3 of 3 written

Lie Groups & Manifolds

The geometry of rotation and motion, done properly, with SO(3)/SE(3), the exponential map, and optimization on curved spaces for orientation and pose estimation.

Part 0

SO(3) & SE(3)

SO(3), SE(3), and the Exponential Map

Rotations and rigid motions as Lie groups, and the exponential map an engine uses to integrate orientation.

SO(3)

Part 1

Lie Algebra & Adjoint

The Lie Algebra, Twists, and the Adjoint

The tangent space of motion (twists) and the adjoint that moves them between frames, the spatial algebra of articulated bodies.

Lie algebra

Part 2

Manifold Optimization

Optimization on Manifolds

Gradient descent that stays on the curved space of rotations, with retraction, for pose estimation and calibration.

manifold optimization