes

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Acknowledgements

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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

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Appendix: Cat Gallop

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Appendix: Validation on β„Žπ‘‘π‘’ β‰  0

Validation on hardware π’Šπ’•π’– = πŸ” 𝒏𝒏

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Appendix: Statistics on CLSS

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Appendix: Simulation VS Hardware

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Appendix: Open Loop Systematic Search

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Appendix: Open Loop Systematic Search

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Appendix: D-S run

Open Loop CPG

𝑀𝑒 [𝑛 βˆ™ π‘‘βˆ’1] 0.25 0.5 0.75 1 Trot Rotary Gallop D-S run

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Appendix: 0.75 Hz Binary Convergence

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Appendix: Robot version 1

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Appendix: Hardware Limitations

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Appendix: PSO Results

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Appendix: PSO Results

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