Recursive linearization of manipulator dynamics models

Techniques from spatial operator algebra are used to obtain closed-form operator expressions for two types of linearized dynamics models, denoted as the direct and the canonical linearized models. Three algorithms are presented. The first describes an O(n ²) recursive method for the computation of the direct model. Previous methods to obtain the canonical linearized model are of O (n³) complexity and are summarized in the second algorithm. They are based on the evaluation of the direct model, the inversion of the mass matrix, and the formation of matrix products. A recursive O(n²) algorithm that does not require these steps for computing the canonical model is then described. The use of spatial operators considerably simplifies the analysis, and allows the use of the operator structure to develop naturally efficient and recursive computational algorithms. Arbitrary single-degree-of-freedom joints are handled in a unified manner. Extensions to linearized models for manipulators with general multi-degree-of-freedom joints are straightforward and result in similar operator expressions and algorithms