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A Humanoid Robot for Research into Kicking Rugby Balls
R. Flemmer and C. Flemmer1
Abstract
This paper describes the design of a life-sized humanoid kicking robot for research into kicking.
Computer vision software finds the goal posts and automatically adjusts the robot’s position to aim at
the centre of the posts. Pneumatic cylinders functioning as the rectus abdominus and quadriceps
muscles operate to get simultaneous maximum speed of the upper and lower leg and a foot speed of 21
m/s. The robot kicks the ball a distance of 45.6 meters +/- 1.2 metres. The distance is well up in the
range of professional kickers and the reproducibility in kicking distance is much better than that of
human kickers. High speed photography elucidates the actual kick.
Secondary pneumatics control the animatronic motions; prior to kicking, the robot takes a step forward
on its left leg, moves its arms and head as though preparing to kick and draws its right leg back into a
cocked position. These animatronic motions make the robot look uncannily human.
The strength, accuracy and reproducibility of the robotic kicker make it an ideal research tool to
investigate the mechanics, kinematics and dynamics of place kicking a rugby ball. Research using
human kickers is limited by the intrinsic variation in their kicking.
Keywords: robotic, humanoid, kicking, animatronic, rugby
1 Introduction
Research into kicking a rugby ball is handicapped by the inherent variation of human kickers; it is not
possible for a human to control the exact foot position, speed and point of contact on the ball from one
kick to the next. The aim of this work was to build a robotic kicking mechanism capable of kicking a
rugby ball in a consistent manner and kicking as far as professional rugby kickers. This could then be
used to research aspects of kicking such as the mechanics, kinematics and dynamics of place kicking a
rugby ball. While the primary aim was to build the research tool, a secondary aim was to make the
robotic kicker look attractive and stimulate interest in robotics. Consequently it was built with an
aesthetically pleasing humanoid form and endowed with animatronics so that it could mimic the
motions of a human kicker preparing to kick. Prior to kicking, the robot steps forward on its left leg,
looks up at the goal posts, looks down at the ball, adjusts its aim, moves its arms together, draws its
right leg back into a cocked position and its left eye glows red when it is locked onto target.
The upper and lower parts of the right (kicking) leg of the robot are moved using large pneumatic
cylinders and computer-controlled timing of the limbs so that the cylinder equivalent of the rectus
abdominus muscle and the cylinder equivalent of the quadriceps muscle mimic the motion of a human
kicker drawing his leg back and kicking while moving the upper and lower leg simultaneously. The
animatronic behaviour is also pneumatically-driven with smaller cylinders and less exacting timing
than is needed for the kicking. The robot is positioned roughly facing the goal posts. Images from a
CCD camera located in the robot’s head are used to find the post position and move a steering
mechanism which adjusts the position of the kicker until it is aiming directly at the goal.
The field of sports robots is reviewed briefly. Thereafter, the design of the kicking robot is described
together with some preliminary performance results.
1
R. Flemmer, C. Flemmer (corresponding author)
School of Engineering and Advanced Technology, Massey University, Private Bag 11 222, Palmerston
North 4442, New Zealand.
Email: [email protected] Tel: 64-6-356-9099 extn 7452 Fax: 64-6-350-5604
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2 Literature Review
A review of sports robots reveals two broad fields. The first and biggest field is research into general
robotics; including kinematics, artificial vision, navigation, obstacle avoidance, object recognition and
manipulation. Here, humanoid robot development is commonly benchmarked using competitions such
as Robocup where variations of autonomous soccer robots are tested against each other [16]. The
GuRoo [27], Qrio [10], DARwIn-OP [5] and Nao [4] robots are humanoid exemplars. There are also
table tennis robots named Kong and Wu [29], a pool playing robot [17], a martial arts robot [13] and
robotic baseball arms (a pitching arm [22] and a batting arm [23]). All of these robots move using
electric motors2 and are consequently very slow and weak [26]. For example, the robotic pitching arm
can achieve a maximum end effector speed of 6 m/s [22] while the top recorded pitch speed for a
human is 45 m/s [9].
The second and smaller field of sports robots is used for sports research and testing. Here, the emphasis
is on producing powerful mechanical machines rather than robots with humanoid form. There are
several robotic golf arms (reviewed in [2]), including Iron Byron used by the United States Golf
Association and by sports companies to test golf clubs and balls [26]. The Enhanced Automatic
Robotic Launcher, EARL, is a robotic arm used by the US Bowling Congress to test ten pin bowling
equipment such as lanes, balls and pins [6]. A robotic footwear tester is under development [20] but it
currently has a much slower impact time than a human and cannot simulate the human force trace [11].
A mechanical kicking machine for soccer and rugby balls is reported by Holmes et al., [8] and Adidas
are sponsoring further research in this area [3]. The kicking machine can get ball speeds in excess of 34
m/s [19]. Kensrud and Smith report the use of a pneumatic sabot style air cannon capable of projecting
balls at speeds up to 60.8 m/s and of commercial baseball pitching machines such as HomePlate and
Sports Tutor [12]. A robotic soccer-ball kicking leg called Roboleg was developed to test soccer balls
and footwear using spring-loaded actuators [20]. However Roboleg was abandoned as a test robot
because of problems with the control system [20].
In summary, sports robots with humanoid form are mostly used for general robotics research rather
than for sports research and testing because they are too slow and too weak to achieve the performance
levels of professional human players. Robotic machines without humanoid form can match (and
surpass) the strength of elite sports players and are used for testing sports equipment. They include
machines for testing golf clubs, ten pin bowling equipment, baseballs and the proprietary kicking
machine developed at Loughborough University [8, 19]. Rugby ball manufacturer, Gilbert, uses human
kickers to test new styles of rugby balls but more objective testing could be done with a robotic tester.
3 Design of the Humanoid Kicking Robot
3.1 Overview
The humanoid kicking robot is shown in Fig. 1. Its design is registered in New Zealand (design number
415366). It is 1.96 m tall, weighs approximately 200 kg and is constructed from aluminium plate.
Behind the robot is a black steel box enclosing the chassis of the robot with a steering mechanism and a
120-amp hour lead-acid battery to power the robot and its air compressor. Wheels on the box can be
lowered down so that the robot can be moved using the front pull bar. When this bar is lowered to the
ground it is used to position the kicking tee (Fig. 2).
The robot stands on its left leg and swings its right leg to kick. The ball is placed upon a standard
kicking tee whose position can be adjusted laterally and longitudinally on the pull bar. A mechanism is
used to position the ball vertically on the tee (Fig. 2) and this is removed before kicking. The kicking
leg is articulated at the knee so that the motion of the foot parallels closely that of a human foot during
kicking.
2
The exception is the Headless Batter, a pneumatically operated, spring-loaded baseball batting arm
described in [15]. However, this was not built for research and its performance is not quantified.
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Fig. 1 Schematic of the humanoid kicking robot
lateral
adjustment
front
adjustment
(a) Pull bar with adjustable kicking tee
(b) Pull bar detail and ball positioning mechanism
Fig. 2 Pull bar and ball positioning mechanism
3.2 Design of the pneumatically controlled kicking leg
Air cylinders are used to power the leg (Fig. 3). The upper cylinder, acting as the rectus abdominus,
has a diameter of 80 mm and the lower, acting as the quadriceps, has a diameter of 65 mm. Since the
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pneumatic system operates at 840 kPa (8.4 bar), these cylinders provide forces of 4,021 N and 2,655 N
respectively. Preliminary calculations indicated that this would give a foot speed comparable with that
of professional kickers.
The pneumatic circuitry for explosive kicking is sophisticated (Fig. 4). Commercial air cylinders are
throttled because excessive rod speed overheats the seals and leads to mechanical failure. Throttling is
achieved firstly by limiting the diameter of the ports and secondly using the back pressure from the
downstream side pressurised air. To overcome this, the ports were drilled as widely as possible and a
rapid-venting diaphragm valve was installed on the downstream side. This valve has a large diaphragm
exhausting to ambient and, when the pressure differential is appropriate, it provides rapid venting.
The strategy was to pressurize the downstream side of both cylinders via a pilot line, bleed the pressure
down until it approached atmospheric, at which point the diaphragm valve would open, and pressurize
the upstream side by means of a very large three-port solenoid valve. A very accurate time delay was
needed between the start of the rectus abdominus stroke and the start of the quadriceps stroke in order
to get both upper and lower legs to reach maximum speed at the point of contact with the ball. A
variation in the delay of 5 milliseconds would change the knee angle at the point of impact, causing the
foot to strike the ball slightly higher or lower, with profound effects on trajectory and speed. This
extreme sensitivity is not surprising because the whole period of contact between ball and foot only
lasts about 10 milliseconds.
Fig. 3 Detail of kicking leg
Immediately after the kick, the leg had to be decelerated carefully so that the pistons would not hit the
end of their travel too rapidly. A carefully timed set of valve closures allowed for a relatively smooth
deceleration. Even so, the jolt of each kick would move the robot out of position. Consequently, an
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automated aiming system was used to adjust the position of the robot before each kick. This is
described in the next section.
Fig. 4 Pneumatic arrangement for kicking
3.3 The animatronics control
The most important aspect of the animatronic control, in terms of kicking performance, is the accurate
aiming of the robot at a target. The robot is manually pulled into roughly the correct position so that the
CCD camera in its nose can see the goal posts. When the robot steps towards the ball on its left leg, it
has stable three-point contact with the ground (the left leg and two points at the rear of the chassis).
The robot is controlled from a laptop and artificial vision software recognises the vertical goal post and
operates a lead screw mounted transversely in the chassis so that the chassis moves until the robot is
positioned correctly (centred between the posts). The lead screw can move the chassis 100 mm on
either side of the centre point. When the robot has moved into position and is ready to kick, red LED’s
light its left eye.
Professional rugby kickers, such as Quade Cooper and Jonny Wilkinson, have a pre-kick ritual to get
correctly positioned. To make the kicking robot look more realistic, it was programmed with a similar
ritual; moving its head (up, down and sideways) as though watching the ball and the posts and bringing
its arms up prior to kicking. Each of these movements is controlled pneumatically with standard air
cylinders fitted with limit switches. Since the timings of these motions are not critical, the air cylinders
did not need any modification.
The kicking leg is very strong and potentially very dangerous. An ultrasonic sensor fitted to the robot’s
midriff ensures that the kicking sequence is only activated if there is no-one standing in front of the
robot.
3.4 Design analysis of performance
Table 1 shows the design parameters of the robotic kicker.
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Table 1 Design parameters
Parameter
Length of leg from hip to toe
Width of leg at the top
Width of leg at the bottom
Inertia of leg about hip joint
Volume of quadriceps cylinder
Swept volume of rectus cylinder3
Valve 1 (quadriceps) effective area
Valve2 (rectus) effective area
Reservoir pressure
Symbol
P0
Value
1.22 m
0.180 m
0.052 m
1.605 kgm2
424.1 cm3
502.7 cm3
34.5 mm2
210 mm2
840 KPa (gauge)
Source
Solidworks™ software
Solidworks™ software
Solidworks™ software
Solidworks™ software
SMC pneumatics
SMC pneumatics
SMC pneumatics
SMC pneumatics
Measured
The upper limit of performance for the robotic leg corresponds to the assumption of negligible energy
loss from aerodynamic drag on the leg as it moves and of zero friction in the tubes and solenoid valves.
If these assumptions are valid, the first law of thermodynamics can be used to calculate the maximum
achievable foot speed and ascertain whether this is similar to the foot speed of an elite kicker.
The first step in the analysis is to estimate the drag on the leg and the pressure losses in the valves and
tubes, to see whether they are, in fact, negligible.
3.4.1 Aerodynamic drag on the leg
The leg can be viewed as a wedge, tapering from a top width, , to a bottom width, , with length, .
Assume that it has a radial velocity, measured about the hip joint, of radians per second. Air flow
around the leg will be turbulent, so the leg has a drag coefficient, , of 1, i.e. that of a cylinder [17].
Obviously the flow near the hip will be laminar but this will make only a small contribution to the total
drag so that this imprecision will have a small conservative effect. Consider an elementary length of the
leg, , at a distance from the hip joint. It will have an elementary area,
of:
(1)
The velocity
at any distance
from the hip joint is:
(2)
So for a foot speed,
, the angular velocity is:
(3)
The drag force,
, acting on the elemental area is:
(4)
where
is the density of air (and at 20 oC and sea level is 1.204 kg/m3).
The elementary moment,
, on the leg about the pivot of the hip joint is:
(5)
which can be integrated over the length of the leg to give:
(6)
3
Note that the swept volume is not the same as the volume of the rectus air cylinder (1,005 cm 3)
because the cylinder is not fully extended at the point where the toe touches the ball.
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Substituting equations (1) to (4) into (6) and assuming the foot speed, , to be 26.4 m/s (that of an elite
kicker [1]) gives a moment, , of 11.5Nm resulting from air resistance to the motion of the leg.
The expected torque produced by the abdominal cylinder,
, is:
(7)
i.e., the magnitude of the cross product of the radial distance vector, , and the force vector from the
air cylinder, . The torque is about 500 Nm as measured from the Solidworks™ model, evaluated at
the point of impact with the ball. It is apparent that the moment due to air resistance is negligible by
comparison with the moment produced by the abdominal cylinder. Since this is evaluated at the point
of highest speed, and therefore greatest drag, the aerodynamic drag on the leg can safely be ignored.
3.4.2 Pressure drop across the solenoid valves
At the instant of opening of the solenoid valves, the flow is zero but, as the flow increases, the line
losses increase as the square of volumetric flow (assuming flow through the valves and tubes is not
laminar).
If flow across the valves was choked, we should have:
(8)
where is the downstream pressure, is the upstream pressure and
air has the value of 1.4. Since the flow is not choked:
is the adiabatic index, which, for
(9)
For a reservoir pressure of 840 kPa (gauge), this implies that the downstream pressure does not fall
below 443 kPa (gauge).
The solenoid valves were provided by SMC Corporation of Japan and conform to the JIS B 8374
standard. For the condition given in equation (9) (subsonic flow), the flowrate across the valve,
in terms of the “effective area” of the valve, ,is specified by SMC to be:
,
(10)
Where
3
3
is the volumetric discharge in dm /min (dm is a decimetre)
is the effective valve area in mm2 (and is shown in Table 1 for the two valves)
is the temperature in Celsius
is the absolute upstream pressure in MPa (i.e., 0.941 MPa)
is the absolute downstream pressure in MPa
For punt kicks in Australian Rules football, the average elapsed time from minimum knee angle to
maximum knee velocity for elite players is 65 milliseconds [1]. However, because these kicks are
executed while running, the leg is not drawn back as far as when place kicking a rugby ball. Therefore,
the duration of a place kick is estimated to be about one and a half times as long as the punt kick, i.e.,
about 100 milliseconds. In this time, each of the two air cylinders moves through the swept volumes
shown in Table 1. Assuming that the temperature, , is 20 oC, this means that the flowrate, , across
the quadriceps valve is:
dm3/min
and the flowrate,
, across the rectus valve is:
dm3/min
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Substituting the design parameters (Table 1) into equation (10) gives a pressure drop across the
quadriceps valve and the rectus valve of 1.8 kPa and 0.2 kPa respectively. This is negligible compared
with the reservoir pressure and the assumption of zero frictional loss across the solenoid valves is valid.
3.4.3 Frictional losses in the tubing
The pneumatic line from the reservoir to the abdominus cylinder is a 3.5 m length of drawn nylon
tubing with an internal diameter of 13mm. The tubing is assumed to be smooth, i.e. to have a relative
roughness of approximately zero.
Assuming that air flow in the tube is adiabatic and that the air behaves like a perfect gas, the pressure
drop along the tube will be [14]:
(11)
Where, is the friction factor, is the cross sectional area of the tube, is the perimeter of the tube,
is the density of air in the tube, is the velocity of air in the tube and
is the Mach number,
defined as:
(12)
Where
is the velocity of sound (and is approximately 343 m/s in dry air at 20 oC).
The combined swept volume of the two air cylinders, , is 0.9268 litres flowing in 100 ms which
implies a velocity, , of 69.8 m/s. From equation (12) this implies a Mach number,
, of 0.2. For
small Mach number, equation (11) reduces to Darcy’s equation [14]:
(13)
Air at atmospheric pressure (101 kPa) has a density of 1.204 kg/m3. The density of air in the tube,
941kPa can be calculated for a perfect gas as:
, at
kg/m3
Reynold’s number,
, is:
(14)
Where is the dynamic viscosity of air and is 1.983 x 10 -5 kg/ms at 20 oC (and is independent of
pressure).
Evaluating equation (14) gives a Reynold’s number of 5.1 x 10 5, which corresponds to a friction factor
of 0.0032 for a smooth pipe [14]. From equation (13) this means that the pressure drop over the 3.5 m
length of tube is 8 kPa. This is negligible compared with the reservoir pressure, so the assumption of
small frictional loss in the tube is valid.
Having established that energy losses due to drag on the leg and friction in the valves and tubes are
negligible, the first law of thermodynamics can be used to calculate the maximum achievable foot
speed.
3.4.4 First law analysis of the system
Consider a closed system that includes the kicking leg and the plumbing and has its boundaries at the
inlet air manifold and at the surface of the air cylinders. The First Law states:
(15)
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The heat supplied to the system by its surroundings, , is nearly zero and the work done on the closed
system (leg plus plumbing), , is zero because the work done on the leg in order to move it against air
resistance has been shown to be negligible. The internal energy of the closed system, , is the increase
in kinetic energy of the leg and the change in internal energy of the air within the tubing and cylinders.
During the kick, and terminating at the instant when the two portions of the limb are exactly straight,
but before the foot strikes the ball, the pistons, together, sweep a system volume V s. If the flow through
the pipes and valves were entirely frictionless, the cylinder pressure at the termination of the stroke
would be the same as that of the reservoir, P 0. Ignoring the small consequences of acceleration of the
air and using an SMC Quick Exhaust Valve to ensure that the exhaust air has little back resistance (on
the rectus air cylinder), equation (15) can be rewritten as:
(16)
Using equations (3) and (16) and the parameters of Table 1, the upper limit of the foot velocity at
impact is 38.0 m/s. Elite kickers have an average foot speed of 26.4 m/s [1] which means that the
robotic kicker should have a similar kicking power.
4 Experimental
The robot kick was tested under varying conditions of tee position, kick duration and differential delay
between the actuation of upper and lower leg air cylinders.
4.1 Measurement of foot speed
Two roundels with crosses were placed on the kicking foot and a Casio Exilim Pro EX-F1 camera
operating at 1200 frames per second (fps) was used to video the kick. Sequential images (such as those
shown in Fig. 5) were extracted from the video and used to measure the position of the markers on the
foot and the position of the ball. The known dimensions of the logo on the ball were used in calibrating
the distance measurements on the images. The measurements were then used to compute the speed of
the markers and the ball.
Fig. 5 Two sequential images showing marker positions, M1 (rear-most marker) and M2 (front marker)
In order to assess the precision of the measurement method, a single video of a kick was measured five
times. The 370 measurements of marker speed had a standard deviation of 0.51 m/s. Fig. 6 shows the
data for Marker 2. The point of impact occurs at about 11 ms on this arbitrary time scale.
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Fig. 6 Marker 2 speed measurement precision
25.0
Speed (m/s)
20.0
15.0
10.0
5.0
0.0
0
5
10
15
20
25
30
Time (ms)
Fig. 7 shows a typical variation in marker speed over time. The toe speed before impact with the ball
was computed from the speeds of the two markers, averaged over 3 kicks. Fig. 8 shows a typical
variation in ball speed with time.
Fig. 7 Marker speed variation over time
25
Speed (m/s)
20
15
contact with ball
M1
10
M2
5
ball leaves foot
0
0
5
10
15
20
25
30
Time (ms)
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Fig. 8 Variation in ball speed over time
30
Speed (m/s)
25
20
15
10
5
0
12
14
16
18
20
22
24
26
28
30
Time (ms)
The pneumatically-controlled kicking leg achieved an average foot speed of 20.8 m/s and Fig. 9 shows
the resulting deformation of the kicked ball. The ball was a Gilbert Virtuo 2011 Rugby World Cup ball
inflated to a pressure of 10 psi. There were cross winds gusting from 3 to 33 km/h but the kicks were
done between gusts, with almost no wind. For 10 kicks, the average kick distance was 45.6 m with a
standard deviation of 1.2 m. The ball speed reached 27 m/s (Fig. 8).
(a) Side view
Prior to kick
Maximum ball deformation
(b) Rear view
Prior to kick
Maximum ball deformation
Fig. 9 Deformation of a kicked rugby ball
The kicking accuracy of individual professional rugby players is not published, but Spamer et al. [24]
report an average place kick distance and accuracy for elite under 16 New Zealand rugby players of
37.6 +/- 4.4 m. Holmes et al. [7] measured the average kick distance of elite rugby union players at
53.7 +/- 5.7 m with an average ball speed of 26.4 +/- 3.0 m/s. The robotic kicker, at 45.6 +/- 1.2 m, has
an acceptable kick-distance and kicks very reproducibly, making it an excellent research tool.
The human-like appearance and behaviour of the kicking robot is captivating and it has received
considerable publicity. For example, it was used to predict the outcome of the 2011 Rugby World cup
and a video of this is available at [27].
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5 Discussion
A First Law analysis led to an estimated upper limit on foot speed of about 38 m/s and the robot
achieved a speed of about 21 m/s. The difference arises from friction in the cylinders, losses in the
fittings and probably, principally from back pressure on the discharge side of the cylinders, only one of
which had a SMC Quick Exhaust Valve.
High speed photography showed that the robot lower limb actually moved backwards at the end of the
kick. Having pondered this observation, we realised that we had missed an obvious point about human
kickers; their abdominus muscles are small compared with their quadriceps muscles. Consequently
their foot does not move backwards during the kick. Also, the major energy going into a human kick
derives from the quadriceps muscle; the knee moves slowly but the foot moves very fast.
We noted that ball placement was crucial; a difference of 3 mm had significant effect on the accuracy.
6 Conclusion
Humanoid robots are commonly moved using electric motors and are generally much slower and
weaker than human sports players. The pneumatically-activated humanoid robotic kicker, described in
this work, can kick almost as far as elite rugby union kickers and the kick distance is more consistent. It
can therefore be used to research the mechanics, kinematics and dynamics of place kicking a rugby
ball. The accuracy of the robot was tested in windless conditions. An anemometer will be fitted in the
robot’s head so that wind speed can be measured and incorporated into the automatic aiming system.
The accuracy of the robot will then be tested in windy conditions.
The robot draws a lot of attention because of its animatronic behaviour. This will be extended so that
when the robot is not kicking it will respond to people moving past; its eye will glow read and it will
move its head and track them with the camera so that it appears to be watching them.
Acknowledgements
The authors acknowledge gratefully the following contributions to this research effort:
Pneumatics company, SMC, donated the pneumatic components used in the robotic kicker. The
contribution was administered by Kevin Buckley of the Palmerston North branch of SMC New
Zealand.
Ian Savage, chief research and development engineer for English rugby ball manufacturer, Gilbert,
provided the rugby balls and insight into human kicking.
Ian Thomas, workshop technician at Massey University, videoed the kicking and provided the CAD
drawings and photographs of the robot.
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