Abstract: A formulation of the hybrid localization envelopment problem is given by using Lie group, Lie Algebra and homogenous space in differential geometry theory. Based on the geometric properties of homogeneous space, the hybrid problem is decomposed into a (symmetric) localization problem and an envelopment problem. An effective hybrid algorithm is proposed to solve the problems. Simulation results show that the proposed algorithm robust, computational efficiency and high accuracy.

Key words: Envelopment algorithm, Euclidean group Lie group, Euclidean transformation, Lie algebra, Workpiece localization, Force analysis, Passive overconstrained PM, Static indeterminacy, Stiffness matrix of constraint wrenches, Weighted Moore-Penrose generalized inverse