On a Hybrid Symbolic-Connectionist Approach for Modeling the Kinematic Robot Map - and Benchmarks for Computer Algebra

Abstract

The kinematics model of a robot arm (we are considering open kinematic chains) is described by a corresponding robot map having the configuration space as its domain and the workspace as codomain. In other words, the robot map assigns to every configuration of the joint parameters a unique point of the workspace of the robot arm. We briefly discuss the general introduction of the robot map where the parameters of a translational joint are represented by points of the real line and the parameters of a rotational joint by points of the unit circle in the real plane, respectively. Thus, in general, a concrete joint configuration (point of the configuration space) is an element of an abelian Lie group being a direct product of some copies of the real line and the unit circle. The position and orientation of the endeffector of a robot arm is represented by an element of the euclidean motion group of real 3-space. The standard problems like the direct kinematics problem, the inverse kinematics problem and the singularity problem can easily be defined.