Linearization of manipulator dynamics using spatial operators

Techniques from the spatial operator algebra are used to obtain closed-form operator expressions for two types of linearized dynamics models: the linearized inverse and forward dynamics models. Spatially recursive algorithms of O(n) and O(n ²) complexity for the computation of the perturbation vector and coefficient matrices for the linearized inverse dynamics model (LIDM) are developed. Operator factorization and inversion identities are used to develop corresponding closed-form expressions for the linearized forward dynamics model (LFDM). Once again, these are used to develop algorithms of O(n) and O(n ²) complexity for the computation of the perturbation vector and the coefficient matrices. The algorithms for the LFDM 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 ³) algorithms