Grassmann-Cayley algebra and robotics
Plücker coordinates are a suitable way to present lines in space for purposes of studying instantaneous motions of robot arms. In this paper the author presents an algebraic structure which is very useful for representing instantaneous motions of robots. He also presents applications to series-parallel mechanisms, rigidity of framework, and splines. He represents Grassmann-Cayley algebra in a concrete fashion, in terms of Plücker coordinates of subspaces. A synthetics geometric condition, expressed in the Grassmann-Caley algebra, and expanded by the shuffle formula, gives a bracket condition. This provides a translation of synthetic geometric conditions into invariant algebraic conditions. An important problem for several of his applications is the reverse translation, a problem is called Cayley factorization. He describes this problem and its role in computer-aided geometric reasoning.
scientific article; zbMATH DE number 746196