1 Articulated Figures Inverse Kinematics Articulated Figures - - PDF document

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Foundations of Computer Graphics Foundations of Computer Graphics (Spring 2010) (Spring 2010)

CS 184, Lecture 25: Inverse Kinematics

http://inst.eecs.berkeley.edu/~cs184

Many slides courtesy James O’Brien

Summary and Outline Summary and Outline

• Inverse Kinematics Lecture
• CS 294-13 Advanced Graphics in the fall
• Course Evaluations
• Best of luck for HW 5, Final

Forward Kinematics Forward Kinematics

• Joints (typically not 6 DOF)
• Pin – rotate about one axis
• Ball – arbitrary rotation
• Prism – translate alone one axis

Joints Joints Pin and Ball Joint 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

Prism Joint Prism Joint

• Translate inboard joint to local origin
• Translate along axis
• Translate origin to location of joint on outboard

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Articulated Figures Articulated Figures

• Composite transformations up

the hierarchy

Inverse Kinematics Inverse Kinematics Inverse Kinematics Inverse Kinematics

Egon Pasztor

2 Segment Arm in 2D 2 Segment Arm in 2D Direct IK Direct IK

• Analytically solve for parameters (not general)

Difficult Issues Difficult Issues

• Multiple configurations distinct in config space
• Or connected in config space

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Infeasible Regions Infeasible Regions Numerical Solution 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 Jacobians and Configuration Space 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)

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Next Semester 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
• Daniel’s path tracer

Wrap Up 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