Biomimetic Robots for Robust Operation in Unstructured Environments

M. Cutkosky and T. KennyStanford University

R. Full and H. KazerooniU.C. Berkeley

R. HoweHarvard University

R. ShadmehrJohns Hopkins University

http://cdr.stanford.edu/touch/biomimetics

Site visit -- Stanford University, Sept. 2, 1990

Main ideas:• Study insects to understand role

of passive impedance (structure and control), study humans to understand adaptation and learning(Full, Howe,Shadmehr)

• Use novel layered prototyping methods to create compliant biomimetic structures with embedded sensors and actuators (Cutkosky, Full, Kenny)

• Develop biomimetic actuation and control schemes that exploit “preflexes” and reflexes for robust locomotion and manipulation (Full, Cutkosky, Howe, Kazerooni, Shadmehr)

BioMimetic Robotics

MURIBerkeley-HarvardHopkins-Stanford

Low-LevelControl

Design & Fabrication

High-LevelControl

MURI

BiomimeticRobots

Issues in studying, designing and building biomimetic robots(and the basic outline for today’s site visit)

1. 2.

3.

Low-LevelControl

Fabrication

High-LevelControl

MURI

What passive properties are found in Nature?

What properties in mechanical design?

How should properties be varied for changing tasks, conditions ?Matching ideal impedance for unstructured dynamic tasks (Harvard)

Guiding questionsGuiding questions

Preflexes: Muscle and Exoskeleton Impedance Measurements (Berkeley Bio.)

Biological implications for RoboticsBasic Compliant Mechanisms for Locomotion (Stanford)Variable compliance joints (Harvard, Stanford)Fast runner with biomimetic trajectory (Berkeley ME)

Fabrication

MURILow-LevelControl High-Level

Control

What strategies are used in insect locomotion and what are their implications?Insect locomotion studies (Berkeley Bio)New measurement capabilities (Stanford)

What motor control adaptation strategies do people use and how can they be applied to robots?

Compliance Learning and Strategies for Unstructured Environments (Harvard & Johns Hopkins)Implications for biomimetic robots (Harvard, Stanford)

Guiding questionsGuiding questions

1 cmdt=10ms dt=30msdt=10msAre preflexes enough?

High-LevelControlMURI

Low-LevelControl

Fabrication

How do we build robust biomimetic structures and systems?Shape deposition manufacturing of integrated parts, with embedded actuators and sensors (Stanford)

How do we build-in tailored compliance and damping?

Effects of Compliance in simple running machine (Stanford, Berkeley ME)

Structures with functionally graded material properties (Stanford)

Guiding questionsGuiding questions

9:30-11:00 Low Level Biomimetic Control

• Results on measurements of muscles, exoskeleton,

compliance, damping (Full ~30)

• Implications for biomimetic robots (Bailey ~20min)

• Matching leg trajectory and scaling (Kazerooni ~15)

• Matching impedance to dynamic task (Matsuoka ~15)

Low-LevelControl

Fabrication

High-LevelControl

MURI

What passive properties are found in Nature?

What properties in mechanical design?

How should properties be varied for changing tasks, conditions ?Matching ideal impedance for unstructured dynamic tasks (Harvard)

Preflexes: Muscle and Exoskeleton Impedance Measurements (Berkeley Bio.)

Biological implications for RoboticsBasic Compliant Mechanisms for Locomotion (Stanford)Variable compliance joints (Harvard, Stanford)Fast runner with biomimetic trajectory (Berkeley ME)

MURI Year One Meeting 1999

University of California at BerkeleyDepartment of Integrative Biology

rjfull@socrates.berkeley.eduhttp://polypedal.berkeley.edu

University of California at BerkeleyDepartment of Integrative Biology

rjfull@socrates.berkeley.eduhttp://polypedal.berkeley.edu

Lower Level ControlProfessor Robert J. FullDaniel DudekDr. Kenneth Meijer

Lower Level Control

Mechanical

HigherCenters Environment

aero- , hydro, terra-dynamic

FeedforwardController

(CPG)

AdaptiveController Sensors

Closed-loop

Open-loop

System(Actuators, limbs)

FeedbackController

Sensors

Behavior

Chain of Reflexes

Cruse Controller

Inspired by

Stick Insects

Rough Terrain

Fractal Surface

Variation -3 times the height of the center of mass

Control Challenge

NeuralNeural

MechanicalMechanical

PreciseNovelSlow

Static

Feedforward

ContinuousFeedback(Reflexes)

ControlControl

Dynamic

Feedforward

GrossRepetitiveRapid

ContinuousFeedback(Preflexes)

PolyPEDAL Control

Musculoskeletal units, leg segments and legs do computations on their own.

Control results from propertiesof parts and their morphology.

Control algorithms embeddedin the form of animal itself.

Lower Level Control

Mechanical

HigherCenters Environment

aero- , hydro, terra-dynamic

FeedforwardController

(CPG)

AdaptiveController Sensors

Closed-loop

Open-loop

System(Actuators, limbs)

FeedbackController

Sensors

Behavior

Contribution to Control

FeedforwardIntrinsic musculo-skeletal properties

PreflexMotor program acting through moment arms

Passive DynamicSelf-stabilization

Mechanical System

Predictive Rapid acting

Neural SystemReflex

ActiveStabilization

Neuralfeedbackloops

Slow acting

MURI Interactions

Muscles and

Rapid PrototypingStanfordMotor Control

& LearningJohns Hopkins

Sensors / MEMSStanford

ManipulationHarvard

MURI

LocomotionUC Berkeley

Robot & Leg MechanismsUC Berkeley

Manufactured Legs

What properties should legs possess? Why?

Act as springs to store and return energy? How?

Act to reject disturbances?

What properties should legs possess? Why?

Act as springs to store and return energy? How?

Act to reject disturbances?

Road Map

1. System Impedance

2. Leg Impedance

3. Muscle Impedance

Spring-Mass SystemsLeggedSIX-

Human

TWO-Legged

Cockroach Crab

LeggedEIGHT-

Dog

LeggedFOUR-Vertical

ForceBody

Weight

ForceTime

Fore-aft

Blickhan 1989

Virtual Leg Stiffness

10

100

0.010.001 0.1 1 10 100Mass (kg)

1

Cockroach

Crab

Quail

Hare

Human

Kangaroo

Dog

rel,legk

HOPPERS

TROTTERSRUNNERSkrel =

F

mg

xx

Blickhan and Full, 1993

Sagittal Plane Model

ORGANISM

Multi-Leg

Spring Loaded Inverted

Pendulum k

m

Leg Springs ?

Road Map

1. System Impedance

2. Leg Impedance

3. Muscle Impedance

Leg as Spring & Damper

∆x

Force

Stiffness, kDamping coefficient, c

Restorative Forcesand Perturbation Damping

. ..

For an Oscillating System:Force = force due to + force due to + force due to mass stiffness damping

Force = kx + cx + mx

Experimental Setup

Oscillate Leg

At Multiple

Frequencies

To Determine

k and c

Oscillate Leg

At Multiple

Frequencies

To Determine

k and c

Servo Motor

Roach leg

Length and Force recording

Leg Oscillation Experiments

Time (s)

Dis

plac

emen

t (m

m)

For

ce (

N)

Small Deflection at 12 Hz

-0.3

0

0.3

0 0.05 0.1 0.15 0.2

-0.03

0

0.03

Displacement Force

Leg Is Spring and Damper

Displacement (mm)

For

ce (

N)

Small Deflection at 12 Hz

-0.03

0.03

-0.3 0.3

Slope ≈ Impedance

Effect of Frequency

Displacement (mm)

For

ce (

N)

k25 Hz > k0.08 Hz

Impedance Increases with Frequency

-0.035

0.035

-0.3 0.3

Force @0.08 Hz Force @25 Hz

45

50

55

60

65

70

75

0.01 0.1 1 10 100

Impedance

Preferred Stride Frequency12 Hz

Impedance of Metathoracic Limb of Cockroach

Impe

danc

e (N

/m)

Frequency (Hz)

Leg Model

• At high frequencies:Force (k1+k2)*(displacement)

• At low frequencies:Force k2*(displacement)

Standard Linear Solid

c k1

k2

Frequency vs Speed

Speed (m/sec)

0

5

10

15

20

0 0.2 0.4 0.6

Cockroach

Str

ide

freq

uen

cy (

Hz)

ImpedanceIncreases

ImpedanceConstant

Alter Leg Spring AngleTake Longer Strides

*

NaturalFrequency?

Impedance

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

-1.25 -0.75 -0.25 0.25 0.75 1.25

Displacement (mm)

Forc

e (

N)

0.25 Hz24 Hz

k24 Hz > k0.25 HzLarge Deflection Non-linear

Perturbation Rejection

RestorativeForce

4x Body Mass

Perturbation

Discoveries

1. Insect leg behaves like a spring and damper system.

2. Strain energy is stored in the leg and returned.

3. Force – displacement relationship shows hysteresis with significant energy dissipation (50% or more).

Discoveries

4. Leg impedance increases with frequency up to 12 Hz, the preferred speed of the animal.

5. Leg impedance remains constant at frequencies above 12 Hz.

6. The leg’s natural frequency is near the frequency used by the animal at its preferred speed.

Discoveries

7. Insect leg could simplify control by rejecting perturbations.

For a deflection of only one mm, the leg produces a force of 0.75-4x body mass.

Road Map

1. System Impedance

2. Leg Impedance

3. Muscle Impedance

MURI Interactions

Muscles and

Rapid PrototypingStanfordMotor Control

& LearningJohns Hopkins

Sensors / MEMSStanford

ManipulationHarvard

MURI

LocomotionUC Berkeley

Robot & Leg MechanismsUC Berkeley

Manufactured LegsWhat properties

should actuators possess? Why?

Act as springs to store and return energy? How?

Act to reject disturbances?

Power generation?

What properties should actuators possess? Why?

Act as springs to store and return energy? How?

Act to reject disturbances?

Power generation?

Horizontal Plane Model

ORGANISM

Multi-Leg

Lateral Leg Spring

Muscle-Apodeme Damped Springs ?

k

m

Muscle Lever

Servo andForce

Transducer

Stimulation Stimulation

Strain

Frequency

- pattern- magnitude- phase

- pattern- magnitude

ControlControl

Workloop Technique

Muscle Capacity

4 6 8 10 12 14

++in vivoin vivo conditions conditions

2 Muscle Action Potentials

in vivoin vivoconditionsconditions**

205 10 15

3 Muscle Action Potentials

Muscle Strain %

179 Powerspace

100

80

60

40

20

0

-200.0

-100.0

0.0

Power(W/kg)

177c Powerspace

Sti

mu

lati

on p

has

e (%

)

Spring

Spring

Damper

Damper

Motor

Musculo-skeletal Model

Force

VelocityInsect Leg

Intrinsic musculo-skeletal properties

Preflexes

Brown and Loeb, 1999

Active+Passive Force

Passive Force

Length Increase

Perturbation Experiments

Servo and ForceTransducer

Stimulation

Passive Muscle Stiffness Significant

Effect of Step Length Increase

Stimulated (Twitch)

Relaxed

Passive resistance

is significant in muscle

177c

Passive resistance

is significant in muscle

177c

(n = 4)

0 1 2 30

20

40

60

Step size (%)

For

ce in

crea

se (

mN

)

Oscillatory Perturbations

0 200-5

0

5

0.5 %

Muscle strain (%)

Force (mN)

Time (ms)

-0.25 0 0.25

-5

5

Muscle strain (%)

Force (mN)

Phase angle

Ecomplex =(Force/Area)/strain

Eviscous/Eelastic=tan(phase angle)

Visco-elastic PropertiesPassive Muscle

Impedance increases with frequency in muscle 179 Impedance independent of frequency in muscle 177cSignificant viscous damping in both muscles.

Passive MuscleImpedance increases with frequency in muscle 179 Impedance independent of frequency in muscle 177cSignificant viscous damping in both muscles.

Frequency (Hz)

tan(phase angle)Ecomplex (N/m2)

Frequency (Hz)0 50 100 150

0

1

2

3

4

5 x 105

0 50 100 1500

0.2

0.4

0.6

0.8

1

M177c (n=3)M179 (n=2)

L=1.075

Effect of Length

0.9 1 1.1 1.2 1.3 1.40

2

4

6

8

10x 10

5

0.9 1 1.1 1.2 1.3 1.40

0.2

0.4

0.6

0.8

1

Length

tan(phase angle)Ecomplex (N/m2)

Length

M177c (n=3)M179 (n=2)

f= 50 Hz

Passive MuscleImpedance increases with lengthContribution viscous damping decreases with length

Passive MuscleImpedance increases with lengthContribution viscous damping decreases with length

Perturbation experiments

00

300

100

Locomotion cycle (%)

Force (mN)

0 100

+

Locomotion cycle (%)

Strain

Locomotor pattern

Sinusoid (A=0.5%,f=200 Hz)

7%

Impedance during workloop.

Multiple Muscle System

Anatomically similar muscles provide

impedance during

different phases of the locomotion

cycle!

Anatomically similar muscles provide

impedance during

different phases of the locomotion

cycle!

Muscle strain (%)

0 100

Impedance (mN)

Locomotion cycle (%)

m177c

m179

Stimulation Phase {

Discoveries1. Passive muscle can reject perturbations.

2. Preflexes comprise passive (fixed) and active

components (adjustable).

3. Passive muscle acts like a visco-elastic

actuator.(Viscous damping is responsible for a significant part of total

force response to perturbation.)

4. Impedance of anatomically similar muscles

is distributed over the locomotion cycle.

Impact on Deliverables

1. Energy storage

2. Reject perturbations

3. Simplify control

4. Penetrate new environments

5. Increase robustness

1. Energy storage

2. Reject perturbations

3. Simplify control

4. Penetrate new environments

5. Increase robustness

Low-LevelControl

Fabrication

High-LevelControl

MURI

What passive properties are found in Nature?

What properties in mechanical design?

How should properties be varied for changing tasks, conditions ?Matching ideal impedance for unstructured dynamic tasks (Harvard)

Guiding questionsGuiding questions

Preflexes: Muscle and Exoskeleton Impedance Measurements (Berkeley Bio.)

Basic Compliant Mechanisms for LocomotionBiological implications for Robotics (Stanford)Variable compliance joints (Harvard, Stanford)Fast runner with biomimetic trajectory (Berkeley ME)

Low-LevelControl

MURILocomotion:

Biomimetic Ideology

• Goal:– Navigate rough terrain with simple, robust, compliant robots

• Mindset shaped by Biology – Tunable, passive mechanical properties– Purpose-specific geometry – Simple control scheme – Robust components

Low-LevelControl

MURI Variable Compliance?: Interpreting Biological Findings

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

-1.25 -0.75 -0.25 0.25 0.75 1.25

Displacement (mm)

Forc

e (

N)

0.25 Hz24 Hz

Force

Displacement

Load

Unload

k24 Hz > k0.25 Hz

• Idea– Desired reaction forces depend on the environment and locomotion speed

• How do we represent these findings?– Not traditional spring or damper elements– Energy spent per cycle independent of frequency (area enclosed by curve is the energy spent)

• Results suggest hysteretic damping

Low-LevelControl

MURIVariable Impedance:

New Design Direction• What’s the difference between compliance and impedance?

– Impedance refers to the relationship: dF/dx– Stiffness refers to particular impedance relationship, namely: dF/dx = k

• Hysteretic Damping– Characteristic of some heterogeneous materials– Loading and unloading create different stress-strain paths– Stress-strain curve is independent of frequency

• Design Implications– Compliance is mainly a function of displacement– Damping has a significant frequency dependant term

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

-1.25 -0.75 -0.25 0.25 0.75 1.25

Displacement (mm)

Forc

e (N

)

0.25 Hz

24 Hz

Force

Displacement

Load

Unload

k24 Hz > k0.25 Hz

Low-LevelControl

MURIVariable Impedance: Design Approach

• Traditional Robotic Compliance– Actuator powered– Proportional feedback control - variable compliance– Complex

• multiple control laws with different objectives must work together

• Low bandwidth - controller delays

k-

+SetPoint

PlantActuatorPosition

Low-LevelControl

MURIVariable Impedance: Design Approach

• Different Approach– Compliant member powered– Adjustable geometry - variable impedance– Simple

• mechanical properties are more predictable

• separate from control law

• intrinsic low level stability

• Biology is telling us what mechanical properties we really need

SDM robot limb withcompliance and damping

Stiffness

Variable Stiffness Joint Concept

Low-LevelControl

MURISprawl 1.0:

Legged Testbed

• Capture the essential locomoting elements in a low DOF robot

• Explore the roles of compliance and damping in locomotion

• Identify areas which can be improved by SDM

Low-LevelControl

MURISprawl 1.0: Biomimetic, not just a copy

• Full’s research highlights certain important locomoting components– Power-producing thrust muscles– Supporting/repositioning hip joints

Low-LevelControl

MURISprawl 1.0:

Thrusting

• Full’s research on power-producing muscles 177a,c,d,e (Ahn, Meijer)

• Thrust production - Decoupled, compliant system

Cockroach Geometry

Force andWorkspace

Femur

Tibia

12

Force andWorkspace

F1 r1 0 1

=F2 0 r2 2

Robotics Analysis

Force andWorkspace

Sprawl 1.0 Geometry

Very LowFrictionPneumaticPiston

Sprawl 1.0 Geometry

Damped, CompliantRC Servo Actuator

Low-LevelControl

MURISprawl 1.0:

Repositioning/Supporting

• Full’s research on Trochanter-Femur joint (Dudek)

• Repositioning/Supporting - Decoupled, compliant system

Cockroach Geometry

g

Actuated Body-Coxa joint

Compliant Trochanter-Femur joint

Low-LevelControl

MURI Sprawl 1.0: Findings

• Good design and passive mechanical properties take burden off control– Compliance and damping– Simple alternating tripod locomotion scheme– Built-in posture control

• Low bandwidth geometry changes– Walking, stopping, turning, and running

• Need for robust components– Traditional components are not robust - poster child for SDM

Low-LevelControl

MURI Sprawl 1.0: Future Work

• Suggestions from Full– Change location of center of mass– Increase gait frequency– Dynamically control middle leg set points– Weaken front leg force

• Work in Progress– Add compliant springs in parallel with constant force pistons– Replace RC servo hip actuators with more biomimetic components