Robust Dynamic Locomotion Through

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Robust Dynamic Locomotion Through
Feedforward-Preflex Interaction
Jorge G. Cham, Sean A. Bailey, Mark R. Cutkosky
Center for Design Research Stanford University
2000 ASME International Mechanical Engineering
Congress and Expo November 9, 2000
This work is supported by ONR and NSF
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Robust Dynamic Locomotion
Background and Motivation
Biological Inspiration
Modeling Approach
Hexapedal Prototypes
Conclusions And Future Work
Biology
Prototypes
Modeling
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Motivation

• Hazardous tasks for humans
• Access to areas inaccessible to wheeled vehicles
• Legged animals are faster and more agile in rough
  terrain

Intro
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Motivation

• Most current robots have neither simplicity of
  wheels
• nor versatility and speed of legged animals

Dante Robot
Raibert Monopod
Intro
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Motivation

• Statically-stable robots
• Robust by maintaining at least three legs on the
  ground
• Limited speed

Dante Robot
Raibert Monopod
Intro
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Motivation

• Dynamically-stable robots
• Fast locomotion that is stable over time
• Limited robustness and versatility

Dante Robot
Raibert Monopod
Intro
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Motivation

• Robust and Dynamic
• Robustness Rapid convergence to desirable
  behavior steady-state despite large disturbances
• Dynamic significant transfers of kinetic and
  potential energies

Deathhead Cockroach
Intro
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Recent Work

• Passively-stable walking (McGeer, 1990)
• Self-stabilizing running (Ringrose, 1997)
• Rhex (Saranli, 2000)

Intro
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Hypothesis

• Robust and Dynamic locomotion can be achieved
  with no sensory feedback
• Disturbance-rejection is a property of the
  mechanical system
• tuned to a feedforward (open loop) activation

Intro
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Biological Inspiration

• Up to 50 body-lengths per second
• Traverse terrain with obstacle three times height
  of center of mass
• Prof. Robert Full, Berkeley Polypedal Lab

Biology
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Biological Inspiration

• When transitioning from flat to rough terrain
• impulses sent to the muscles did not noticeably
  change
• Similar activation despite large changes in
  events

Flat terrain
Rough terrain
Biology
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Biological Inspiration

• Implies exclusion of sensory feedback
• No precise foot-placement or follow-the-leader
  gait
• But still able to traverse rough terrain..!

Biology
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Preflexes

• Passive properties of the mechanical system
• that stabilize and reject disturbances
• Immediate response
• No delays associated with sense-compute-command
  loops

Biology
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Preflexes Self-Stabilizing Posture

• Sprawled posture
• Individual leg function
• Front legs decelerate, hind legs accelerate
• Self-correcting forces with respect to the
  geometry

Biology
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Preflexes Visco-elastic Properties

• Exoskeleton and muscle properties
• Compliance
• Damping

Biology
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Control Hierarchy
Neural System (CPG)

• Preflexes provide immediate stabilization for
  repetitive task
• Reflexes and neural feedback adapt to changing
  conditions
• through the feedforward pattern

Feedforward Motor Pattern
Sensory Feedback (Reflexes)
Mechanical System (muscles, limbs)
Mechanical Feedback (Preflexes)
Environment
Passive Dynamic Self-Stabilization
Locomotion
Biology
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Modeling

• Initial attempts at characterizing stability and
  performance
• of a feedforward activation pattern
• applied to a properly designed passive
  mechanical system

Modeling
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Modeling - Mode Transitions

• Locomotion is a series of transitions between
  modes
• Here, modes are determined by the feedforward
  pattern
• especially if we dont account for a flight phase

Modeling
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Modeling Linear systems

• Show that feedforward mode transitions
• result in stable, converging periodic motion

Modeling
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Modeling Non-linear 2 DOF
Servo

• Simple model
• Opposing legs with passive properties
• At fixed times, legs are given an impulse
  extension

Sagittal plane
k, b, ?nom
Planar Quadruped simplified model
Modeling
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Modeling Non-linear 2 DOF

• At beginning of mode

Modeling
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Modeling Non-linear 2 DOF

• At beginning of mode
• the mass moves

Modeling
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Modeling Non-linear 2 DOF

• At beginning of mode
• the mass moves
• according to the modes dynamics

Modeling
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Modeling Non-linear 2 DOF

• At a fixed time

Modeling
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Modeling Non-linear 2 DOF

• At a fixed time
• the system transitions to the new mode
• carrying the state conditions into the next mode

Modeling
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Modeling Non-linear 2 DOF

• Simulations show that for a wide range of system
  parameters
• trajectories converge to stable periodic motion
• despite large disturbances

Modeling
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Modeling Floquet Analysis

• Behavior is confirmed by Floquet analysis
• Small perturbation analysis
• Floquet multipliers indicate attractiveness of
  periodic motion

Modeling
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Modeling System Behavior

• Chasing an equilibrium
• Equilibrium changes at fixed times according to
  activation pattern
• System parameters influence trajectory within mode

Modeling
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Prototypes

• Built prototypes based on biological principles
  described
• No active sensing
• Fixed cycle of tripod activation

time
Feedforward Activation Pattern
Prototypes
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Prototype - Design

• Sprawled Posture
• Leg function
• Compliant joints

Prototypes
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Prototype - Design

• Passive compliant hip joint in sagittal plane
• Piston thrusts along direction of hip

Prototypes
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Prototype - Fabrication

• Fabrication for robustness
• Active components embedded inside structure
• Integrated soft-hard materials in joints

Cycle of Integrated Fabrication of Robot
Prototypes
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Prototype - Performance

• Dynamic running
• Speeds of up to 3 body-lengths per second (40
  cm/sec)

Prototypes
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Prototype - Performance

• Obstacles of hip-height
• Slopes of up to 18 deg.

Prototypes
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Prototype - Movie
gtOgt
Prototypes
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Conclusions

• Findings from biomechanics suggests that robust
  dynamic locomotion
• can be achieved without sensory feedback
• Prototypes and simulations confirm fast, stable
  performance

Future
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Future Work

• Characterize role of system properties
• to design for appropriate performance
• Using higher level feedback (reflexes) for
  adaptation

Future
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Questions?Acknowledgements

• ONR, NSF
• Jonathan Clark, Pratik Nahata, Ed Froehlich
• Stanford DML and RPL

Intro
Biology
Prototypes
Modeling
Future