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Fast and Robust Legged Locomotion Inspired by Biological Systems

This study explores the design and analysis of legged robotic systems capable of fast and robust traversal over rough terrain. Inspired by the efficient locomotion of biological organisms like the death-head cockroach, the focus is on achieving high speeds and stability through passive dynamic stabilization and compliant mechanical systems. The report discusses functional biomimesis and the implementation of advanced robotic mobility solutions designed for applications such as mine clearing and urban reconnaissance. Performance metrics, mechanical properties, and design considerations are presented, highlighting novel approaches to legged robot design.

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Fast and Robust Legged Locomotion Inspired by Biological Systems

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  1. Fast and Robust Legged Locomotion Sean Bailey Mechanical Engineering Design Division Advisor: Dr. Mark Cutkosky May 12, 2000

  2. Overview Intro Design Biomimesis Analysis Conclusions • Introduction • Functional Biomimesis • Robot Design • Model Analysis • Conclusions

  3. Fast, Robust Rough Terrain Traversal Intro Design Biomimesis Analysis Conclusions • Why? • Mine clearing • Urban Reconnaissance • Why legs? • Basic Design Goals • 1.5 body lengths per second • Hip-height obstacles • Simple

  4. Traditional Approaches to Legged Systems Intro Design Biomimesis Analysis Conclusions • Statically stable • Tripod of support • Slow • Rough terrain • Dynamically stable • No support requirements • Fast • Smooth terrain

  5. Biological Example Intro Design Biomimesis Analysis Conclusions • Death-head cockroach Blaberus discoidalis • Fast • Speeds of up to 10 body/s • Rough terrain • Can easily traverse fractal terrain of obstacles 3X hip height • Stability • Static and dynamic

  6. Biomimesis Options Intro Design Biomimesis Analysis Conclusions Too complex! Functional Biomimesis “Biomimetic” configuration Extract fast rough terrain locomotion capabilities

  7. Biological Inspiration Intro Design Biomimesis Analysis Conclusions • Control heirarchy • Passive component • Active component

  8. Is Passive Enough? Intro Design Biomimesis Analysis Conclusions • Passive Dynamic Stabilization • No active stabilization • Geometry • Mechanical system properties

  9. Geometry Intro Design Biomimesis Analysis Conclusions Cockroach Geometry Functional Biomimesis Robot Implementation • Passive Compliant Hip Joint • Effective Thrusting Force • Damped, Compliant Hip Flexure • Embedded Air Piston • Rotary Joint • Prismatic Joint

  10. Sprawlita Intro Design Biomimesis Analysis Conclusions • Mass - .27 kg • Dimensions - 16x10x9 cm • Leg length - 4.5 cm • Max. Speed - 39cm/s 2.5 body/sec • Hip height obstacle traversal

  11. Movie Intro Design Biomimesis Analysis Conclusions • Compliant hip • Alternating tripod • Stable running • Obstacle traversal

  12. Mechanical System Properties Intro Design Biomimesis Analysis Conclusions • Prototype: Empirically tuned properties • Design for behavior ? Mechanical System Properties Modeling

  13. “Simple” Model Full 3D model Symmetry assumption Planar model Intro Design Biomimesis Analysis Conclusions K, B, nom • Body has 3 planar degrees of freedom • x, z, theta • mass, inertia • 3 massless legs (per tripod) • rotating hip joint - damped torsional spring • prismatic leg joint - damped linear spring • 6 parameters per leg 18 parameters to tune - TOO MANY! k, b, nom

  14. Simplest Locomotion Model g g Intro Design Biomimesis Analysis Conclusions • Body has 2 planar degrees of freedom • x, z • mass • 4 massless legs • freely rotating hip joint • prismatic leg joint - damped linear spring • 3 parameters per leg 6 parameters to tune, assuming symmetry k, b, nom Biped Biped Quadruped

  15. Modeling assumptions g State x 0 Leg Set Leg Set Leg Set Leg Set 1 2 1 2 T T T T Time Stride Period = state trajectory Intro Design Biomimesis Analysis Conclusions • Time-Based Mode Transitions • Clock-driven motor pattern • “Groucho running”1 • One “reset” mode • Two sets of legs - Two modes • Symmetric - treat as one mode • Mode initial conditions • Nominal leg angles • Instant passive component compression 1 McMahon, et al 1987

  16. Modeling assumptions g T T T T = state trajectory Intro Design Biomimesis Analysis Conclusions • Time-Based Mode Transitions • Clock-driven motor pattern • “Groucho running”1 • One “reset” mode • Two sets of legs - Two modes • Symmetric - treat as one mode • Mode initial conditions • Nominal leg angles • Instant passive component compression t = 2T- State x 0 Leg Set Leg Set Leg Set Leg Set 1 2 1 2 Time Stride Period 1 McMahon, et al 1987

  17. Modeling assumptions g t = 2T+ State x 0 Leg Set Leg Set Leg Set Leg Set 1 2 1 2 T T T T Time Stride Period = state trajectory Intro Design Biomimesis Analysis Conclusions • Time-Based Mode Transitions • Clock-driven motor pattern • “Groucho running”1 • One “reset” mode • Two sets of legs - Two modes • Symmetric - treat as one mode • Mode initial conditions • Nominal leg angles • Instant passive component compression 1 McMahon, et al 1987

  18. Modeling assumptions g t = 2T + 1/3T State x 0 Leg Set Leg Set Leg Set Leg Set 1 2 1 2 T T T T Time Stride Period = state trajectory Intro Design Biomimesis Analysis Conclusions • Time-Based Mode Transitions • Clock-driven motor pattern • “Groucho running”1 • One “reset” mode • Two sets of legs - Two modes • Symmetric - treat as one mode • Mode initial conditions • Nominal leg angles • Instant passive component compression 1 McMahon, et al 1987

  19. Modeling assumptions g t = 2T + 2/3T State x 0 Leg Set Leg Set Leg Set Leg Set 1 2 1 2 T T T T Time Stride Period = state trajectory Intro Design Biomimesis Analysis Conclusions • Time-Based Mode Transitions • Clock-driven motor pattern • “Groucho running”1 • One “reset” mode • Two sets of legs - Two modes • Symmetric - treat as one mode • Mode initial conditions • Nominal leg angles • Instant passive component compression 1 McMahon, et al 1987

  20. Modeling assumptions g t = 3T- State x 0 Leg Set Leg Set Leg Set Leg Set 1 2 1 2 T T T T Time Stride Period = state trajectory Intro Design Biomimesis Analysis Conclusions • Time-Based Mode Transitions • Clock-driven motor pattern • “Groucho running”1 • One “reset” mode • Two sets of legs - Two modes • Symmetric - treat as one mode • Mode initial conditions • Nominal leg angles • Instant passive component compression 1 McMahon, et al 1987

  21. Modeling assumptions g t = 3T+ State x 0 Leg Set Leg Set Leg Set Leg Set 1 2 1 2 T T T T Time Stride Period = state trajectory Intro Design Biomimesis Analysis Conclusions • Time-Based Mode Transitions • Clock-driven motor pattern • “Groucho running”1 • One “reset” mode • Two sets of legs - Two modes • Symmetric - treat as one mode • Mode initial conditions • Nominal leg angles • Instant passive component compression 1 McMahon, et al 1987

  22. Modeling assumptions g t = 3T + 1/3T State x 0 Leg Set Leg Set Leg Set Leg Set 1 2 1 2 T T T T Time Stride Period = state trajectory Intro Design Biomimesis Analysis Conclusions • Time-Based Mode Transitions • Clock-driven motor pattern • “Groucho running”1 • One “reset” mode • Two sets of legs - Two modes • Symmetric - treat as one mode • Mode initial conditions • Nominal leg angles • Instant passive component compression 1 McMahon, et al 1987

  23. Non-linear analysis tools = state trajectory = fixed points xk+1 = xk = x* State x 0 Leg Set Leg Set Leg Set Leg Set 1 2 1 2 T T T T Time Stride Period = state trajectory Intro Design Biomimesis Analysis Conclusions • Discrete non-linear system • Fixed points • numerically integrate to find • exclude horizontal position information

  24. Non-linear analysis tools = nominal trajectory Intro Design Biomimesis Analysis Conclusions • Floquet technique • Analyze perturbation response • Digital eigenvalues via linearization - examine stability • Use selective perturbations to construct M matrix Numerically Integrate

  25. Non-linear analysis tools Intro Design Biomimesis Analysis Conclusions • Floquet technique

  26. Perturbation Response Intro Design Biomimesis Analysis Conclusions

  27. Analysis trends 0.075 2.8 Horizontal Velocity Recovery Rate 2.6 0.07 2.4 0.065 2.2 0.06 X_dot (m/s) 1/max[eig(M)] 2 0.055 1.8 0.05 1.6 0.045 1.4 0.04 1.2 6.5 7 7.5 8 8.5 9 9.5 10 Damping (N-s/m) Intro Design Biomimesis Analysis Conclusions • Relationships • damping vs. speed and “robustness” • stiffness, leg angles, leg lengths, stride period, etc • Use for design • select mechanical properties • select other parameters • Insight into the mechanism of locomotion

  28. Design Example Robustness Speed Intro Design Biomimesis Analysis Conclusions Damping Damping Damping Stiffness Stiffness Stiffness Speed = 0 Speed = 13 cm/s Speed = 23.5 cm/s

  29. Locomotion Insight Intro Design Biomimesis Analysis Conclusions • Body tends towardsequilibrium point • Parameters andmechanical propertiesdetermine how Trajectory Mode Equilibrium Statically Unstable Region Initial condition Leg Extension Limit Leg Pre- Compressions

  30. Summary and Conclusions Intro Design Biomimesis Analysis Conclusions • Current leg systems are either fast or can handle rough terrain • Biology suggests emphasis on good mechanical design • enhances capability • simplifies control • Purely clock-driven systems can be fast and robust • Floquet technique can be used to indicate locomotion robustness • Trends can be established to improve design and provide insight

  31. Future Work Intro Design Biomimesis Analysis Conclusions • Extend findings and insights to more complex models • Develop easily modeled 4th generation robot • Utilize sensor feedback in high level control • Examine other behaviors

  32. Thanks! Intro Design Biomimesis Analysis Conclusions • Center for Design Research • Dexterous Manipulation Lab • Rapid Prototyping Lab • Mark Cutkosky • Jorge Cham, Jonathan Clark

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