Reading. Realistic Character Animation. Modeling Realistic Motion. Two Approaches

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1 Realistic Character Animation Reading Jessica Hodgins,,et.al,Animating Human Athletics,, SIGGRAPH 95 Zoran Popović, Changing Physics for Character Animation,, SIGGRAPH 00 2 Modeling Realistic Motion Model muscles Environment forces Energy consumption Individual style Two Approaches Simulate robot controllers Solve a large optimization that obeys laws of physics and minimized energy consumption 3 4

2 Control Systems Robot Controllers in Animation Desired Forces and behavior torques User Control Model State Numerical Integrator Graphics 5 6 Where do the control laws come from? Observation Biomechanical literature Optimization Intuition Hierarchy of control laws 1. State machine 2. Control actions 3. Low level control 7 8

3 Hierarchy of control laws Running state machine 1. State machine 2. Control actions 3. Low level control Ball of foot Leaves ground unloading flight Heel touches ground loading Knee extended Knee bends Toe contact Percentage of stance phase complete Heel and Toe contact Heel contact Ball of foot touches ground 9 10 Hierarchy of control laws Flight duration 1. State machine 2. Control actions 3. Low level control 11 12

4 Forward Velocity Ground speed matching Balance: roll, pitch, yaw Mirroring: hips and shoulders 15 16

5 Control laws for all states Neck: turn in desired facing direction Shoulder: mirror hip angle Elbow: mirror magnitude of shoulder Wrist: constant angle Waist: keep body upright Hierarchy of control laws 1. State machine 2. Control actions 3. Low level control Low level control τ = k( θ θ) + k ( θ θ) d v d Difference between walking and running Walking: double support Running: flight phase Energy transfer patterns Inverted pendulum Pogostick 19 20

6 Spacetime Optimization 21 Captured Motion Works well only for small deformations No high-level editing constructs High Level Control Get a limp walk by making one leg stiff Reduce gravity to get a moon walk Change the position and timing of foot placements Make a quiet run by reducing the floor impact forces 23 24

7 The New Approach Outline Complex Model Transform existing motion Spacetime constraints formulation Simplified character representation Get the best of both worlds: Expressiveness of captured data Controllability of the spacetime model Original motion Fitting Spacetime motion model Motion Library Spacetime Editing Final motion Reconstruction Simplified Model Transformed spacetime motion Outline Complex Model Simplified Kinematics Original motion Final motion Fitting Reconstruction Simplified Model Spacetime motion model Spacetime Editing Transformed spacetime motion Human Run Human Jump 27 28

8 Motion Synthesis As Constrained Optimization Outline Complex Model Body, muscle and force DOFs: q(t) Constraints: Pose C p Mechanical C m Dynamics C d Objective E(q(t)) q m a minimize E q ( t ) q(t) R C p q () t = 0 F subject to q S f m C ma q t f () = 0 C q () t = 0 T F = m a " t q k a C d m f f C p U V W Original motion Fitting Spacetime motion model Motion Library Spacetime Editing Final motion Reconstruction Simplified Model Transformed spacetime motion Outline Complex Model Spacetime Editing Original motion Fitting Spacetime motion model Final motion Spacetime Editing Reconstruction Simplified Model Transformed spacetime motion Change pose and environment constraints Foot placement and timing Introduce a new obstacle Change the objective function Minimize floor impact forces Make dynamic balance more important 31 32

9 Spacetime Editing Change explicit character parameters Short leg Redistribute mass Modify muscle characteristic Gravity Example: Human Run Original model has 59 DOFs Simplified model has 19 DOFs Optimizations are done on one gait cycle Each optimization completes within 2 minutes Example: Human Broad Jump Original model has 59 DOFs Simplified model has 11 DOFs Entire upper body reduced to a mass point No joint angle DOFs 35 36

10 Hopper y x z z y x y Prismatic Joint 37