## 4 Experimental Results
### The Influence of Various Parameters
#### 4.2.3 The Influence of Basic Structure Parameters  
To study the influence of the actual structure parameters of the mobile platform on the controller, we compared the controller with the system parameters to that without the system parameters. The specific parameters were as follows:  
**Situation 11**: The novel hybrid controller without error in the parameters of the mobile platform:  
\[L_{1}^{s11}(k)=0.10\cdot L_{1}(k);\quad L_{2}^{s11}(k)=0.25\cdot L_{1}(k);\quad L _{3}^{s11}(k)=0.25\cdot L_{1}(k); \tag{55}\]  
Figure 7: Circular trajectory tracking results of the mobile platform using the HILC controller with a speed limit. (**a1**) Path change tracking using HILC law (51). (**a2**) Final speed of the two-wheels tracking using HILC law (51). (**a3**) Maximum tracking error change tracking using HILC law (51). (**b1**) Path change tracking using HILC law (52). (**b2**) Final speed of the two-wheels tracking using HILC law (52). (**b3**) Maximum tracking error change tracking using HILC law (52). (**c1**) Path change tracking using HILC law (53). (**c2**) Final speed of the two-wheels tracking using HILC law (53). (**d1**) Path change in tracking using HILC law (54). (**d2**) Final speed of the two-wheels tracking using HILC law (54). (**d3**) Maximum tracking error change tracking using HILC law (54).  
**Situation 12:** The novel hybrid controller with error in the parameters of the mobile platform:  
\[\begin{array}{c}L_{1}^{s12}(k)=\left[\begin{array}{cc}\cos(q)&\sin(q)&1\\ \cos(q)&\sin(q)&-1\\ \end{array}\right];\\ L_{2}^{s12}(k)=0.5\cdot L_{1}^{s12}(k);\qquad L_{3}^{s12}(k)=0.5\cdot L_{1}^{ s12}(k);\end{array} \tag{56}\]  
**Situation 13:** The other controller without the control matrix parameters of mobile platforms:  
\[\begin{array}{c}L_{1}^{s13}(k)=0.1\left[\begin{array}{cc}0.5&0.2&B_{rs}/R_{ rs}\\ \cos(q)&\sin(q)&-B_{rs}/R_{rs}\\ \end{array}\right];\\ L_{2}^{s13}(k)=2.5\cdot L_{1}^{s13}(k);\qquad L_{3}^{s13}(k)=2.5\cdot L_{1}^{ s13}(k);\end{array} \tag{57}\]  
By selecting different Iterative learning controllers, we obtained the different dynamic iterative trajectory graphics and the final trajectory result of the mobile platform, as shown in Figure 8.  
(1) Comparing Figure 8a1-a3,b1-b3, the controller without the basic system parameters can still track the circular trajectory, which proves that the iterative controller designed in this article does not depend on the actual parameters.  
(2) Comparing Figure 8b1-b3,c1-c3, the designed controller cannot effectively track the given trajectory when the gain matrix \(L_{1}(k)\) does not conform to the movement characteristics of mobile platforms,.  
Figure 8: Circular trajectory tracking results of the mobile platform using the HILC controller with different structure parameters. (**a1**) Path change tracking using HILC law (55). (**a2**) Final path tracking using HILC law (55). (**a3**) Maximum tracking error change using HILC law (55). (**b1**) Path change tracking using HILC law (56). (**b2**) Final path tracking using HILC law (56). (**b3**) Maximum tracking error change using HILC law (56). (**c1**) Path change tracking using HILC law (57). (**c2**) Final path tracking using HILC law (57). (**c3**) Maximum tracking error change using HILC law (57).