Slide 1
Slide 2
Motivation
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Hazardous tasks for humans |
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Access to areas inaccessible to wheeled
vehicles |
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Legged animals are faster and more
agile in rough terrain |
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Motivation
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Most current robots have neither
simplicity of wheels… |
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…nor versatility and speed of legged
animals |
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Motivation
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Statically-stable robots |
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Robust by maintaining at least three
legs on the ground |
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Limited speed |
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Motivation
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Dynamically-stable robots |
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Fast locomotion that is stable over
time |
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Limited robustness and versatility |
Motivation
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Robust and Dynamic |
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Robustness: Rapid convergence to
desirable behavior steady-state despite large disturbances |
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Dynamic: significant transfers of
kinetic and potential energies |
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Recent Work
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Passively-stable walking (McGeer, 1990) |
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Self-stabilizing running (Ringrose,
1997) |
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Rhex (Saranli, 2000) |
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Hypothesis
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Robust and Dynamic locomotion can be
achieved with no sensory feedback… |
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Disturbance-rejection is a property of
the mechanical system… |
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…tuned to a feedforward (open loop)
activation |
Biological Inspiration
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Up to 50 body-lengths per second |
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Traverse terrain with obstacle three
times height of center of mass |
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Prof. Robert Full, Berkeley Polypedal
Lab |
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Biological Inspiration
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When transitioning from flat to rough
terrain… |
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…impulses sent to the muscles did not
noticeably change |
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Similar activation despite large
changes in events |
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Biological Inspiration
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Implies exclusion of sensory feedback |
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No precise foot-placement or
“follow-the-leader gait” |
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But still able to traverse rough
terrain..! |
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Preflexes
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Passive properties of the mechanical
system… |
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…that stabilize and reject disturbances |
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Immediate response |
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No delays associated with
sense-compute-command loops |
Preflexes – Self-Stabilizing
Posture
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Sprawled posture |
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Individual leg function |
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Front legs decelerate, hind legs
accelerate |
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Self-correcting forces with respect to
the geometry |
Preflexes – Visco-elastic
Properties
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Exoskeleton and muscle properties |
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Compliance |
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Damping |
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Control Hierarchy
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Preflexes provide immediate
stabilization for repetitive task |
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Reflexes and neural feedback adapt to
changing conditions… |
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…through the feedforward pattern |
Modeling
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Initial attempts at characterizing stability
and performance… |
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…of a feedforward activation pattern… |
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…applied to a properly designed passive
mechanical system |
Modeling - Mode Transitions
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Locomotion is a series of transitions
between modes |
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Here, modes are determined by the
feedforward pattern… |
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…especially if we don’t account for a
flight phase |
Modeling – Linear systems
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Show that feedforward mode transitions… |
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…result in stable, converging periodic
motion |
Modeling – Non-linear 2 DOF
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Simple model |
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Opposing legs with passive properties |
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At fixed times, legs are given an
impulse extension |
Modeling – Non-linear 2 DOF
Modeling – Non-linear 2 DOF
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At beginning of mode… |
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…the mass moves… |
Modeling – Non-linear 2 DOF
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At beginning of mode… |
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…the mass moves… |
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…according to the mode’s dynamics |
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Modeling – Non-linear 2 DOF
Modeling – Non-linear 2 DOF
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At a fixed time… |
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…the system transitions to the new
mode… |
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…carrying the state conditions into the
next mode |
Modeling – Non-linear 2 DOF
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Simulations show that for a wide range
of system parameters… |
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…trajectories converge to stable
periodic motion… |
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…despite large disturbances |
Modeling – Floquet Analysis
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Behavior is confirmed by Floquet
analysis |
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Small perturbation analysis |
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Floquet multipliers indicate
attractiveness of periodic motion |
Modeling – System Behavior
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“Chasing an equilibrium” |
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Equilibrium changes at fixed times
according to activation pattern |
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System parameters influence trajectory
within mode |
Prototypes
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Built prototypes based on biological
principles described |
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No active sensing |
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Fixed cycle of tripod activation |
Slide 30
Prototype - Design
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Passive compliant hip joint in sagittal
plane |
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Piston thrusts along direction of hip |
Prototype - Fabrication
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Fabrication for robustness |
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Active components embedded inside
structure |
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Integrated soft-hard materials in
joints |
Prototype - Performance
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Dynamic running |
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Speeds of up to 3 body-lengths per
second (40 cm/sec) |
Prototype - Performance
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Obstacles of hip-height |
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Slopes of up to 18 deg. |
Prototype - Movie
Conclusions
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Findings from biomechanics suggests
that robust dynamic locomotion… |
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…can be achieved without sensory
feedback |
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Prototypes and simulations confirm
fast, stable performance |
Future Work
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Characterize role of system properties… |
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…to design for appropriate performance |
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Using higher level feedback (reflexes)
for adaptation |
Questions?
Acknowledgements
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ONR, NSF |
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Jonathan Clark, Pratik Nahata, Ed
Froehlich |
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Stanford DML and RPL |