Synthesis of Control Systems for Manipulators Using Multivariable Robust Servomechanism Theory

This paper describes a framework for synthesizing control laws for manipulators based on robust servomechanism theory for multivariable linear systems. This framework takes into account the coupled and nonlinear nature of the differen tial equations describing the manipulator as well as the fact that the inputs and outputs are subject to large excursions. The robust servomechanism theory is applied to the linear system that results when the overall, nonlinear, dynamic system is split, in the standard manner, into a nominal sys tem and a (linear) system linearized about the nominal. A control law for the linear system is then derived on the basis of linear quadratic regulator theory. To ensure good dynamic response, the implicit model-following technique is used to choose the weights in the resulting performance index. The theory is then applied to design a control law for a two-degree-of-freedom spatial manipulator following a pre scribed trajectory. The effect of changing the speed and iner tias of the manipulator on the gains prescribed by the control law is also discussed.