A TRAJECTORY CONTROL METHOD FOR NONLINEAR DIFFERENTIALLYFLAT SYSTEMS

Abstract

The paper presents a trajectory control method for nonlinear differentially flat control systems, referred to as the generalized Computed Torque Control (CTC) method. It is shown that the classical Computed Torque Control, traditionally applied to serial manipulators, can be regarded as a special case of a general trajectory control method for a specific class of flat systems, denoted as class A systems. An approach to the linearization of such systems is proposed, based on class C coordinate transformations, which transform the original nonlinear control system into an equivalent trivial linear control system while preserving equivalence in the sense of control system theory. It is noted that class C transformations admit hardware implementation using physically realizable signal-processing elements. It is shown that flat systems of class A possess a flat output depending only on the current state of the system, which extends the applicability of the proposed method to other nonlinear control objects, including certain types of mobile robots. In addition, the analysis of the classical CTC method makes it possible to formulate a disturbance rejection criterion for the linear controller included in the trajectory control scheme.