Fast and Robust Legged
Locomotion
Overview
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Introduction |
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Functional Biomimesis |
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Robot Design |
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Model Analysis |
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Conclusions |
Fast, Robust Rough
Terrain Traversal
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Why? |
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Mine clearing |
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Urban Reconnaissance |
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Why legs? |
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Basic Design Goals |
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1.5 body lengths per second |
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Hip-height obstacles |
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Simple |
Traditional Approaches to
Legged Systems
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Statically stable |
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Tripod of support |
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Slow |
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Rough terrain |
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Dynamically stable |
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No support
requirements |
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Fast |
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Smooth terrain |
Biological Example
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Death-head cockroach Blaberus
discoidalis |
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Fast |
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Speeds of up to 10 body/s |
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Rough terrain |
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Can easily traverse fractal terrain of
obstacles 3X hip height |
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Stability |
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Static and dynamic |
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Biomimesis Options
Biological Inspiration
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Control heirarchy |
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Passive component |
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Active component |
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Is Passive Enough?
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Passive Dynamic Stabilization |
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No active stabilization |
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Geometry |
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Mechanical system properties |
Geometry
Sprawlita
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Mass - .27 kg |
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Dimensions - 16x10x9 cm |
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Leg length - 4.5 cm |
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Max. Speed - 39cm/s
2.5 body/sec |
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Hip height obstacle traversal |
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Movie
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Compliant hip |
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Alternating tripod |
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Stable running |
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Obstacle traversal |
Mechanical System
Properties
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Prototype: Empirically tuned properties |
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Design for behavior |
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“Simple” Model
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Body has 3 planar degrees of freedom |
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x, z, theta |
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mass, inertia |
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3 massless legs (per tripod) |
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rotating hip joint - damped torsional
spring |
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prismatic leg joint - damped linear
spring |
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6 parameters per leg |
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18 parameters to tune - TOO MANY! |
Simplest Locomotion Model
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Body has 2 planar degrees of freedom |
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x, z |
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mass |
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4 massless legs |
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freely rotating hip joint |
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prismatic leg joint - damped linear
spring |
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3 parameters per leg |
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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
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Discrete non-linear system |
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Fixed points |
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numerically integrate to find |
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exclude horizontal position information |
Non-linear analysis tools
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Floquet technique |
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Analyze perturbation response |
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Digital eigenvalues via linearization -
examine stability |
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Use selective perturbations to
construct M matrix |
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Non-linear analysis tools
Perturbation Response
Analysis trends
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Relationships |
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damping vs. speed and
“robustness” |
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stiffness, leg angles, leg
lengths, stride period, etc |
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Use for design |
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select mechanical properties |
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select other parameters |
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Insight into the mechanism of
locomotion |
Design Example
Locomotion Insight
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Body tends towards
equilibrium point |
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Parameters and
mechanical properties
determine how |
Summary and Conclusions
Future Work
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Extend findings and insights to more
complex models |
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Develop easily modeled 4th generation
robot |
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Utilize sensor feedback in high level
control |
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Examine other behaviors |
Thanks!
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Center for Design Research |
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Dexterous Manipulation Lab |
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Rapid Prototyping Lab |
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Mark Cutkosky |
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Jorge Cham, Jonathan Clark |