DelftUniversity ofTechnology
Identification of Joint Impedance
Erwin de Vlugt, PhD
tools for understanding the human motion system,treatment selection and evaluation
Lecture 12 SIPE 2010Case Studies
DelftUniversity ofTechnology
Delft-Leiden Research Connection
Frans van der Helm, Erwin de Vlugt, Alfred Schouten, Herman van der Kooij, David Abbink, Riender Happee, Winfred Mugge, Alistair Vardy, Judith Visser, Stijnvan Eesbeek
Mission: development of SIPE technology to analyze the human neuromuscular control system
Laboratory for Kinematicsand Neuromechanics
Hans Arendzen, Jurriaan de Groot, CarelMeskers, Frans Steenbrink, Erwin de Vlugt, Asbjorn Klomp, Hanneke van derKrogt, Andrea Maier, Bob van Hilten, Rob Nelissen
Mission: application and validation of SIPE technology in the clinical practice to improve efficacy of intervention
DelftUniversity ofTechnology
• Mechanical energy transfer to the biological system
• Measurement of forces and movement
Robots for System Identification
http://fogonazos.blogspot.com/2006/12/la-ertica-del-robot_26.html
DelftUniversity ofTechnology
Robots for System Identification
- Natural tasks- Perturbations - Closed loop- Interpretable
parameters
DelftUniversity ofTechnology
System Identification & Parameter Estimation (SI-PE)
Physical Systeminput output
Identification(SI)
minimal a prioriknowledge required
System Behavior
Parameterization(PE)
A priori knowledgerequired
Physical Properties
DelftUniversity ofTechnology
Three case studies
1. Linear SIPE: intrinsic and reflexive properties of the shoulder (1DOF)
2. Linear SIPE: … but now for 3DOF (shoulder, elbow, wrist)
3. Nonlinear PE: intrinsic and reflexive torque of the ankle in stroke
DelftUniversity ofTechnology
Linear systems: Frequency domain analysis of mass-damper-spring
2
1
2
( )H sMs Bs K
s fπ
=+ +
=
10-1 100 101
10-4
10-3
Gai
n
10-1 100 101
-150
-100
-50
Frequency [Hz]
Pha
se [d
eg]
Stiffness Damping Mass
• H is causal• H is an admittance
0
2
KMBKM
ω
β
=
=
DelftUniversity ofTechnology
OptimalAdmittance Control
• Simulations indicate that contribution of reflexes decrease with frequency of torque input.
De Vlugt et al. 2001
DelftUniversity ofTechnology
Short Intro toOptimal Admittance Control
Joint Admittance• is the dynamic relationship between joint angle and joint torque• the result of visco-elasticity and torque generated by reflexes• important for posture maintenance
Research Questions• does admittance depend on the dynamic properties of external
load, e.g. damping ?• how does admittance change with joint angle?
DelftUniversity ofTechnology
Case 1: 1DOF shoulder joint control
DelftUniversity ofTechnology
Recordings
DelftUniversity ofTechnology
Procedures
• External damping BE: 0 – 400 Ns/m• External mass ME: 0.6 – 10 kg• Unpredictable force disturbances
• 40 s (0.1-20 Hz)• Grip displacements ≈ 3 mm (SD)• EMG of four shoulder muscles• n=5 (healthy)
DelftUniversity ofTechnology
Force perturbations: closed loop
EnvironmentΣF
ΣXREF
D
-
XεHuman
DelftUniversity ofTechnology
Force perturbations: closed loop
NeuralDelay
Activation
MuscleSpindles
Intrinsic Arm
Environment
pv kk +sDTe s−
1+sA1
τ kbm1
2 ++ ssΣ
F
ΣXREF
D
Σ
X
-
-
Human Arm
A
EEkb +sL+
2
Em s
DelftUniversity ofTechnology
SI Results: Frequency Response Functions
damper offdamper on
DelftUniversity ofTechnology
Parameter Estimation (PE)
D
Fhand
Xhand
Linear Endpoint Model
FRF Estimation
Parameter Fit
FRF Simulation
Hold position
DelftUniversity ofTechnology
PE Results: stretch reflex estimates
De Vlugt et al. 2002
DelftUniversity ofTechnology
Results: optimized stretch reflex
DelftUniversity ofTechnology
Reflexive Admittance Control: no environment
DelftUniversity ofTechnology
Reflexive Admittance Control: with External Damper
DelftUniversity ofTechnology
Case 2: SIPE in the 3DOF Shoulder
DelftUniversity ofTechnology
2DOF FRFs
datamodel
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PE Result: intrinsic parameters
De Vlugt et al. 2006
DelftUniversity ofTechnology
Stiffness Ellipses
datamodel
reflexes turned of / turned on
DelftUniversity ofTechnology
Case 3: Nonlinear case: Ramp-hold Ankle rotation in stroke
De Vlugt et al. 2010
DelftUniversity ofTechnology
Nonlinear case: Ramp-hold Ankle rotation
• stroke (n = 19)
Goal:• estimate passive visco-elasticity
and stretch reflex dynamics andcompare to Ashworth Scale
DelftUniversity ofTechnology
Direct Physical Parameterization
DelftUniversity ofTechnology
No Identification, Direct Parameterization
direct parameterization of anonlinear model in time domain
Parameters:• inertia• tissue viscosity• tissue elasticity• activation dynamics• contractile dynamics
DelftUniversity ofTechnology
Main Result
• Detailed parameterizationpossible:- Accurate (VAF > 90%)- Valid (low parameter SEM)
• Viscosity decreased withmovement velocity
• Passive stiffness correlatedto Ashworth Scale
DelftUniversity ofTechnology
Challenges: SIPE during movement
• Time Varying Joint Admittance• Wavelets and subspace techniques• Collaboration between the fac. of 3ME (DCSC, BMechE) and
Aerospace Eng.
DelftUniversity ofTechnology
Summary
• Linear behavior: frequency domain can be used and provides direct qualitative information about the human joint dynamics.
• Nonlinear behavior: time domain analysis by direct parameterization of a physical nonlinear model of the human joint.
• Towards Time Varying System Identification….
DelftUniversity ofTechnology
Graduate Student Master Projects
• Master Projects at NMC Lab involves a mixture of SIPE, physiology and clinical issues
• Many (international) opportunities for Graduate Students• internship (stage), preferably outside the Netherlands• fundamental projects: TUD• clinical projects: LUMC, Erasmus MC, VUMC
Identification of Joint ImpedanceDelft-Leiden Research ConnectionRobots for System IdentificationRobots for System IdentificationSystem Identification & Parameter Estimation (SI-PE)Three case studiesLinear systems: Frequency domain analysis of mass-damper-springOptimal�Admittance ControlShort Intro to�Optimal Admittance ControlCase 1: 1DOF shoulder joint controlRecordingsProceduresForce perturbations: closed loopForce perturbations: closed loopSI Results: Frequency Response FunctionsParameter Estimation (PE)PE Results: stretch reflex estimatesResults: optimized stretch reflexReflexive Admittance Control: no environmentReflexive Admittance Control: with External DamperCase 2: SIPE in the 3DOF Shoulder2DOF FRFsPE Result: intrinsic parametersStiffness EllipsesCase 3: Nonlinear case: Ramp-hold Ankle rotation in strokeNonlinear case: Ramp-hold Ankle rotationDirect Physical ParameterizationNo Identification, Direct Parameterization Main ResultChallenges: SIPE during movementSummaryGraduate Student Master Projects