sports games: artificial intelligence and physics

Sports Games: Artificial Intelligence and

Physics

Topics

Sports Game Design and Development◦Architectures◦Class Structures

Agent Cooperation◦Team based cooperation and Optimization

Physics◦Object physics◦Agent physics◦Dead Reckoning

Strategy Development◦Artificial and Human Elements

Challenges

Simulating a natural, well-known environment◦Modeling fields, courts, rinks, etc.◦Modeling player personalities and animations◦Physics engine

Strategy◦Sports are a form of Real-Time strategy◦Strategies while confined to a set of rules and

the size of the field, are numerous and constantly changing

A Brief History

A well known fact: Video game detail has improved over the years

From Tecmo Bowl to Madden 2008◦Better player models◦Larger fields, increased atmosphere◦More intelligent AI◦More modes, styles of play

Arcade versus Simulation Longer play modes Online play

Building an Sports AI Architecture

Building a Sports AI Architecture

A Sports game has many CPU-Intensive tasks◦Player animation◦Route planning◦Physics modeling◦Strategy development

Breaking these down in a high level architecture confined by the rules of the game can help ease the complexity of the development


Layering the architecture


Plans◦ Offensive

Pass Shoot Drive to the basket

◦ Defensive Position the defender Double team the ball handler

◦ Shared Rebound Set up for a free throw

Plans enable the players to move freely and determine their own best routing methods

This level of abstraction provides a sense of realism to the game


Example planning classClass AgentPlan{

float EvaluateInitiation();float EvaluateContinuation();void Initiate();void Update();

}Initiation and continuation are very important concepts

because they determine if a plan is working and where to go next◦ Common return values are between -1.0 and 1.0

Update is called for every tick to update the AI


High level strategy module sets a goal◦ An opportunity is seen to complete a through pass in front of

the goal for a scorePlan is created

◦ An opportunity is seen to complete a through pass in front of the goal for a score

Route finding plots course◦ Each player (opponent and team) is considered,

momentum(team and player), and even ball planningExecute plan

◦ Not all plans will work out◦ Depending on the skill level of the other team and unforeseen

occurrences, this leaves the game interesting


States◦A game can be broken into states with

responsibilities and transition points. Moving from an offensive state to a defensive state

◦These states can govern the types of plans that will be used

◦In an offensive state you wouldn’t push all your defenders back Well you might But more often than not you will push defenders up so

that they can support an offense and keep momentum moving in the positive direction


Agent AI◦Well thought out collection of utility functions and

data used by the plans◦Determine a player’s chance of success◦Determine the likelihood of certain actions

Dunks, lay-ups, bicycle kicks, etc Based on real-world player abilities and conditions of

the game◦Perform the action and determine the type of

action that can be performed by providing a wrapper to the mechanics


Agent Mechanics◦Considered to be low-level AI◦Manage and select animations to be used◦Some of these decisions are determined through the use

of a random number This gives the effect that the game is more real Humans do not always react to the same situation in the same

way◦This level also takes into consideration the kinds of

commands that users would input into the system Run Shoot Pass

Dead Reckoning

Dead Reckoning

Originally developed as a tool for navigators◦Determining the position of his ship given

parameters such as direction, intended course, and speed

Estimating position based on past position and trajectory◦This becomes more complicated when other

factors are taken into consideration Wind or current

Dead Reckoning

Inertia◦Dead Reckoning at its most basic level reduces to

Newton’s first law of motion Knowing an object’s position and speed, we can assume the

object will continue to travel in a straight line.◦Pt = P0 + vt

◦Px,t+1 = Px,t + vx

◦Py,t+1 = Py,t + vy

◦Pz,t+1 = Pz,t + vz

◦These calculations can sometimes prove to be “too good” Incorporating an error calculation might help Even the best quarterbacks have a bad game

Dead Reckoning

Pseudo- Brownian Motion◦An extremely maneuverable object is harder to

predict velocity vectors over lengths of time In the case of a UFO which can do whatever it pleases

(Or so we assume), knowing the velocity magnitude can only help us determine a spherical region of possible positioning

◦In sports games this can be observed as objects in motion which experience seemingly random movement which is an effect of outside forces As a pass is being completed, a strong wind may blow

and knock the ball off of its intended course.

Dead Reckoning

Kinematics◦If the object’s initial velocity is unknown, it can

be computed from observation by plotting the curve of its position for an arbitrary interval and computing speed as the first derivative of the position curve.

◦Adding an estimate of its acceleration vector can help in estimating the object’s future trajectory.

◦P = P0 + v0t + 0.5at2

Dead Reckoning

Uses in sports games◦Shooting a ball or puck◦Passing a ball or puck

Dead reckoning is useful for planning the trajectory of players to determine if a player can make it to an open position to complete the pass.

Good examples of this can be found in soccer games◦Players will often link passes together by passing to a

teammate when faced with a defender and running past the defender to accept a return pass up the pitch

Dead Reckoning

Online play◦Dead Reckoning can be used in games to minimize

the effects of network latency Each player periodically broadcasts a packet containing

his avatar’s location, velocity, and acceleration During the intervals between packets, each machine

runs a dead reckoning algorithm to compute the approximate positions and orientations of all other players

When a new incoming packet from another player is received, the local state of the world is updated accordingly, and the process starts anew

Dead Reckoning

Inferring goals◦Dead Reckoning can help to infer another

players goals and try to intercept them This can be seen as interceptions in football and

soccer

Interceptions

Interceptions

Interceptions occur in many sportsThe interesting aspect of calculating

interceptions is that the same theories apply as in Dead Reckoning, but the system is less planned◦Meaning that, interceptions are not intentional◦Games should include interceptions as

incidental and unplanned from an AI perspective in order to accurately model a sports game

Interceptions

Interceptions

An object is at a position PbIt travels in a straight line with velocity VbAnother object is at a Pp and wants to

intercept the first object◦The intercepting object has a set speed it can

move atA velocity to intercept, Vp, is calculated

This is a simplified model

Interceptions

For instance:◦A basketball bouncing off of a rim has a path

that is parabolic in shape◦Break the model down into two submodels

Altitude of the ball Motion in the ground plane

◦The ground plane motions are orthogonal to the altitude axis These motions can be considered in isolation

Interceptions

Another simplification occurs in the previously described model◦No turning radius◦Infinite Acceleration◦Indefinite travel at maximum velocity

Error isn’t always frowned upon…by developers◦Passes are missed. It happens.◦Other methods can be used to calculate for

heading changes

Interceptions

Interceptions

For an interception to occur, the position of the ball and the player must be the same at some time t

If Vp is known prior, then the function can look like◦ Pb + Vbt = Pp + Vpt

However Vp is the variable that needs to be solved for◦ Distance between the player’s initial position and the ball

at time t: |(Pb – Pp) + Vbt| If the player can move a distance equivalent to how distant the

ball is, the player can intercept the ball at time t |(Pb – Pp) + Vbt| = sit

Interceptions

|P + Vt| = st

(P +Vt)*(P+Vt)=(st)2

P*P + 2P * Vt + V*Vt2 = s2t2

(V*V – s2)t2 + (2P*V)t + (P*P) = 0Now the equation is a second-order

polynomial of tNow it’s time to use the quadratic equation

stVtPVtP )(*)(

Interceptions

Category of solution is determined by the expression in the radical◦b2 – 4ac

A better form to look at our equations from◦b2-4ac = (2P*V)2 – 4(V*V-s2)(P*P)◦…◦(P*V)2 + (s2 – V*V)(P*P)

Interceptions

No Real Roots◦The radicand(quantity with the radical) is negative

There are no real roots The ball cannot be intercepted

◦This occurs when the ball travels at a speed greater than the maximum speed of the player

◦S2 – V*V must be negative◦S<|V|◦The player has to be able to move faster than the

ball if he hopes to intercept it

Interceptions

One Real Root◦Border case between whether or not the player can

intercept the ball◦Only one point in time for interception◦The radicand must be zero◦Two Special Cases

(P*V)<0◦ The ball’s velocity is toward the interceptor and can be caught

(P*V)>0◦ The ball’s velocity is not toward the receiver

This happens because the interception theoretically happened in the past

Interceptions

Two Real Roots◦Does not require the speed of the player to be

greater◦Two positive roots

The player is close to the line of motion and able to catch the ball anytime

◦Two negative roots Impossible interception. Negative time.

◦One positive and one negative root The player is moving faster than the ball and can

meet at any time to meet it in the positive direction

Dead Reckoning

Dead Reckoning

Error correction◦The translational error between the real

position of an agent and the estimate provided by dead reckoning can become unbounded with time. The agent will compute its own short-term map of

its surroundings The short-term map is compared with the a priori

map using pattern recognition techniques Small, incremental corrections are applied on the

fly

Agent Cooperation

Agent Cooperation

Coordination and communication are key amongst human teams and the same goes for the PS3, Xbox360, and Commodore 64

The first step is to define behaviors for the agents.

In the case of baseball:◦Baserunning◦Fielding◦Hitting◦Pitching

Agent Cooperation

Hitting and Pitching◦ Not too complex

Very much animation based◦ The pitch is thrown◦ It is hit, or not hit◦ The ball will have a determined path◦ Once the ball is hit, its initial velocity an angle are the only real

factors of importance These two factors in addition to existing baserunners directly affect

how the ball is fielded◦ Ball hit and ball pitched act more like events

Prepare to field Field Prepare to run

Agent Cooperation

Fielding Behaviors◦Assignments happen off of two main triggers

(events) Ball Hit Ball Fielded

◦Players should react differently to these situations Only one player fields a ball, so the other players

watch, or prepare for other strategies

Agent Cooperation

Agent Cooperation

Class StructureClass BasicBehavior{…void Entry(Cplayer*);void Exit(Cplayer*);void Process(Cplayer*);…}

Each derived behavior has a transition table to switch between behaviors and actions◦ Many times this can result in a similar behavior being performed◦ Transition tables do not always lead to a distinctly different behavior

Agent Cooperation

Initial Behavior Assignments◦In the case of a ball hit event, once the initial

angle and velocity are known, it is easy to determine where the ball will land, and what actions and behaviors to disperse

◦Determining the Hit Type and Hit Zone can be done using physics and trigonometry The Hit Type and Hit Zone values can be used to

control values across the entire field

Agent Cooperation

Hit Types◦ Ground ball◦ Fly ball◦ Line drive◦ Popup◦ Deep drive

In the case of a hit type ground ball Zone 7 ◦ The first baseman and right fielder should motion to the

Behavior Field Ball◦ The rest of the infielders will move to Behavior Cover Base,

with exception to the second baseman who will assume Cutoff or Field Ball depending on velocity

◦ Left and Center Field are in Behavior Back Up

Agent Cooperation

Hit Zones

Agent Cooperation

Initial Behavior Assignments for Runners◦Hit Types

Ground Ball – Behavior Go or Behavior Go Back A runner on second, not forced will assume Behavior

Go on any ball hit in a right-hand zone Hit type fly ball will throw Behaviors Go Halfway, or Tag

Up◦The runners evaluate situations exactly like humans

do They check proximities of fielders to the ball, evaluate

the actions of other runners and make a best decision on what to do

Agent Cooperation

Agent Cooperation

Throw Determination◦Fly balls

95 percent of the balls either go to second or home

Or throw to the cutoff man and let him decide◦Rundowns

We have enough information to run the player down every time (100 percent success rate)

So the better approach to take is to make it interesting and allow the runner to fool with the window

Real Time Strategy Development


Sports games are confined to sets of rules and the development of strategies both team-wide and personal that confine themselves to the rules of physics and the rules of the game

This does not limit however the amount of work and planning that is done by each individual player, who has to model the abilities and limitations of his or her real-life component.

Team dynamic is equally important◦ Some teams have characteristically strong defense◦ Some players communicate better than others, and are

more intelligent


Soccer Games◦Real time strategy in the sense of team control◦Moving offense/defense forward and back◦Controlling player motions

Many of the players use advanced AI techniques to predict good strategies to use with you

Games can allow you to change offense and defensive strategies on the fly.

Different players have different abilities◦This skill set in some ways can become very detailed◦Some famous players are known for their speed, shooting,

defensive abilities and a knowledgeable player can exploit these to their own advantage


Positions and zones are of extreme importance◦Players have roles◦Like in RTS games, some characters cannot perform

well on certain terrain◦The same goes for players playing in muddy

conditions or snowTeams have characteristics and players that

make them more powerful against other teams◦Not a division on race and inherent abilities◦A division based on skill and communication

There are optimal configurations


A new trend is also to give you manager control◦This involves more long term planning

regarding player trading, development, and economics

◦Played over a long period of time, your decisions affect your win percentages and offers you receive. This kind of play rewards players who are very

tied to the individual sport


Skills Vs. Strategy◦An interesting development in sports gaming is that of

providing you with additional skills◦Managing a team from the top level, while managing a

player’s actions on a lower level are becoming increasingly common

◦FIFA 2008 included a new mode titled “Be a Pro” which allows the user to master skills such as dribbling and tackling at a level that goes beyond simply pressing A or B

◦This type of a game feature can almost be compared to some aspects of RPG gaming, where a player levels up and is rewarded with experience points and abilities

Final Notes

Sports games have the difficult task of being true to the sport and physics◦Accurate player modeling◦Robust physics engines

Sports games incorporate features from many different genres◦Real-time strategy styles◦RPG-type player development

Through the years sports games have advanced significantly to allow a deeper level of play

Questions?

sports games: artificial intelligence and physics

Documents

sports ai architecturebuilding

sports ai architecturelayering

physics sports games

game interestingbuilding

video game

high level architecture

skill level

modeling player personalities