Target Tracking Project

We designed image processing and control algorithms for a two-degree-of-freedom laser workbench equipped with a monocular camera, enabling stepper motor control for target identification and tracking.

Task specification

1. fitting inverse kinematics(optional and not done in video).
2. Scan the QR code to get a color sequence.
3. Use laser to point corresponding target both statically and dynamically.
4. Change next color with step 3.

6-DOF Robotic Arm Sorting Project

We developed forward and inverse kinematics and trajectory planning algorithms for a 6 dof robotic arm platform, achieving dart positioning and transportation.

Task specification

1. Taking a photo of the plane and get their position(not shown in video).
2. Mark half of the darts as the destination of the other half.(e.g. 3 origination 3 destination for 6 darts)
3. Place every dart to their assigned destination steadily and accurately.
4. Reset to the initial position.

Least Squares

This is note1 based on Linear Algebra And Learning From Data by Gilbert Strang.

Least Squares

Many applications lead to unsolvable linear equations $Ax=b$. The least squares method chooses $\hat x$ to make $||b-A\hat x||^2$ as small as possible. Which is $(Ax-b)^T(Ax-b)$. Minimizing erorr means its derivatives are zero which leads to normal eqautions $A^TA\hat x=A^Tb$.

Four ways to solve

1.The SVD of A leads to its pseudoinverse $A^+$. Then $\hat x = A^+b$ :one short formula (This note)
2.$A^TA\hat x=A^Tb$ can be solved directly when A has independent columns
3.The Gram-Schmidt idea produces orthogonal columns in Q which... read more