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SI. ~"'. Cllllomla .Ju..1tt3WP5 -14:50Destabilizing effects of muscular co-contraction

human-machine interactionin

5[

Karin HollerbachGraduate Group in Bioengineering

H. KazerooniDepartment of

Mechanical Engineering

C. F. RamosNeurosciences Division

University of California, Berkeley, CA 94720

[3] or is moving an exercise machine or an orthoticdevice. In systems of this nature, the human armdynamics are integrated with the machine dynamics,resulting in behavior specific to the total system. Theperformance and stability of the system taken as awhole are both functions of not only the machinedynamics, but also the human arm dynamics. Evideocefor instability in a human-machine system involving aninteraction force between the human and the machine,as well as force feedback compensation within themachine, has been shown [1,3]. The goal of this articleis to determine whether increasing muscular co-contraction levels may be a cause of such instability.

Abstract

We are studying the control of human arm movementsthat are constrained by physical interaction with amachine such as a hand controller or a teleroboticsystem. One of the difficulties in controlling this typeof constrained interaction is instability in the humanarm-machine system. In this article, we presentsimulation results showing that increasing muscular co-contraction destabilizes human-machine interaction.Results of this work may have an impact on the designof machines that are to interact with humans.

NomenclatureKazerooni [1] has demonstrated a relationship

between stability in active hand controllers andcompliance in the hand controller and in the humanarm. (Active hand controllers are defined as powered.multi-degree-of-freedom joystick-like mechanisms thatare maneuvered by a human to generate commandsignals.) In order to guarantee stability. somecompliance in either the hand controller or in thehuman arm is required. We extend these results bypresenting simulation results that demonstrate thedestabilizing effects of increasing arm impedance byincreasing muscular co-contraction levels explicitly.

agonist muscleantagonist muscle

LR

-

aBhBpBvL,RfL,RJpK}K2KpDL,R

tL,RTv

VL,R

XL,Re

-

Empirical evidence has shown that "rigidity" of alimb is increased by simultaneous co-contraction ofantagonist muscles, resulting in more effective }X>SbJralmaintenance [5,9]. Furthermore, model simulationstudies have shown that high co-contraction levelscause a strong resistance to low-frequency disturbingforces [5,10]. We note, however, that the focus of ourstudies is not posture maintenance in the presence ofdisturbing forces and torques; instead, we are interestedin the behavior of the arm-machine system as the annis constrained by continuous contact with the machine.The instability in this type of interaction may bedescribed as an increasing tremor in the ann, rather thanan inability to reject disturbing forces. The hypothesisof the present study is that increased co-contractionlevels in the human arm contribute significantly to

instability in the human-machine system.

joint accelemtionmuscle damping constantpassive tissue dampingmuscle damping elementactual muscle tensionpassive tissue inertiamuscle spring stiffnessmuscle spring stiffnesspassive tissue stiffnessneural input to musclehypothetical muscle tensiontime constantjoint velocitymuscle velocitymuscle position

joint position

Instability in human-machine interaction

1.

When the human arm is interacting directly witha machine, its movement is constrained throughphysical contact with the machine; i.e., the human armmoves in such a way that the machine continuouslyexerts a dynamic constraint on the arm. Examples ofconstrained movements can be seen when the arm isoperating a hand controller [1] or a telerobotic system

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2.

Simulation study

In the simulation study described here, we used anon-linear, lumped-parameter, antagonist muscle modelof single-joint movements of the human arm[4,7,8,10]. A brief description of the model and ofexternal torques ("load disturbances") and positionconstraints applied to the model in the present study isshown in Figure 1. The undisturred agonist-antagonistmuscle model is described by the following set ofequations:

LR

agonist muscleantagonist muscle

-

9:..0dd(iXLd"(h:XR

d-y

dtd~tLd"(h:tR

fL

fR

BVL

v=

VL

VR

Figure 1. Model used In simulation studies.The model consists of an antagonist pair of

muscles, a passive load, and neurologicalcontrol signals to each muscle. Disturbances

modeling machine Input to the human arm maybe Imposed as load disturbances or as position

constraints.

a

-~ --BVL -

-~--BVR-

-Kg9-Bgv+fL -fR -= ] -pnL -tL= T

= DR -tR

T

K1 (eK2(XL-8) -1)

K1 (eK2(XR-G) -1)1.25 tL

Bh + IVLI

1.25 tRBh + IvRI

-

In the first three sets of simulations, we appliedan external, time-varying load disturbance andexamined the response of the system to the appliedtorque. These simulations involve predictable(constant or periodic) applied torques on the simulatedarm. The model was simulated with varying 00-contraction levels. Load disturbance amplitudes and co-contraction levels were normalized in the model, withminimum muscle forces at 80 grams and maximummuscles forces at 10,000 grams. The simulations wererun for several seconds to observe long-term trends.However, plotted in each figure are the first 1000milliseconds only, as this time proved to be sufficientto show the observed behavior.

=

BVR =

The disturbances and constraints applied to theantagonist muscle model were used to model thepossible modes of interaction of the human arm withthe machine: it is possible for the machine to eitherapply a specific joint torque to the human arm, whileallowing the human to determine the position; on theother hand, the machine may impose a positionconstraint, while the human imposes forces on themachine.

In the first set of simulations, we applied aconstant joint torque with an amplitude of 1000,comparable to a muscle force of 1<XX> grams (Figure 2).Co-contraction levels were varied from 6(XX) grams to10,000 grams. In the results, increased levels of co-contraction correspond to an overall decrease in theposition response (a smaller deviation from the initialposition), and an increase in joint oscillation. Thedecrease in the amplitude of the position responserepresents an increase in the arm's ability to maintainits posture. The increase in joint oscillation (tremor)with increasing co-contraction levels, however,suggests a decrease in stability when the arm isdisturbed by external forces. The frequency of dle

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oscillations that result from a constant, externallyapplied joint torque in the presence of high co-contraction levels. is approximately 10 Hz.

deq Joint Position

Figure 3. Joint position as a function of timein response to a sinusoidal applied torque with

amplitude = 1000 grams and frequency = 10Hz. Co-contraction levels varied from 5000

grams to 8000 grams and 10,000 grams.

In the third set of simulations (Figure 4) weexamined the system's response to varying frequenciesin the applied torque. The torque frequency was variedin order to determine whether the behavior pattern inresponse to the 10 Hz load is specific to 10 Hz loads.In Figure 4, the disturbance amplitude is 1000 grams,and co-contraction levels are high, at 9(XX) grams. Anincrease in disturbance frequency from 1 Hz to 5 Hzmay be observed to cause a decrease in the amplitude ofthe position response. A further increase in frequencyto 10 Hz decreased the mean position response butincreased the amplitude.

msec

Figure 2. Joint position and acceleration asrunctlons or time In response to a load

disturbance with amplitude = 1000 grams. Co-contraction levels varied from 6000 grams to

7000, 8000, and 10,000 grams.

In the second set of simulations, we applied asinusoidal torque disturbance with an amplitude of1000 and a frequency of 10 Hz (Figure 3). In thesteady st3te, the increase in co-conU'action levels, from5<XX> grams to 10,<XX> grams, caused an increase in theamplitude and a small decrease in tre phase shift of theoscillations. As before, the increasing amplitude of theoscillations with increasing levels of co-conU'actionsuggests a decrease in the st3bility of the arm.

Figure 4. Joint position as a function of timein response to sinusoidal applied torque withamplitude = 1000 grams and frequencies = 1

Hz,S Hz, and 10 Hz. Co-contraction was kepthigh, at 9000 grams.

In the final set of simulations, we added adisturbance to the system, in the fonn of a positionconstraint imposed upon the ann. As before, wesimulated the resulting model under varying mean co-contraction levels. The position constraint was takenfrom data measured in experiments with a real arm andmachine; the resulting simulated contact force (between

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the human arm and the hypothetical machine imposingthe position consbaint in the simulation) was calculatedand compared with the actual, experimental force data.The simulation, in this case, was run for severalseconds. The applied position consbaint is shown inFigure 5. Simulations were carried out at threedifferent levels of co-contraction, 2000 grams, 5000grams, and 9(XX) grams. The contact force, between thearm's endpoint (hand) and a hypothetical machineimposing the position constraint, was calculated and isshown in Figure 6. The force behavior at all three co-contraction levels is qualitatively similar to thatobserved in the laboratory. Increasing co-contractionlevels, however, increases the amplitude of the contactfocce resJX}nse.

3. Discussion

It has been observed [1,2] that increasing humanarm impedance leads to instability in human-machineinteroction. The significance of the work. presented hereis to examine the specific link between increasingmuscular co-contraction levels in the arm andinstability. In order to test the hypothesis thatincreased co-contraction leads to instability, wesimulated single joint arm behavior with loaddisturbances and position constraints that might beimposed on the arm by an octual machine.

Figure 7. The contact force between the arm(hand) and the machine, as measured by

sensors in the machine. The contact force wasgenerated in response to the imposed position

constraint shown in Figure 5. For moreinformation on how these data were gathered,

the reader is referred to (2).

Figure S. The joint position as a function oftime. The position constraint shown here was

Imposed upon the arm, and the resultingcontact forces between the human arm (hand)

and a hypothetical machine imposing theconstraint were calculated In the simuiation

and are shown in Figure 6.

Our simulations indicate that high co-conb"OCtionlevels lead to smaller steady-state displacements of thearm, in response to applied load disturbances; i.e., highco-contraction levels improve the disturbance rejectionproperties of the arm. This result supports previousdata [5,10] regarding the role of co-contraction levels inposture maintenance. However, our simulation resultsindicate that, in the presence of soch externally imposedconstraints, high co-contraction levels do lead toincreasing transient oscillation of the arm. Thisoscillation, unless it is sufficiently filtered out by themachine, could be enough to cause growingoscillations. leading to total (unbounded) instability ofthe human-machine system.

sec

The model used in the simulations pennitted us tospecify the co-contraction levels explicitly. We testedthe effects of co-contraction levels in several sets ofcircumstances. The first included constant and periodicapplied joint torques. In all cases, increasing co-contraction in the muscles led to increased tremor.Increased co-conb'aCtion in the presence of applied jointtorques, thus, tended to destabilize the system. In thelast set of simulations, a position constraint was

Figure 6. The contact force between the humanarm (hand) and a hypothetical machine

imposing the position constraint shown InFigure 5. The contact force is shown for three

different co-contraction levels, 2000 grams,5000 grams, and 9000 grams.

applied to the arm, and the resulting contact force wascalculated at three different co-contraction levels. Theposition constraint data were taken directly from anexperiment using a real machine and human. In thatexperiment, the machine was commanded to movealong a trajectory, imposing the position constraintshown in Figure 5. The contact forces in the resulting,unstable system were measured and are shown in Figure7, for comparison with the calculated contact forcesshown in Figure 6. We note the similarity of the lowfrequency components of the measured force in Figure71 to the calculated force in Figure 6. In addition, weobserve that. while qualitatively the force response issimilar at all co-conb'action levels, the amplitude of thefooce increases with increasing co-contraction. Thus, thesimulations that were used to verify the arm model'spredictions appear to be in agreement with experimentaldata gathered using a real machine and human.

5.

References

[1] Kazerooni, H., 1990, Human-robot interaction viathe transfer of power and information signals. IEEETrans. on Systems and Cybern., Vol. 20, No.2, 450-463.

[2] Kazerooni, H., 1992, Human-induced instabilityin powered hand controllers. Proc. of the 1992 IEEEInti. Conf. on Robotics and Automation.

[3] Kazerooni, H., Tsay, T .1., and Hollerbach, Karin,1993, A controller design framework for teleroboticsystems (to apJX';ar).

[4] Kim, W. S., Lee, S. H., Hannaford, B. and Stark,L., 1984, Inverse Modeling to obtain head movementcontroller signal. Proc. of the IEEE 20th Annual Confon Manual Control. 601-620.

The results of the preceding sections indicate thatco-contraction of the muscles in the human arm plays arole in determining the relative stability of the humanarm-machine-load system. Increasing co-contractionincreases the magnitude of the arm's impedance. Whenit becomes great enough, the magnitude of theimpedance causes at least a conservative Nyquiststability condition describing the human-machinesystem to fail [2] As a result, the stability of thesystem can no longer be guaranteed. Thus, the modelpredicts one cause of instability in the arm-machine-load system: increasing muscular co-contraction.

[5] Murray, W. R. and Hogan, N., 1989,Experimental observations on the maintenance of elbowposture in the presence of disturbances. Issues in TheModeling and Control of Biomechanical Systems(Edited by J. L. Stein, J. A. Ashton-Miller, and M. G.Pandy), pp. 19-28. ASME.

[6] Ogata, K., 1970, Modern control engineering.Prentice-Hall, Inc., pp. 407-417.

[7] Ramos, C. F. and Stark, L., 1987, Simulationstudies of descending and reflex control of fastmovements. J. Motor Behav. 19:38-62.

Summary4.In this article, we use a model of the human ann

to predict one cause of instability in a human arm-machine-load system: increased co-contraction of thearm muscles. This prediction is based on experimentalobservations indicating that varying arm impedancecauses instability. The prediction of the model isverified using data from a simulation and compared withexperimental observations. Other factors that may playa significant role in causing instability include machineand compensator design. It is the interaction of each ofthese factors that ultimately determines the stability ofthe system, and it is the understanding of thisinteraction that is the goal of this research. In futureresearch, we plan to test these simulation results withan actual machine simulating the modeled armbehavior.

[8] Ramos, C. F., Hacisalihzade, S. S., and Stark.L., 1990, Behavior Space of a stretch reflex model andits implications for the neural control of voluntarymovements. Med. & Bioi. Eng. & COmpUl., 28:15-23.

[9] Wilkie, D. R., 1950, The relation between forceand velocity in human muscle. J. Physiol. KilO, pp.248-280.

[10] Winters, J. M. and Stark, L., 1985, Analysis offundamental human movement patterns through the useof in-depth antagonistic muscle models. IEEE Trans. onBiomed. Engr. BME32, 10,826-839.

1 The high frequency components of the force shown inFigure 7 represent unmodeled dynamics of the sensors in thereal robot and should not be expected to be duplicated in thesimulation results.

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