CS184 Section 10
Inverse Kinematics and CS184 Extensions
Brandon Wang
April 16, 2013
Material adapted from Carlo Sequin.
CS184 Section 10
Today
Final project proposals due tomorrow!
- CS184 Extensions
- Inverse Kinematics
- Tell me about your projects
Future Classes
If you liked CS184, you can take more classes in graphics!
- CS274 - Computational Geometry
- CS280 - Computer Vision
- CS283 - Advanced Comptuer Graphics
- CS284 - Computer Aided Geometric Design
- CS285 - Solid Modeling
- CS294 - Animation, Simulation, Computational Photography, etc
CS274 - Computational Geometry
Make meshes to render
CS280 - Computer Vision
Graphics, but backwards
(Requires CS188 as well.)
CS280 - Computer Vision
CS283 - Advanced Computer Graphics
Continuation of CS184, goes more in-depth about theory.
CS283 - Advanced Computer Graphics
CS284 - Computer Aided Geometric Design
Make the tools that people use to design things.
(Lots of splines, subdivision, etc)
CS285 - Solid Modeling
Make things.
(Mix of splines, meshes, but kind of like an art class)
Path Tracing
Fabrication/CAD
Computational Photography
Computational Photography
Computer Vision
Sound
Berkeley's Research
http://graphics.berkeley.edu/Unreal Engine 4
Wreck-It Ralph
Inverse Kinematics
You have an arm, and joints. Now you need to figure out how to get the end to some position.
Jacobian
E=f(q)
E is of dimension n, the number of constraints. (i.e. x,y,z of your goal)
q is of dimension m, the degrees of freedom of the linkage. (i.e. each angle of each joint)
We want to find J in
dE=J(q) dq
J, the Jacobian matrix, is the n by m matrix of partial derivaties where the (i,j)th element of J is given by
J_{ij}=\frac{df_i}{dq_j}
Inverse Jacobian
dE=J(q) dq
dq=J^{-1} dE?
J not always invertible!
SVD (with 1/0 to 0):
J=QSP^T
J^{-1}=PS^{-1}Q^T
Jacobian Transpose
Cyclic Coordinate Descent - use many 1 DoF IK problems. Essentially loop over your joints from leaf to root.
Jacobian
Write out the Jacobian for the 3-link spider leg with respect to height H of its end effector above the ground plane.
Theta1 = Theta2 = 90 degrees
