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Controlling Animation

Controlling Animation. Boundary-Value Problems Shooting Methods Constrained Optimization Robot Control. Computer Animation. Story (concept, storyboard) Production (modeling, motion, lighting). Motion. Keyframing Interpolates motion from “key” positions Perfect control

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Controlling Animation

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  1. Controlling Animation Boundary-Value Problems Shooting Methods Constrained Optimization Robot Control

  2. Computer Animation • Story • (concept, storyboard) • Production • (modeling, motion, lighting) Slide 2

  3. Motion • Keyframing • Interpolates motion from “key” positions • Perfect control • Can be tedious • No realism Slide 3

  4. Motion • Simulation • Solves equations of motion to compute motion • Realistic motion • Automatic generation • Difficult to control Slide 4

  5. Controlling Simulation • What initial velocity will cause the hat to land on the coatrack? ? Slide 5

  6. Production • Story dictates the motion. Animator’s must control the behavior. Slide 6

  7. initial velocity simulator Simulation Function S(t, u) nonlinear not continuous Slide 7

  8. How do we compute S(t, u)? • Solve an initial-value problem: numerically integrate the first-order differential equation...detect collisions...apply impulses when collisions occur. Slide 8

  9. Boundary-Value Problem • A solution to an initial value problem is a motion that is the solution to a differential equation with the specified initial value. A solution to a boundary value must also solve the ordinary differential equation and match the specified boundary values (initial, final, or any other). ? Slide 9

  10. Boundary-Value Problem • What initial velocity will cause the hat to land on the coatrack? Slide 10

  11. Solution by Shooting • Shooting Method • Pick initial linear and angular velocity u = (v, ω) • Simulate with initial value q0=(x0, R0, u) to compute the simulation function S(t, u) • Repeat until S(t, u) matches the other boundary value x1, R1 • Problem • The initial linear and angular velocity are described by 6 parameters. • Exploring a parameter space of high-dimension requires many samples: number of points in a uniform grid grows exponentially. Slide 11

  12. Shooting Method • We can combat the high dimensional parameter spaces with clever sampling techniques or derivative-based methods. • Sampling techniques • Importance Sampling • Markov Chain Monte Carlo • Derivative-based Methods • Gradient descent • Newton’s root finding method • Human assistance (interaction) Slide 12

  13. Interactive Control Slide 13

  14. Interactive Control Slide 14

  15. Interactive Control Slide 15

  16. update Interactive Control Slide 16

  17. surface simulator gravity More Parameters velocity … Slide 17

  18. simulator More Constraints velocity surface gravity … Slide 18

  19. simulator More Bodies velocity surface gravity … Slide 19

  20. Active Characters • What about objects that have self-propelling muscles and forces. How can we compute their motion automatically? Slide 20

  21. Constrained Optimization • Body, muscle and force degrees of freedom: q(t) • Constraints • Pose Cp • Mechanical Cm • Dynamics Cd • Objective Function E(q(t)) Slide 21

  22. Controller Approach • Roboticists address almost identical problems in robot design. How should we control a robot to make it walk or run? Similar techniques have been applied for problems in computer animation. • Biomechanics data and observations • Feedback controllers • designed by hand • simulated annealing • generate-and-test strategy • parameter estimation and parallel optimization techniques Slide 22

  23. Next Time • Research in the MIT Computer Graphics Group Slide 23

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