Motion control of mobile under-actuated manipulators by implicit function using support vector machines

In this study, the authors propose implicit control using least square support vector machines (LS-SVMs) approximation for the motion control of wheeled under-actuated manipulators. For approximating the multi-input and multi-output non-linear system, an LS-SVM matrix operator is proposed. Further, by using implicit function with SVMs, a control is constructed to obtain motion tracking of wheeled under-actuated manipulators. The relative degree of the regulated output is assumed to be known enabling the system feedback linearisable. It is shown that the tracking error can be controlled in a small neighbourhood of zero through Lyapunov´s direct method. The methodology is applicable to minimum phase observable and stabilisable systems of unknown but finite dimension, as long as the relative degree is known. The effectiveness of the proposed control method is substantiated by the simulation results.