An efficient method for linearization of dynamic models of robot manipulators

Abstract

An efficient method for linearizing dynamic models about a nominal trajectory is developed from the straightforward Lagrangian formulation. The method is very simple and systematic. It can be applied to compute the feedforward control law (i.e. the generalized forces or torques) about the desired nominal trajectory and to design the feedback controller that reduces or eliminates any deviations from the desired nominal trajectory. The salient advantage of the method is that the number of computations for deriving the complete linearized dynamic models for a manipulator is so few as to allow real-time computation on a mini- or microcomputer. The total number of computations to derive the complete linearized dynamic models (including the computation of the joint generalized forces or torques) about the nominal trajectory for a manipulator with six degrees of freedom is at most 2600 multiplications and 2711 additions. Computationally, this method is the fastest of all existing methods.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>