Adaptive Neural Network-Based Tracking Control for Full-State Constrained Wheeled Mobile Robotic System
In this paper, an adaptive neural network (NN)-based tracking control algorithm is proposed for the wheeled mobile robotic (WMR) system with full state constraints. It is the first time to design an adaptive NN-based control algorithm for the dynamic WMR system with full state constraints. The constraints come from the limitations of the wheels’ forward speed and steering angular velocity, which depends on the motors’ driving performance. By employing adaptive NNs and a barrier Lyapunov function with error variables, then, the unknown functions in the systems are estimated, and the constraints are not violated. Based on the assumptions and lemmas given in this paper and the references, while the design and the system parameters chose properly, our proposed scheme can guarantee the uniform ultimate boundedness for all signals in the WMR system, and the tracking error converge to a bounded compact set to zero. The numerical experiment of a WMR system is presented to illustrate the good performance of the proposed control algorithm.
Considering the exciting NN-based methods in –, we can notice the fact that NN is an important tool to solve the intelligent control problem. The NNs can approximate different types of nonlinear equations with arbitrary precision under certain conditions –, and have been widely used in control algorithm for the uncertain nonlinear systems –. By introducing NNs to uncertain nonlinear systems with constraints, several typical NN-based algorithm for nonlinear systems with constraints are shown in  and –. In  and , the control algorithms were designed for the strict feedback nonlinear systems with constant output constraints  and time-varying output constraints , respectively. In , –, and  the adaptive NN-based control was introduced to a class of nonlinear systems with full state constraints. Noticing the effectiveness of the NN-based algorithm to deal with the nonlinear systems with constraints, we can conclude that NN-based methods may be an efficacious way to deal with the WMR systems with constraints, which is a kind of typical nonlinear system. In  and , some works based on NNs for the WMR systems with constraints have done. In view of these researches, the research work for the tracking control of WMR with constraints has important scientific significance. But, the existing works for WMR tracking control does not give enough consideration on the tracking control with full state constraints.
This paper considering the tracking control problem for the dynamics model of the WMR system ,  with full state constraints. The main contributions of this paper are as follows. 1) It is the first time to propose a tracking control algorithm for the dynamic WMR system with full state constraints. 2) Based on WMR systems, a study of constrained NN control is carried out, which provides a new paradigm for NN research and enhances the development of NNs with constraint.
Using the approximation property of the NNs, we have proposed an adaptive NN-based tracking control algorithm for. WMR systems with full state constraints. The unknown parts of the robotic system are approximated by NNs, and then, considering the full states constrains, a new adaptive NN-based tracking control algorithm is developed by employing the BLF, and suitable controllers and adaptive laws are given. When the design and system parameters are chosen appropriately, the trajectory of the WMR positional can track the desired positional trajectory with a good performance. Tracking errors converge to a small neighborhood of zero, and the boundedness of the controllers and the adaptive laws are obtained. Thus, all signals in the WMR system are proved to be uniformly ultimately bounded. A numerical experiment is performed to demonstrate the validity of the proposed control algorithm for this kinds of WMR systems. By employing the Nussbaum Gain theorem , , and , the research on intelligent control of time-varying constrained system with unknown control direction will be carried on in the future.
 P. F. Muir and C. P. Neuman, “Kinematic modeling for feedback control of an omnidirectional wheeled mobile robot,” in Autonomous Robot Vehicles. New York, NY, USA: Springer, 1990, pp. 25–31.
 D. Chwa, “Sliding-mode tracking control of nonholonomic wheeled mobile robots in polar coordinates,” IEEE Trans. Control Syst. Technol., vol. 12, no. 4, pp. 637–644, Jul. 2004.
 R. Martínez, O. Castillo, and L. T. Aguilar, “Optimization of interval type-2 fuzzy logic controllers for a perturbed autonomous wheeled mobile robot using genetic algorithms,” Inf. Sci., vol. 179, no. 13, pp. 2158–2174, Jun. 2009.
 S. S. Ge and Y. J. Cui, “New potential functions for mobile robot path planning,” IEEE Trans. Robot. Autom., vol. 16, no. 5, pp. 615–620, Oct. 2000.
 ¸ S. Yildirim and S. Sava¸s, “Tracking control of a nonholonomic mobile robot using neural network,” in Handbook of Research on Advancements in Robotics and Mechatronics. Hershey, PA, USA: IGI Global, 2015, pp. 631–661.
 H. Q. Wang, X. P. Liu, and K. F. Liu, “Robust adaptive neural tracking control for a class of stochastic nonlinear interconnected systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 27, no. 3, pp. 510–523, Mar. 2016.
 W. He, Y. T. Dong, and C. Y. Sun, “Adaptive neural impedance control of a robotic manipulator with input saturation,” IEEE Trans. Syst., Man, Cybern., Syst., vol. 46, no. 3, pp. 334–344, Mar. 2016.
 T. P. Zhang and S. S. Ge, “Adaptive neural network tracking control of MIMO nonlinear systems with unknown dead zones and control directions,” IEEE Trans. Neural Netw., vol. 20, no. 3, pp. 483–497, Mar. 2009.
 M. Chen, “Disturbance attenuation tracking control for wheeled mobile robots with skidding and slipping,” IEEE Trans. Ind. Electron., vol. 64, no. 4, pp. 3359–3368, Apr. 2017.
 H. Q. Wang, B. Chen, and C. Lin, “Adaptive neural tracking control for a class of stochastic nonlinear systems with unknown dead-zone,” Int. J. Innov. Comput. Inf. Control, vol. 9, no. 8, pp. 3257–3269, Aug. 2013