Partial nonlinear state feedback methods for fast varying parameters: an example in robotics

Under the assumption of robust model, nonlinear state feedback decoupling methods can be used for the control of robotized systems. In this case, classically, a partial decoupling of the only grand motion axes is more suitable. Then state variables of the effector appear as parameters in the decoupling state equations. We show here, that if these parameters are slowly varying before the dynamics of the grand motion axes (the exact mathematical meaning of this notion is given in this article), the classical decoupling methods remain valid with parametrized laws, but if parameters dynamic are non negligible before the decoupling dynamic, we are in the fast varying parameters case, and we show in this case that decoupling methods operators must be changed in order to include these dynamical effects, which lead by using the classical decoupling methods, to non-efficient control. The computation of the static and dynamic feedback laws are given in the case of nonlinear decoupling, linearization and rejection of perturbations. An robust example in robotics is given, and the contribution of parameters dynamic is shown