Movement AI

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Movement AI

• John See
• 19, 26 Nov 2010

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Movement AI in Millingtons Model
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Movement AI vs. Animation

• Many games rely solely on some movement AI, and
  very little advanced decision-making
• Movement AI vs. Animation overlap
• Movement AI movement of characters around the
  game level and NOT movement of limbs/faces/parts
  etc.

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Movement algorithm structure
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2D Movement - Statics

• Characters as Points
• Static structure
• Position of character (two linear coordinates in
  a 2D vector)
• Orientation (floating point value in radians)
• 2D movement commonly take place on the x-z plane
  with y axis fixed to zero
• In standard game engines by default, a character
  is looking down the z-axis at zero orientation

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Kinematics

• Movement (velocity) calculated based on position
  and orientation alone
• No acceleration involved? A little unrealistic,
  but works fine for many games. Simpler to
  implement.
• Kinematic structure
• Position of character (2D or 3D vector)
• Orientation (floating point value indicating
  degree of facing)
• Velocity (2D or 3D vector indicating speed and
  direction)
• Rotation (floating point value indicating
  rotation speed)
• Steering structure
• Return accelerations (for movement and rotation)
  to change velocities of character

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Updating Position and Orientation

• High-school physics equations for motion
• s vt 0.5at2
• If frame rate high, update time is small, the
  square is even smaller, contribution of
  acceleration is negligible
• Common to see the 2nd term removed from the
  update loop for fast movement updates (less
  computation too)
• s vt

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Kinematic Movement Algorithms

• Use static data (position orientation, no
  velocities) to output a desired velocity
• No acceleration used
• Abrupt changes in velocity can be smoothed over
  several frames to give realistic look
• Further simplification Force orientation of
  character to be in the direction it is traveling
  (without any smooth rotation)

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Seek (Kinematic)

• Input Characters and Targets static data
  (position orientation)
• Calculates
• Velocity direction (vector) from the character to
  the target by subtracting position of character
  from position of target)
• No rotation
• Perform normalization on the direction vector to
  obtain unit vector, which will then be multiplied
  with the max speed of character

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Flee (Kinematic)

• Simply reverse the calculation of the velocity
  direction vector, to move away from the target
• Calculate from target to character

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Arrive (Kinematic)

• SEEK is designed for chasing
• If the character seeks a particular location in
  the world at constant maximum speed, it is likely
  to overshoot an exact point, wiggle backward and
  forward trying to get there.
• Arrive introduces
• A radius of satisfaction (to check if the
  character is nearing location)
• A time-to-target value (to slow character down if
  it is within radius of satisfaction)
• Inside radius, Velocity Dist. from location /
  Time-to-target
• This reduces as the character is nearing location

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Wander (Kinematic)

• Character meanders randomly (like a random walk)
  in a forward direction
• Always moves in the direction of the current
  orientation at maximum speed
• Direction of orientation is randomized here
• Take a random number between 1 and 1 (where
  values around zero are more likely), and multiply
  by a fixed maximum rotation speed), to get new
  rotation velocity

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Steering Behaviors

• Extend kinematic algorithms by adding velocity
  and rotation as input thus characters have
  acceleration
• 2 categories
• Fundamental steering behaviors
• Behaviors built from combination of fundamental
  behaviors
• Input Kinematic values of a moving character
• Target information can be from another moving
  character, collision geometry of the world, or
  specific path geometry

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Variable Matching

• Simplest form of steering behaviors involve
  matching variables from character with variables
  from target.
• Matching
• Position of target (Seek, Arrive)
• Orientation of target (Align)
• Velocity of target (Velocity Matching)
• Delegation or Combination of various kinematic
  elements
• There could be opposite behaviors that will
  intend to unmatch as much as possible.

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Seek Flee

• Seek match position of character with position
  of target.
• Direction vector from character to target.
• Velocity/speed of character needs to be clipped
  from exceeding its maximum value, since
  acceleration will cause its speed to grow larger
  and larger.
• Acceleration is applied to the direction to the
  target, limited by a maximum value
• Introduce additional drag to prevent orbiting of
  target
• Flee Direction vector from target to character

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Arrive

• Similar to (Kinematic) Arrive, this (Dynamic)
  Arrive intends to slow the character down as it
  approaches the target so that it arrives exactly
  at the right location

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Arrive

• Uses 2 radii
• Arrival Radius lets character get near enough
  to target w/o letting small errors keep it in
  motion
• Slowdown Radius slows character down when it
  passes into this radius. Ideal speed is
  calculated using time-to-target method (like
  before). Upon entering this radius, speed is
  maximum. Zero speed when arrive successfully.
• The target velocity (speed) is interpolated using
  distance from target
• When a character is moving too fast to arrive at
  right time, target velocity lt actual character
  velocity, acceleration will be negative, or
  acting to slow it down

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Leave

• Opposite behavior to Arrive
• No point in implementing Unlikely to want to
  accelerate and build up speed if leaving.
• Just using Flee (move at maximum velocity)

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Align

• Match orientation of the character with that of
  target
• Pays no attention to position/velocity of
  character/target
• Idea Subtract character orientation from target
  orientation, and convert result into range (-p,
  p) radians
• Algorithm is similar to Arrive

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Velocity Matching

• Idea Use acceleration to get to the target
  velocity
• Subtract velocity of character from velocity of
  target to get velocity difference
• Use time-to-target method to find
  acceleration/deceleration to be applied to
  character
• How is matching velocities useful?
• Also becomes much more useful when combined with
  other behaviors (e.g. flocking steering behavior)

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Delegated Behaviors

• More complex behaviors that make use of the basic
  fundamental steering behaviors
• Seek, Align and Velocity Matching are the
  fundamental behaviors that can be used
• Programming Tip Polymorphic style needed to
  capture these dependencies

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Pursue

• When seeking a moving target, constantly moving
  towards the targets current position is not
  sufficient!
• Going in circles? Inefficient? Look unrealistic?
• Instead of aiming at its current position, how
  about predicting where it will be at some time in
  the future, and aim towards that point?

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Pursue

• Does not need sophisticated algorithms
  Overkill!
• Assumption Target will continue moving with same
  velocity as it currently is.

• Work out distance between character and target,
  and how long it takes to get there
• Use this time interval as prediction time
• Calculates position of target based on the
  assumption
• Use new position as target for Seek

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Evade

• Simply the opposite behavior to Pursue
• Instead of delegating to Seek, delegate it to Flee

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Face

• Makes character look at its target
• Delegates to Align behavior to perform rotation,
  but calculates target orientation first
• Target orientation generated from relative
  position of target to character

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Looking Where Youre Going

• To enable character to face in the direction it
  is moving
• Using Align, give the character angular
  acceleration to make it face the right way while
  moving this method causes gradual facing change
  (more natural)
• Method of implementation is similar to Face
  behavior except for target orientation which is
  calculated using current velocity of character

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Wander

• In Kinematic version, direction of character is
  perturbed by a random amount of rotation each
  time it was run. Result Erratic rotation
• This can be smoothen by making orientation of the
  character indirectly reliant on random numbers.
• OR, think of it as a delegated Seek behavior.
• Idea 1 Constrain the target to a circle around
  the character

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Wander

• Idea 2 Improve it by moving the circle out in
  front of the character and shrink it down
• Face or Look Where Youre Going behaviors can be
  used to align the characters orientation to the
  direction it is moving
• A maximum wander rate can be used to constrain
  the random numbers to an interval within the
  previous wander direction to prevent too much
  erratic rotation

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Path Following

• Steering behavior that takes a whole path as a
  target
• Move along path in one direction
• A Delegate behavior
• Calculates position of target based on current
  character location and shape of path
• Hands over its target to Seek

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Path Following

• 2 stages
• Current character position is mapped to nearest
  point along path. Curved paths or paths with many
  line segments can increase computation
  complexity.
• Target is selected further along the path than
  the mapped point by a fixed distance. Seek the
  target.

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Predictive Path Following

• Predictive version
• Predict where the character will be in a short
  time.
• Map this to the nearest point on the path. This
  is the candidate target for seeking.
• If the new candidate target has not been placed
  farther along the path than it was at the last
  frame, then change to new target.

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Predictive Path Following

• Upside Smoother for complex paths with sudden
  direction change
• Downside Cutting-corner behavior Character may
  miss a whole section of the path if two sections
  of a path come close together

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How to Construct Path?

• For ease of use in graphic/rendering systems,
  paths are normally represented using a single
  parameter (normally floating-point, constraint to
  a range) that increases monotonically along the
  path (can be seen as distance along path)

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Separation

• Commonly used for crowd simulations (where number
  of characters are heading roughly same direction)
• Acts to keep characters from getting too close
  and crowded.
• Does not work when characters move across each
  others path
• Zero output in terms of movement!

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Separation

• Idea If behavior detects another character
  closer than some threshold, it acts like evade
  to move away
• Strength of the evade movement is related to
  the distance from the target
• 2 common calculations
• Strength maxAcceleration (threshold
  distance) / threshold
• Strength min(k distance distance,
  maxAcceleration)
• For each case,
• distance distance between character and nearby
  neighbor
• threshold min distance for separation to occur
• maxAcceleration max acceleration of character
• k strength decay constant

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Steering Family Tree
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Other Delegated Steering Behaviors

• Collision Avoidance
• To avoid collision between various moving
  characters
• Obstacle/Wall Avoidance
• To avoid collision between character and
  unanimated obstacles or walls
• Read from textbook

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Combining Steering Behaviors

• A moving character usually needs more than one
  steering behavior to model it more realistically
• E.g. To seek its goal, avoid collision with
  others, avoid bumping into walls
• Some special behaviors may require more than one
  steering behavior to be active at once.
• E.g. To steer in a group towards a goal,
  maintaining a good separation distance from group
  members, and to match each members velocities
• How?

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Combining Steering Behaviors

• Blending
• Execute all steering behaviors and combining
  their results using some set of weights or
  priorities
• Arbitration
• Selects one or more steering behaviors to have
  complete control over character. Many schemes
  available nowadays.
• Many steering systems combine elements of both
  blending and arbitration to maximize advantages

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Weighted Blending

• Use weights to combine steering behaviors
• Example Riot crowd AI
• Character does not just do one thing. It does a
  blend or synthesis of all considered behaviors.
• Idea
• Each steering behavior is asked for its
  acceleration request
• Combine the accelerations using a weighted linear
  sum, coefficients specific to each behavior
• If final acceleration from sum is too great, trim
  it accordingly

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Flocking

• Original research by Craig Reynolds, to model
  movement patterns of flocks of simulated birds
  (boids).
• Flocking relies on simple weighted blend of 3
  behaviors
• Separation move away from boids that are too
  close
• Alignment move in the same direction and at the
  same velocity as flock
• Cohesion move towards the center of mass of the
  flock
• Simple flocking Equal weights for all
• Any of the behaviors seemed more important?

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Flocking

• In most implementations, flocking behavior is
  modified to ignore distant boids for efficiency
• A neighborhood is specified to consider only
  other boids within the area
• Shape Radius or angular cut-off

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Flocking
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Flocking Equilibria Problems

• Unstable equilibria Character trying to do more
  than one thing at a time, resulting in doing
  nothing (as long as enemy is stationary), then
  skirts around before making a move
• Stable equilibria Character could make it out of
  equilibrium slightly, but heads back into
  equilibrium within basin of attraction

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Flocking Constrained Environments

• Obstacles vs. Target Character tries to avoid
  obstacle while pursuing enemy. Blending causes
  resulting direction even farther from correct
  route to capture enemy
• Narrow Doorways Character tries to move at acute
  angles through narrow doorways to get to target.
  Obstacle avoidance causes character to move past
  the door missing the target

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Flocking Nearsightedness Problem

• Nearsightedness Due to the behaviors acting
  locally in their immediate surroundings, a
  character can avoid a wall, but takes the wrong
  side of the wall due to method of computing
  change of orientation.
• Does not realize the wrong path!
• Can be addressed by incorporating pathfinding.

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Priority-based Blending

• Some steering behaviors do not produce
  acceleration as output (collision avoidance,
  separation, arrive, etc.) HOW?
• Example Seek (always max acceleration)
  Collision Avoidance (minimal change of movement
  to avoid).
• Seek always dominates if blended equally!

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Priority-based Blending

• Idea
• Arrange behaviors in groups with regular blending
  weights
• Place groups in order of priority, and consider
  each group accordingly
• If total result is very small (less than some
  threshold), ignore it and consider next group
• If total result is reasonable (more than some
  threshold), use the result to steer character
• Example Pursuing character with 3 groups in
  priority 1st Collision avoidance, 2nd
  Separation, 3rd Pursuit

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Equilibria Fallback

• Priority-based approach can cope with stable
  equilibria problem.
• If a group of behaviors in equilibrium, total
  acceleration will be near zero drop down to the
  next group in priority
• Example Falling back to Wander

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Cooperative Arbitration

• In priority blending, a prioritized behavior may
  have an drastic effect on the character movement
  (not smooth) when it changes to other behaviors
  of less priority
• In weighted blending, one of the main behaviors
  may be diluted by the output of another behavior
• Context-sensitive or cooperation between
  different behaviors can help create more
  realistic and less-dramatic movement

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Cooperative Arbitration Steering Pipeline
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Other Movement Topics

• Physics (Predictive and Non-predictive)
• Jumping
• Coordinated Movement (to some extent using group
  AI)
• Formations
• Motor Control