JCS&T Vol. XX No. Y Month 2012 A Neural Compensator based on the Integral Sliding Mode Control Design for the Trajectory Tracking of a Nonholonomic Mobile Robot with Kinematics Disturbances Nardênio Almeida Martins 1,3 nardenio@din.uem.br, nardenio@das.ufsc.br Maycol de Alencar 1 Warody Claudinei Lombardi 2 Douglas Wildgrube Bertol 3 Edson Roberto De Pieri 3 Humberto Ferasoli Filho 4 1 Universidade Estadual de Maringá, Departamento de Informática, Avenida Colombo, 5790, 87020-900, Maringá, PR, Brasil 2 Lyon Université, INSA - Institut National des Sciences Appliquées, 20, avenue Albert Einstein, 69621 Villeurbanne Cedex, French, http://www.insa-lyon.fr 3 Universidade Federal de Santa Catarina, Departamento de Automação e Sistemas, Grupo de Pesquisa Robótica, C. P. 476, 88040-900, Florianópolis, SC, Brasil 4 Universidade Estadual Paulista Júlio de Mesquita Filho, Faculdade de Ciências, Departamento de Computação, Av. Luiz E. C. Coube, C. P. 473, 17033-360, Bauru, SP, Brasil ABSTRACT An integral sliding mode controller in the trajectory tracking problem for a nonholonomic mobile robot with kinematic disturbances is proposed. To circumvent the chattering phenomenon, a neural compensator is designed by a modeling technique of Gaussian radial basis function neural networks and does not require offline training. Stability analysis is guaranteed by the Lyapunov method. Simulation results of the proposed approach are provided. Keywords: Nonholonomic mobile robot, trajectory tracking, kinematic disturbances, integral sliding mode controller, neural networks, Lyapunov method. 1. INTRODUCTION The wheeled mobile robot of the type (2,0) is usually studied as a typical example of the nonholonomic system [1]. Many approaches have been proposed to treat the motion control design of this type of mobile robot [2]. Thus, this paper describes the design of a kinematic controller for this mobile robot, which is based on the integral sliding mode theory, considering the presence of kinematic disturbances. Sliding mode control design (SMC), which consists, by means of a discontinuous action, in constraining the system motion along manifolds of reduced dimensionality in the state space, is known as being a robust approach to solve the control problems of nonlinear systems [3], such as stabilization and tracking. Due to robustness properties against various kinds of uncertainties such as modeling imprecision and disturbances, the SMC has become very popular and used in many application areas [3]. However, a drawback of the classical SMC is that the trajectory of the designed solution is not robust on a time interval preceding the sliding motion, even to disturbances satisfying the matching condition. Also, this control scheme has important drawbacks that limit its practical applicability, such as high frequency switching (chattering) and large authority control, which deteriorate the system performance. The first drawback mentioned is due to control actions that are discontinuous on the sliding surfaces, which causes the high frequency switching in a boundary of the sliding surfaces. This high frequency switching might excite unmodeled dynamics and impose undue wear on the actuators, so that the control law would not be considered acceptable. The second drawback mentioned, is based on the requirement of a prior knowledge of the boundary of uncertainty in compensators. If boundary is unknown, a large value has to be applied to the gain of discontinuous part of control signal and this large control gain may intensify the high frequency switching on the sliding surfaces. In order to solve the reaching phase problem an integral sliding mode design concept was proposed [3]. The basic idea is to define the control law as the sum of a continuous nominal control and a discontinuous control. The nominal control is responsible for the performance of the nominal system, i. e., without disturbances; and the discontinuous control is used to reject the disturbances. An integral term is included in the sliding manifold, this guarantees that the system trajectories will start in the manifold from the first time instant. Researches have been developed using softcomputing methodologies, such as artificial