csce 552 spring 2011 inverse kinematics & ai by jijun tang
TRANSCRIPT
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