Linearization of manipulator dynamics using spatial operators

Linearized dynamics models for manipulators are useful in robot analysis, motion planning, and control applications. In this paper we use techniques from the spatial operator algebra to obtain closed form operator expressions for two types of linearized dynamics models, the Linearized Inverse and Forward Dynamics Models. We rst develop spatially recursive algorithms of O(n) and O(n) complexity for the computation of the perturbation vector and coe cient matrices for the Linearized Inverse Dynamics Model. Subsequently, operator factorization and inversion identities are used to develop corresponding closed form expressions for the Linearized Forward Dynamics Model. Once again, these are used to develop algorithms of O(n) and O(n) complexity for the computation of the perturbation vector and the coe cient matrices. The algorithms for the Linearized Forward Dynamics Model do not require the explicit computation of the mass matrix nor its numerical inversion and are also of lower complexity than the conventional O(n) algorithms.