CSCE 552 Spring 2011

Inverse Kinematics & AI

By Jijun Tang

Announcements

Second presentation: April 11th and 13th In class Each group 12 minutes

What to show: Detailed designs of layers/modules/classes Progress report with demo 3D/2D Models, graphics, etc Schedules and milestones Problems and planned changes

Frustum and Frustum Culling

Hemisphere Lighting

Normal Mapping Example

Specular Lighting

Environmental Map

Inverse Kinematics

FK & IK Single Bone IK Multi-Bone IK Cyclic Coordinate Descent Two-Bone IK IK by Interpolation

FK & IK

Most animation is “forward kinematics” Motion moves down skeletal hierarchy

But there are feedback mechanisms Eyes track a fixed object while body moves Foot stays still on ground while walking Hand picks up cup from table

This is “inverse kinematics” Motion moves back up skeletal hierarchy

Example of Inverse Kinematics

Single Bone IK

Orient a bone in given direction Eyeballs Cameras

Find desired aim vector Find current aim vector Find rotation from one to the other

Cross-product gives axis Dot-product gives angle

Transform object by that rotation

Multi-Bone IK

One bone must get to a target position Bone is called the “end effector”

Can move some or all of its parents May be told which it should move first

Move elbow before moving shoulders May be given joint constraints

Cannot bend elbow backwards

Cyclic Coordinate Descent

Simple type of multi-bone IK Iterative: Can be slow May not find best solution: May not

find any solution in complex cases But it is simple and versatile: No

precalculation or preprocessing needed

Procedures

Start at end effector Go up skeleton to next joint Move (usually rotate) joint to minimize

distance between end effector and target Continue up skeleton one joint at a time If at root bone, start at end effector again Stop when end effector is “close enough” Or hit iteration count limit

Properties

May take a lot of iterations Especially when joints are nearly

straight and solution needs them bent e.g. a walking leg bending to go up a step 50 iterations is not uncommon!

May not find the “right” answer Knee can try to bend in strange directions

Two-Bone IK

Direct method, not iterative Always finds correct solution

If one exists Allows simple constraints

Knees, elbows Restricted to two rigid bones with a rotation

joint between them Knees, elbows!

Can be used in a cyclic coordinate descent

Two-Bone IK Constraints

Three joints must stay in user-specified plane: e.g. knee may not move sideways

Reduces 3D problem to a 2D one Both bones must remain original length Therefore, middle joint is at intersection of

two circles Pick nearest solution to current pose, or one

solution is disallowed: Knees or elbows cannot bend backwards

Example

Allowedelbow

position

Shoulder

Wrist

Disallowedelbow

position

IK by Interpolation

Animator supplies multiple poses Each pose has a reference direction

e.g. direction of aim of gun Game has a direction to aim in Blend poses together to achieve it Source poses can be realistic

As long as interpolation makes sense Result looks far better than algorithmic IK with

simple joint limits

Example

One has poses for look ahead, look downward (60

。), look right, look down and

right Now to aim 54

。right and 15

。 downward,

thus 60% (54/90) on the horizontal scale, 25% (15/60) on the downward scale Look ahead (1-0.25)(1-0.6)=0.3 Look downward 0.25(1-0.6)=0.1 Look right (1-0.25) 0.6=0.45 Look down and right (0.25)(0.6)=0.15

IK by Interpolation results

Result aim point is inexact Blending two poses on complex

skeletons does not give linear blend result

But may be good enough from the game perspective

Can iterate towards correct aim

Attachments

e.g. character holding a gun Gun is a separate mesh Attachment is a bone in character’s skeleton

Represents root bone of gun Animate character Transform attachment bone to world space Move gun mesh to that pos+orn

Attachments (2)

e.g. person is hanging off bridge Attachment point is a bone in hand

As with the gun example But here the person moves, not the bridge Find delta from root bone to attachment bone Find world transform of grip point on bridge Multiply by inverse of delta

Finds position of root to keep hand gripping

Artificial Intelligence:Agents, Architecture, and Techniques

Artificial Intelligence

Intelligence embodied in a man-made device

Human level AI still unobtainable The difficulty is comprehension

Game Artificial Intelligence:What is considered Game AI?

Is it any NPC (non-player character) behavior? A single “if” statement? Scripted behavior?

Pathfinding? Animation selection? Automatically generated environment?

Possible Game AIDefinition

Inclusive view of game AI:

“Game AI is anything that contributes to the perceived intelligence of an entity, regardless of what’s under the hood.”

Goals of anAI Game Programmer

Different than academic or defense industry

1. AI must be intelligent, yet purposely flawed2. AI must have no unintended weaknesses3. AI must perform within the constraints4. AI must be configurable by game designers

or players5. AI must not keep the game from shipping

Specialization ofGame AI Developer

No one-size fits all solution to game AI Results in dramatic specialization

Strategy Games Battlefield analysis Long term planning and strategy

First-Person Shooter Games One-on-one tactical analysis Intelligent movement at footstep level

Real-Time Strategy games the most demanding, with as many as three full-time AI game programmers

Game Agents

May act as an Opponent Ally Neutral character

Continually loops through the

Sense-Think-Act cycle Optional learning or remembering step

Sense-Think-Act Cycle:Sensing

Agent can have access to perfect information of the game world May be expensive/difficult to tease out useful info Players cannot

Game World Information Complete terrain layout Location and state of every game object Location and state of player

But isn’t this cheating???

Sensing:Enforcing Limitations

Human limitations? Limitations such as

Not knowing about unexplored areas Not seeing through walls Not knowing location or state of player

Can only know about things seen, heard, or told about

Must create a sensing model

Sensing:Human Vision Model for Agents

Get a list of all objects or agents; for each:1. Is it within the viewing distance of the agent?

How far can the agent see? What does the code look like?

2. Is it within the viewing angle of the agent? What is the agent’s viewing angle? What does the code look like?

3. Is it unobscured by the environment? Most expensive test, so it is purposely last What does the code look like?

Sensing:Vision Model

Isn’t vision more than just detecting the existence of objects?

What about recognizing interesting terrain features? What would be interesting to an agent? How to interpret it?

Sensing:Human Hearing Model

Human can hear sounds Human can recognize sounds and

knows what emits each sound Human can sense volume and indicates

distance of sound Human can sense pitch and location

Sounds muffled through walls have more bass

Where sound is coming from

Sensing:Modeling Hearing

How do you model hearing efficiently? Do you model how sounds reflect off every

surface? How should an agent know about sounds?

Sensing:Modeling Hearing Efficiently

Event-based approach When sound is emitted, it alerts

interested agents Observer pattern

Use distance and zones to determine how far sound can travel

Sensing:Communication

Agents might talk amongst themselves! Guards might alert other guards Agents witness player location and spread

the word Model sensed knowledge through

communication Event-driven when agents within vicinity of

each other

Sensing:Reaction Times

Agents shouldn’t see, hear, communicate instantaneously

Players notice! Build in artificial reaction times

Vision: ¼ to ½ second Hearing: ¼ to ½ second Communication: > 2 seconds

Sense-Think-Act Cycle: Thinking

Sensed information gathered Must process sensed information Two primary methods

Process using pre-coded expert knowledge

Use search to find an optimal solution

Thinking:Expert Knowledge

Many different systems Finite-state machines Production systems Decision trees Logical inference

Encoding expert knowledge is appealing because it’s relatively easy Can ask just the right questions As simple as if-then statements

Problems with expert knowledge: not very scalable

Finite-state machine (FSM)

Production systems

Consists primarily of a set of rules about behavior

Productions consist of two parts: a sensory precondition (or "IF" statement) and an action (or "THEN")

A production system also contains a database about current state and knowledge, as well as a rule interpreter

Decision trees

Logical inference

Process of derive a conclusion solely based on what one already knows

Prolog (programming in logic)

mortal(X) :- man(X). man(socrates).

?- mortal(socrates). Yes

Thinking:Search

Employs search algorithm to find an optimal or near-optimal solution Branch-and-bound Depth-first Breadth-first

A* pathfinding common use of search Kind of mixed

Depth and breadth-first

Thinking:Machine Learning

If imparting expert knowledge and search are both not reasonable/possible, then machine learning might work

Examples: Reinforcement learning Neural networks Decision tree learning

Not often used by game developers Why?

Thinking:Flip-Flopping Decisions

Must prevent flip-flopping of decisions Reaction times might help keep it from

happening every frame Must make a decision and stick with it

Until situation changes enough Until enough time has passed

Sense-Think-Act Cycle:Acting

Sensing and thinking steps invisible to player

Acting is how player witnesses intelligence Numerous agent actions, for example:

Change locations Pick up object Play animation Play sound effect Converse with player Fire weapon

Acting:Showing Intelligence

Adeptness and subtlety of actions impact perceived level of intelligence

Enormous burden on asset generation Agent can only express intelligence in terms

of vocabulary of actions Current games have huge sets of

animations/assets Must use scalable solutions to make selections

Extra Step in Cycle:Learning and Remembering

Optional 4th step Not necessary in many games

Agents don’t live long enough Game design might not desire it

Learning

Remembering outcomes and generalizing to future situations

Simplest approach: gather statistics If 80% of time player attacks from left Then expect this likely event

Adapts to player behavior

Remembering

Remember hard facts Observed states, objects, or players Easy for computer

Memories should fade Helps keep memory requirements lower Simulates poor, imprecise, selective human

memory For example

Where was the player last seen? What weapon did the player have? Where did I last see a health pack?

Rememberingwithin the World

All memory doesn’t need to be stored in the agent – can be stored in the world

For example: Agents get slaughtered in a certain area Area might begin to “smell of death” Agent’s path planning will avoid the area Simulates group memory

Making Agents Stupid

Sometimes very easy to trounce player Make agents faster, stronger, more accurate Challenging but sense of cheating may

frustrate the player Sometimes necessary to dumb down

agents, for example: Make shooting less accurate Make longer reaction times Engage player only one at a time Change locations to make self more vulnerable

Agent Cheating

Players don’t like agent cheating When agent given unfair advantage in speed, strength, or

knowledge People notices it

Sometimes necessary For highest difficultly levels For CPU computation reasons For development time reasons

Don’t let the player catch you cheating! Consider letting the player know upfront No one wants to fight a stupid enemy, trade-off

Common Game AI Techniques

A* Pathfinding Command Hierarchy Dead Reckoning Emergent Behavior Flocking Formations Influence Mapping …

A* Pathfinding

Directed search algorithm used for finding an optimal path through the game world

Used knowledge about the destination to direct the search

A* is regarded as the best Guaranteed to find a path if one exists Will find the optimal path Very efficient and fast

Command Hierarchy

Strategy for dealing with decisions at different levels From the general down to the foot soldier

Modeled after military hierarchies General directs high-level strategy Foot soldier concentrates on combat

US Military Chain of Command

Dead Reckoning

Method for predicting object’s future position based on current position, velocity and acceleration

Works well since movement is generally close to a straight line over short time periods

Can also give guidance to how far object could have moved

Example: shooting game to estimate the leading distance

Emergent Behavior

Behavior that wasn’t explicitly programmed

Emerges from the interaction of simpler behaviors or rules Rules: seek food, avoid walls Can result in unanticipated individual or

group behavior

Flocking

Example of emergent behavior Simulates flocking birds, schooling fish Developed by Craig Reynolds: 1987

SIGGRAPH paper Three classic rules

1. Separation – avoid local flockmates2. Alignment – steer toward average

heading3. Cohesion – steer toward average position

Formations

Group movement technique Mimics military formations Similar to flocking, but actually distinct

Each unit guided toward formation position Flocking doesn’t dictate goal positions Need a leader

Flocking/Formation

Influence Mapping

Method for viewing/abstracting distribution of power within game world

Typically 2D grid superimposed on land Unit influence is summed into each grid cell

Unit influences neighboring cells with falloff Facilitates decisions

Can identify the “front” of the battle Can identify unguarded areas Plan attacks Sim-city: influence of police around the city

Mapping Example

Level-of-Detail AI

Optimization technique like graphical LOD Only perform AI computations if player will

notice For example

Only compute detailed paths for visible agents Off-screen agents don’t think as often