Robotic problems over a configurational manifold of vector parameters and dual vector parameters
The kinematics of a manipulator involves the Euclidean group. A vector parametrization of SO(3), obtained using the Cayley transformation, allows to introduce a group action of the Lie group of vector parameters (the composition law is: \(c.d = {c + d + c \wedge d\over 1 - c^ t d}\) where \(c\), \(d\) belong to \(\mathbb{R}^ 3\)) on the trivialized tangent bundle of SO(3) (which is also a Lie group). An other description using Plücker coordinates allow to use revolute and prismatic joint variables of the manipulator and to introduce a ``dual'' matrix and vector notation. The same vector parametrization is used and leads also to an elegant and efficient description of manipulator kinematics.
scientific article; zbMATH DE number 746198