Unit 12 You ’ re supposed to shake hands. Section B Period 2 (3a — 4)
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Transcript of Department of Applied Mechanics – Budapest University of Technology and Economics Dynamics of...
Department of Applied Mechanics – Budapest University of Technology and Economics
Dynamics of Dynamics of rehabilitation robots –rehabilitation robots – shake hands or hold shake hands or hold
hands?hands?G. Stépán, L. Kovács
Department of Applied MechanicsBudapest University of Technology and Economics
Department of Applied Mechanics – Budapest University of Technology and Economics
Contents- Introduction: force control
- Motivation
- Turbine blade polishing
- Human force control
- Rehabilitation robotics
- 1 DoF model of force control
- Digital effect: sampling
- Theoretical and experimental stability charts
- Conclusion: bifurcations
Department of Applied Mechanics – Budapest University of Technology and Economics
Position control
1 DoF models x
Blue trajectories:Q = 0
Pink trajectories: Q = – Px – Dx
.
Department of Applied Mechanics – Budapest University of Technology and Economics
Force control
Desired contact force:Fd = kyd ;
Sensed force: Fs = ky
Control force: Q = – P(Fd – Fs) – DFs + Fs or d
.
Department of Applied Mechanics – Budapest University of Technology and Economics
Stabilization (balancing)
Control force:Q = – Px – Dx
Special case of force control: with k < 0
.
Department of Applied Mechanics – Budapest University of Technology and Economics
Modelling digital control
Special cases of force control:- position control with zero stiffness (k = 0)- stabilization with negative stiffness (k < 0)
Digital effects:- quantization in time: sampling – linear - quantization in space: round-off errors at ADA converters – non-linear
Department of Applied Mechanics – Budapest University of Technology and Economics
Alice’s Adventures in Wonderland
Lewis Carroll (1899)
Department of Applied Mechanics – Budapest University of Technology and Economics
Contents- Introduction: force control
- Motivation
- Turbine blade polishing
- Human force control
- Rehabilitation robotics
- 1 DoF model of force control
- Digital effect: sampling
- Theoretical and experimental stability charts
- Conclusion: bifurcations
Department of Applied Mechanics – Budapest University of Technology and Economics
Motivation
- Polishing turbine blade(Newcastle/Parsons robot)
- Rehabilitation robotics(human/machine contact)
- Coupling force control (CFC)(between truck and trailer)*
- Electronic brake force control(added to ABS systems)** Knorr-Bremse
Department of Applied Mechanics – Budapest University of Technology and Economics
Motivation
- Polishing turbine blade(Newcastle/Parsons robot)
- Rehabilitation robotics(human/machine contact)
- Coupling force control (CFC)(between truck and trailer)*
- Electronic brake force control(added to ABS systems)** Knorr-Bremse
Department of Applied Mechanics – Budapest University of Technology and Economics
Motivation
- Polishing turbine blade(Newcastle/Parsons robot)
- Rehabilitation robotics(human/machine contact)
- Coupling force control (CFC)(between truck and trailer)*
- Electronic brake force control(added to ABS systems)** Knorr-Bremse
Department of Applied Mechanics – Budapest University of Technology and Economics
Motivation
- Polishing turbine blade(Newcastle/Parsons robot)
- Rehabilitation robotics(human/machine contact)
- Coupling force control (CFC)(between truck and trailer)*
- Electronic brake force control(added to ABS systems)** Knorr-Bremse
Department of Applied Mechanics – Budapest University of Technology and Economics
Contents- Introduction: force control
- Motivation
- Turbine blade polishing
- Human force control
- Rehabilitation robotics
- 1 DoF model of force control
- Digital effect: sampling
- Theoretical and experimental stability charts
- Conclusion: bifurcations
Department of Applied Mechanics – Budapest University of Technology and Economics
Turbine blade polishing
Department of Applied Mechanics – Budapest University of Technology and Economics
Mechanical model of polishing
mr = 2500 [kg] br = 32 [Ns/mm] C = 150 [N]
ms = 0.95 [kg] bs = 2 [Ns/m(!)] ks = 45 [Ns/mm]
me = 4.43 [kg] be = 3 [Ns/m(!)] ks = 13 [Ns/mm]
Fd = 50 [N]
Department of Applied Mechanics – Budapest University of Technology and Economics
Experimental stability chart
Department of Applied Mechanics – Budapest University of Technology and Economics
Self-excited oscillation – Hopf bifurcation
Department of Applied Mechanics – Budapest University of Technology and Economics
Time-history and spectrum
Department of Applied Mechanics – Budapest University of Technology and Economics
Contents- Introduction: force control- Motivation- Turbine blade polishing- Human force control- Rehabilitation robotics- 1 DoF model of force control- Digital effect: sampling- Theoretical and experimental stability charts- Conclusion: bifurcations
Department of Applied Mechanics – Budapest University of Technology and Economics
Human force control
“Good memory causes trouble”
Meeting others on narrow corridors oscillations
caused by the delay of our reflexes
Why do we “shake” hands?
Department of Applied Mechanics – Budapest University of Technology and Economics
Hemingway, E., The Old Man and the Sea (1952)
Santiago plays arm-wrestling in a pub of Casablanca
Department of Applied Mechanics – Budapest University of Technology and Economics
Human-robotic force control
Dextercartoon
Department of Applied Mechanics – Budapest University of Technology and Economics
Contents- Introduction: force control
- Motivation
- Turbine blade polishing
- Human force control
- Rehabilitation robotics
- 1 DoF model of force control
- Digital effect: sampling
- Theoretical and experimental stability charts
- Conclusion: bifurcations
Department of Applied Mechanics – Budapest University of Technology and Economics
Rehabilitation roboticsIRB 1400 H
IRB 140
Couch
Touch screen
Control panelOperationmode selector
Safety switch
Etc.
Instrumented orthosis
Frame
Stack lights
Start pedal
Department of Applied Mechanics – Budapest University of Technology and Economics
The safety relaxer
Department of Applied Mechanics – Budapest University of Technology and Economics
The instrumented orthosis
Robot
Safety relaxer mechanism (SRM)
6 DOF force/torque transducer #1Quick changer #1
6 DOF force/torque transducer #2
Quick changer #2
Orthosis shell
Handle (the so-called safeball)
Teaching-in device
Department of Applied Mechanics – Budapest University of Technology and Economics
Mechanical model of relaxer
Department of Applied Mechanics – Budapest University of Technology and Economics
Force control during teaching-in
Sampling time at outer loop with 60 [ms]
Sampling time at force sensor with t 4 [ms]
Fd
0Fe,n xd,n
xn-1
xd,n
DSP (or PC)
xn-L Fm,n
force controlrobot -
controllerrobot arm +
teaching-in device
force / torqueacquisition
deadtime 400ms !
Department of Applied Mechanics – Budapest University of Technology and Economics
Delay and vibrations
Department of Applied Mechanics – Budapest University of Technology and Economics
Delay and vibrations
Department of Applied Mechanics – Budapest University of Technology and Economics
Delay and vibrations
Department of Applied Mechanics – Budapest University of Technology and Economics
Contents- Introduction: force control
- Motivation
- Turbine blade polishing
- Human force control
- Rehabilitation robotics
- 1 DoF model of force control
- Digital effect: sampling
- Theoretical and experimental stability charts
- Conclusion: bifurcations
Department of Applied Mechanics – Budapest University of Technology and Economics
1 DoF model of force control
Equation of motion:
Equilibrium:
Force error: (Craig ’86)
Stability for ,
)(sgn
)(
))(()()( or tyC
F
tky
FtkyPtkytmy
d
d
.. .
kFy dd /)1/(or/ PCPCF
0 Pkxmx)()( txyty d ..0P
Department of Applied Mechanics – Budapest University of Technology and Economics
Contents- Introduction: force control
- Motivation
- Turbine blade polishing
- Human force control
- Rehabilitation robotics
- 1 DoF model of force control
- Digital effect: sampling
- Theoretical and experimental stability charts
- Conclusion: bifurcations
Department of Applied Mechanics – Budapest University of Technology and Economics
Modelling sampling
Time delay andzero-order-holder(ZOH)
Dimensionless time/tT
Department of Applied Mechanics – Budapest University of Technology and Economics
Modelling sampling
Sampling time is , the j th sampling instant is tj = j
Natural frequency:
Sampling frequency: dim.less time: T = t/Dimensionless equations of motion:
x(j), x’(j) B1,B2
),[),()()( jjjdj ttttkyFtkyPtQ
)2/(/)2/( mkf nn /1sf
)1()1()()()()( 22 jxPTxTx nn )1,[ jjT
)()()( TxTxTx ph
)1()1()sin()cos( 21 jxPtBtB nn
Department of Applied Mechanics – Budapest University of Technology and Economics
Contents- Introduction: force control
- Motivation
- Turbine blade polishing
- Human force control
- Rehabilitation robotics
- 1 DoF model of force control
- Digital effect: sampling
- Theoretical and experimental stability charts
- Conclusion: bifurcations
Department of Applied Mechanics – Budapest University of Technology and Economics
Stability of digital force control
stability
Parameters: and
jj Azz 1
)(
)(
)1(
jx
jx
jxjz
)cos()sin()sin()1(
)sin()cos())cos(1)(1(
0101
nnnnn
nnn
P
Pn
A
0)det( AI
13,2,1
snn ff /)2/()( P
Department of Applied Mechanics – Budapest University of Technology and Economics
Checking |1,2,3|<1 algebraically
Routh-Hurwitz
Department of Applied Mechanics – Budapest University of Technology and Economics
Stability chart of force control
Vibration frequency: 0 < f < fs/2
Maximumgain:
Minimumforce error:
CF )3/2(min,
5.1max P
Department of Applied Mechanics – Budapest University of Technology and Economics
Effect of viscous damping
Damping ratio : 0.04 and 0.5
)1()1()(
)()()()(2)(2
2
jxP
TxTxTx
n
nn
Department of Applied Mechanics – Budapest University of Technology and Economics
Experimental verification
Department of Applied Mechanics – Budapest University of Technology and Economics
Experimental verification
Damping ratio = 0.04 P
[ms]
Department of Applied Mechanics – Budapest University of Technology and Economics
Differential gain D in force control
Sampling at the force sensor with t = q :
)1()()1()1()(
)()()(2
2
jxDjxP
TxTx
nn
n
)()()()( jjdj tkytykDFtkyPtQ
q
qjxjxjx
)1()1()1(
jjTj qjxjxjxjx Azzz 1)1()1()()(
Department of Applied Mechanics – Budapest University of Technology and Economics
Stability chart and bifurcations
Dimensionless differential gain Dn = 0.1
Department of Applied Mechanics – Budapest University of Technology and Economics
Stability chart and bifurcations
Dimensionless differential gain Dn = 1.0
Department of Applied Mechanics – Budapest University of Technology and Economics
Conclusions
- All the 3 kinds of co-dimension 1 bifurcations arise in digital force control(Neimark-Sacker, flip, fold)
- Application of differential gain leads to loss of stable parameter regions
- Force derivative signal can be filtered with the help of sampling, but stability properties do not improve
- Do not use differential gain in force control
Department of Applied Mechanics – Budapest University of Technology and Economics