A new method for linearization of dynamic robot models

Abstract

A method for linearizing dynamic models for robot manipulators along a nominal trajectory for robot manipulators is developed from the straightforward Lagrangian formulation. The method is very simple and systematic. It can be applied both to the computation of the feedforward control law (i.e. the joint generalized forces/torques) along the desired nominal trajectory and to the design of the feedback controller that reduces or eliminates any deviations from the desired nominal trajectory. The salient advantage of using this method is that the amount of computation required for deriving the complete linearized dynamic model for a manipulator is so small that it makes the real-time computation on a mini- or microcomputer possible. The computation for a general manipulator with six degrees of freedom requires at most 2000 multiplications and 1700 additions. For most industrial manipulators with six degrees of freedom, it requires at most 1400 multiplications and 1300 additions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>