# Application of Improved Sliding Mode and Artificial Neural Networks in Robot Control
## 3 Results  
The MATLAB/Simulink diagram simulating the proposed method for the Mobile robot is shown in Figure 4.  
The block diagram under analysis in Figure 4 in this study likely outlines an advanced control system framework for a mobile robot, integrating Intelligent Sliding Mode Control (ISMC) with a Radial Basis Function (RBF) neural network. This synthesis suggests a sophisticated mechanism that aims to refine the robot's trajectory tracking in the presence of uncertainties and non-linearities typical of robotic systems. At the outset, the Input Block defines the desired trajectory or setpoint for the robot, providing a benchmark for its motion. The Summing Junction then computes an error signal by contrasting this reference with the feedback from the robot, signifying the deviation of the robot's actual path from the intended course. Subsequently, an Integrator Block accumulates the error, suggesting a possible inclusion of an integral component in the control strategy, which could be indicative of a PID controller's influence or another integrative control methodology. The Mux Block consolidates multiple signals into one, implying a synthesis of error information, possibly amalgamating the instantaneous and cumulative error signals for input into the control system. Central to the diagram is the ISMC-RBF Controller Block, which embodies the core intelligence of the system. It leverages a fusion of ISMC for its robustness against uncertainties and the adaptive nature of RBF neural networks to fine-tune control laws dynamically. This adaptive ability ensures the controller's responsiveness to the complex dynamics of the mobile robot. The code used in this block is mentioned in Appendix A. The Robot Block symbolizes the actual mobile robot that acts on the control signals. It reflects the robot's physical response to the inputs, with its dynamics and movement patterns forming the output of this block. The Demux Block, situated downstream, disperses the combined input into separate streams, which likely represent distinct state variables of the robot's movement for subsequent processing or feedback. A critical component of the system is the Feedback Loop, which circulates the robot's state back to the Summing Junction. This closed-loop feedback is instrumental in real-time control adjustments, allowing for a self-correcting mechanism that aligns actual performance with targeted outcomes. Lastly, the bidirectional communication between the robot and the ISMC-RBF Controller indicates a two-way exchange of information: the robot provides its state data to the controller, and the controller, in turn, relays control instructions back to the robot. The diagram encapsulates a dynamic and intelligent control strategy that caters to the demanding requirements of mobile robot navigation, promising enhanced precision, swift  
Figure 4: MATLAB/Simulink diagram simulating the ISMC-RBF controller. response, and steadfastness, even when subjected to external disturbances and intrinsic dynamic complexities. The parameters of the robot used in the simulation are presented in Table 1.  
The parameters of the proposed controller are presented in Table 2.  
The response of the ISMC-RBF method between \(x_{d}\) and \(x_{W}\), and \(y_{d}\) and \(y_{W}\) with the Tricuspid curve is presented in Figure 5. Observing Figure 5, it can be seen that \(x_{W}\) converges towards \(x_{d}\), with a rise time (\(t_{r-x}\)) of 0.0710 s, a settling time (\(t_{ss-x}\)) of 0.0978 s, a steady-state error (\(e_{ss-x}\)) of 0 m, and a percent overshoot (\(POT_{x}\)) of 0.0040%; and \(y_{W}\) converges towards \(y_{d}\), with a rise time (\(t_{r-y}\)) of 0.0646 s, a settling time (\(t_{ss-y}\)) of 0.0902 s, a steady-state error (\(e_{ss-y}\)) of 0 m, and a percent overshoot (\(POT_{y}\)) of 0.0042%. Figure 6 displays the control signals of the ISMC-RBF controller.