Notes

Outline

Fast and Robust Legged Locomotion

Overview Introduction Functional Biomimesis Robot Design Model Analysis Conclusions

Fast, Robust Rough Terrain Traversal Why? Mine clearing Urban Reconnaissance Why legs? Basic Design Goals 1.5 body lengths per second Hip-height obstacles Simple

Traditional Approaches to Legged Systems Statically stable Tripod of support Slow Rough terrain Dynamically stable No support requirements Fast Smooth terrain

Biological Example 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

Biomimesis Options

Biological Inspiration Control heirarchy Passive component Active component

Is Passive Enough? Passive Dynamic Stabilization No active stabilization Geometry Mechanical system properties

Geometry

Sprawlita Mass - .27 kg Dimensions - 16x10x9 cm Leg length - 4.5 cm Max. Speed - 39cm/s    2.5 body/sec Hip height obstacle traversal

Movie Compliant hip Alternating tripod Stable running Obstacle traversal

Mechanical System Properties Prototype: Empirically tuned properties Design for behavior

“Simple” Model 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!

Simplest Locomotion Model 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

Modeling assumptions

Modeling assumptions

Modeling assumptions

Modeling assumptions

Modeling assumptions

Modeling assumptions

Modeling assumptions

Modeling assumptions

Non-linear analysis tools Discrete non-linear system Fixed points numerically integrate to find exclude horizontal position information

Non-linear analysis tools Floquet technique Analyze perturbation response Digital eigenvalues via linearization - examine stability Use selective perturbations to construct M matrix

Non-linear analysis tools Floquet technique

Perturbation Response

Analysis trends 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

Design Example

Locomotion Insight Body tends towards equilibrium point Parameters and mechanical properties determine how

Summary and Conclusions

Future Work Extend findings and insights to more complex models Develop easily modeled 4th generation robot Utilize sensor feedback in high level control Examine other behaviors

Thanks! Center for Design Research Dexterous Manipulation Lab Rapid Prototyping Lab Mark Cutkosky Jorge Cham, Jonathan Clark