Affine Transformations in Solving Robot Control Problem

Abstract

An affine transformation is a mapping that transforms points and vectors from one space to another, in a way that preserves the ratios of distances. Inverse kinematics is defined as the mapping from Cartesian space to joint space, i.e., computation needs to find the joint angles for a given Cartesian position and orientation of the end effectors. This computation is fundamental to control robot arms but it is very difficult to calculate an inverse kinematics solution of robot manipulator. Solving the inverse kinematics problem for robot manipulators is a challenging task; the difficulty of the solution arises from the nonlinear equations(trigonometric equations) that occur during the transition between joint and Cartesian spaces.

Keywords: Affine transformation, Cartesian space, Denavit–Hartenberg (DH) Parameters, robot manipulator, rotation matrix transformation matrix, the translation matrix