Analysing and classifying wheelchair movements from motion capture data

Analysing and classifying wheelchair movements from

motion capture data

Tilde Arvedson Anna Lundemo tildea@kth.se lundem@kth.se

Degree Project in Engineering Physics, First Cycle, SA104X

Supervisor: Kjetil Falkenberg Hansen, Ludvig Elblaus Examiner: Mårten Olsson

Abstract

This is a project that describes a part of the development of a tool intended for wheelchair users in their learning process of new and important movements in everyday life and in sports. The process began with an investigation, with the help of people with wheelchair experience, of which movements that were considered important and which were considered useful in sports and in everyday life. The project was first focused on improving the technical skills of athletes practicing wheelchair sports. After studies and discussions it however changed focus, to also deal with obstacles in everyday life and to help people using wheelchairs to learn more everyday movements. After practical workshops, a mechanical analysis of the wheelchair was made. Some types of movement patterns, such as balancing on the rear wheels and turning, was considered essential to study and the goal was also to get information about for example the speed and acceleration of the wheelchair. This was to be analysed in real time and then sonified in later steps. We developed a code to recognize and assess these movements, which is the product of the project.

Sammanfattning

Detta är ett projekt som beskriver en del av utvecklingsprocessen för ett verktyg ämnat för rullstolsåkare i deras inlärningsprocess av nya och viktiga rörelser i vardagen och i sportsammanhang. Processen började med en undersökning, med hjälp av rullstolsburna, av vilka rörelser som ansågs svåra och vilka som ansågs användbara inom sport och i vardagen. Projektet var först inriktat mot att förbättra tekniken hos idrottsutövare inom rullstolssporter. Efter undersökningar och diskussioner bytte det dock senare bana, till att även handla om hinder i vardagen och att hjälpa rullstolsåkare att lära sig vardagligare rörelser. Efter praktiska workshops gjordes en mekanisk analys av rullstolen. Vissa typer av rörelsemönster, till exempel balansering på bakhjul och sväng, ansågs vara viktiga att studera och målet var även att få information om till exempel rullstolens hastighet och acceleration. Detta skulle analyseras i realtid för att sedan sonifieras i senare steg. Vi utvecklade en kod för att känna igen och bedöma dessa rörelser, vilket är produkten av projektet.

Contents

2.3 Different types of wheelchairs . . . 7

2.4 Sports studied . . . 8 2.4.1 Classification . . . 8 2.4.2 Wheelchair rugby . . . 8 2.4.3 Wheelchair basketball . . . 9 3 Method 10 3.1 Experimental setup . . . 10 3.2 Workshop . . . 10 3.3 Field research . . . 13 3.3.1 Observing athletes . . . 13 3.3.2 Interview . . . 14 3.3.3 Conclusion . . . 15 3.4 Taxonomy . . . 15 3.4.1 Movements . . . 16 3.4.2 Definition of stability . . . 17 3.5 Coding . . . 18 3.5.1 Tools . . . 18 3.5.2 Calculations . . . 19 4 Result 23 4.1 Distinguishing the movements . . . 24

5 Discussion 25 5.1 Future research . . . 26

6 Acknowledgments 27

List of Figures

1 Scheme of the classification procedure in wheelchair rugby . . . 9

2 Placements of the rigid bodies . . . 12

3 Scheme of the wheelchair . . . 16

4 Timeline of the coordinates . . . 20

5 Scheme of compatible movements . . . 23

6 Scheme of the output for each movement . . . 24

List of Tables

1

Introduction

The development of new wheelchair techniques has in the last twenty years of the twentieth century not been noticeably advancing. In 1970 the first competitions in wheelchair slalom were held in Sweden, leading to an increasing public interest of wheelchair sports. Also, new wheelchair techniques were developed by the athletes. Wheelchair slalom had already been practiced for twenty years in other parts of the world, but 1988 the sport was removed from Paralympics. Then, the interest for wheelchair slalom decreased in Sweden and fewer new wheelchair techniques were developed [1]. Therefore it is necessary not to be satisfied with the current technology but to continue to push forward towards new innovations. This study is a part of a greater research project performed by The Institution for Media Technology and Interaction Design at Kungliga Tekniska Högskolan. The purpose of the project is to develop an efficient method for learning how to maneuver a wheelchair and the idea is to produce a program that can identify specific wheelchair movements and connect these to different sounds. The later process is called sonification. The sound is to tell the executor if the movement is being properly done. This could be essential for people wanting to sharpen their techniques or for people who have recently become chair bound. The program is also supposed to function as a way of creating music by moving the wheelchair around.

The focus of this report is how to model certain important wheelchair movements and how to classify and distinguish them. These specific movements are further described in Section 3.4.1. This project demanded both a mechanical analysis as well as implementing code. Also, a lot of background research had to be done before starting the actual project in order to obtain a greater understanding of the wheelchair, the person managing it and which movements that are difficult and/or important. Hopefully, the research project will after completion be a useful tool for people using wheelchairs in their learning and improvement process.

2

Background

2.1 Sonification

Sonification refers to the technique to provide sound response to data and is the core com-ponent of Auditory Display which includes all comcom-ponents of a human-machine interaction system, from the technology like headphones and speakers to the gathering of data to the processing. It is an interdisciplinary field of research and is used in, among others fields, bio-medicine, psychology and pedagogy [2]. In this project, sonification will be used as a response to certain components of wheelchair movements.

2.2 Related Work

One of the studies looked at early in the process was Movement and muscle activity pat-tern in wheelchair ambulation by persons with para-and tetraplegia by Schantz, Björkman, Sandberg and Andersson. In this study, the maximum speed and arm-stroke frequency between people with paraplegia and tetraplegia respectively, was compared [3]. People with different injuries may have different difficulties when maneuvering a wheelchair, and a wider understanding of these handicaps was proven to be important in the process of this project. Paraplegia is the concept of a spinal chord lesion that has caused paralysis in legs and trunk whereas tetraplegia means paralysis in legs, trunk and arms [4].

The technique of sonification for athletic purposes has been used before, for example by Schaffer and Gehret who used it to optimize the technique of rowers [5]. The goal of their research was similar to the purpose of this project: that with help of sonification aid athletes to achieve maximum results in their training. The technique was used and evaluated in training with the German Rowing Association. The idea was that changes in certain movements that is difficult to discover at eyesight, could affect the rowing boat significantly. Shaffer and Gehret states that the system of sonification successfully helped the rowers to improve their techniques.

2.3 Different types of wheelchairs

In order to find which movements that would be interesting to study, a brief investigation of how a wheelchair is built and how the human body can affect its movements was made. Wheelchairs can either have straight or tilted wheels. Tilted wheels are used in several wheelchair sports as for example basketball, rugby and dancing [6], while straight wheels are used in daily life as well as for example in extreme wheelchairing [7].

One advantage with a wheelchair with tilted wheels is that it is laterally more stable and does therefore not flip over as easily as a wheelchair with straight wheels [8]. This is partly due to a friction force from the ground onto the wheels. In a static state, the force from the ground onto the wheels will be represented by the total gravitational force of the human body and the wheelchair. Thus, there is no friction force from the ground onto wheels that are straight. On the other hand, the force on a tilted wheel can be decomposed into one force perpendicular to the wheel axis and one force parallel to the ground [9].

However, tilted wheels result in a higher momentum on the wheel axes. The force on one wheel can be decomposed into forces perpendicular and parallel to the wheel axis. The perpendicular force, F , will with the moment arm x cause a momentum, M , as M = x · F on the wheel axis. This will cause a risk for it to break. For the case with straight wheels, this will not be a risk since there will ideally not be a force parallel to the wheel axis.

Furthermore, the pressure, P , on the wheels should be smaller in the case with straight wheels since a greater wheel area, A, is in contact with the ground P = F

A [9].

The human body’s effect on the movements of a wheelchair was further investigated in Section 3.2.

2.4 Sports studied

2.4.1 Classification

Many wheelchair sports use a form of ranking system to classify the athletes’ functional abilities. Officials evaluate the athletes’ ability to perform sport specific movements. The athletes are thereafter given a point corresponding to their abilities. Figure 1 [10] shows the classification system of wheelchair rugby described below.

2.4.2 Wheelchair rugby

Famous from the Academy Award nominated documentary Murderball [11], which is the original name of the sport, wheelchair rugby is played professionally in 25 countries, with Australia as the top-ranked nation. The athlete is after the classification process divided into one of seven groups, where each group is associated to a point ranging from 0.5 to 3.5, with 0.5 corresponding to the athletes with the most disability for rugby playing. Each team has a maximum of four players on the court at any time and these four players’ points are allowed to sum up to a maximum of eight. To decide the athlete’s group, officials observe the athlete when performing a variety of movements, including stopping, tackling and pushing. The athletes’ limbs are judged on characteristic rugby qualities like strength and flexibility and they are evaluated on how well they can perform typical movements, like throwing a ball. The wheelchair handling skills are evaluated both at practice and during games [10].

Figure 1: Scheme of the classification procedure in wheelchair rugby

2.4.3 Wheelchair basketball

Wheelchair basketball is with its estimated 100 000 practitioners one of the largest handicap sports in the world. The rules are similar to those of standard basketball, but somewhat modified. For example, it is against the rules to touch the wheels more than twice after receiving or dribbling the ball. The athlete must instead pass, bounce or shoot the ball before touching the wheels again. In basketball the classification system goes from 1.0 to 4.5 and a team cannot have more than 14 points in total on the court at the same time. There are three main points that classifiers look at to determine a persons point; trunk function, lower limb function and upper limb function [12].

3

Method

3.1 Experimental setup

The workshop (see Section 3.2) was held in a newly build motion capture laboratory at the campus of Kungliga Tekniska Högskolan in Stockholm. The laboratory was approximately 25 m2 large and equipped with 16 infrared cameras that emitted infrared light and detected the rigid bodies that reflected this light. The cameras, that are of the model Prime 41 by the brand Opritrack, has a resolution of 4.1 MP (2048x2048) and takes 180 frames per second [13].

3.2 Workshop

It was necessary to hold a first workshop to obtain a greater understanding of which move-ments that are difficult to master, which parts of the body that are most involved in each movement and other questions that only people with wheelchair experience could answer. The participant in the workshop was a 16-year-old male, with a congenital Cerebral palsy disorder. He is currently in a wheelchair rugby team, but has only driven a wheelchair by himself daily for about five or six years. He believes that the body parts most involved during the practice of his sport are the shoulders, upper back, the chest and the triceps. The wrist is more important in everyday life than during rugby practices, the reason being that you during the practices often use a sort of glue to get a better grip on the wheels. Many players have very little movement in the wrist and the glue helps them with this. The workshop participant said that it is very common for people in wheelchairs to have spina bifida (split spine) and therefore not have that much strength in the torso, which is a disadvantage.

One movement that the participant expressed that he wanted to master was to turn the chair without using his hands and arms. He said that this would be very beneficial in his sport because then the turn would be faster, since using the hands slows the chair down. Five rigid bodies, each consisting of three markers, were fastened on the wheelchair and on the participant’s body, as shown in Figure 2. A thin bar with the three markers in a horizontal row was placed over the ankles in the front of the wheelchair (Figure 2c). Three markers in a triangular formation were fastened on each of the wheels (Figure 2b), on the upper arm and on the lower arm (Figure 2a). The thought behind the placement of the markers was to get a good orientation of where the wheelchair was in the room and to track the arm movements, since the participant during the interview said that the relative movements of the under- and overarm is important in steering, turning and stopping. The markers were placed on his right side, since that is his strongest side.

Several movements were recorded: going straight forward, backwards, going in a circle, zigzag and going up on, balancing and driving a little bit on the rear wheels. The last mentioned is a very important movement since it is required for going over thresholds and similar situations [1]. The limitations were the small space and also that the participant, as he himself stated, is not a world class rugby player.

(a) (b)

(c)

3.3 Field research

3.3.1 Observing athletes

To investigate what movements that are essential or hard to master for high levelled athletes, a training session with Akropol BBK’s wheelchair basketball team was attained. The team won silver medal in the Swedish championship 2015 [14] and several of the athletes were professionals. There were six athletes and one trainer, who were not himself in a wheelchair. The athletes had their own wheelchairs and the training lasted for one hour.

In an interview with the athletes after the workout the following was told: First, everybody had their own personally made wheelchair with different features. All of them had two rear wheels and two small wheels in the front. However, some chairs had one small wheel in the back, just behind the rear wheels, whereas others had two. The difference was that with one wheel in the back the wheelchair turns more easily but it will at the same time be more unstable. Secondly, there is a huge difference between daily life wheelchairs and wheelchairs used for sports. One interesting difference is that in sport wheelchairs the centre of mass is behind the wheel axis of the chair, as opposed to everyday life chairs where it is right above the wheel axis. This results in the sport wheelchair responding better when turning and that it does not flip over as easy as an every day life wheelchair. Furthermore, a wheelchair with a high chair has the advantage of the athlete being closer to the basket, whereas a wheelchair with a low chair has the centre of mass close to the ground and is thus more stable and appropriate for athletes with bad balance. Last, the more tilted wheels the better the rotation of the wheelchair.

Moreover it is important to have a good connection between arms and body in every movement. Also, the position of the torso and the hip play a great role in every movement and what type of injury one has affects greatly what movements one manages.

The trainer further stated some differences in trainings for beginners and athletes on elite level. In the lower levels, the technique exercises mainly treat changing movements, for example changing between going straight forward, turning, stopping and going backwards. On elite level the focus is primarily on controlling the basketball within the movements. Furthermore, observations were made during the workout. A scheme describing some in-teresting movements follows.

Reaching high speed: The athletes’ bodies were tilted forward and following the arm movements during the entire movement. According to the trainer, two of the athletes were especially good at reaching high speed. When trying to observe the difference between these two and the other athletes, one could notice a slight difference in the way their bodies moved. The body movements of the two especially talented athletes were smoother and followed the movement patterns of the arms more adequately, resulting in the wheelchair

movement also being smoother. For all the athletes the wheelchair alternated between having weight on the front wheels and the rear wheels. According to the athletes, it is desirable to reduce the tilting of the chair as much as possible, in order to maximize the effect in the direction parallel to the floor.

Rotating: When going straight forward, a rotation could be done by simply moving one of the wheels backwards.

Turning: A turn could either be done with one hand, two hands or with no hands. With two hands, it could be done by moving one wheel forward and one backwards. With one hand it could be done by only moving one wheel forward or only moving one wheel backwards. When one or two hands were used it varied if the upper part of the body were used or not. Some athletes tilted the body a lot, whereas others did not. If no hands were used, it was the tilting of the upper part of the body that resulted in the wheelchair turning. According to the trainer the movement of the trunk and the hip is often essential when turning.

Stopping: Stopping could either be done by tilting the body to one side while moving the opposite wheel backwards with the respective hand. It could also be done by stopping the wheels with both hands and tilt the body backwards.

Tilting: The athletes stated that tilting the wheelchair up on one of the rear wheels, was a difficult movement. According to the trainer it is important to manage this movement since it is essential to get closer to the basket. When one of the athletes showed this movement, the chair balanced on one rear wheel and one front wheel. According to the athletes, factors that play a main role when doing this movement, other than technique and balance, is the height of the chair, the size of the wheels and if leg muscles are present or not. However the athletes had different opinions on whether or not there was an influence of the later category.

Zigzag: Since this was a basketball team and the ball needs to be bounced by one hand (see Section 2.4.3), the athletes managed the movement often called zigzag. It was done by first moving the right wheel forward with the right hand and thereafter moving the left wheel forward with the left hand. Thereafter the right hand was again used to move the right wheel and so on.

3.3.2 Interview

In order to get a better perception of what stability on a wheelchair means, a rugby athlete was interviewed. First, he claimed and demonstrated that it is possible for the wheelchair to be completely still when balancing on the rear wheels. However, he said that this movement is difficult to learn.

Secondly, the athlete also claimed that one problem when learning how to balance is the lack of courage when tilting backwards, especially for drivers that have recently been injured. It is essential to tilt backwards enough to reach the equilibrium state of the wheelchair. There can be different equilibrium states, depending on if the driver’s body is tilted forward, backwards or being straight in the wheelchair. All wheelchairs have natural balancing states, i.e. equilibrium states, depending on how the body is orientated.

Furthermore, he stated that almost always when driving without balancing, both of the rear wheels are in contact with the ground. Thus, there should be no point in defining stability as how often a wheel is in contact with the ground, as previously thought. Last, the athlete described the two different ways of passing an edge, for example a kerb, from above. One option is to gain speed and then jump from the edge. The other way is to stop at the edge, start balancing on the rear wheels and then fall from the edge. Ideally, in both cases, one would like to land on the rear wheels and the front wheels simultaneously.

3.3.3 Conclusion

After the workshop, the observation of athletes and the analysis of different wheelchairs in Section 2.3, it was concluded that the body movements of the person in the wheelchair was to a great extent determined by which kind of handicap or what degree of paralysis they have. For this reason, the construction of wheelchairs is done in such a way that the chair is able to be greatly adjusted. The conclusion that was drawn from the workshop and the meetings with wheelchair experienced people was that it would be unnecessarily difficult to generalize the bodily movements of the person in a wheelchair and it would be more beneficial to only model the movements of the wheelchair. The task would have been too complex for this project. Moreover the goal is for this tool to be used by many different people with different handicaps, without grand adjustments to the program. It was thus decided that the task would be to model only the movements of the wheelchair and ignore the person’s impact on it. It was also decided only to analyse the movements of a straight wheeled wheelchair. A few crucial movements were decided and the analysis of them is described in Section 3.4.1.

3.4 Taxonomy

A taxonomy, meaning a classification of several key movements in wheelchair driving, was constructed. The mathematical algorithms that was later used in analyzing the movements were developed in this stage. The importance was to distinguish one movement from another. How could one see for example, with only data coordinates, that the current movement is a turn and not a stationary rotation?

3.4.1 Movements

To get a clear view of the different parts of each movement, the wheelchair was divided into three parts: Rear wheel 1, Rear wheel 2 and Front wheels. These were analysed separately. Front wheels means the front part of the wheelchair, as indicated in Figure 3, since the front wheels cannot move independently of each other. The reason behind these distinctions is that the rigid bodies would be placed on these three places. Rear wheel 1 and Rear wheel 2 do not refer to specific wheels, it just means that one of the wheels behave in the described way and the other in the other way described. They could thus both refer to either the left wheel or the right wheel.

Figure 3: Scheme of the wheelchair

Movement Description Rear wheel 1 Rear wheel 2 Front wheels

Turning The wheelchair is moving along a curved line

Moving in circu-lar line

Moving in circu-lar line, radius of curvature dif-ferent from rear wheel 1

Stationary rotating

The wheelchair is rotating around its own axis

Moving in circu-lar line

Ideally station-ary, or having a very small radius of curvature Rear

wheel balancing

The front wheels do not have contact with the ground No contact with the ground Going straight Ideally moving along a straight line Ideally infi-nite radius of curvature Ideally infi-nite radius of curvature Ideally infi-nite radius of curvature Falling from height Starting from height, leaving it and falling to the ground

Speed in -ˆz Speed in -ˆz Speed in -ˆz

Table 1: Table analysing the movements studied

The empty squares in Table 1 indicates that the category does not need to be checked in order to classify the movement.

3.4.2 Definition of stability

In each movement a definition of stability is used to describe how stable the movement was. However, “stability” could be defined in several different ways. Here, four different definitions were used. First, when balancing on the rear wheels, the height difference of the front wheels was used to describe the stability of the wheelchair. Also, the equilibrium state when balancing should be measured for each individual before the program is run.

Then, the difference between the actual height and the height of the equilibrium state can be sonified. Since the equilibrium state can vary, see Section 3.3.2, the participant needs to specify the position of the body in advance, and be consequent when balancing on the rear wheels.

The second stability defined was the ability to follow the direction of a movement. For example, when going straight forward or backwards, perfect stability means going on a perfectly straight line. When turning, perfect stability would mean that the line in which the turn is done is a perfect circular curve, and when rotating perfect stability means that the inner wheel has the same position throughout the movement. In order to investigate the stability for these three cases, a radius of curvature was defined, see Equation 9. Thus, for perfect stability, the radius of curvature should be infinite in every time step t, when going straight. When turning, the radius of curvature should be the same throughout the turn, and when rotating the radius of curvature of the inner wheel should be zero.

The third type of stability studied is when the wheelchair is falling from an edge to the ground. As stated in Section 3.3.2, one would like to have both rear wheels at the same height at all times during the fall, to increase the likelihood of landing evenly on the ground. Last, if someone is secure and experienced in balancing on the rear wheels, the person can stand very still, both regarding the front wheels as previously described, and in moving the rear wheels. For someone less experienced, this person will move the rear wheels forward and backwards a little to become more stable. In excess of the height fluctuations of the front wheels, in the movement of balancing, the stability regarding the movements in the rear wheels is also computed.

3.5 Coding

3.5.1 Tools

The main parts of the process from the raw data obtained from the motion capture system to the sonification can be described by this figure:

M oCap ⇒ [ ] ⇒ Analysis ⇒ [ ] ⇒ Sonif ication

MoCap is the motion capture system, in which data is gathered. In the first empty box the data obtained from the motion capture system is processed, in order for it to be analysed in Analysis. In the second empty box, the format of the analysed data is once again changed, in order for it to be sonified in Sonification.

The part of this figure that this report touches upon is the Analysis. It is supposed to analyse the data coordinates from the motion capture markers and to pass on information

to the sonification program. The programming language used during this process was Python 3.3.

As mentioned in Section 3.4, the analysis is based on the assumption that the motion capture system register three rigid bodies, each one composed by three markers. The positions of the rigid bodies is set to be in the middle of the three markers. One rigid body is fastened on each of the rear wheels as in Figure 2b and one over the ankles as in Figure 2a. The data is coming in as three dimensional euclidean coordinates and the markers on the rear wheels also gives information about the rotational speed of the wheel as quaternions. This gives sufficient data to compute speed, acceleration, position etc. at a minimal load of data. It is necessary to have rigid bodies on each of the rear wheels that it for example will be possible to see if both wheels hit the ground at the same time in a fall. The markers at the front wheels are necessary to see if the wheelchair is going forward or backwards and to distinguish balancing on the rear wheels.

3.5.2 Calculations

Certain movements, described in Section 3.4.1, were chosen to be modelled and explained mathematically in Python. A description of the features that is needed to describe the movements follows. The features are being calculated in real time, with data incoming from the motion capture system, see Section 3.5.1. In order for the program to work, the motion capture system must be calibrated and the neutral height z0 specified before the

measurements start. k represents the coordinate (x, y, z) at the current time, k0 represents

the coordinate a time t earlier and k₁ the coordinate in between. Before the program is run, some parameters must be specified.

z0 is a vector with the height over the ground for the three rigid bodies. It is measured

when the wheelchair stands on the ground, without balancing or being on a height. zf all is the height of the front wheels when the wheelchair flips over backwards from a

balancing state.

zdif f is the height difference between the rear wheels and the front wheels. This can be

calculated from z₀.

Furthermore, initial values must be specified. r0, the initial radius, and v0, the initial

velocity, are initially set to zero, and the initial coordinate values k₀ and k₁ are specified. When the program is run, z0, zdif f and zf all have the same values throughout the whole

session, while r0, v0, k0and k1are constantly being redefined. If k is the current coordinate

and k0 was the coordinate a time t earlier, the following will happen before the program is run again, with k as the current coordinate: k0 = k01, k1 = k0 and v0 = v0, as illustrated

Figure 4: Timeline of the coordinates

Velocity: The velocity is calculated in each time step t as the distance travelled, k − k0,

divided by the time step t.

v = ∆k/∆t = k − k0

t (1)

Acceleration: The acceleration is calculated in each time step t, as the difference in velocity v − v0 divided by the time step t.

a = ∆v/∆t = v − v0

t (2)

Height: The height of the front wheels is the difference in the ˆz direction of k and z0.

Since the ground could be slightly uneven, a minimal height difference was defined. Under this limit no height difference will be shown. However, if the difference is greater than the limit height the movement will be interpreted as the wheel in question lifting.

h = ∆z = z − z0 (3)

Direction: This function investigates if the wheelchair is moving forward or backwards. Here, the difference between the coordinates of the front wheels kF and the rear wheels kR

are compared with the velocity. The values of the coordinates in the ˆx direction are first compared. If the coordinate difference between the front wheels and rear wheels is zero, i.e. the wheelchair does not move in the ˆx direction, the values in the ˆy direction are instead investigated. The result will be the same regardless of which of the ˆx or ˆy directions that is investigated first, thus the order does not matter. Looking in the ˆx direction:

kFx − kˆ Rx > 0 and v ˆˆ x > 0 ⇒ the wheelchair is moving forward

kFx − kˆ Rx > 0 and v ˆˆ x < 0 ⇒ the wheelchair is moving backwards

kFx − kˆ Rx < 0 and v ˆˆ x < 0 ⇒ the wheelchair is moving forward (4)

kFx − kˆ Rx < 0 and v ˆˆ x > 0 ⇒ the wheelchair is moving backwards

kFx − kˆ Rx = 0 ⇒ check the ˆˆ y direction

Angle velocity: This function gives information about the angle velocity of a wheelchair when turning. It is thus not the angle velocity of the wheels that is received. The angle between the two vectors k and k0is calculated and divided by the time step t. The function

also calculates laps per second, laps per meter and laps per meter per second. Angle velocity:

ω = cos−1 k0· k |k0||k|



/t (5)

Laps per second:

n_laps/s = ω

2π (6)

Laps per meter:

nlaps/m=

ω 2π ·

1

|v| (7)

Laps per meter per second:

n_laps/m·s= ω 2π·

1

Radius of curvature: In order to calculate the radius of curvature for a wheel, three position coordinates are needed, one at k, one at k0 and one at k1. The formula used is:

W = |k − k0|, H =     k1− k − k0 2     , R = W 2 8H + H 2 [15] (9) Centripetal Acceleration: Here, the centripetal acceleration in a turn is calculated. It is calculated as the square of the angle velocity multiplied by the radius of curvature.

a = ω2r (10)

Except for these functions that treat straightforward definitions of movements, a few defi-nitions of stability were made, as described in Section 3.4.2.

Steady path: This definition of a steady driving path is that the radius of curvature is constant during the entire movement.

Steady height: The function investigates the stability of the wheels when lifted up from the ground. The stability is defined as the fluctuation in height, i.e. the two ˆz-coordinates in one time step t are compared.

Steady wheel: The rotation of the rear wheels is a measure of the stability when balancing. As stated before, the rotation is detected in the motion capture system as quaternions. This definition was however not implemented in the code.

Steady fall: When the wheelchair is in free fall, the height difference between the rear wheels is calculated. If the difference is zero, the wheelchair has perfect stability.

4

Result

Figure 5: Scheme of compatible movements

The scheme shown in Figure 5 indicates in which order the movements are checked in the program. They are checked from the top to the bottom in the figure. When a new coordinate enters the program, it is first investigated if the wheelchair is moving or standing still. If it is moving, the four movements connected to Moving are checked. First it is checked if the wheelchair is moving forward or backwards. Secondly the type of movement is investigated, i.e. if it is a turn, a rotation or if it is going straight. Thereafter, independently of whether the wheelchair is at a standstill or moving, it is tested if the wheelchair is on the ground or over the ground. Finally, if the wheelchair is on the ground, it is checked whether it is balancing or not. However, if the wheelchair is over the ground it is also checked if it is falling.

The movements that are parallel to each other in the scheme are not compatible, whereas all movements that are on different levels in the scheme could be combined, except for Still and Falling. Thus, the total movement of the wheelchair is described by one and only one movement from each level in the scheme. However, the movements that are connected with Moving are not compatible with Still, as the scheme indicates.

Figure 6: Scheme of the output for each movement

The output of the program is two lists. The first list has a position for each movement, which contains 1 or 0 depending on if the movement is active or not. The other list contains most of the calculated data described in Section 3.5.2. In Figure 6 the output for each movement is shown. The reason that for example Not balancing is not shown in the figure, is that no further information than what is calculated in the former levels of Figure 5 will be added to the output list.

4.1 Distinguishing the movements

The procedure used to distinguish the movements follows the classification from Section 3.4.1. First, the magnitude of the velocity of the front wheels is checked and if it is greater than a certain threshold limit value, the wheelchair will be registered as Moving. The threshold value is essential, since it must be taken in consideration that even if the wheelchair is still, it can make small movements. If it is moving, Equation 4 is used to see whether the wheelchair is moving forward or backwards.

Thereafter, Equation 9 is implemented to calculate the radius of curvature of the wheelchair. The radius will of course be different for the different rigid bodies (placed on the different wheels), but in the case of a straight motion, all the wheels will have close to an infinite

radius of curvature. Only one of the wheels needs to be checked to characterize a straight movement, for simplicity one of the rear wheels is used. If the radius of curvature of the studied wheel is not very large, it is checked if it is very small, close to zero. If it is, it is certain that the movement is a Rotation. If it is not close to zero, the other rear wheel is checked, and if that as well differs from a very small limit value, the movement is a Turn. The values that will be used to distinguish between the movements must be specified (see Section 5).

Continuing, the ˆz-coordinate of one of the rear wheels is compared to the z0 value of this

specific wheel (see Section 3.5.2). If it differs by a value greater than a limit value, it is obvious that the wheelchair is over the ground. The reason that a limit value has to be specified is that there can be irregularities on the ground. If the difference is smaller than the limit value, the wheelchair is standing on the ground and the front wheels are checked to see if it balances. If its ˆz-coordinate differs from the ˆz-coordinate of the rear wheels by less than z_{dif f}, (again, see Section 3.5.2), it is balancing. Returning to the case where the wheelchair is over the ground, as seen in Figure 5, there are three possibilities. First, the speed in the ˆz direction is checked for one of the rear wheels. If it is not zero, the wheelchair is in the air, falling from an edge. If it is zero, the same procedure as described above is used to see if it is balancing on this edge.

5

Discussion

When trying to find important movements to study it has been very helpful to meet peo-ple with wheelchair experience. Since we started this project without any knowledge of wheelchair driving it has also been essential to meet a variety of people, with different kinds of injuries and different kinds of experiences. We have met people that have had wheelchair experience their whole life, and people who got injured as grown ups. Listening to different stories and comparing movements from people with different backgrounds has been helpful when trying to get a greater understanding of wheelchair driving.

Moreover, observing athletes when practicing different movements has widened our percep-tion of wheelchair driving. There were various movements that the athletes showed during the training session with Akropol’s BBK which we had no idea existed or did not think were possible to manage with such great precision. On the other hand, conversing with people with wheelchair experience resulted in a greater understanding for difficulties in wheelchair driving, and also made it easier to decompose movements into smaller parts in order to analyse them.

As described in the introduction, this report covers, among others, a part of a process which is supposed to lead to a program in which people who want to improve their wheelchair technique will get real time feedback on their movements. In order for the program that

has been developed in our part of the process to work properly, the values of the radius of curvature that is used to distinguish between Turn, Rotation and Straight needs to be specified. Recordings in which a participant has to do these three different movements must be done, and for each movement the radius of curvature must be calculated according to the formula described in Equation 9. Then, one value that distinguishes Straight and Turn and one value that distinguishes Turn and Rotation will be found. However, there were not time to do this in this project.

As indicated in Section 2.1, a sonification process follows this project. The aim is to have different sounds for the different movements and to sonify the features connected to each movement (see Figure 6). Hopefully, when the sonificiation process is completed, the program will be an efficient tool for helping people in wheelchairs improve their technique.

5.1 Future research

While working with this project some interesting ideas for further research arose. In Sec-tion 3.3.1 the smoothness in the movement of the wheelchair when having high speed was discussed. It would be interesting to study how the body movements should be done in or-der for the efficiency forward to be as great as possible, i.e. how to increase the smoothness. Furthermore, it should be interesting to investigate how the movements of a wheelchair are affected by the body movements when turning, since these seem to differ a lot between ath-letes. Another interesting aspect would be to analyse how to change movement efficiently, which the trainer for Akropol BBK’s wheelchair basketball team pointed out was difficult to master for beginners and semi professionals (see Section 3.3.1). It would be interesting to investigate the effect of the body on the changes and how the speed of the movements of the torso affects the change of movement. Finally, one should investigate how different movements are affected by different injuries and in what movements the absence of certain abilities play the biggest role.

Another difficult and therefore interesting movement that was explained by one of the inter-viewed athletes is to climb up an edge, for example a kerb, with the wheelchair. According to him, the rate of difficulty depends on the injury, i.e. the lack of musculature.

In this study, for reasons described in Section 3.3.3, only the wheelchair was analysed. Though, for one of the most common movements beginners are struggling with, that may not be enough. One of the athletes, who himself had worked with beginners, said that it demanded a lot of practice to find a good arm movement just to go forward. To get an even acceleration and speed, one needs to do a continuous pendulum motion with the arms, in order to follow the wheels with arms and hands. Many beginners are afraid to let go of the wheels and they therefor "stop" the movement and slow down the chair rapidly when the chair is in motion. This could also be interesting to research further.

6

Acknowledgments

We would like to thank our supervisor Kjetil Falkenberg Hansen and the other members of our team Ludvig Elblaus and Andreas Almqvist Gref. Also, we would like to thank Malcolm Halvarsson, Stefan Jansson and team members in Norrbacka HIF rugby team, Mike Perry and the basketball team Akropol BBK, Martin Bretz and Sebastian Forsén.

7

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