September 23, 2015 @WeB02.4, 15:20 to 15:40 pm, Regular CCA Session, Modeling, Room Cutler

Hybrid Nonlinear Model of McKibben Pneumatic Artificial Muscle Systems Incorporating a Pressure-Dependent Coulomb Friction Coefficient

Kentaro Urabe Nara Institute of Science and Technology, Japan Kiminao Kogiso University of Electro-Communications, Japan

2015 IEEE Multi-Conference on Systems and Control 21-23 September 2015, Novotel Sydney Manly Pacific, Sidney, Australia

Supported by JSPS Grant-in-Aid for Young Scientists (A)

Outline

2

Introduction

Model of PAM System

Analysis

Validations

Conclusion

PAMs (ActiveLink, Co.)

Introduction

3

McKibben Pneumatic Artificial Musclehigh power/weight ratio, flexibility

appropriate use for power assist and rehabilitation system, as a soft actuator.

nonlinearities such as hysteresis, hydrodynamics, friction,…

Modeling and control of the PAM are known to be challenging issues. [Tondu, CSM 00]

solenoid

air

L

M

M

L l0

compressure

valve

100 200 300 400 500 600 700

0

0.1

0.2

0.3

pressure [kPa]

ε

M [kg]= 3M [kg]= 6M [kg]= 9

rubber tube� mesh�

hysteresis

expansion

contraction

Nonlinear model under inner pressure range of 0.2 to 0.7 [kPa] (flexible & stiff)

Hybrid modeling with a proportional directional control valve

Heuristic parameter estimation based on model analysis

Gray-box modeling with consideration of load-dependent parameters

Gray-box modeling in game-theoretic learning

Numerical consideration of PID vs MPC using our model

Our interests: We can get the model more precise? Our proposed model is general?

Basically, linear model under inner pressure range of 0.5 to 0.7 [kPa] (stiff)

Tracking control using inverse model and state feedback

Positioning control for polynomial model using PI-type hysteresis compensator

Maxwell-slip model to capture the force/length hysteresis

Piecewise-affine modeling and constrained control

Introduction

4

Existing works

Our previous works

[T.V. Minh et al., 10]

[L. Udawatta et al., 07]

[T. Itto, et al., ICIT11]

[Kogiso, et al., IROS12]

[Kogiso, et al., IROS13]

[Kogiso, et al., AIM13]

[T.V. Minh et al., 11]

[Urabe, et al., ISIC15]

[G. Andrikopoulos et al., 13]

Introduction

5

Objective of this studyTo obtain a precise model of the PAM system,

propose to replace a Coulomb coefficient with a pressure-dependent one,

check if the proposed model enables to have behaviors of different commercial PAMs.

100 200 300 400 500 600 700

0

0.05

0.10

0.15

0.20

0.25

pressure [KPa]

contr

action

rat

io

Satisfy the previous result?

ActiveLink TAA10（Φ10 0.25 m）

What if the PAM was discontinued?

Simulation

Experiment&

Analysis

6

Dominant parameters

x(t) = f�(x(t), u(t))

y(t) = h(x(t))

x(t) 2 S�

x := [✏ ✏ P ]T y := [✏ F ]T

Switched system with 12 subsystems

if L0

D0

D1 D2 D3

M

K

RT

✓

ccA0

Cq1

Cq2

k1 k2cv

Ptank

Pout

k

: natural diameter of PAM [m]: natural length of PAM [m]

: source absolute pressure [Pa]

: coefficients for PAM volume [m^3]

: atmospheric pressure [Pa]

: specific heat ratio for air [-]: ideal gas constant [J/kg K]: absolute temperature [K]: coefficient of elasticity [N/m^3]: initial angle btw braided thread & cylinder long axis [deg] : correction coefficient [-]: correction coefficient [1/Pa]: Coulomb friction [N]

: viscous friction coefficient [Ns/m]

: orifice area of PDC valve [m^2]

: polytropic indexes [-]

: mass of weight [kg]

Analysis result: For the PAM system model,its steady-state behavior is characterized by

and its transient behavior is characterized by

A0 k1 k2 cv

load-dependent parameters:

parameters:

K(M) �(M) Cq1(M) Cq2(M) cc(M)

h ccP (t)h

updated!

[Kogiso, et al., IROS12]

Validation

7

Equipment

proportional directional

control valve

Validation: Model Precision

8

0.18

0.20

0.22

0.24

0.26

0.28

0 5 10 15 20 25 30 35 40

0 5 10 15 20 25 30 35 40time [s]

300350400450500550600650700

contr

acti

on r

atio

pre

ssure

[kP

a]

experimental resultsimulation result

Comparison

transient responsesteady-state response

proposed

previous

c0c = hcc

P (t)

100 200 300 400 500 600 700

0

0.05

0.10

0.15

0.20

0.25

pressure [KPa]

contr

action

rat

io

100 200 300 400 500 600 700

0

0.05

0.10

0.15

0.20

0.25

pressure [KPa]

contr

action

rat

io

ActiveLink TAA10（Φ10 0.25 m）

c0c = cc

Validation: Model Precision

9

2

4

6

8

10

1 2 3 4 5 6 7 8 9M [Kg]

cc (pressure-dependent)

cc (consntant)

x 103

erro

r bet

wee

n r

espon

ses

0.5

1.0

1.5

2.0

2.5

3.0

3.5x 105

1 2 3 4 5 6 7 8 9M [Kg]

cc (pressure-dependent)

cc (consntant)

erro

r bet

wee

n r

espon

ses

Errors over up to 9 kg weights

steady-state response transient response

proposed

previous

previous

proposed

ActiveLink TAA10（Φ10 0.25 m）

Model Validation

10

ActiveLink TAA10（Φ10 0.25 m） FESTO DMSP-10-250N（Φ10 0.25 m）

FESTO DMSP-20-200N（Φ20 0.20 m） Kanda AirMuscle（Φ1.25 in 0.20 m）

Four types of commercial PAMs

(discontinued)

Model Validation: Parameters

11

ActiveLink TAA10 DMSP-10-250N DMSP-20-200N Kanda AirMuscle

[Kogiso, et al., IROS13]

cc

Model Validation

12

DMSP-10-250NActiveLink TAA10

0

0.05

0.10

0.15

0.20

0.25

contr

acti

on r

atio

100 200 300 400 500 600 700pressure [kPa]

0

0.05

0.10

0.15

0.20

0.25

contr

acti

on r

atio

100 200 300 400 500 600 700pressure [kPa]

100 200 300 400 500 600 700pressure [kPa]

0

0.05

0.10

0.15

0.20

0.25

contr

acti

on r

atio

100 200 300 400 500 600 700pressure [kPa]

0

0.05

0.10

0.15

0.20

0.25

contr

acti

on r

atio

Kanda AirMuscleDMSP-20-200N

Steady-state response

Model Validation

13

DMSP-10-250NActiveLink TAA10

Kanda AirMuscleDMSP-20-200N

0

0.05

0.10

0.15

0.20

0.25

contr

acti

on r

atio

100 200 300 400 500 600 700pressure [kPa]

0

0.05

0.10

0.15

0.20

0.25

contr

acti

on r

atio

100 200 300 400 500 600 700pressure [kPa]

100 200 300 400 500 600 700pressure [kPa]

0

0.05

0.10

0.15

0.20

0.25

contr

acti

on r

atio

100 200 300 400 500 600 700pressure [kPa]

0

0.05

0.10

0.15

0.20

0.25

contr

acti

on r

atio

Steady-state response

Model Validation

14Kanda AirMuscleDMSP-20-200N

250300350400450500

0.180.20

0.220.240.26

5 10 15 20 25 30 35 400time [s]

5 10 15 20 25 30 35 400

pre

ssure

[kP

a]co

ntr

acti

on r

atio

0.040.060.080.100.120.14

5 10 15 20 25 30 35 400time [s]

5 10 15 20 25 30 35 400250300350400450500

pre

ssure

[kP

a]co

ntr

acti

on r

atio

5 10 15 20 25 30 35 400time [s]

5 10 15 20 25 30 35 400250300350400450500

pre

ssure

[kP

a]

0.080.10

0.120.140.16

contr

acti

on r

atio

5 10 15 20 25 30 35 400time [s]

5 10 15 20 25 30 35 400250300350400450500

pre

ssure

[kP

a]

0.120.14

0.160.180.20

contr

acti

on r

atio

DMSP-10-250NActiveLink TAA10

Transient response

Model Validation

15Kanda AirMuscleDMSP-20-200N

DMSP-10-250NActiveLink TAA10

250300350400450500

0.180.20

0.220.240.26

5 10 15 20 25 30 35 400time [s]

5 10 15 20 25 30 35 400

pre

ssure

[kP

a]co

ntr

acti

on r

atio

0.040.060.080.100.120.14

5 10 15 20 25 30 35 400time [s]

5 10 15 20 25 30 35 400250300350400450500

pre

ssure

[kP

a]co

ntr

acti

on r

atio

5 10 15 20 25 30 35 400time [s]

5 10 15 20 25 30 35 400250300350400450500

pre

ssure

[kP

a]

0.080.10

0.120.140.16

contr

acti

on r

atio

5 10 15 20 25 30 35 400time [s]

5 10 15 20 25 30 35 400250300350400450500

pre

ssure

[kP

a]

0.120.14

0.160.180.20

contr

acti

on r

atio

Transient response

Conclusion

16

SummaryIntroduction Model of PAM System replaced Coulomb coefficient w/ the pressure-dependent one.

Analysis introduced dominant parameters of the proposed model.

Validation enable to get model’s precision better. enable to catch behaviors of commercial McKibben PAMs.

Future works to consider an effective model reduction, in order to obtain an appropriate model for controller design. to develop a flexible actuator of antagonistic pairs of PMAs, in order to realize a position/force control system.

17

Thank you for your attention.