Linear Algebra Continuous Dynamic

This paper presents a novel methodology to deal with the problem of trajectory tracking in WMR. This new approach uses the dynamic model of WMR and allows perfect velocities tracking. Generally, the classic control approaches applied to the dynamic model of the robot solve the problem of trajectory tracking in two stages. In the first one is designed a controller that ensures the perfect tracking of the velocities considering only the kinetic structure of the model. The second stage solves the problem of tracking velocities using the dynamics of the system [1,2]. In our work, the procedure arises naturally when looking for the conditions that a system must meet in order to have an exact solution. The control action is obtained by solving a linear system, even though the original system model is nonlinear. Compared with other literature methods (back stepping, look-ahead methods, finite-time techniques, etc.), only algebra knowledge is needed to understand and apply this methodology. The controller performance is evaluated and compared with other controllers of the literature through laboratory experiments in PIONEER 3DX mobile robot. The paper is ordered as follows. In Section 2 are described the mathematical model of the mobile robot and the control design of the proposed controller. Section 3 presents the experimental results using a mobile robot Pionner 3DX. Finally, Conclusions are detailed in Section 4.