This paper proposes a new adaptive controller for three-wheeled mobile robots (3WMRs) called the ABHSMC controller. This ABHSMC controller is developed through a cooperative approach, combining a backstepping controller and a Radial Basis Function (RBF) neural network-based Hierarchical Sliding Mode Controller (HSMC). Notably, the RBF neural network exhibits the remarkable capability to estimate both the uncertainty components of the model and systematically adapt its parameters, leading to enhanced output trajectory responses. A novel navigational model, constructed by the connection to the adaptive BHSMC controller, Timed Elastic Band (TEB) Local Planner, and A-star (A*) Global Planner, is called ABHSMC navigation stack, and it is applied to effectively solve the tracking issue and obstacle avoidance for the 3-Wheeled Mobile Robot (3WMR). The simulation results implemented in the Matlab/Simulink platform demonstrate that the 3WMRs can precisely follow the desired trajectory, even in the presence of disturbances and changes in model parameters. Furthermore, the controller’s reliability is endorsed on our constructed self-driving car model. The achieved experimental results indicate that the proposed navigational structure can effectively control the actual vehicle model to track the desired trajectory with a small enough error and avoid a sudden obstacle simultaneously.

This paper proposes a new approach to robustly control a 2D under-actuated overhead crane system, where a payload is effectively transported to a destination in real time with small sway angles, given its inherent uncertainties such as actuator nonlinearities and external disturbances. The control law is proposed to be developed by the use of the robust hierarchical sliding mode control (HSMC) structure in which a second-level sliding surface is formulated by two first-level sliding surfaces drawn on both actuated and under-actuated outputs of the crane. The unknown and uncertain parameters of the proposed control scheme are then adaptively estimated by the fuzzy observer (FO), where the adaptation mechanism is derived from the Lyapunov theory. More importantly, stability of the proposed strategy is theoretically proved. Effectiveness of the proposed adaptive FO-based HSMC approach was extensively validated by implementing the algorithm in both synthetic simulations and real-life experiments, where the results obtained by our method are highly promising.