Design of an Affine Control Law for the Position Control Problem of Robotic Systems Based on the Development of a Linear Dynamic Model

One of the frequent tasks of a robotic system is to go from an initial position to another location or to change its actual configuration to some desired one. Thus, an efficient as well as simple control law should be applied to achieve such objective. Despite the presence of several control approaches of robotic systems, this work proposes mainly a design method of an affine state-feedback controller for the problem of position control and by considering the general form of the nonlinear dynamics. The adopted methodology is chiefly based on the development of a linear dynamic model defined around the desired position. Moreover, the linear matrix inequality technique is used to compute the feedback gains of the control law. An illustrative example and a comparison with the CTC controller are given at the end to show the validity and efficiency of the proposed design and control approach.