World Space Servoing for Character Animation Under Simulation

World Space Servoing for Character Animation Under Simulation Pawel Wrotek Electronic Arts Chad Jenkins Brown University Morgan Mc. Guire 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 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 Wa Wd v

A Note about Axis-Angle (Source code in our Sandbox paper) • Torques determined by desired angular acceleration – i. e. , Proportional to 2 nd derivative of rotation • 1 D Hinge [Hodgins 95]: t 2 q/ t 2 • 3 D Ball joint: t 2[rotation]/ t 2 – …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 1 D problem… • 3 D Ball joint:

Early Results • Gain Tuning • Cartwheel with object

More Recent Results • Obstacle course – Parent space – World space Parent 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 G 3 D and ODE user communities “Innovating Game Development” Guest Lecturers • A-Lab

Robo. Cup Dynamical Soccer • cjenkins@cs. brown. edu • morgan@cs. williams. edu