MODELING THE EFFECTS OF INERTIAL REACTIONS ON OCCUPANTS OF MOVING POWER WHEELCHAIRS

Debarag Banerjee, Lawrence M. Jordan and Michael J. Rosen Department of Biomedical Engineering University of Tennessee Memphis, Tennessee U.S.A.

ABSTRACT

Sagittal torso and arm motions induced by fore-and-aft accelerations in power wheelchairs may adversely affect control performance for people with disabilities. Susceptibility to uncontrolled bucking is an example. A control systems model of this phenomenon has been developed which requires a simplified biomechanical model of the human torso. Experiments have been performed on able-bodied human subjects to evaluate the model and to find values for effective torso stiffness and damping. These results are a first step towards understanding potentially dangerous phenomena and specifying clinical guidelines to avoid them.

BACKGROUND

A common problem in the design of mobility-aids for physically challenged individuals is the compromise between stability and responsiveness. While this is a general problem in any feedback control system, it arises for wheelchairs in the following way: When a person driving a power wheelchair attempts to accelerate the vehicle forward or backward an inertial force acts on his body. If the musculature of the person involved is not strong enough to withstand this force then it may throw the limb manipulating the joystick controller opposite to the direction intended, i.e., backwards while speeding up and forward while braking.. Thus, the vehicle performs the opposite task (e.g., braking when speeding was intended) thereby initiating a similar event train in an opposite sense. This leads to oscillations in the man-machine system which may be sustained or transient. In such a situation, the person may attempt to correct the oscillatory behavior by applying proper muscular effort through voluntary intent. Due to the delays inherent in the system this may actually aggravate the effect instead of correcting for it. A similar phenomenon of interactive man-machine system instability has been investigated in vivo by Jagocinski et al.,[1] for head-switch equipped power chairsBennett[2] has investigated the bucking effect using a crude dummy of a hand holding the joystick controller. An analysis has also been performed by Brubaker [3] regarding factors affecting manual wheelchair performance. Power wheelchair controller issues have also been delved into by Cooper[4]. However, in order to quantifiably model such a phenomenon a concise model describing the effect of acceleration of the seat on the upper torso and the joystick hand is required. It has been strongly conjectured by Winter et al.[5] that the human musculoskeletal system components can be functionally modelled as a combination of masses attached to linear springs and dampers. Though characteristics of individual muscles have been thoroughly established study of the performance of multi-jointed systems like the torso have been rare.

RESEARCH QUESTIONS

Long Term

The long term objective of the research is to develop and demonstrate prescriptive procedures for selecting or designing dynamical performance parameters (viz control systems, joystick characteristics, structural design) for the safe operation of power wheelchairs by severely disabled persons. In order to reach the goal, suitable modeling of the occupant-chair system under significant inertial effects is necessary.

Short Term

In order to develop an objective model of the interactive dynamics of the occupant and the wheelchair, a necessary prerequisite is knowledge of the behavior of human torso as a kinematic system. Though there is ample biomechanical data[6] pertaining to the mass distribution of the torso, no such research has been done for finding the spring and damping constants of the same. The following experiment is aimed at finding the linear spring and damping coefficients that best describe a single degree-of-freedom model of the torso.

METHOD

An experiment has been performed for determining the dynamic behavior of the human torso in the sagittal plane as well as for parameterizing the human-wheelchair interaction in an open-loop scenario. Setup An able-bodied human subject was seated in an XPR ArrowTM power wheelchair. The wheelchair joystick output was disconnected from the control system circuitry and an external sinusoidal voltage generator was used to excite the wheelchair at the port receiving the former joystick output. Thus the effective control of the wheelchair was relinquished by the user to the voltage generator. The wheelchair front casters were locked and it was further constrained only in the fore-and-aft direction by a pair of rails. The wheelchair was otherwise conformant to ones in regular use.

Data Collection

The wheelchair was made to move against a graduated planar background. Reflective markers were placed on strategic observable points on the chair and on the human subjects. The entire setup was then recorded on a VHS video camera facing perpendicular to the background. The joystick output and the excitation input were directly recorded on a computer after suitable sampling and digital to analog conversion. An example frame from the videograph is shown in Fig1.

Procedure

The subject sat on the wheelchair in a normal posture holding the joystick as one normally would have for controlling the wheelchair, except that she was asked not to perform any voluntary movements. A mechanical resstraint was also used on the S's shoulders to prevent protraction and retraction. The wheelchair control was then excited by a sinusoidal voltage signal from the generator. This caused the chair to oscillate linearly along the guide-rails. The S's torso was thus subjected to

Figure 1: Subject seated in remotely controlled wheelchair during chair oscillation test.

inertial acceleration due to the oscillatory motion. Because of the motion, the joystick hand of the S experienced a similar motion. However, the joystick being disconnected from the control circuitry, the human-machine loop remained open, enabling separate observation of the control input and the fed- back signal from the machine-man path. Also the motion of the torso in the sagittal plane was recorded by the camera -the reflective markers serving as points of reference. A light bulb positioned in the camera's field of view was controlled by the on-off switch of the voltage generator in order to synchronize the data gathering of the computer and the camera. The excitations were performed at frequencies 0.2 Hz to 1 Hz at intervals of 0.1 Hz and 1Hz to 2 Hz at interval of 0.5 Hz.

Initial Data Analysis

Pending procurement of the automated digitiser, portions of the videograph has been manually digitised by viewing it in still mode on a high-resolution monitor through a transparent calibrated rectangular grid. The positions of the markers on the S's shoulder and on the axle, wheelrim and pushbar of the chair were noted for each frame of the videograph. The relative movement of the upper torso with respect to the chair and the horizontal velocity of the chair was determined from the dynamicity in these marker positions. For small amplitudes of upper torso motion, it can be shown that the torso-wheelchair combination behaves like a linear second-order dynamical system whose frequency response is governed by the transfer function:

where, m = Mass of torso l = Height of the center of mass of the torso from pelvic pivot point k = Ratio of Shoulder height to l K= Effective rotational spring constant of the torso C= Effective rotational damping constant of the torso QT=Angle of inclination of torso AC= Linear acceleration of the chair

Among these parameters, K and C were unknown while the rest were obtained from direct observation and anthropometric data. Since the controller was excited by sinusoidal voltages at various frequencies the velocity dynamics of the chair and hence that of the torso were also roughly sinusoidal at the excitation frequencies.

RESULTS

Estimating the chair velocity and the horizontal relative motion of the torso from the video data and comparing their respective amplitudes and phase at a number of frequencies yielded the observed frequency response of this system shown in Fig. 2. These points were then fitted to a generic second-order frequency response function (theoretical curves shown in Fig. 2) to yield the spring and damping characteristics of the torso (K and C). The subject used in the experiment was a 150 lb medium dimensioned female whose torso parameters were Mass = 90 lb Height of CG from pelvic center of rotation = 18 inches Rotational spring constant = 558 lb-in/rad Rotational damping constant = 54 lb-in/rad/sec As a redundancy check, the parameter k had been kept indeterminate. The fitted equation returned a value of k within 1.25% of the observed value. As a final corroboration of the model, a computer-aided simulation of the experiment was performed using the mechanical parameters obtained. The simulation validated the model within ranges of reasonable experimental error and simulation assumptions (see Fig. 2). Hence, a concise modeling of moderate sagittal movements of the human torso has been performed.

Figure 2: Frequency response of torso. The gain and phase of the transfer function are plotted on separate scales against frequency. Theoretical response has been computed from transfer function equation while the simulated response is obtained from time-step integrated computer simulation of the experiment.

DISCUSSION

The inaccuracies and the data-processing time can be greatly reduced by use of more sophisticated equipment. A good alternative might have been the use of CCD camera equipment usually used in gait labs instead of the regular VHS equipment. Such equipment was not available at the time these experiments were scheduled. Another improvement can be conceived in using an automated frame- grabber instead of manually digitizing the videograph. Nonetheless the experiment can be considered a success insofar as the obtainment of reasonable values of spring and damping constants of the torso are concerned. A mechanical mannikin incorporating these kinematic parameters is now under construction. It is hoped that when the mannikin is used as a substitute for a real occupant it will help illuminate various aspects of the system under study, without unduly inconveniencing human subjects. We also plan to use more sophisticated equipment (viz ViconTM systems) for these studies on the mannikin.

REFERENCES

1. Jagocinski RJ, Hawthorne DL, Childress DS, VanVorhis R and Strysik J: ÒUsing a Time Delay to Alleviate Head Oscillations with an Electric WheelchairÓ RESNA 10th Annual Conf 1987.

2. Bennett L: "Powered Wheelchair" Bucking J of Rehab Res. 24(2):81-86, 1987.

3. Brubaker CE: "Wheelchair Prescription: an analysis of factors that affect mobility and performance" J of Rehab Res 23(4): 19-26, 1986.

4. Cooper R: "Intelligent Control of Power Wheelchairs" IEEE Engg in Medicine and Biology 423-431, July/Aug 1995.

.5. Winters J, Stark L and Seif-Naraghi AH: ÒAn Analysis of the Sources of Musculoskeletal System Impedance" J. Biomechanics 21:1011-1025, 1988.

6. Adrian MJ and Cooper JM: "Biomechanics of Human Movement"Benchmark Press, 1989.

ACKNOWLEDGEMENTS

We gratefully acknowledge Jim Weidhass for his helpful assistance in constructing the experimental setup. We also thank Faunne Anderson and Kizmet Tennial for serving as the human subjects in our experiments.

Debarag Banerjee Biomedical Engineering Dept University of Tennessee, Memphis 810 Madison Ave Suite 801 Memphis, TN 38163 Ph: (901) 448-7099 FAX: (901) 448-7387

Modeling Occupants of Wheelchairs

Modeling the Effects of Inertial Reactions on Occupants of Moving Power Wheelchairs