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 uncertain nonstrict nonlinear system with dead-zone input, an adaptive neural network (NN)-based finite-time online optimal tracking control algorithm is proposed. By using the tracking errors and the Lipschitz linearized desired tracking function as the new state vector, an extended system is present. Then, a novel Hamilton-Jacobi-Bellman (HJB) function is defined to associate with the nonquadratic performance function. Further, the upper limit of integration is selected as the finite-time convergence time, in which the dead-zone input is considered. In addition, the Bellman error function can be obtained from the Hamiltonian function. Then, the adaptations of the critic and action NN are updated by using the gradient descent method on the Bellman error function. The semiglobal practical finite-time stability (SGPFS) is guaranteed, and the tracking errors convergence to a compact set by zero in a finite time.

In this paper, a dynamic model of a wheeled mobile robotic (WMR) system with coupled control input is developed, which will increase the complexity of its tracking control with time-varying advance angle. To deal with this problem, a partial reinforcement learning neural network (PRLNN)-based tracking algorithm is proposed for the WMR systems. The main contributions of the PRLNN adaptive tracking control method is that it is the first control method to introduce the PRLNN adaptive control to the WMR system, which determines to solve the WMR tracking control with the time-varying advance angle. The critic neural network (NN) and action NN adaptive laws for the decoupled controllers are designed using the standard gradient-based adaptation method. According to the Lyapunov stability analysis theorem, the uniform ultimate boundedness of all signals in the WMR system can be guaranteed with the design parameters chose properly, and the tracking error converge to a small compact set nearby zero. A numerical simulation is presented to verify the effectiveness of the proposed control algorithm.

In this paper, an optimal control algorithm is designed for uncertain nonlinear systems in discrete-time, which are in nonaffine form and with unknown dead-zone. The main contributions of this paper are that an optimal control algorithm is for the first time framed in this paper for nonlinear systems with nonaffine dead-zone, and the adaptive parameter law for dead-zone is calculated by using the gradient rules. The mean value theory is employed to deal with the nonaffine dead-zone input and the implicit function theory based on reinforcement learning is appropriately introduced to find an unknown ideal controller which is approximated by using the action network. Other neural networks are taken as the critic networks to approximate the strategic utility functions. Based on the Lyapunov stability analysis theory, we can prove the stability of systems, i.e., the optimal control laws can guarantee that all the signals in the closed-loop system are bounded and the tracking errors are converged to a small compact set. Finally, two simulation examples demonstrate the effectiveness of the design algorithm.

Resistance coefficient (RC) is an important measure when designing wheel-driving mechanisms and accurate dynamic models for real-time mobility control of wheeled mobile robots (WMRs). This measure is typically formulated as a constant that depends on the wheel load, wheel dimensions, and soil that the WMR is designed for. This article proposes a novel variable RC that responds to terrain deformation. This variable RC is then applied to controllers for WMRs that estimate driving torques and slip ratios on deformable terrain. Simple yet accurate models of RC are developed from both experimental results and theoretical analysis, and these models are then compared with other methods. The proposed RC models give more accurate and more computationally efficient estimations of driving torques and slip ratios for WMRs, with average estimation errors less than 6% and the shortest computation time in experiments. The two proposed estimators are then applied to the design of the tracking-control systems for a WMR running on deformable terrain. Experiments with simulated sandy terrain demonstrate that both proposed control systems are feasible, and the slip estimation effectively decreases velocity tracking errors from more than 20% to less than 10%.

In this paper, an adaptive dynamic programming-based online adaptive tracking control algorithm is proposed to solve the tracking problem of the partial uncertain time-delayed nonlinear affine system with uncertain resistance. Using the discrete-time Hamilton-Jacobi-Bellman function, the input time-delay separation lemma, and the Lyapunov-Krasovskii functionals, the partial state and input time delay can be determined. With the approximation of the action and critic, and resistance neural networks, a near-optimal controller and appropriate adaptive laws are defined to guarantee the uniform ultimate boundedness of all signals in the target system, and the tracking error convergence to a small compact set to zero. A numerical simulation of the wheeled mobile robotic system is presented to verify the validity of the proposed method.