Kiru Lab / Embodied Control: Kinematics and the Inverse Jacobian
The Jacobian
Differentiate the forward map and you get the matrix that relates joint velocity to hand velocity.
In this module you will
- Derive the manipulator Jacobian analytically and numerically
- Interpret its columns and its rank
- Diagnose a singularity from its singular values
The Velocity Jacobian
The same object you met in track two, now with physical units: how fast the hand moves per unit of joint rate.
Code Walkthrough · 40m
Singularities and Conditioning
When the Jacobian loses rank, an entire direction of motion becomes unreachable and naive inversion explodes.
Concept · 30m