Basic principles of mechanical theorem proving in elementary geometrics
Journal of Automated Reasoning
Applications of Gro¨bner bases in non-linear computational geometry
Mathematical aspects of scientific software
Algebraic methods for geometric reasoning
Annual review of computer science: vol. 3, 1988
On geometric and topological reasoning in robotics
Annals of Mathematics and Artificial Intelligence
Modeling Connectionist Network Structures: Some Geometric and Categorical Aspects
Annals of Mathematics and Artificial Intelligence
Journal of Automated Reasoning
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Improvements in cad-based quantifier elimination
Improvements in cad-based quantifier elimination
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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.