Application of 2D PGA as an Subalgebra of CRA in Robotics

摘要

We present a concept of 2D Projective Geometric Algebra (PGA) as a subalgebra of Compass Ruler Algebra (GRA) to handle problems in computer graphics and engineering efficiently in terms of an algebra with minimal dimension. In this case, we can benefit from both CRA and PGA simultaneously. When we deal with complex problems, we can use CRA objects such as circles but at the same time we can switch to PGA as a subalgebra of CRA to handle operations with flat-objects more efficiently without the change of structure of any further implementation. We demonstrate this approach on example of inverse kinematics of a planar 3-link manipulator.