rbm: Rigid Body Motion Library

A library to handle rigid body motion in 3D space using Lie Group.

Dependancies

• This library depends on vma for basic linear algebra. The linear algebra routines depend on
  • Apple's Accelerate framework on macOS, iOS, etc.
  • libopenblas and libgfortran on other OSes, behind the scene.
• For unit test, this repository automatically fetches Google's GTest toolkit.

Basic Functionalities

To represent the orientation in 3D space, this library implements SO(3) (Special Orthogonal) Group. The orientation and position are represented as an element in SE(3) (Special Euclidean) Group, which can be considered as the combination of the SO(3) and 3-dimensional vector space.

The following functions are available in the library:

• Mapping between so(3) and SO(3), i.e., matrix exponential on so(3) and logarithm on SO(3).
• Generation of the rotation matrix (an element in SO(3) space) from Euler angle representations.
• Inverse of the elements in SO(3).
• Interpolation of orientation using a similar methodology as Bezier curves.
• Mapping between se(3) and SE(3), i.e., matrix exponential on se(3) and logarithm on SE(3).
• Generation of the SE(3) elements from SO(3) and a 3-dimensional vector.
• Combination of mappings in SE(3), inverse mapping, etc.