Determination of Conditions on Feedback Gains for the Position Control of Robotic Systems Under an Affine PD-Based Control Law

Among the most important tasks, in order to control the robotic system to achieve some desired goal, is the design of the controller to be applied as well as the right choice of gains to be used. Despite the presence of several effective controllers that can be used, it remains the judicious choice of the adequate values of the feedback gains that will define the control and then the stabilization of the robot system from some initial configuration towards a desired one. This work mainly proposes some conditions that can help to make the right choice of the feedback gains to solve the problem of position control of robotic systems via an affine PD-based control law. Such control law is designed through the linearization of the nonlinear dynamics of the robotic system around the desired state. The methodology used is mainly based on the linear matrix inequality (LMI) techniques and lies on determining the conditions on the feedback gains ensuring the stability of the linear dynamic model and the nonlinear dynamics under the adopted controller. An illustrative example of a two-degree-of-freedom manipulator robot is considered to illustrate the different adopted determination methods of conditions on the feedback gains.