In this paper, we will propose the controller of a 2-DOF head in a snake robot for effective image data reading when the snake robot is driving, and present an error-based adaptive robust radial base function neural network back-stepping controller. The snake robot head system is a nonlinear system, and there are unmeasurable disturbances that occur while driving. To solve this problem, we use back-stepping controller and radial basis function neural network to compensate for unmeasurable disturbances to improve the steady state. In order to further compensate for the network approximation error that occurs during training or large signal changes, we use adaptive coefficients and error functions to approximate the network approximation error and design adaptive robust terms. Compared to the previous controller, the proposed controller can actively compensate for large signal changes and has the advantage of not generating residual input in a steady state. The proposed controller is based on Lyapunov function candidate to design an adaptive law and prove the system stability. The stability of the control system is proven through Lyapunov analysis and bounded. The proposed controller compared and verified the controller performance for two inputs through simulation and presented the efficiency of the controller.

This paper proposes a quadrotor system control scheme using an intelligent–proportional–integral–differential control (I-PID)-based controller augmented with a radial basis neural network (RBF neural network) and the proposed adaptive robust term. The I-PID controller, similar to the widely utilized PID controller in quadrotor systems, demonstrates notable robustness. To enhance this robustness further, the time-delay estimation error was compensated with an RBF neural network. Additionally, an adaptive robust term was proposed to address the shortcomings of the neural network system, thereby constructing a more robust controller. This supplementary control input integrated an adaptation term to address significant signal changes and was amalgamated with a reverse saturation filter to remove unnecessary control input during a steady state. The adaptive law of the proposed controller was designed based on Lyapunov stability to satisfy control system stability. To verify the control system, simulations were conducted on a quadrotor system maneuvering along a spiral path in a disturbed environment. The simulation results demonstrate that the proposed controller achieves high tracking performance across all six axes. Therefore, the controller proposed in this paper can be configured similarly to the previous PID controller and shows satisfactory performance.

Image stabilization is important for snake robots to be used as mobile robots. In this paper, we propose an adaptive robust RBF neural network nonsingular terminal sliding mode control to reduce swinging in the snake robot’s head while it is being driven. To avoid complex dynamic problems and reduce interference during driving, we propose a 2-DOF snake robot’s head system. We designed the control system based on the nonsingular terminal sliding mode control, which ensures a fast response and finite time convergence. To reduce chattering, we incorporated an RBF neural network that can compensate for disturbances. Additionally, we included an adaptive robust term to address the disadvantages of neural network-based control. The adaptive robust term generates control inputs based on the error and is used in conjunction with the reverse saturation function to eliminate chattering. The update law of the neural network and the adaptive robust term is designed based on Lyapunov’s theory. We proved the stability of the proposed controller by investigating finite time convergence before and after the reverse saturation function operation section. Finally, we verified the performance of the proposed controller through computer simulation. The simulation evaluates the controllers using a sinusoidal reference signal similar to snake robot movement and a mixed reference signal considering the controller’s waste case. The proposed controller has excellent tracking performance and improved chattering compared with the previous controller.

This paper proposes a robust control scheme combining prescribed performance-based time-delay estimation (TDE) with a radial basis function neural network (RBF-NN). The proposed prescribed-performance-based time delay control constructs desired error dynamics through transformed errors to achieve prescribed performance. This design preserves the simple control structure of traditional time-delay control (TDC) while maintaining its stability condition and M stability analysis, enabling the application of existing design methodologies. RBF-NN is incorporated to compensate residual TDE error, and Lyapunov analysis establishes stability of the overall system. The approach is validated in simulation on a 3-DOF robotic manipulator under cases without and with payload variations and additive joint disturbances, demonstrating satisfaction of the prescribed-performance bounds and improved tracking relative to the TDC while retaining simplicity.