# Application of Improved Sliding Mode and Artificial Neural Networks in Robot Control
## 1 Introduction  
Mobile robots, as semi-autonomous or autonomous systems, have the capability to navigate unstructured environments without direct human intervention [1; 2; 3]. These systems are equipped with sensors, processors, and locomotive mechanisms, enabling them to execute a wide range of tasks from simple to complex, such as cargo transport, space exploration, or providing assistance in medical and industrial applications. Mobile robots can autonomously locate and navigate [4; 5; 6] using algorithms and technologies such as artificial intelligence (AI), machine learning, and sensor-based mapping, efficiently interacting with their surroundings. They can also be remotely controlled via wireless connections. The field of mobile robotics continues to evolve with ongoing research and development aimed at enhancing automation capabilities and optimizing task performance across various industries. In recent years, the robotics domain has made significant strides, propelled by the amalgamation of sophisticated control strategies and computational intelligence. Notably, Sliding Mode Control (SMC) [7; 8] and Artificial Neural Networks (ANNs) [9] have emerged as key technologies to enhance the precision and adaptability of robotic systems. SMC is known for its robustness and effectiveness in dealing with non-linearities and system uncertainties, making it an ideal choice for dynamic and complex environments. Conversely, ANNs play a crucial role by introducing learning capabilities to robots, thereby facilitating real-time decision-making and adaptation based on sensory input. Accurate trajectory tracking is a crucial component in robotic applications, underscoring the importance of advanced control methodologies. Various control strategies have been developed and implemented to enhance the precision and responsiveness of robots in following designated paths. Among these, linear trajectory control based on the kinematic model of the robot has been explored in [10], where the principles of linearization help in simplifying the control of complex robotic motions. Adaptive sliding control, detailed in [11], adjusts to changes in robot dynamics and environmental conditions to maintain path accuracy. Fuzzy control, discussed in [12], achieved target precision and maintained it within 2.23 s with a maximum error of less than 1 mm, showcasing its effectiveness in dealing with uncertainties and non-linearities. Furthermore, Proportional-Integral (PI) control presented in [13], and the Proportional-Derivative Plus (PD+) method developed in [14], where the Integral of Squared Error (ISI) was notably high at 8,705,235.5, with Root Mean Squared Error (RMSE) indices of 46.41 and 6.56, respectively, highlight the different approaches to minimizing steady-state error and improving settling time. Dynamic PI sliding control proposed in [15] integrates the robustness of sliding mode control with the simplicity of PI control, enhancing stability and reducing overshoot. Nonlinear adaptive control, designed and simulated in [16], successfully demonstrated a circular robot trajectory within 0.5 s without overshoot, maintaining negligible steady-state error. Additionally, Model Predictive Control (MPC) with friction compensation developed in [17] tested on an eight-shaped trajectory, showed Integral Absolute Error (IAE\({}_{\text{xy}}\)) and Integral Angular Error (IAE\({}_{\text{g}}\)) of 1.517 m and 1.2907 rad, respectively, with corresponding Mean Absolute Errors (MAE\({}_{\text{xy}}\) and MAE\({}_{\text{g}}\)) of 0.0997 m and 0.0655 rad, underscoring MPC's capability to predict and correct future trajectory errors efficiently. Despite these advancements, the issue of chattering in sliding control laws, particularly noted in studies [11; 15], has not been sufficiently addressed, indicating an area for further research and improvement in control strategies for mobile robots. This introduction sets the stage for discussing innovative control solutions that enhance trajectory tracking while minimizing the drawbacks of existing methods.