# Application of Improved Sliding Mode and Artificial Neural Networks in Robot Control
## 3 Results
These control signals exhibit small amplitudes and low oscillation frequencies compared to the constant speed approach law and exponential function, with signum in [33] using the same parameters with this robot. This indicates that the proposed control method has successfully mitigated the chattering phenomenon commonly associated with sliding control. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Description** & **Value** \\ \hline \(I_{b}\) & Robot Moment of Inertia & 11.25 kgm\({}^{2}\) \\ \(M\) & Robot Mass & 9.4 kg \\ \(L\) & Distance Between & 0.178 m \\ \(k\) & Driving Gain Factor & 0.448 \\ \(c\) & Viscous Friction Factor & 0.1889 kgm\({}^{2}\)s\({}^{-1}\) \\ \(I_{W}\) & Moment of Inertia of Wheel & 0.02108 kgm\({}^{2}\) \\ \(r\) & Radius of Wheel & 0.0245 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of a Three-Wheeled Omnidirectional Mobile Robot model. Figure 5: Response of the ISMC-RBF between \(x_{d}\) and \(x_{W}\), and \(y_{d}\) and \(y_{W}\) with the Tricuspid curve. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline \(\kappa\) & \(diag([15,\,15,\,8])\) \\ \(\eta\) & \(diag([200,\,200,\,200])\) \\ \(\epsilon\) & \(diag([0,\,15,\,0,\,15,\,0,\,15])\) \\ \(\lambda\) & \(diag([15,\,15,\,15])\) \\ \(\alpha\) & \(diag([12,\,12,\,12])\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the proposed controller. Figure 7 presents the sliding surface \(\mathbf{s}=\left[s_{1}\,s_{2}\,s_{3}\right]^{\text{T}}\) of the proposed controller. Initially, the surface starts according to the sliding coefficient values. Then, s quickly reaches a convergence point and continues to slide around \(\mathbf{s}=0\). The Tricuspoid trajectory response of the ISMC-RBF controller is depicted in Figure 8.  
Figures 9 and 10 showcase the trajectory responses of the ISMC-RBF controller to the Tricuspoid and Lissajous curves under the influence of noise at the robot's output (assuming sensor noise with a power of 0.0005 w and a sampling time of 0.0001 s). The robot's actual trajectory still converges to the reference trajectory within a finite time, with the error converging to zero. The simulation results presented in Figures 8-10 provide compelling evidence of the effectiveness of the proposed ISMC-RBF controller in tracking desired trajectories with high precision and reliability. Figure 8 illustrates the actual trajectory of the mobile robot compared to the desired Tricuspoid trajectory. The close alignment between the actual trajectory (red) and the desired trajectory (blue dashed lines) demonstrates the controller's high precision in trajectory tracking. The minimal deviation observed indicates that the controller effectively minimizes tracking errors, ensuring that the robot follows the intended path accurately. The smoothness of the trajectory reflects the controller's capability to manage the robot's movements without significant oscillations, further emphasizing its precision. Figure 6: Control signals \(\mathbf{u}\) of the ISMC-RBF. Figure 7: Sliding surfaces \(\mathbf{s}\). Figure 9 shows the robot's trajectory response under the influence of sensor noise while following the same Tricuspid curve. Despite the presence of noise, the actual trajectory remains close to the desired trajectory, highlighting the robustness of the ISMC-RBF  
Figure 8: Trajectory response of the ISMC-RBF controller for the robot with the Tricuspid curve. Figure 10: Trajectory response of the ISMC-RBF controller for the robot with the Lissajous curve under noise. Figure 9: Trajectory response of the ISMC-RBF controller for the robot with the Tricuspoid curve under noise. controller against disturbances. Although some oscillations and deviations are introduced due to noise, the controller successfully compensates for these disturbances, maintaining the overall shape and direction of the desired trajectory. This robustness to noise is crucial for practical applications where environmental disturbances are common.