1 Articulated Figures Inverse Kinematics Articulated Figures - PDF document

Summary and Outline Summary and Outline Foundations of Computer Graphics Foundations of Computer Graphics  Inverse Kinematics Lecture (Spring 2010) (Spring 2010)  CS 294-13 Advanced Graphics in the fall CS 184, Lecture 25: Inverse Kinematics  Course Evaluations http://inst.eecs.berkeley.edu/~cs184  Best of luck for HW 5, Final Many slides courtesy James O’Brien Forward Kinematics Joints Forward Kinematics Joints  Joints (typically not 6 DOF)  Pin – rotate about one axis  Ball – arbitrary rotation  Prism – translate alone one axis Pin and Ball Joint Pin and Ball Joint Prism Joint Prism Joint  Translate inboard joint to local origin  Translate inboard joint to local origin  Rotate about axis (for pin), arbitrary (for ball)  Translate along axis  Translate origin to location of joint on outboard  Translate origin to location of joint on outboard 1

Articulated Figures Inverse Kinematics Articulated Figures Inverse Kinematics  Composite transformations up the hierarchy Inverse Kinematics 2 Segment Arm in 2D Inverse Kinematics 2 Segment Arm in 2D Egon Pasztor Direct IK Direct IK Difficult Issues Difficult Issues  Analytically solve for parameters (not general)  Multiple configurations distinct in config space  Or connected in config space 2

Infeasible Regions Numerical Solution Infeasible Regions 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 Back to 2 Segment Arm Back to 2 Segment Arm Jacobians and Configuration Space Jacobians and Configuration Space Solving for Joint Angles Solving for Joint Angles Issues 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) 3

Next Semester Wrap Up Next Semester Wrap Up  CS 294-13 (maybe CS 283) Advanced Graphics  Good luck on HW 5 and Final  Follow-on of this course, discuss current research  Great teaching the course; hope to see more of  Take it if did well and enjoyed 184, want to learn more some of you next semester and beyond  Or are considering industry or graduate school in area  Course Evaluations  Tentative Topics / Assignments  Scores taken seriously in instructor evaluations  Path Tracer  Comments feedback important for future iterations  Real-Time or Image-Based Rendering  Subdivision Surfaces  Have a great end of semester  Physical Simulation  http://inst.eecs.berkeley.edu/~cs294-13/fa09  Daniel’s path tracer 4