## 4 Experimental Validation
### Discussion  
QR code-navigated AGVs are widely used in agriculture, industrial automation, healthcare, logistics, and other fields. There are a large number of researchers contributing to QR code navigation, localization, path planning, etc. in the related literature. With the development of industrial automation, visual navigation is widely adopted because of its high accuracy and low latency. However, single navigation still faces many problems, such as a long processing time and high sensor requirements. Ref. [7] proposed to use EKF combined with an internal encoder and external QR code to correct the cumulative error generated by attitude estimation. This method can effectively solve the error problem and improve the positioning accuracy, providing a new reference for navigation methods. However, the error increases as the distance of the QR code paste increases.  
In this article, EKF can only calculate the a posteriori estimate of the state through the current measurement value and the a priori estimate, and cannot directly consider the influence of historical data, so it is susceptible to the cumulative error of the sensor. EKF assumes that the noises in the system model and the measurement model are linear Gaussian distributed, but there may be nonlinear noises and non-Gaussian distributed noises in the actual application, which may lead to the filtering results of accuracy degradation. Our work meets the positioning requirements of high-precision navigation systems in terms of adaptive tuning, positioning accuracy, and navigation time.  
When in a suitable environment, the navigation and positioning scheme proposed by some researchers can achieve 100% positioning and permanently eliminate accumulated errors. The method proposed by [8] can achieve 100% accuracy and complete given commands under suitable circumstances. It has achieved a qualitative leap in the field of navigation and positioning. However, due to its use of RGB sweep detection, when encountering bright light environments, or when obstacles are similar in color to the transported object, it can adversely affect the results to detect the completion of instructions.  
[PERSON], [PERSON], and [PERSON], [PERSON] et al. [29; 30] proposed different fusion methods to improve the positioning accuracy and reduce the time required for navigation. However, when AGVs are in an environment similar to a long corridor, they are prone to map distortion, incorrect judgement of current position, continuing along the wrong route and collision problems.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Number of Cycles**} & \multirow{2}{*}{**Algorithm**} & \multicolumn{2}{c}{**Number of**} & \multirow{2}{*}{**Cumulative Time**} & \multirow{2}{*}{**Maximum/Minimum**} & \multirow{2}{*}{**Maximum/Minimum**} \\  & & & & & **Recovery Time (s)** & \\ \hline \multirow{3}{*}{10} & AMCL & 17 & 51.64/3.04 & 2.59/1.75 & 22.81/15.69 \\  & Improved AMCL & 2 & 1.18/0.59 & 0.12/0.06 & 3.88/1.72 \\  & AMCL & 31 & 79.04/2.54 & 2.78/1.16 & 19.26/10.71 \\  & Improved AMCL & 3 & 1.56/0.52 & 0.21/0.02 & 4.33/2.28 \\  & AMCL & 44 & 119.68/2.72 & 2.13/1.54 & 21.16/9.31 \\  & Improved AMCL & 5 & 2.26/0.45 & 0.51/0.03 & 3.29/1.61 \\  & AMCL & 60 & 146.28/2.44 & 2.88/1.02 & 18.74/11.26 \\  & Improved AMCL & 8 & 3.28/0.40 & 0.96/0.02 & 5.10/2.13 \\  & AMCL & 71 & 162.64/2.29 & 1.35/0.97 & 16.89/8.92 \\
50 & Improved AMCL & 10 & 4.18/0.41 & 0.29/0.05 & 3.77/1.02 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Measurements of the occurrence of kidnappings.  
Through the simulation experiments and scenario tests in this section, a large number of experimental comparisons can be made to conclude the superiority of the proposed method in this paper, which is better than similar methods in terms of the adaptive adjustment time, positioning accuracy, and navigation time.