Toward a Competitive Pool-Playing Robot

C O V E R F E A T U R E

46 Computer

Toward a

Competitive

Pool-Playing Robot

rom behind a closed door in a university cam-

pus hallway comes the distinctive clacking

sound of a pool game in progress. This isn’t a

student lounge, but rather a laboratory where

we’re developing a vision-based, intelligent

robotic system to play competitive pool. Named Deep

Green, the system currently shoots at a better-than-ama-

teur level, and our goal is to advance the system to be able

to challenge a proﬁcient human opponent, ultimately at

a championship level.

Pool—by which we loosely refer to all cue sports,

including billiards, carom, and snooker—is somewhat

misunderstood, more likely to evoke images of shifty

characters in smoky bars than advanced robotics. It

evolved in the royal courts of medieval Europe as an

indoor version of croquet. Today, pool is enjoying a

resurgence of popularity worldwide. Variations are

played in almost every country, and pool was recognized

as a demonstration sport in the 1998 Nagano Olym-

pics. According to a 2005 survey,

more than 35 million

people played pool that year in the US alone, and pool

ranked as the eighth most popular participation sport,

just after cycling and ﬁshing.

The ﬁrst attempt to automate pool was the Snooker

Machine developed at the University of Bristol in the late

1980s,

which culminated with a televised game on BBC’s

science program QED.

Since then, researchers have

developed a number of pool-playing robotic systems

4-6

well as a training system that has a computer vision com-

ponent but doesn’t involve robotic actuation.

7,8

DEEP GREEN

As Figure 1 shows, Deep Green is centered on a

3-degree-of-freedom (DOF) industrial gantry robot,

which is mounted to the ceiling to avoid impeding human

access to the table. A digital camera, the global vision

system (GVS), is attached to the ceiling aiming down

toward the table, accompanied by an array of directional

lights. Attached to the gantry’s vertical post is a 3-DOF

spherical robotic wrist that, combined with the gantry’s

linear motion, affords the robot complete reachability

over the workspace.

The end-effector, illustrated in Figure 2, includes two

distinct cue devices, one based on a linear electromag-

netic motor and the other actuated pneumatically. The

electromagnetic cue can be ﬁnely controlled to strike up

to a velocity of 3 meters per second, which is sufﬁcient for

normal play, whereas the pneumatic cue is used solely for

power breaks and strikes at 12 m/s. A small eye-in-hand

camera, the local vision system (LVS), is also attached to

the end-effector, as is a pick-and-place vacuum tool for

ball-in-hand conditions and automatic racking.

The table itself is a standard 4-foot × 8-foot coin-oper-

ated pool table, and all devices are connected to a single

Deep Green is a vision-based, intelligent robotic system that currently shoots pool at a

better-than-amateur level, with the ultimate goal of challenging a proficient human

opponent at a championship level.

Michael Greenspan, Joseph Lam, Marc Godard, Imran Zaidi,

and Sam Jordan, Queen’s University

Will Leckie, Nortel

Ken Anderson, Larus Technologies

Donna Dupuis, University of British Columbia

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January 2008

PC. While the system has been designed to play

the popular game of 8 Ball, with slight modiﬁca-

tions it could play any other variation of pool.

Figure 3 shows a number of example shots.

ROBOTICS

Rather than build our own hardware, we

based Deep Green on standard commercially

available, albeit customized, components. This

makes the system relatively inexpensive and

quick to deploy, and it allowed us to focus our

effort on the computational challenges.

Camera calibration

The system’s robotic aspects rely primarily on

computer vision. Before using the cameras, we

had to calibrate them so that they could accu-

rately determine the ball locations within the

table’s metric coordinate reference frame. Using

standard techniques, we determined the cam-

eras’ intrinsic parameters, including factors to

correct for the radial distortion inherent to optical sys-

tems. It was also necessary to rectify the table plane to

compensate for perspective distortions that result from

the GVS retinal plane not being aligned exactly parallel

to the table surface, which is difﬁcult to achieve manu-

ally to the desired accuracy.

The retinal plane and the table are related by a trans-

formation known as a homography, a mapping between

two planes. The standard technique for determining a

homography involves extracting a minimum of four cor-

responding point locations between a planar pattern and

its image. This technique is awkward to apply in Deep

Green as the pattern must be large (the table’s size) as

well as very ﬂat and accurate.

Alternatively, we exploit an invariant property of the

projective space that uses a simple target comprising

perpendicular lines, such as a large carpenter’s square.

This technique lets us integrate measurements taken at

various positions on the table into a single homography,

which we estimate up to an afﬁnity. With a few addi-

tional simple measurements, we can then recover the

remaining rotation and scale parameters that map the

image pixels to metric locations on the table surface.

Ball localization and identification

At runtime, Deep Green acquires a GVS image when

the balls come to rest and unwarps it to remove the radial

and perspective distortions. It then compares this image

with a set of statistics—pixel means and variances—

acquired from a set of approximately 30 background

images of the table, without any balls present. For each

pixel, if the difference between the foreground and back-

ground pixel values exceeds some threshold value of the

background standard deviation, the system judges that

pixel to be foreground, that is, possibly a ball.

Because this ﬁlter passes signiﬁcant noise, the system

applies a connected-components algorithm and only

admits those regions large enough to be valid balls. It

then processes these ball regions using circle-extraction

and best-ﬁt routines, leading to an accurate estimate of

each ball’s center location.

Once Deep Green has accurately identiﬁed the ball

locations, it sends the circular subregions deﬁning each

ball to a color-indexing routine to determine the ball

identities. It must know the exact identity (number) of

each ball, as the formal rules for 8 Ball require nominat-

ing a ball and pocket for each shot. Ofﬂine, the system

forms a 2D histogram in normalized RGB space for each

of the 16 ball types from a collection of images of each

ball, taken at different aspects and at various locations

on the table. At runtime, it compares the color space his-

togram of each ball region with this database and uses a

histogram similarity metric to classify the ball.

Despite strong similarities between the colors of differ-

ent ball types, and reuse of colors among the stripes and

Figure 1. Deep Green robotic pool-playing system. The system is centered

on a 3-degree-of-freedom gantry robot mounted to the ceiling to avoid

impeding human access to the table.

Figure 2. End-effector components.

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48 Computer

C O V E R F E A T U R E

solids, the color-indexing method can reliably determine

each ball’s identity. Once the system has accurately local-

ized and identiﬁed each ball, it can simulate the table

state for shot planning.

Robot calibration

The challenge in using a standard gantry platform is its

limited accuracy, as industrial robotics tend to be highly

precise and repeatable but not terribly accurate. While

it’s possible to design a gantry robot with ﬁne-grained

accuracy, such a device would be expensive, delicate,

and unlikely to maintain its accuracy while absorbing

the impacts required to place shots. A more reasonable

approach is to demand less accuracy from the primary

positioning device and rely upon the vision system for

calibration and correction.

One calibration technique involved both the LVS and

GVS cameras.

We repeatedly positioned the robot over

a series of circular patterns placed on the table surface.

We then used the correspondence between the robot

joint encoder values and the centers of the extracted cir-

cles within the GVS image to determine the functional

relationship between the robot coordinate frame and the

table plane. This technique reduced robot positioning

error from the order of centimeters to within 0.6 mm on

average, with a standard deviation of 0.3 mm.

Eye-in-hand visual servoing

While robot calibration rendered an improvement, a

positioning accuracy of 0.6 mm is insufﬁcient to success-

fully pot many long shots. It may be possible to further

reﬁne our calibration technique, successively unraveling

the robot’s many mysterious nonlinearities. However,

the likely result of such an effort would be a very brittle

system—any change in the system parameters, due to

aging or other extrinsic conditions such as vibrations or

temperature, would require a tedious recalibration.

To improve positioning accuracy, we have developed

an eye-in-hand visual-servoing system in which the LVS

camera is mounted on the end-effector with its optical

axis pointing roughly along the direction of the cue.

The LVS uses the known ball locations determined by

the GVS as visual landmarks to detect and compensate

for positioning errors accumulated during the gantry’s

coarse motion.

LVS correction. Consider the nearly perfect straight shot

illustrated in Figure 4. In this GVS image, the inscribed

line is deﬁned by the extracted center locations of the

Figure 3. Example shots. (a) 9 ball in the side pocket—composite of three images. (b) Combination shot: 4 ball in the corner pocket,

off of the 7 ball—composite of four images. (c) Combination shot: 6 ball in the corner pocket, off of the 1 ball—composite of four

images. (d) 5 ball in the corner pocket—time-exposure image.

(a)

(b)

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January 2008

cue and object balls prior to placing the shot. The

rendered circles are a sequence of three extracted

positions of the object ball, at times t

to t

, once the

shot has been placed. The centers of these circles fall

on or close to the line, indicating that the robot was

positioned to make a very accurate straight shot.

The ﬁnal resting positions of the cue and object balls

at time t

also fall on this line, further supporting the

shot’s quality.

From the LVS’s vantage, this is the ideal line. When

the robot is servoed to its shot position, as deter-

mined by the GVS, it accumulates error. By analyz-

ing the LVS image, and comparing the line connect-

ing the current cue and object ball centers with the

ideal line, the system can calculate transformations

that correct for the robot positioning error.

Figure 5a shows an LVS image acquired after the

robot has been servoed to its shot position, using

only the information from the GVS. The current

(red) and ideal (green) lines aren’t aligned, indi-

cating positioning error. After the system executes the

automatic alignment procedure, the current line overlaps

almost exactly with the ideal line, as shown in Figure

5b, and the shot will therefore be very close to a perfect

straight shot.

Alignment methods. We have developed two different

methods to align the robot position with the LVS ideal

line.

The simpler one is iterative and based entirely on

2D LVS image data. The other method uses knowledge of

the 3D rigid transformation between the robot wrist coor-

dinate reference frame and the LVS optical frame. This

transformation, known as the tool control frame (TCF)

matrix, is determined ofﬂine in a calibration stage.

Figure 6 plots the result of an experiment designed to

characterize the performance of these two methods. A

total of 90 straight shots were executed. Thirty of these

shots used only information from the GVS and robot

calibration, 30 more applied alignment using the image-

based method, and the ﬁnal 30 used the position-based

method. We calculated the angular error of each shot by

extracting the object-ball center locations at a number

of (at least two) positions along their trajectories using

the GVS and comparing the angle of this line with the

line deﬁned by the cue and object balls prior to placing

the shot (similar to Figure 4).

We plotted the angular errors for each of the 3

sets of 30 shots in ascending order. Alignment using

either method signiﬁcantly reduced the angular error.

Without alignment, the mean absolute error was

1.8 degrees. With alignment, the error was reduced

by more than two thirds, to 0.51 degrees and 0.56

degrees for the image- and position-based methods,

respectively. While the accuracy is similar for both

alignment methods, the position-based method is

approximately 40 percent faster. Once the straight

shot is aligned accurately, the TCF matrix can be used

to further rotate and translate the cue around the cue-

ball center to execute a cut shot of any desired angle and

spin.

GAMING

For those who play pool only casually, skill is the limit-

ing factor, and sinking the current ball is usually the sole

concern. For more advanced players, however, strategy

Figure 4. Straight shot. Intermediate object ball locations fall on a line

defined by initial cue and object ball locations.

Figure 5. LVS correction. (a) Current (red) and ideal (green) lines

before alignment. (b) After alignment, current and ideal lines

overlap.

(b)

(a)

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50 Computer

C O V E R F E A T U R E

becomes a key element of the game, and professionals are

known to plan ﬁve or more shots ahead for a given table

state. For a robotic system to play competitively, it must

therefore strategize computationally, which involves both

predicting and planning future table states. This requires

the interplay of physics simulation and search.

Physics simulation

To predict the table state after a shot so that subse-

quent shots can be planned, an accurate physics model

is necessary. Spin is an essential element of the game,

and imparting spin on the cue ball by displacing and

angling the cue at impact is a technique used to control

the interaction and placement of balls following a shot.

The physics model therefore involves conserving not only

linear but also angular momentum.

We have developed a physics simulator that predicts a

shot’s outcome from a derived physics model.

Unlike

physics simulators that use the more common numerical

integration approach, our method operates in the con-

tinuous domain, predicting the times of pending events

such as collisions or transitions between motion states.

Our technique returns an exact analytic solution based

on a parameterization of the separation of two moving

balls as a function of time. The resulting equation is a

quartic polynomial that can be solved either iteratively

or in closed form to determine the collision time. A simi-

lar derivation exists for other events, such as ball-rail and

-pocket collisions and transitions from sliding-to-rolling

and rolling-to-stationary states.

Compared to integration, our approach is more

accurate, requiring no discrete time step; and

time efﬁcient, requiring approximately two to three

orders of magnitude fewer computations per shot.

This added efﬁciency is especially important when the

physics simulator is used in expanding a game tree, as

many different shots—sometimes tens of thousands or

more—might need to be simulated prior to making a

decision.

Our physics simulator was the basis for the Compu-

tational 8 Ball Tournaments at the 10th and 11th Inter-

national Computer Olympiads.

These tournaments let

teams develop different strategy engines and compete

using the common physics simulator.

One consideration in modeling the physics was shot

noise. When a human or robotic player takes a shot, error

in the cue’s position and velocity makes each shot noni-

deal. To make the simulation more realistic and the com-

petition more challenging, we added zero-mean random

Gaussian noise to each of the ﬁve shot parameters that

determine the outcome of a shot: two angles (θ,φ), two

offsets (a, b), and the striking speed V.

The sigma values

of each distribution were empirically determined to cause

one missed shot every 10 shots on average, a success rate

similar to that of advanced human play. When planning

a shot for robotic play, a noise model based on the robot’s

calibrated positioning accuracy can be used to determine

the probability of a given shot’s success.

With the physics simulator’s ability to predict a shot’s

outcome, it’s then necessary to evalu-

ate many possible shot sequences to

determine the best shot to place given

the current table state. Our approach

to this search is based on the mini-

max game tree used in games like

chess and checkers.

15,16

While the

basic concept is the same as in chess,

one difference is that pool is played in

a continuous, rather than a discrete,

domain. The size of the search space

for any particular shot is therefore

truly inﬁnite, rather than the huge

but ﬁnite search space of chess.

Another unique consideration in

pool is shot noise. In practice, each of

the ﬁve shot parameters has an element

of uncertainty that can be modeled as

a probability distribution. For this rea-

son, we have adapted the expectimax

search tree, which has been applied to

games like backgammon that have a

probabilistic component. Because pool

is played in a continuous domain, the

chosen tree search algorithm incorpo-

•

1 3 5 7 9 11 13 15 17 19 21 23 2725 29

Shots (in ascending order)

Angle error (degree)

Without LVS

LVS image-based

LVS position-based

Figure 6. Angular error in straight shot tests with LVS correction. Alignment reduced

the error by more than two thirds, to 0.51 degrees and 0.56 degrees for the image- and

position-based methods, respectively.

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January 2008

rates statistical sampling to account for uncertainty in shot

execution. The utility of a future table state is weighted by

its probability of occurrence, and the weighted utilities of

the children of each node are combined when considering

which path to traverse.

Empirical evaluation of strategic play

To explore the beneﬁts of strategic play in pool, we

executed a set of experiments using this tree-search

framework.

Methodology. We simulated a series of 8 Ball tourna-

ments involving 19 competitors, all with identical shot-

generation algorithms. Eighteen of the competitors used

different tree-search depths, tree-scoring variations, and

evaluation-function variations; the 19th used a depth-

zero “greedy” shot-selection algorithm based solely on

the probability of the current shot’s success with no

regard for the resulting table state or future shots. This

greedy player had the same skill level as the other com-

petitors but thought like an amateur.

Three tournaments were played with three different

noise models reﬂecting the players’ technical skill level.

For the high-noise model, about 80 percent of balls were

sunk as planned; for low noise, about 90 percent; and for

zero noise, all shots were executed exactly as planned. All

players in each tournament used the same noise model and

search algorithm. Each tournament therefore isolated per-

formance as a function of tree-search depth and evaluation-

function variation. A search depth of 1, for example, con-

siders not only the current shot but also all shots resulting

from the current shot. The various scoring and evaluation

functions differed in how they rated a leaf node’s utility as

well as in how they combined the information from child

nodes in propagating back up the tree.

This is similar to comparing two human players by

categorizing their play in two areas:

technical skill—precision in executing shots; and

level of strategic play—how far ahead in the game

•

the player looks, and how the player controls the cue

ball position for the next shot.

We examined numerous combinations of tree-scor-

ing variations—Monte Carlo, probabilistic, or success-

weighted—and evaluation-function variations: average,

maximum, or weighted. Within each tournament, the

players with common search algorithm/evaluation func-

tions (but varying search depth) played 200-game matches

against one another and against the greedy player in a

round-robin format. The winning player of each game

received a total of 10 points, and the losing player received

one point for each pocketed ball of its color group (stripes

or solids), for a maximum of seven points. The match

score was the sum of the game scores.

Results. Table 1 summarizes the results from these

experiments. Players are ranked by their overall perfor-

mance by averaging the percentage of games won, points

scored, point differential, miss rate, and percentage of

shots resulting in a ball-in-hand. The percentage of shots

resulting in a BIH indicates not only how often a player

fouled, but more importantly how often it left itself with

no shot. The greedy player was more heavily penalized

by this setting because it never considered the table state

resulting from its chosen shot.

In the zero-noise tournament, the deeper-searching

players consistently outplayed their shallower-searching

competitors. For a given search type/evaluation function

variant, the depth 2 player always defeated the greedy

player easily and then defeated the depth 1 player in

turn. The greedy player was defeated in all matches in

the zero-noise tournament, winning at best 16.5 percent

of the games in its match against one player. Against the

greedy player, all of the depth 2 players scored more wins

with a higher point differential than the corresponding

depth 1 player.

Look-ahead. Positional play in the form of look-ahead

is clearly an important consideration in pool. Choosing

the easiest shot, or the shot with the highest probability

Table 1. Summary across search depths for zero-, low-, and high-noise tournaments.

Average Average

Average wins Average points Average point misses ball-in-hand

Noise Player (percent) scored differential (percent) (percent)

Zero Greedy 9.9 771.6 –1,093.3 0.0 10.3

All depth 1 61.1 1,390.8 278.4 0.0 2.5

All depth 2 79.9 1,622.5 814.9 0.0 2.5

Low Greedy 19.9 963.1 –791.0 6.3 12.0

All depth 1 62.7 1,458.8 323.9 2.6 3.6

All depth 2 67.4 1,523.9 467.1 1.6 3.4

High Greedy 36.5 1,301.7 –314.6 11.8 14.3

All depth 1 54.8 1,484.4 114.2 8.9 10.4

All depth 2 58.7 1,519.9 200.4 9.3 9.0

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52 Computer

C O V E R F E A T U R E

of success, doesn’t result in a competitive player; plan-

ning strategically using look-ahead does. These results

mirror the expectation for human players similarly char-

acterized by technical skill and level of strategic reason-

ing. Players are always limited by their technical skill,

regardless of how strategically they plan shots. However,

for sufﬁciently skilled players, the beneﬁts of strategic

reasoning and cue-ball placement in the form of look-

ahead always dominate over less strategic play.

While these experiments have evaluated look-ahead

only to a depth of 2, the beneﬁts of look-ahead should

continue to be apparent for search depths up to 8, at

which point all game tree branches will have terminated,

with all balls sunk and the game completed. In practice,

expanding the game tree to greater depths can be quite

time expensive, and so tournament competitors have

restricted their searches to depths of 2 or 3.

ADVANTAGES OF MACHINE PLAY

In many ways, pool is an ideal game for automation.

A great deal of human pool instruction and practice is

oriented toward establishing an accurate and repeatable

stroke. Machines routinely outperform humans at posi-

tioning accuracy and repeatability, and they function

consistently, without the performance-degrading effects

of muscle fatigue. They also aren’t susceptible to psy-

chological pressure, a signiﬁcant source of variation and

failure in human play.

In addition, a machine like Deep Green can sense the

balls’ absolute metric locations in the table coordinate

reference frame. Humans can ascertain the balls’ geo-

metric arrangement based on their relative positions on

the table, allowing them to plan and execute challenging

shots, but in certain situations even skilled humans have

difﬁculty perceiving the correct angles. For example, shots

that involve multiple banks are inherently difﬁcult to per-

ceive, and humans often use inexact systems based on

table landmarks (diamonds) to augment their perception.

In contrast, the machine resolves the metric location of

all balls and table elements such as rails and pockets. This

allows for more exact geometric planning, and enhances

the machine’s ability to predict a shot’s outcome.

Another advantage of the machine is its computational

simulation of the table’s physics. Most human players

rely on an intuitive understanding of this aspect of the

game. Typically with little or no formal knowledge of

physics, they develop heuristics to predict the subsequent

table state that results from the multiple interactions of

any particular shot. While often useful, these heuris-

tics have limited ﬁdelity. In contrast, the machine has

an executable physics model and, so long as a handful

of parameters have been estimated through calibration,

can use a physics simulator to predict the resulting table

state both accurately and efﬁciently.

Moreover, the cue end-effector provides precise con-

trol of stroke speed. The electromagnetic linear actua-

tor responsible for the forward motion of Deep Green’s

stroke has a dedicated digital control unit that can be

commanded in either position or velocity modes. The

cue’s speed can range from almost stationary to approxi-

mately 3 m/s, with an average error of approximately 0.1

percent. In contrast, humans tend to strike with one of

six speeds: slow, medium-slow, medium, medium-fast,

fast, or break. The added graduation in controlling cue

speed translates to an increased ability to place the cue

ball and predict and control the table state.

Once the mechanics of placing a shot have been mas-

tered, pool becomes a strategic game, and here too the

machine has a potential advantage. The essence of pool

strategy is the ability to look ahead and predict the table’s

state following a potential shot or series of potential

shots. This same capability lets computers outperform

people at chess and other games recently believed to be

only within the realm of human mastery.

NEED FOR INTELLIGENCE

The Deep Green project has inspired polar opposite

responses on the degree of difﬁculty required to attain our

goal. Some people who are familiar with technology but

not with pool have regarded it as a straightforward task,

requiring only standard robotic techniques to provide a

solution. In contrast, proﬁcient players who have no spe-

cial relationship with technology tend to argue that pool is

a distinctly human activity, requiring human intelligence

and skill, and that automating it is impossible.

Our view lies somewhere between these two extremes.

We believe that developing a robotic system to play pool

competitively against a proficient human opponent is

achievable. The technical problems are both interesting and

sufﬁciently challenging to motivate advanced research, but

not so difﬁcult as to evade a meaningful solution.

Another question that Deep Green raises is whether

computational intelligence is necessary for robotic pool.

Isn’t an accurate positioning system and simple shot

planning based purely on geometry sufﬁcient? There are

two answers to this question. First, accurate positioning

of a standard gantry robot is itself a challenging goal

requiring sensor-based methods for calibration and cor-

rection. Second, even if perfectly accurate positioning

were possible, it’s still advantageous to play strategically

and plan ahead a number of shots, as evidenced by our

experiments with zero-noise tournaments.

eep Green currently plays at a better-than-ama-

teur level, planning and executing difﬁcult combi-

nation and rail shots from across the table. It has

pocketed runs of four consecutive balls, and it’s only a

matter of time before it can consistently run the table.

Several research challenges must be addressed to advance

the system further. The most difﬁcult will emerge in com-

peting against proﬁcient human opponents. Humans are

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January 2008

crafty competitors, able to efﬁciently recognize and exploit

weaknesses in their opponents. To play at a competitive

level, Deep Green must incorporate insights from machine-

learning and opponent-modeling techniques. ■

Acknowledgments

The authors thank Precarn Inc., the Institute for Robot-

ics and Intelligent Systems, the Canada Foundation for

Innovation, and the Natural Sciences and Engineering

Research Council of Canada for their ﬁnancial support,

and Elisha Hardwick for her photographic work. They

also thank the many students who have contributed long

hours to the development of the Deep Green system.

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puter Eng., Queen’s Univ., Kingston, Canada, 2007.

11. D.G. Alciatore,

The Illustrated Principles of Pool and Bil-

liards, Sterling, 2004.

12. W. Leckie and M. Greenspan, “Pool Physics Simulation by

Event Prediction 2: Collisions,” Int’l Computer Games Assoc.

J., Mar. 2006, pp. 24-31.

13. M. Greenspan, “Pickpocket Wins Pool Tournament,”

Int’l

Computer Games Assoc. J., Sept. 2006, pp. 153-156.

14. W. Leckie and M. Greenspan, “Pool Physics Simulation by

Event Prediction 1: Motion Transitions,” Int’l Computer

Games Assoc. J., Dec. 2005, pp. 214-222.

15. W. Leckie and M. Greenspan, “Monte-Carlo Methods in Pool

Strategy Game Trees,” Proc. 5th Int’l Conf. Computers and

Games (CG 06), LNCS 4630, Springer, 2007.

16. M. Smith, “PickPocket: A Computer Billiards Shark,”

Artifi-

cial Intelligence, Nov. 2007, pp. 1069-1091.

Michael Greenspan is an associate professor in the Depart-

ment of Electrical and Computer Engineering and in the

School of Computing, Queen’s University, Kingston,

Ontario, Canada, and is spending the year as a visiting sci-

entist at the University of Coimbra, Portugal. His research

focuses on problems in computer vision and computer gam-

ing. Greenspan received a PhD in systems and computer

engineering from Carleton University, Ottawa. Contact

him at michael.gr[email protected]a.

Joseph Lam is a PhD candidate in the Department of Elec-

trical and Computer Engineering at Queen’s University.

His research interests include computer vision and visual

servoing. Contact him at jctlam@gmail.com.

Marc Godard is a bachelor’s student in the School of

Computing, Queen’s University. His research interests

include computer vision, cognitive models, and prediction

algorithms. Contact him at 4mg12@qlink.queensu.ca.

Imran Zaidi is a bachelor’s student in the School of Com-

puting, Queen’s University. Contact him at 3aiz@qlink.

queensu.ca.

Sam Jordan is a master’s student in the Department of

Electrical and Computer Engineering at Queen’s Univer-

sity. His research interests include robotics, augmented

reality, and human-computer interaction. Contact him

at 3sj1@queensu.ca.

Will Leckie is an electro-optics hardware designer with

Nortel at its Carling Campus in Ottawa. His research

interests include robotics and artificial intelligence. Leckie

received a master’s degree in electrical and computer engi-

neering from Queen’s University. Contact him at will.

leckie@ece.queensu.ca.

Ken Anderson is a software engineer at Larus Technologies

in Ottawa. His research interests include robotics, single-

agent search, and computer games. Anderson received a

master’s degree in computing science from the University

of Alberta. Contact him at anderson@cs.ualberta.ca.

Donna Dupuis is a master’s student in the Department of

Electrical Engineering at the University of British Colum-

bia, Vancouver, British Columbia, Canada. Her research

interests include computer vision, robotics, and artificial

intelligence. Contact her at dupuisd@mech.ubc.ca.

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