1. Foundations of Computer Graphics (Spring 2010) CS 184, Lecture 25: Inverse Kinematics http://inst.eecs.berkeley.edu/~cs184 Many slides courtesy James O’Brien

2. Summary and Outline  Inverse Kinematics Lecture  CS 294-13 Advanced Graphics in the fall  Course Evaluations  Best of luck for HW 5, Final

3. Forward Kinematics  Joints (typically not 6 DOF)  Pin – rotate about one axis  Ball – arbitrary rotation  Prism – translate alone one axis

4. Joints

5. Pin and Ball Joint  Translate inboard joint to local origin  Rotate about axis (for pin), arbitrary (for ball)  Translate origin to location of joint on outboard

6. Prism Joint  Translate inboard joint to local origin  Translate along axis  Translate origin to location of joint on outboard

7. Articulated Figures  Composite transformations up the hierarchy

8. Inverse Kinematics

9. Egon Pasztor

10. 2 Segment Arm in 2D

11. Direct IK  Analytically solve for parameters (not general)

12. Difficult Issues  Multiple configurations distinct in config space  Or connected in config space

13. Infeasible Regions

14. Numerical Solution  Start in some initial config. (previous frame)  Define error metric (goal pos – current pos)  Compute Jacobian with respect to inputs  Use Newton’s or other method to iterate  General principle of goal optimization

15. Back to 2 Segment Arm

16. Jacobians and Configuration Space

17. Solving for Joint Angles

18. Issues  Jacobian not always invertible  Use an SVD and pseudo-inverse  Iterative approach, not direct  The Jacobian is a linearization, changes  Practical implementation (see longer slides)  Analytic forms for prism, ball joints  Composing transformations  Or quick and dirty: finite differencing  Cyclic coordinate descent (each DOF one at a time)

19. Next Semester  CS 294-13 (maybe CS 283) Advanced Graphics  Follow-on of this course, discuss current research  Take it if did well and enjoyed 184, want to learn more  Or are considering industry or graduate school in area  Tentative Topics / Assignments  Path Tracer  Real-Time or Image-Based Rendering  Subdivision Surfaces  Physical Simulation  http://inst.eecs.berkeley.edu/~cs294-13/fa09 http://inst.eecs.berkeley.edu/~cs294-13/fa09  Daniel’s path tracerpath tracer

20. Wrap Up  Good luck on HW 5 and Final  Great teaching the course; hope to see more of some of you next semester and beyond  Course Evaluations  Scores taken seriously in instructor evaluations  Comments feedback important for future iterations  Have a great end of semester