Interpolation Based Controller for Trajectory Tracking in Mobile Robots

Abstract

In this work, a novel algorithm for trajectory tracking in mobile robots is presented. For the purpose of tracking trajectory, a methodology based on the interpolation of trigonometric functions of the wheeled mobile robot kinematics is proposed. In addition, the convergence of the interpolation-based control systems is analysed. Furthermore, the optimal controller parameters are selected through Monte Carlo Experiments (MCE) in order to minimize a cost index. The MCE is able to find, the best set of gains that minimizes the tracking error. Experimental results over a mobile robot Pionner 3AT are conclusive and satisfactory. In addition, a comparative study of control performance is carried out against another controllers.

Tracking Control Design in Nonlinear Multivariable Systems: Robotic Applications

“…In the results presentation, the controller based on kinematic model developed in continuous time will be called C1 (Section 3); the controller developed in discrete time and Euler approximation will be called C2 (Section 4.1); the controller based on trapezoidal approximation will be noted as C3 (Section 4.2); the controller based on dynamic model and Euler approximation will be called C4 (Section 3.2); and the controller developed considering uncertainties (Section 5) will be called C5. e controller and system parameters used for the experimentation are obtained from [8,16,21,24,26], respectively.…”

“…e kinematic continuous time control of a mobile robot will be used to illustrate the procedure. e details of this application can be seen in [16]. A simple nonlinear kinematic model for a mobile robot is given by (7).…”

“…In 9, k x , k y , and k θ are positive constants allowing the performance adjustment of the proposed control system. ey should be k x > 0, k y > 0, and k ψ > 0 to ensure that the tracking errors (10) tend to zero (see [16]). (iv) In the four step, the reference for the sacrificed variables is defined to provide an exact solution to (9).…”

“…(iii) In the next step, the conditions in order that system (16) has exact solution will determine the sacrificed variables reference, leading to…”

“…is methodology has been accepted and applied by different authors (see, for instance [11,12]), being referenced as an alternative to solve the path tracking problem (see, for instance [13][14][15]). In [16], the design in CT is presented using the kinematic model of the mobile robot. In that study, we have only one sacrificed variable, and different approximations were used.…”