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CS184 Section 10

Inverse Kinematics and CS184 Extensions

Brandon Wang

April 16, 2013

Material adapted from Carlo Sequin.

Inverse Kinematics and CS184 Extensions

Brandon Wang

April 16, 2013

Material adapted from Carlo Sequin.

Final project proposals due tomorrow!

- CS184 Extensions
- Inverse Kinematics
- Tell me about your projects

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

Make meshes to render

Graphics, but backwards

(Requires CS188 as well.)

Continuation of CS184, goes more in-depth about theory.

Make the tools that people use to design things.

(Lots of splines, subdivision, etc)

Make things.

(Mix of splines, meshes, but kind of like an art class)

You have an arm, and joints. Now you need to figure out how to get the end to some position.

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}

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.

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