## 4 Experimental Results
### The Influence of Various Parameters  
#### 4.2.1 The Influence of the Control Coefficients and the Error Signals  
To study the influence of the error signals and the control coefficients on the trajectory tracking problem, we selected the circular path as the research task for the trajectory tracking with the mobile platform. In the second task, the modified iterative learning control law was selected as the basic controller, and different error signals and the control coefficients were taken as variable parameters. The specific controller settings were as follows:  
**Situation 4:** The \(e_{i}(k+1)\) only uses as the feedback error signal, and the control law (17) is selected as the basic controller. The corresponding gain parameters are described as follows:  
\[ \begin{array}{l}L_{1}^{s4a}(k)=0.1\cdot L_{1}(k);\\ L_{1}^{s4b}(k)=1.0\cdot L_{1}(k);\\ L_{1}^{s4c}(k)=10\cdot L_{1}(k);\end{array}  \tag{48}\]  
**Situation 5:** The \(e_{i}(k+1)\) and \(e_{i+1}(k)\) are used as the feedback error signal, and the control law (17) is selected as the basic controller. The corresponding gain parameters are described specifically expressed as follows:  
Figure 5: Other typical trajectories tracking results of mobile platform using the HILC law (47) with Initial error. (**a1**) Path change of mixed the arc and line closed trajectory tracking using HILC law (47). (**a2**) Final path of mixed the arc and line closed trajectory tracking using HILC law (47). (**a3**) Average error of the arc and line mixed closed trajectory tracking using HILC law (47). (**b1**) Path change of the cardioid-like trajectory tracking using HILC law (47). (**b2**) Final path of the cardioid-like trajectory tracking using HILC law (47). (**c1**) Path change of the spiral-like trajectory tracking using HILC law (47). (**c2**) Final path of the spiral-like trajectory tracking using HILC law (47). (**c3**) Average error of the spiral-like trajectory tracking using HILC law (47). \[ \begin{array}{ll}L_{1}^{\text{56a}}(k)=0.1\cdot L_{1}(k);&L_{2}^{\text{56a}}(k)=0.5 \cdot L_{1}(k);\\ L_{1}^{\text{56b}}(k)=0.1\cdot L_{1}(k);&L_{2}^{\text{56b}}(k)=1.0\cdot L_{1}(k); \\ L_{1}^{\text{56c}}(k)=0.1\cdot L_{1}(k);&L_{2}^{\text{56c}}(k)=10\cdot L_{1}(k); \end{array}  \tag{49}\]  
**Situation 6:** The feedback error signal includes \(e_{i}(k+1)\), \(e_{i+1}(k)\), and \(e_{i+1}(k-1)\) and the control law (17) is selected as the basic controller. The corresponding gain parameters are specifically expressed as follows:  
\[ \begin{array}{ll}L_{1}^{\text{56a}}(k)=0.1\cdot L_{1}(k);&L_{2}^{\text{56a}} (k)=1\cdot L_{1}(k);&L_{3}^{\text{56a}}(k)=0.1\cdot L_{1}(k);\\ L_{1}^{\text{56b}}(k)=0.1\cdot L_{1}(k);&L_{2}^{\text{56b}}(k)=1\cdot L_{1}(k); &L_{3}^{\text{56b}}(k)=1.0\cdot L_{1}(k);\\ L_{1}^{\text{56c}}(k)=0.1\cdot L_{1}(k);&L_{2}^{\text{56c}}(k)=1\cdot L_{1}(k); &L_{3}^{\text{56c}}(k)=20\cdot L_{1}(k);\end{array}  \tag{50}\]  
By selecting different controller coefficients and different error parameters, we obtained different dynamic iterative trajectory graphics and the final trajectory result of the mobile platform with 100 iterations, which are shown in Figure 6. To determine the influence of the control coefficient and the error parameter, we compared the various dynamic iterative trajectory graphics, as shown in Figure 6.  
(1) Comparing a, b, and c in Figure 6 with different controller coefficients, the number of the iterations required for trajectory tracking can be continuously reduced by increasing the control coefficient within a reasonable range (0.1 to 10). However, if the control  
Figure 6: Circular trajectory tracking results of the mobile platform using the HILC controller with different parameters. (**a**) Using the HILC law with \(k1=0.1\). (**b**) Using the HILC law with \(k1=1\). (**c**) Using the HILC law with \(k1=0.1\). (**d**) Using the HILC law with \(k1=0.1\), \(k2=0.5\). (**e**) Using the HILC law with \(k1=0.1\), \(k2=1\). (**f**) Using the HILC law with \(k1=0.1\), \(k2=10\).