On geometric and topological reasoning in robotics

The interplay of AI and symbolic mathematical computation and traditional mathematics is discussed here on the basis of some selected aspects from geometric, topological and logical reasoning in the classical Al field of robotics. The kinematics model of a robot arm is considered in detail and methods from symbolic computation are applied to inverse kinematics and singularity problems. It is shown how methods from classical geometry and topology can give support to work on typical robotics questions like the existence of singular configurations. Finally a novel approach for logical modeling in robotics is sketched based on so-called logical fiberings.