Augmenting Locomotion in an Anthropomorphic System

Derek L. WightSystems Design Engineering, University of Waterloo

Waterloo, Ontario, N2L 3G1, Canada

Eric G. KubicaSystems Design Engineering, University of Waterloo

Waterloo, Ontario, N2L 3G1, Canada

David W.L. WangElectrical Engineering, University of Waterloo

Waterloo, Ontario, N2L 3G1, Canada

ABSTRACT

A powered orthosis has applications ranging fromassisting the elderly to augmenting astronauts. Anassistive control scheme is developed that uses theforce from a slave actuator to augment the force ofa master actuator. This can be used to augmenta closed-loop control scheme applied to the masteractuator. Initially, actuator augmentation is exploredboth theoretically and experimentally using a simplemechanical system. The control scheme is thenapplied to a scale model of human lower limbs on astationary bicycle to investigate the feasibility of apowered orthosis using pneumatic muscle actuators.

Keywords: Actuator Augmentation, PneumaticMuscle, Exoskeleton, Powered Orthosis

1. INTRODUCTION

Statistics Canada reports that 10.5% of Canadianshave some form of mobility disability [1]. This in-cludes difficulties walking on flat hard surfaces, climb-ing stairs, carrying a 5 kilogram object for 10 meters,or standing for 20 minutes. A powered orthosis couldassist physically limited patients to increase their mo-bility and quality of life.

The objective of this research is the analysis, de-sign and development of technology to augment ananthropomorphic system during locomotion. The gen-eral philosophy is that the performance of an actu-ated mechanical or biomechanical system can be im-proved if supplementary actuators are integrated intothe framework. In particular, this analysis is per-formed with a view towards augmenting human loco-motion with powered exoskeletal devices (also calledorthotic devices). The benefit of a powered ortho-sis ranges from rehabilitating and assisting patientswith weakened or poor motor control, to augmentinghealthy individuals to increase their endurance andstrength [2, 5, 6].

Many of the exoskeletal devices developed to dateare based on position control to track the motions ofthe user e.g. [2]. For the device to support an exter-nal load, it must act between the user and the loadsuch that the orthosis bears the weight. Althoughthis configuration relieves the user from supportingthe weight of the external load and the assistive de-vice, it does not assist the movement of the user’sbody. If a controller is implemented that is force-basedrather than position-based, the orthosis can amplifythe user’s forces and reduce the required effort to per-form an activity. The benefits of this approach aredemonstrated both theoretically and experimentallyin this work.

2. ACTUATOR AUGMENTATION

A general control scheme is developed that allows aslave actuator to augment the function of a master ac-tuator. In the context of this research, the master isthe human user, and the slave is the powered orthosis.To implement actuator augmentation, a closed-loopcontrol algorithm, such as PD, is applied to the mas-ter actuator and the force output is measured. Thismeasured force is used as the reference input to a forcecontroller that drives the slave actuator operating inparallel. The force generated by the slave actuatoraugments the force from the master actuator, thusreducing the force output required from the masteractuator while achieving a similar system output.

Consider a typical ideal DC motor model as shownin Figure 1. The model can be separated along thedotted line to split the electrical from the mechanicalcomponents and gain access to the torque, which isnecessary to determine the effect of multiple actuatorscoupled to a common mechanical system.

To assist the DC motor with a second DC motor,consider Figure 2. The master actuator, Motor1, iscontrolled in a typical manner using a PD controlscheme. The torque, τ1, applied by Motor1 on the me-

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1Ls+R

i K 1Js+B

Kf

1tt q+

-V

V

Ref

BackEMF

Electrical Components Mechanical Components

Figure 1: Typical DC motor model.

PDControl

Motor

ii

ii

Motor1Ref

2

MechanicalSystem

1s

1

2

t

t

tKt1

11

12

2

q

q

+

-

Figure 2: Proposed control scheme.

chanical system (which includes the mechanical com-ponents of the motors) can be determined indirectlyby measuring the current, i1, and multiplying it bythe torque constant Kτ1 . This torque is multiplied bya proportional gain KGain, and the result is convertedback to a current using Kτ2 . This current, i2, is usedto drive the slave actuator Motor2 to act on the com-mon mechanical system and assist Motor1. Note thatthe θ̇ output of the large common gear is used to cal-culate the back-EMF of Motor1. Also note that sinceMotor2 is driven by a current source, it is independentof the back-EMF.

The theoretical viability of the actuator augmen-tation scheme is explored with a simple systemconsisting of two electric motors that are indepen-dently geared to drive a large common gear as shownin Figure 3. The large gear is coupled to a wheelsuspending a mass that creates a load torque on thesystem.

Proposition: Given the mechanical system shown inFigure 3, and the control system in Figure 2, a stableposition controlled system can be found using a PDcontroller with suitable gains.

The output equations from the two motors are asfollows:

τ1 = Kτ1i1 (1)τ2 = Kτ2i2

= Kτ2

[(Kτ1)(KGain)

(1

Kτ2

)i1

]= (Kτ1)(KGain)i1 (2)

Motor1 and Motor2 are each coupled to a gear ofradius r1 and r2 respectively, which drive the largecommon gear of radius rG. The small gears include the

SuspendedMass

Motor

CommonGear

Figure 3: Dual motor experiment.

inertia and damping of the motors and are driven byτ1 and τ2. The common gear supports the load massthat applies a torque τM . The dynamic equations forthe mechanical components are as follows:

JGΘ̈G = τM − τ1G − τ2G (3)

J1Θ̈1 + B1Θ̇1 = τ1 − τ1G (4)

J2Θ̈2 + B2Θ̇2 = τ2 − τ2G (5)

To combine these equations, the following constraintsare required:

Θ1 = −rG

r1ΘG (6)

Θ2 = −rG

r2ΘG (7)

Substituting into Equations 3, 4, and 5 and combining:

[JG +

(rG

r1

)J1 +

(rG

r2

)J2

]Θ̈G +

[(rG

r1

)B1 +

(rG

r2

)B2

]Θ̇G

= τM − τ1 − τ2

Finally, converting to the Laplace domain (and assum-ing zero initial conditions):

ΘG =τM − τ1 − τ2[

JG +(

rGr1

)J1 +

(rGr2

)J2

]s2 +

[(rGr1

)B1 +

(rGr2

)B2

]s

From this equation, it can be seen that the torqueinputs τ1 and τ2 from Motor1 and Motor2 are a linearsummation. Finally, substituting Equations 1 and 2:

ΘG =τM − (Kτ1 )(1 + KGain)i1[

JG +(

rGr1

)J1 +

(rGr2

)J2

]s2 +

[(rGr1

)B1 +

(rGr2

)B2

]s

(8)

42 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 3 - NUMBER 1 ISSN: 1690-4524

The result of Equation 8 indicates that the systemwill behave the same as if a single, larger motor wasused to drive the common gear. Closing the remainingfeedback loops and applying Routh Hurwitz results insimilar stability criteria as for a single motor.

This analysis of the system suggests that if the mas-ter motor (representing the human) is operated usingclosed-loop position control, the slave motor (repre-senting the powered orthosis) can assist the master ina stable fashion using the proposed actuator augmen-tation scheme. With ideal electric motors, the prob-lem simplifies to a system using a single, larger motor.However, in order to make the response of the dualmotor system identical to that of a single motor, thecontrol parameters have to be adjusted to compen-sate for the additional torque, inertia and damping.This signifies that for a powered orthosis, some train-ing may be required by the users in order to matchtheir assisted gait to their desired gait.

3. DUAL MOTOR EXPERIMENTALRESULTS

Although the theoretical case suggests that the actu-ator augmentation scheme should be stable, the the-ory does not include friction, backlash, filter delay, orother nonlinear effects. To demonstrate that the sys-tem will work in practice, experimental results wereconducted with the setup depicted in Figure 3.

The results of position control are shown in Fig-ure 4 (the reference is a step response from 0 to 5000counts). Note that during the unassisted position con-trol, the slave motor was mechanically disconnectedfrom the system so the master actuator did not haveto drive the inertia and friction of the inactive slavemotor.

0 1 2 3 4 5 6 7 8

−20

−10

0

10

20

30

40

Tor

que

(mN

m)

Time (s)

UnassistedAssisted

0 1 2 3 4 5 6 7 8−4

−2

0

2

4

6

Enc

oder

Pos

ition

(10

00 C

ount

s)

Figure 4: Position control results.

The results demonstrate that the addition of thesecond actuator, with an assistive gain of one, reducesthe torque required by the primary actuator by 46%

compared to a theoretical decrease of 50% (some ofthe assistive torque is lost to the friction of the slaveactuator). The time to reach steady state is slightlyfaster for the assisted case as more torque is available.Note that transients during the rising edge of the stepresponse are not at the average assistance level. Thisis in part due to a low pass filter used to remove noisefrom the current measurement of the master motor,as well as amplifier saturation.

To more clearly demonstrate the torque reduc-tion, the control scheme for the master actuator waschanged to a velocity regulating PI control. After theinitial zero-load resting position, the results presentedin Figure 5 clearly show a reduction of the torque out-put of the master actuator without any amplifier sat-uration or transients to complicate comparison. Thishighlights another important aspect of the actuatoraugmentation scheme. No modifications of the slaveactuator control were required to change between po-sition and velocity control. The slave actuator willprovide assistance regardless of the control scheme ap-plied to the master actuator because it utilizes theexisting control loop.

2 3 4 5 6 7 8

0

10

20

30

Tor

que

(mN

m)

Time (s)

2 3 4 5 6 7 8−2

0

2

4

6

8

10V

eloc

ity (

1000

Cou

nts/

s)UnassistedAssisted

Figure 5: Velocity control results.

Two extreme cases of the assistive scheme revealsome interesting results. In theory, there is no limitto the assistive gain with the appropriate control mod-ifications. The torque required by the master actuatoronly needs to be large enough to provide a referencesignal for the slave actuator. However, the maximumassistive gain is limited by the noise in the system. Inthis experiment, it was found that with a first orderlow pass filter of approximately 600Hz applied to thecurrent measurements, the assistive gain could stillbe set well above 100, with the appropriate controllergain modifications, before the quality of the output be-gan to significantly degrade. By decreasing the band-width of the filter on the current measurements, theassistive gain can be further increased, but with someimpact on the performance of the system.

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The other extreme case to consider is low loads onthe common mechanical system. When the externalload is removed, the only force opposing motion isfriction. In this case, the benefits of the second ac-tuator are almost negligible because at an assistivegain of one, all of the torque generated by the slaveis used to overcome its own friction. Friction may bethe primary determinant of the benefits of actuatoraugmentation. Depending on the external load com-pared to the friction between the actuators and thecommon mechanical system, the benefits of actuatoraugmentation can vary from significant to negligible.

Outside of the application of powered orthotics, thiscontrol scheme may be useful to retrofit underpoweredsystems, or where physical constraints do not permita single actuator of appropriate size.

4. AUGMENTING HUMANPERFORMANCE WITH A POWERED

ORTHOSIS

The human body effectively achieves position controlduring gait by placing the limbs in such a way thatstable motion is obtained. Drawing an analogy to thedual motor system, consider Figure 6. The forces of

F

F

FFEstimate

1

K

EMG

Proprioceptive Feedback

Human Mechanical System(Human Body & Orthosis)

1

K

HumanMuscleInput

ForceEstimator

HighLevel

Control

Slave Actuator

Slave Actuator

Figure 6: Augmenting human muscles.

the human muscles (the master actuators) act on theskeleton (the common mechanical system) to producea desired motion. To augment the human, estimates ofthe muscle forces can be inferred with techniques suchas electromyography (EMG), which monitor the elec-trical activity in a contracting muscle. The force esti-mates are used as reference inputs to a force controllerthat drives the slave actuators, which in turn act onthe human. Locally the orthosis operates under open-loop position control, but by integrating the humaninto the actuator augmentation scheme, the humanuser closes the position feedback loop with proprio-ceptive and kinesthetic feedback mechanisms. As theapparent force required to achieve the desired motionbecomes reduced, so does the user’s neural drive toindividual muscles. This reduces the reference inputsto the orthosis slave actuators, which reduces theirforce output, thus closing the position control loop.While the use of EMG as a force estimate for a pow-ered orthosis has been demonstrated before [5, 6], theactuator augmentation control scheme provides a the-

oretical basis on which any actuator or appropriateforce sensor can be used.

As discussed in the dual motor experimental re-sults, the benefit of an assistive actuator is limited bythe friction between the slave actuator and the com-mon mechanical system. The relatively low frictionmuscular-skeletal system allows the human body toconserve energy by making use of the natural pendu-lum motion of the leg during the swing phase of gait.If relatively small electric motors were used as the as-sistive actuator in a lower limb orthosis, substantialgearing would be required, which would reduce theback-drivability and bandwidth of the actuator. Usinga highly geared electric motor would require that themotor be driven throughout the entire gait cycle, los-ing the energy savings of the pendulum motion. Also,without actuator compliance, any lag in the systemcould result in user discomfort [5].

A more appropriate selection of actuator is thePneumatic Muscle Actuator (PMA). PMA’s are con-structed by combining a rubber lining with a heli-cal braided mesh shell. When the PMA is pressur-ized, the structure produces an axial contraction withthe radial expansion. PMA’s are naturally compli-ant which is a benefit in terms of back-drivability andsafety, but requires the application of nonlinear con-trol techniques to compensate for the nonlinearitiesand achieve accurate control. Despite the nonlinear-ities associated with PMA’s, a preliminary analysis[3], which considers the feasibility of the entire sys-tem, indicates PMA’s are the most promising actua-tor technology for this application. In particular, thisis due to the high power-to-weight (1000 W/kg) andpower-to-volume (1.1 W/cm3) ratios [4].

5. PNEUMATIC MUSCLE BICYCLEEXPERIMENT

In order to demonstrate the actuator augmentationcontrol scheme on an anthropomorphic system, a onedegree of freedom scale model of human lower limbswas constructed and mounted on a stationary bicycle(see Figure 7). The limbs are assisted by two PMA’saffixed to the thighs that generate torques at the kneejoints. An electric motor is coupled to the crank, andthe applied torque is inferred from the drive current.

To investigate actuator augmentation on the bicy-cle model, two controllers are implemented. The mo-tor, representing the human contribution, is veloc-ity controlled with a PI controller and an adaptivefeed-forward component to compensate for the non-linearities of the mechanical system. The PMA’s arecontrolled using a lookup table to determine the re-quired operating pressure to achieve the desired refer-ence torque. The level of assistance is governed witha proportional controller that scales the motor torquemeasurements used in the PMA lookup table.

The experimental results in Figure 8 demonstratethe beneficial nature of the actuator augmentation

44 SYSTEMICS, CYBERNETICS AND INFORMATICS VOLUME 3 - NUMBER 1 ISSN: 1690-4524

Proportional Piezo Valves

Motor & Encoder

Crank

PneumaticMuscle

Figure 7: PMA bicycle experimental apparatus.

control scheme. In the assisted case, the PMA ac-tuators reduce the power requirements of the masteractuator (representing human) by 40%. Simulationspredicted an improvement of 52% [3] in the regionsoutside of pressure saturation (grey), but the differ-ence can be attributed to modelling nonlinearities.

0 50 100 150 200 250 300 3500

0.5

1

1.5

2

2.5

Crank Angle (Crank Vertical at 0 and 180 deg)

Tor

que

(Nm

)

UnassistedAssisted

Figure 8: PMA bicycle experimental results.

The frequent variations in torque are due to sig-nificant backlash in the gear train of the electric mo-tor. Since the backlash is not representative of humanfunction, this motor is being replaced and more de-tailed results of this experiment will be presented in afuture paper.

6. CONCLUSIONS

This work has demonstrated the development and ap-plication of actuator augmentation. The application

of this control scheme to the dual motor experimentclearly shows the benefit of using slave actuators toreduce the load on a master actuator. The potentialapplication of this control scheme to a powered ortho-sis was explored through the use of a scale model ofhuman lower limbs mounted on a stationary bicycle.Pneumatic muscles were used to successfully augmentan electric motor representing the human pedalling.

The use of actuator augmentation for a full scaleorthosis is particularly promising because the humanbecomes an integral part of the control loop. The hu-man body is a difficult subject from which to draw ac-curate force measurements, but by incorporating thehuman into the control loop, the orthosis automati-cally gains the human’s flexibility and adaptiveness tonew environments. Balance, coordination, gait pat-terns, path planning, knowledge of the environment,and obstacle avoidance are all imparted on the ortho-sis by the actions of the user. Since actuator aug-mentation makes use of the existing control schemesapplied to the master actuator, the human user is notrestricted to specific activities.

7. REFERENCES

[1] Statistics Canada, “A Profile of Disability inCanada, 2001”, Ministry of Industry, Catalog No.89-577-XIE, Dec. 2002.

[2] Y. Umetani, Y. Yamada, T. Morizono, T.Yoshida, S. Aoki, “Skil Mate, Wearable Exoskele-ton Robot”, IEEE SMC ’99 Conference Proceed-ings Systems, Man, and Cybernetics, Vol. 4, pp.984-988, Oct., 1999.

[3] D.L. Wight, “Control of a Pneumatically PoweredOrthosis”, MASc Thesis, University of Waterloo,ON, Canada, 2004.

[4] D.W. Repperger, C.A. Phillips, D.C. Johnson,R.D. Harmon, K. Johnson, “A Study of Pneu-matic Muscle Technology for Possible Assistancein Mobility”, Proceedings of the 19th Annual In-ternational Conference of the IEEE Engineeringin Medicine and Biology Society, Vol. 5, pp. 1884-1887, Oct., 1997.

[5] H. Kawamoto, Y. Sankai, “Comfortable Power As-sist Control Method for Walking Aid by HAL-3”,IEEE International Conference on Systems, Manand Cybernetics, Vol. 4, pp. 6-9, Oct., 2002.

[6] Daniel P. Ferris, Joseph M. Czerniecki, BlakeHannaford, “An Ankle-Foot Orthosis Powered ByArtificial Muscles”, 25th Annual Meeting of theAmerican Society of Biomechanics, Aug. 2001.

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