Dynamo Dynamic, Data-driven Character Control with Adjustable Balance Pawel Wrotek Electronic Arts Chad Jenkins Brown University Morgan McGuire Williams.

Dynamo Dynamic, Data-driven Character Control with Adjustable Balance

Pawel Wrotek Electronic Arts

Chad Jenkins Brown University

Morgan McGuire Williams College

First, a video…First, a video…

Character MotionCharacter Motion

• An integral part of modern video gamesFIFA 2006 (EA)

San Andreas (Rockstar)

Antigrav (Harmonix)

Kinematic Character MotionKinematic Character Motion

• Expressed by rigid body kinematics

– Rigid bodies connected by joints

– Character pose defined by rotation

of joints

– Vector θ(t) represents pose

at a given instant of time

Motion Generation:Motion Generation:Mocap and KeyframingMocap and Keyframing

• (+) path of least resistance

• (+) absolute control “wyciwyg”

• (-) not physically dynamic

– static and partial snapshot of the dynamics occurred at the time of creation

• Production animation, not interactive games

God of War 2 (Sony)

Motion Generation:Motion Generation:Procedural AnimationProcedural Animation

• Rules/algorithms to automatically generate motion

• Three categories of approaches:

– Indirectly emulate physical plausibility

• [Perlin,Goldberg 94] [Popovic, Witkin 99] [Kovar et al. 02]

– Simulate physics only when necessary

• [Shapiro et al. 03] [Zordan et al. 05]

– Simulate physics directly and persistently

• [Hodgins et al. 95] [Laszlo et al. 00]

Procedural AnimationProcedural Animation

• Indirectly emulate physical plausibility

– Scripting [Perlin,Goldberg 94]

– Blending [Rose et al. 98]

– Optimization [Liu et al. 05] [Arikan et al. 03]

(+) creators retain control

Creators define all rules for movement

(-) violates the “checks and balances” of motion

Motion control abuses its power over physics

(-) limits emergent behavior

Procedural AnimationProcedural Animation

• Simulate physics directly

– Ragdolls

– Controllers to generate motor forces

[Zordan, Hodgins 02] [Faloutsos et al. 01][Popovic et al. 00]

– (+) proper “separation of powers”

• Physics, control, AI

• Allows for emergent, natural interactions

– (-) inherit problems that plague robotics

PhysicsController

Procedural AnimationProcedural Animation

• Simulate physics only when necessary– Dynamic response:

[Shapiro et al. 03] [Zordan et al. 2005] [Natural Motion Endorphin]

– Mocap for “normal” dynamics

– Simulation for disturbance dynamics

(+) the best of mocap and simulation

(-) limited to passive response

• Falling, getting hit, etc.

• No persistent interaction

Fundamental QuestionFundamental Question

• Can we have practical methods for physically simulated characters?

• Revisit the broader picture for autonomous control

– Decision making (AI): objectives, current state (x[t]) → desired motion (xd[t])

– Motion Control: desired motion (xd[t]), current state (x[t]) → motor forces (u[t])

– Physics: current state (x[t]) → next state (x[t+1])

PhysicsMotionControl

DecisionMaking

objectives

x[t+1]

u[t]xd[t]

u[t]=MC(xd[t]-x[t]) x[t+1]=P(x[t],u[t])xd[t]=AI(x[t])

The Autonomous Physical Motion The Autonomous Physical Motion Control ProblemControl Problem

MotionControl

DecisionMaking

objectives

x[t+1]

u[t]xd[t]

u[t]=MC(xd[t]-x[t])xd[t]=AI(x[t])

Physicsu[t]

x[t+1]=P(x[t],u[t])

The Autonomous Physical Motion The Autonomous Physical Motion Control ProblemControl Problem

• Simulating physics

– Download ODE

– Buy Havoc

– Implement Guendelman et al. 03

MotionControl

DecisionMaking

objectives

x[t+1]

u[t]xd[t]

u[t]=MC(xd[t]-x[t])xd[t]=AI(x[t])

The Autonomous Motion Control The Autonomous Motion Control ProblemProblem

• AI for autonomous decision making

– Someone else’s problem

– Interface point for decision making

– Focus on motion control

• Motion capture as decision making placeholder

MotionControl

x[t+1]

u[t]xd[t]

u[t]=MC(xd[t]-x[t])

Mocapdata

Motion Control: ImpedimentsMotion Control: Impediments

• Gain tuning for motion control

• Balance for upright motion

MotionControl

x[t+1]

u[t]xd[t]

u[t]=MC(xd[t]-x[t])

Mocapdata

Motion Control: ImpedimentsMotion Control: Impediments

• Gain tuning for motion control

• Balance for upright motion

MotionControl

x[t+1]

u[t]xd[t]

u[t]=MC(xd[t]-x[t])

Mocapdata

Problem: parent space control?

Motion Control: ImpedimentsMotion Control: Impediments

• Gain tuning for motion control

• Balance for upright motion

MotionControl

x[t+1]

u[t]xd[t]

u[t]=MC(xd[t]-x[t])

Mocapdata

Problem: parent space control?Solution: world space control?

Segway Analogy Segway Analogy

Segway Analogy Segway Analogy

Segway Analogy Segway Analogy

• Parent PD-servo

– Torque u about an axis

• Appropriate kp and kd values

are necessary for stable control

– Tedious and difficult

– Holdover from robot rotational sensing

Feedback Motion ControlFeedback Motion Control

u

u[t]=kp(θd[t] - θ[t]) + kd(θd[t] - θ[t])..

D. Brogan

World Space PD-ServoWorld Space PD-Servo

• τ = kp (v · θ) + kd (ωd – ωa)Wd = desired world space rotation matrix

Wa = actual world space rotation matrix

T = Wd * Wa-1

(transformation from Wa to Wd)

v, θ = rotation axis, angle derived from T

ωd = desired world space angular velocity

ωa = actual world space angular velocity

Wd

Wa

v

θ

A Note about Axis-AngleA Note about Axis-Angle(Source code in the paper)(Source code in the paper)

• Torques determined by desired angular acceleration

– i.e., Proportional to 2nd derivative of rotation

• 1D Hinge [Hodgins95]: 2/t2

• 3D Ball joint: 2[rotation]/t2

– …but Matrix/Quat derivatives produce denormalized results under ODE’s Euler integration and are awkward to convert to torques

– Rotation axis is fixed anyway during the Euler timestep, so reduce to a 1D problem…

• 3D Ball joint: )(],[ ; 1012

2

tt MMaxisAnglevt

v

Early ResultsEarly Results

• Gain Tuning

• Cartwheel with object

Super-balancingSuper-balancing

• An artifact of world space control

• Retain “separation of powers”

– Desired pose relative to character root (Person space)

– Desired root orientation specified by AI

– Actual position and orientation determined by physics

Root-spring controlRoot-spring control

• Spring only opposes gravity (no rotation about FG)

• Torque-limited and breaks under excessive strain

2

G

rootGGrootbalance

F

FF

balanceTorque limit Breaking point

balance

maximum

= 0

Applied Torque

ResultsResults

• Obstacle course

– Parent space

– Person space

• User interaction

• Balance comparison

• Ballistic

– Person space (meathook)

– Person space (root spring), Parent space

• In-game boxing

Parent space

Dynamo

ResultsResults

• Obstacle course

– Parent space

– Person space

• User interaction

• Balance comparison

• Ballistic

– Person space (meathook)

– Person space (root spring), Parent space

• In-game boxing

ResultsResults

• Obstacle course

– Parent space

– Person space

• User interaction

• Balance comparison

• Ballistic

– Person space (meathook)

– Person space (root spring), Parent space

• In-game boxing

ResultsResults

• Obstacle course

– Parent space

– Person space

• User interaction

• Balance comparison

• Ballistic

– Person space (meathook)

– Person space (root spring), Parent space

• In-game boxing

ResultsResults

• Obstacle course

– Parent space

– Person space

• User interaction

• Balance comparison

• Ballistic

– Person space (meathook)

– Person space (root spring), Parent space

• In-game boxing

Future WorkFuture Work

• AI for goal-oriented motion generation

• Experimental parent vs. world analysis

• Biomechanical character constraints

• Embodied perception

ConclusionConclusion

• Physically dynamic characters are practical

• World-space control yields

– Implicit character balance

– Easier gain tuning

• Path to emergent behavior for interactive characters

AcknowledgementsAcknowledgements

• NSF Award IIS-0534858

• Dan Byers

• Sam Howell

• mocap.cs.cmu.edu

• G3D and ODE user communities

• “Innovating Game Development”

Guest Lecturers

• A-Lab

RoboCup Dynamical SoccerRoboCup Dynamical Soccer• [email protected]

• [email protected]