I want to use scipy.optimize package to solve a rigid body optimization problem (finding optimal translation and rotation of a object).
A way to parametrize this problem is through lie group theory and the lie algebra se(3) (often called twist coordinates). This means the state vector is composed of 6 parameters (i.e. pose = [rho_x, rho_y, rho_z, theta_0, theta_1, theta_3]) from which the SE(3) Transformation matrix (a composition of translation vector and rotation matrix) can be obtained through the so called 'wedge' or 'hat' operator and the matrix exponentiation. (I found this cheat-sheet to be an excellent overview)
Now my question: Can scipy be used to optimize a 3D pose that is parametrized by the twist coordinates? I read somewhere that such problems require 'on manifold optimization' methods. So can I use scipy's least_square() or minimize(method="BFGS") for this? or do these only work for flat euclidean spaces?
Alternatively it would also help me a lot if anyone knows of any example where scipy is used to solve a 3D pose optimization problem. I have been looking for examples for the last couple of days but without much success.
This question is a implementation specific part of a more general question I posted on the robotics stackexchange here.