Dead reckoning in Sports and Strategy Games

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Dead reckoning in Sports and Strategy Games

• Ushhan D. Gundevia
• November 8, 2004

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François Dominic Laramée

• In the Gaming business since 1991
• Worked on over 20 Games
• Editor and Principal Author of
• Game Design Perspectives
• Secrets of the Game Business
• francoislaramee_at_videotron.ca

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Some other interesting articles by him

• Advanced Genetic Programming New Lessons from
  Biology
• AI Game Programming Wisdom 2 Sec. 11.5
• A Rule-Based Architecture using Dempster - Shafer
  Theory
• Using N-Gram Statistical Models to Predict Player
  Behavior
• Genetic Algorithms Evolving the Perfect Troll
• All in AI Game Programming Wisdom
• Character-Based Game Design
• http//www.gignews.com/fdlcharacterdesign.htm
• The Developer's Life
• http//www.gignews.com/devlife/
• Chess Programming Part I VI
• http//www.gamedev.net/reference/list.asp?category
  id18

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Dead Reckoning

• What is Dead Reckoning?
• Predicting the motion of an object based on its
  previous state
• Uses in the Gaming Industry
• In Sports Games, AI needs to predict a players
  position to pass/avoid him
• In Online Games, its used to offset latency
• Predicting Goals of the Human Player

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Origins of DR

• Originally developed as a tool for Navigation,
  e.g. Navigating in Heavy Fog without GPS
• It does not take into account the effects of
  outside forces, which leads to less reliable
  estimates

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Equations for DR

• Based on the properties of motion, an article can
  be tracked with the help of
• Inertia
• Pseudo-Brownian Motion
• Kinematics

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Inertia

• Everyone remember Newtons First Law of motion
• Px Px0 vxt
• Py Py0 vyt In 3D
• Pz Pz0 vzt
• In situations which are relatively free of
  outside influence, it works well
• Sometimes, may be too well. In these cases we
  might have to insert evaluation errors.

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Pseudo-Brownian Motion

• In cases where objects are extremely maneuverable
  or have many external influences, its impossible
  to predict its velocity vector over some large
  interval
• Hence, from an observers point of view, they
  appear exhibiting Random Brownian Motion

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What to do then?

• The best that can be done is to compute the
  average displacement among a number of such
  particles.
• In case of objects that are very maneuverable,
  the best we can do is to calculate a radius of a
  spherical region in space in which it could have
  moved
• In case of a floating mine, we can assume the
  radius to be a lot less (half or even its root)

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Kinematics

• If an objects initial velocity u is unknown
• Plot a curve of its position for an arbitrary
  interval, and compute speed as its first
  Derivative
• To add an estimate of acceleration, add the
  acceleration vector

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How to add Acceleration?

• For free falling objects, its gravity
• For a human, it can be calculated by the buttons
  he presses
• For everything else, its the second derivative
  of the curve
• P P0 v0t 0.5at2

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DR in Sports Games

• We apply DR in two situations
• AI is trying to shoot pass a human obstacle
• AI is trying to pass to a human player

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DR in Military Stimulations

• Examples
• In WWII scenario, the human flies a
  reconnaissance aircraft over an enemy fleet/army.
  The bombing raid can be planned with the help of
  DR
• In contemporary warfare, DR can assist in missile
  tracking and firing counter measures
• In Submarine simulations, DR can be used to avoid
  floating mines which are not always visible
  through RADAR.

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Example of a Paradoxical Situation

• Both cars are going head-to-head while passing
  the line
• Due to delay, counter player position arrives
  late, position of opponents car is out-of-date
• ? Both players believe that they are the winner

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DR in Online Games

• DR can be used to mitigate effects of network
  latency
• Each player broadcasts a packets containing is
  location, velocity and acceleration
• During intervals between packets, the AI uses DR
• When a new packet arrives, the local world state
  is updated
• How often to send a packet will depend on the
  games domain.

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Defeating Lag With Cubic Splines
Pt P0 vt
P P0 v0t 0.5at2
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Using Cubic Splines

• Using cubic splines to create a path is a matter
  of simple algebraic equations. The input for
  these equations are four (x,y) coordinates.
• Coordinate 1  Starting position
• Coordinate 2 Position after 1 second using
  starting velocity Coordinate1
  StartVelocity
• Coordinate 3 Position after 1 second using
  reversed ending velocity
  Coordinate4 EndVelocity
• Coordinate 4 Ending position

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Using Cubic Splines

• Here are the parametric equations used to form
  the spline.
• x At3 Bt2 Ct D
• y Et3 Ft2 Gt H
• t is the time variable. It ranges from 0 at the
  initial point to 1 at the end point.
• A x3 3x2 3x1 x0B 3x2 6x1 3x0C
  3x1 3x0D x0E y3 3y2 3y1 y0F 3y2
  6y1 3y0G 3y1 3y0H y0

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Finally
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Inferring Goals

• In cases when the world is not fully accessible,
  the AI can use DR to predict the Human Players
  future goals and decide its interception strategy

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Correcting Errors in DR

• The estimate provided by DR can become unbounded
  over time
• A constant bound might be possible by using a
  Priori map (evidence grid)
• The Agent computing its own position maintains a
  local short map of its surroundings
• This short term map is compared with the priory
  map using PR techniques
• Small, incremental corrections are applied to the
  agents trajectory

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Demonstration - Targeting

• Targeting in Real-Time Network Games

The reality of network games what everyone sees
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Effects of Latency in a Game
Latency causes the game to go in different
directions for each player
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Compensating??
Overly compensating for latency makes the game
look bad.
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Targeting
The target (the blue thing) has two elements A
position, and a velocity.
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Pseudo Code

• for each frame
• target.x_velocity target.x_velocity
  target.x_acceleration
• target.y_velocity target.y_velocity
  target.y_acceleration
• target.z_velocity target.z_velocity
  target.z_acceleration
• target.x_position target.x_position
  target.x_velocity
• target.y_position target.y_position
  target.y_velocity
• target.z_position target.z_position
  target.z_velocity
• laser.x (laser.x target.x_position) / 2
• laser.y (laser.y target.y_position) / 2
• laser.z (laser.z target.z_position) / 2

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Final Effect
The server and other clients can calculate where
the laser is on your screen (the target), but
rather than just placing it there, it makes the
laser quickly converge to that target. This
makes the game run more smoothly for everybody
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Conclusion

• DR is an easy way to predict trajectories of
  objects
• The calculations are based on the information
  readily available and hence there is no inherent
  cheating
• Its execution time is linear wrt the no. of
  objects being tracked

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References

• Dead Reckoning in Sports and Strategy Games AI
  Game Programming Wisdom 2
• Targeting - A variation of Dead Reckoning - Chris
  Haag http//www.gamedev.net/reference/articles/art
  icle1370.asp
• Defeating Lag With Cubic Splines - Nick Caldwell
• http//www.gamedev.net/reference/articles/article
  914.asp
• Suitability of Dead Reckoning Schemes for Games
• http//netmedia.kjist.ac.kr/courses/dic1623-2002f
  a/reports/Sehchan-Case20(Networked20Game2).ppt1
  
• A Dead-Reckoning Technique for Streaming Virtual
  Human Animation
• http//ligwww.epfl.ch/thalmann/papers.dir/ieeetr
  _csvt.PDF