###### Abstract  
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 [PERSON]'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. s +
Footnote †: journal: Applied  
**Citation:** [PERSON]-[PERSON]. the locomotion of the snake robot may result in decreased driving speed or drift during driving, and other factors such as ground friction and other locomotion are not considered. Moreover, their findings lack a rigorous analysis of driving performance. As far as the author is aware, there has been no detailed study on the dynamic control method yet. To consider the dynamics, the snake robot system has many degrees of freedom (DOF) and is subject to complex nonlinearity. Additionally, ground friction also significantly affects the robot's motion, making control challenging. Nevertheless, for effective control considering various conditions, it is necessary to develop a robust nonlinear controller considering disturbance. Sliding mode control is a well-known nonlinear controller used to handle system nonlinearity and unmeasurable disturbance [29; 30; 31; 32]. The fundamental aspect of widely used sliding mode control is the generating of the domain of attraction around a defined switching surface, also known as a sliding manifold, by using a discontinuous control input. The desired control performance is achieved by setting the switching term in the ideal sliding mode. Sliding mode control is based on the principles of asymptotic stability and [PERSON]'s theory, with the linear sliding surface specifying the expected control performances. The Lipschitz condition for ordinary differential equations underpins asymptotic stability. However, a characteristic of asymptotic stability is that the closer the system dynamics are to the equilibrium point, the slower the state convergence and it does not guarantee that the system state can reach the equilibrium point in a finite time. In actual application, this may not pose a problem for sliding mode control, but it may not be feasible when high precision is required. To address this issue, a control method called terminal sliding mode control was developed [33; 34; 35]. Terminal sliding mode control includes an exponential term in the sliding surface, enabling the system to reach within a finite time. However, there was a problem of singularity, which led researchers to propose nonsingular terminal sliding mode control [36; 37]. The nonsingular terminal sliding mode exhibits good control performance, but chattering exists. If the control gain of the switching term is increased in order to be robust against external disturbances, chattering occurs significantly.