World Space Servoing for
Character Animation Under
Simulation
Pawel Wrotek Electronic Arts
Chad Jenkins Brown University
Morgan McGuire Williams College
Character Motion
• An integral part of modern video games
FIFA 2006 (EA)
San Andreas (Rockstar)
Antigrav (Harmonix)
Kinematic 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
Issues with Canned Motion
Physically Simulated
Canned Mocap
Issues with Canned Motion
Physically Simulated
Canned Mocap
Issues with Canned Motion
Physically Simulated
Canned Mocap
Motion Generation:
Mocap 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:
Procedural 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 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 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
Controller
• Allows for emergent, natural interactions
– (-) inherit problems that plague robotics
Physics
Procedural 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 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])
xd[t]=AI(x[t])
objectives
Decision
Making
u[t]=MC(xd[t]-x[t])
xd[t]
Motion
Control
x[t+1]=P(x[t],u[t])
u[t]
x[t+1]
Physics
The Autonomous Physical
Motion Control Problem
xd[t]=AI(x[t])
objectives
Decision
Making
u[t]=MC(xd[t]-x[t])
xd[t]
Motion
Control
x[t+1]=P(x[t],u[t])
u[t]
x[t+1]
Physics
The Autonomous Physical
Motion Control Problem
xd[t]=AI(x[t])
objectives
Decision
Making
u[t]=MC(xd[t]-x[t])
xd[t]
Motion
Control
u[t]
x[t+1]
• Simulating physics
– Download ODE
– Buy Havoc
– Implement Guendelman et al. 03
The Autonomous Motion Control
Problem
u[t]=MC(xd[t]-x[t])
Mocap
data
xd[t]
Motion
Control
u[t]
x[t+1]
• AI for autonomous decision making
– Someone else’s problem
– Interface point for decision making
– Focus on motion control
• Motion capture as decision making placeholder
Motion Control: Impediments
u[t]=MC(xd[t]-x[t])
Mocap
data
xd[t]
Motion
Control
u[t]
x[t+1]
• Gain tuning for motion control
• Maintaining upright balance
Motion Control: Impediments
u[t]=MC(xd[t]-x[t])
Mocap
data
xd[t]
Motion
Control
u[t]
x[t+1]
• Gain tuning for motion control
• Maintaining upright balance
Problem: parent space control?
Motion Control: Impediments
u[t]=MC(xd[t]-x[t])
Mocap
data
xd[t]
Motion
Control
u[t]
x[t+1]
• Gain tuning for motion control
• Maintaining upright balance
Problem: parent space control?
Solution: world space control!
Segway Analogy
• Parent space
– Wheel-centric
coordinates
Segway Analogy
• Parent space
– Wheel-centric
coordinates
• Wheel rotation =
you falling
Segway Analogy
• Parent space
– Wheel-centric
coordinates
• Wheel rotation =
you falling
• Artifact of rotational
sensing
Segway Analogy
• World space
– Earth-centric
coordinates
– Sensed by MEMS
accelerometers
– Separate rider and
wheel orientation
Feedback Motion Control
• Parent PD-servo
– Torque u about an axis
.
.
u[t]=kp(θd[t] - θ[t]) + kd(θd[t] - θ[t])
u
• Appropriate kp and kd values
need for stable control
– Tedious and difficult to find critical
damping
D. Brogan
World Space PD-Servo
τ = kp (v · θ) + kd (ωd – ωa)
Wd = desired world space rotation matrix
θ
Wa = actual world space rotation matrix
Wa
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
v
A Note about Axis-Angle
(Source code in our Sandbox paper)
• Torques determined by desired angular acceleration
– i.e., Proportional to 2nd derivative of rotation
• 1D Hinge [Hodgins95]:
t  2q/t2
• 3D Ball joint:
t  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:
  2q

t  v 2 ; [q , v ]  axisAngle( M t 1M t10 )
t
Early Results
• Gain Tuning
• Cartwheel with object
More Recent Results
• Obstacle course
– Parent space
Parent space
– World space
• User interaction
• Balance comparison
• In-game boxing
Dynamo
More Recent Results
•
•
•
•
Obstacle course
User interaction
Balance comparison
In-game boxing
More Recent Results
• Obstacle course
• User interaction
• Balance comparison
– Green: world space
– Orange: person space
– Purple: person w/ knockout
• In-game boxing
More Recent Results
•
•
•
•
Obstacle course
User interaction
Balance comparison
In-game boxing
Future Work
• AI for goal-oriented motion generation
• Experimental parent vs. world analysis
• Biomechanical character constraints
• Embodied perception
Conclusion
• Physically dynamic characters are practical
• World-space control yields
– Implicit character balance
– Easier gain tuning
• Path to emergent behavior for interactive
characters
Acknowledgements
•
•
•
•
•
•
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 Soccer
• cjenkins@cs.brown.edu
• morgan@cs.williams.edu