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Procedia lEinjEineineriiig 2 (22010) 3121-3126

Procedia Engineering

www.elsevier.com/locate/procedia

8th Conference of the International Sports Engineering Association (ISEA)

Development of low cost on-boarE velocity and position measurement system for wheelchair sports

Hai Xua*, Jang Ching Chuab, Michael Burtonb, Kefei Zhanga, Franz Konstantin Fussb,

AleksanEar Subicb

aSchool of Mathematical and Geospatial Sciences, RMIT University, 124 La Trobe Street, Melbourne, Victoria 3001, Australia bSchool of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Plenty Road, Bundoora, Victoria 3083, Australia

Received 31 January 2010; revised 7 March 2010; accepted 21 March 2010

Abstract

There has been an increase in popularity of wheelchair sports. It is necessary to develop mobile on-board systems to do measurements in field. This paper presents a low cost on-board velocity and position measurement system for field environments. In the system, two MEMS gyroscopes and two GPS receivers are fixed on the rear wheels' axles. A Kalman filter is used to integrate position data with velocity data to produce accurate velocity and displacement estimations. The wheelchair's kinematics can be identified by using the estimations. All of the measurement data are transferred to a computer via a wireless network.

© 2010 Published by Elsevier Ltd.

Keywords: Wheelchair sports; On-board instrumentation; Mobile measurement

1. Introduction

In the last twenty years there has been an increase in the popularity of wheelchair sports [1]. As with all sports, the desire to improve performance is one of the primary concerns of coaches and competitors [2]. A number of offboard wheelchair sports monitoring systems have already been developed [3]. The popular approach used in these systems is to put the monitoring system on a static wheelchair ergometer which is a machine used to simulate the action of propelling a wheelchair for the purpose of training. Much research has been carried out in an attempt to correlate ergometer data and identify information relevant to making a real wheelchair 'go-faster'. However there are vital differences between performing practice drills on a static ergometer and playing on a court. The best ergometer for athletes is one which closely matches their training or competition.

It is necessary to develop mobile technologies and on-board systems which allow measurements in the field. A recent and increasingly analytical approach is to install the monitoring system on the wheelchair. Some on-board wheelchair monitoring devices, which claim to measure virtually every aspect of a wheelchair athlete's technique,

* Corresponding author. Tel.: +61-3-9925-1014; fax: +61-3-9663-2517. E-mail address: hai.xu@rmit.edu.au.

1877-7058 © 2010 Published by Elsevier Ltd. doi:10.1016/j.proeng.2010.04.121

have been developed and are available in the current market place [4]. However, current devices are relatively expensive, heavy and to some extent affecting the athletes' performance [5].

The rapid development of integrated circuit and micro-electro-mechanical systems (MEMS) technology has accelerated research and application of inertial sensors. The MEMS inertial sensors, including gyroscopes have many advantages in size, weight, integration, cost, power consumption and some additional features. But the MEMS inertial sensor is prone to significant instrument biases and drifts due to the noise, device instability and operational environments. For a long period of operation, the MEMS inertial sensor accuracy can be greatly degraded due to its drifting problem.

For wheelchair sports, the capability to provide reliable and accurate position is required and sometimes as well as the capability of continuous positioning and high updating rate. Global Positioning System (GPS) has become a widely used technique for positioning and tracking. However, signal jamming, obstruction, interference and the relatively low update rate are still the major limitations of the low-cost GPS receivers.

In order to improve the performance of measurements and increase the update rate of the positioning system, this paper deals with algorithmic developments of GPS and inertial sensor integrated measurement system. On one hand, the inertial sensor is a self-contained, high update rate device, which does not suffer the signal propagation problems, such as the multipath effects and obstructions, and can produce more continuous positioning estimations. The integration of GPS and inertial sensor system, to some extent, can overcome the problems caused by GPS outage and the update rate can be significantly increased by using the low-cost, high update rate inertial sensor. On the other hand, the GPS positioning method is drift-free, so it can be used as the reference in the inertial sensor error models to deal with the drifting problem. An Extended Kalman Filter (EKF) based algorithm is developed to integrate these two systems.

Nomenclature

r radius of wheel

L length between two wheel-axles

Wleft rotational speed of left wheel

Wright rotational speed of right wheel

m turning angular speed of wheelchair

e deflection angle of wheelchair

Vleft linear speed of left wheel-axle

bright linear speed of right wheel-axle

Vmid linear speed of middle point between two wheel-axles

xleft x-coordinate of position of left wheel-axle end

yleft y-coordinate of position of left wheel-axle end

flight x-coordinate of position of right wheel-axle end

bright y-coordinate of position of right wheel-axle end

xmid x-coordinate of middle point between two wheel-axles

Jmid y-coordinate of middle point between two wheel-axles

2. On-board Velocity and Position Measurement System

2.1. Structure

Two three-dimension (3-D) MEMS gyroscopes and two low cost GPS receivers are used in this on-board measurement system. Fig. 1 is the structure diagram of a rugby wheelchair. One 3-D gyroscope and one GPS receiver are mounted on the axle end of the left wheel, seen in Fig. 1(a), and the other 3-D gyroscope and GPS receiver are on the axle end of the right wheel, showed in Fig. 1(a) and (b).

As shown in Fig. 2(b), one device integrated with a 3-D gyroscope and a GPS receiver is mounted on the axle of the right wheel. The other one is mounted on the axle of the left wheel.

Fig. 1. (a) Front-view of the rugby wheelchair; (b) left side-view of the rugby wheelchair.

2.2. Algorithm

A wheelchair with an athlete is a physical example of a dynamic system. The motions of the wheelchair and the athlete are governed by laws of motion that depend upon their current positions and velocities. As the wheel radius is r, the relationship between the rotational speed of the left wheel wleft and the linear speed of the left wheel vleft can be written as

Wleft = Vleft / r , or Vkft = Wf r

And the relationship between the rotational speed of the right wheel Wright and the linear speed of the right wheel bright can be written as

Wright = Vright / r , or Vright = Wright r (2)

Consider the fact that the difference between vleft and vright will produce the deflection of the wheelchair. Let the initial deflection angle 00 = 0, as diagramed in Fig. 3(b), for any instant t, the relationship between the turning angular speed m and the deflection angle 0 can be written as

m = d0/dt (3)

Fig. 3. Diagram of on-board velocity and position measurement algorithm. (a) overhead view of the movement of a wheelchair with an athlete; (b) diagram of the movement, describing the variables and the relationship among them.

As the length between the two wheel-axles is L, illustrated in Fig. 3(b), one can obtain the following relations:

Vleft = Vmid - mL / 2 , Vright = Vmid + mL / 2 (4) For the wheelchair position, the general form can be written as

-left = -mid - (L COS0)/ 2 , yleft = Jmid - (L slu0)/ 2 (5)

bright = -mid + (L COS0)/ 2 , yright = ymid + (L Slu0)/ 2 (6) Through measuring the rotational speed and position of the two wheel-axles, one can obtain

*mid = bright + -^left) / 2 (7)

ymid = (yright + yleft) / 2 (8)

Vmid = (Wright r + Wleft r) / 2 (9)

0 = tg_1[(yright - yleft) / (-right - -left)] (10)

m = (Wright r - Wleft r) / L (11)

2.3. EKF Algorithm

The EKF is used in the algorithm for integration positioning in order to provide a continuous and reasonably accurate measuring and positioning service. Let xmid, y^, v^d, m, 9 and L be state variables, and xleft, yleft, wleft, xright, yight and WjigM observation variables. They are collected into two single vectors:

S = [Xmid ymid Vmid 9 m L]T (12)

z = [xleft yieft wleft xright Jright Wrightf (13)

Suppose that a measurement has been made at time tk and that the information it provides is to be applied in updating the estimate of the state x at time tk. The measurement interval is At. The following discrete-time equations relate the state at the previous time step k-1 to the state at the current time step k

1 0 -Aisin0 0

0 1 Ai cos- 0 0 0

0 0 1 0 0 0

0 0 0 1 Ai 0

0 0 0 0 1 0

0 0 0 0 0 1

The discrete-time observation equation is given by

1 0 0 0 0 cosQ

0 1 0 0 0 sin Q

1 0 0 0 0 cosQ

0 1 0 0 0 sin Q

0 0 1 0 L 2 0

0 0 1 0 L 2 0

The position measured by GPS may not represent the wheelchair's current position but these values provide a significant contribution in eliminating the gyroscope drifts. That is because the kinematics of the user is relatively low (with the speed of less than 10 m/s) and the measurements by GPS are drift-free even though they contain errors caused by the GPS positioning errors. The EKF is implemented and provides the estimation of the errors in position and velocity determinations according to the referencing measurement generated from the GPS. These estimated errors are then used to correct the gyroscope velocity estimation.

3. Experiments

The low cost on-board velocity and position measurement system for wheelchairs includes two MinimaxX modules. Each of them contains a tri-axis 100 Hz MEMS gyroscope, a low cost 5 Hz GPS receiver and a wireless network transmitter. Fig. 4 shows the two axes positioning results with the reference true position values and EKF filtered position value. The significant drift in gyroscope is greatly eliminated by the integrated GPS. The

1 f'l-, f / atCiA

True value

0 600 1000 1600 2000 2500 3000 3500 4000 4600

Fig. 4. the positioning results comparison. (a) X-axis position, (b) Y-axis position, (c) velocity value, (d) velocity angle.

measurement system, which uses EKF for smoothing the GPS positioning estimations, provides low positioning and velocity error RMS.

4. Conclusion

A low cost on-board velocity and position measurement system is developed for wheelchair sports with two gyroscopes and two GPS receivers. A new algorithm of integrating the gyroscope estimation and GPS positioning has also been developed. The algorithm uses an EKF combining the gyroscope local geographic navigation frame mechanization and the GPS approach together. It improves the positioning update rate from 5 Hz to 100 Hz and maintains the positioning accuracy. Theoretically, this integration method can provide more reliable estimation based on the wheelchair kinematic characteristics rather than simply smoothing the estimations.

References

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[2] Chowa John W. , Chae Woen-Sik. Kinematic analysis of the 100-m wheelchair race. Journal of Biomechanics 40, 2007; p. 2564-2568.

[3] Faupin Arnaud, Campillo Philippe, Weissland Thierry, Gorce Philippe, Thevenon André. The effects of rear-wheel camber on the mechanical parameters produced during the wheelchair sprinting of handibasketball athletes. Journal of Rehabilitation Research & Development Vol. 41, No. 3B May/June 2004; p. 421-428.

[4] Koontz Alicia M., Cooper Rory A., Boninger Michael L., Yang Yusheng, Impink Bradley G., van der Woude Lucas H. V.. A kinetic analysis of manual wheelchair propulsion during start-up on select indoor and outdoor surfaces. Journal of Rehabilitation Research & Development Vol. 42, No. 4 July/August 2005; p. 447-458.

[5] Dabonnevillea M., Kauffmanna P., Vaslina P., de Saint R'emy N., Cou'etard Y., Cid M.. A self-contained wireless wheelchair ergometer designed for biomechanical measures in real life conditions. Technology and Disability 17, 2005; p. 63-76.