## 4 Improved ACO for Global Path Planning  
### Fuzzy Control of \(\alpha\) and \(\beta\)  
In ACO, the \(\alpha\) and \(\beta\) have a great influence on the performance of the algorithm. The value of \(\alpha\) indicates the degree to which the pheromone remaining on each node is valued. The larger value of \(\alpha\), the easier it is for ants to choose a path traveled before. A larger \(\alpha\) keeps ants away from local optimality but reduces the search randomness. The value of \(\beta\) indicates the degree to which the heuristic function is valued. The larger the value of \(\beta\), the easier it is for ants to choose a closer node. If the values of \(\alpha\) and \(\beta\) are not obtained properly, the result will be poor. This section will use fuzzy control to dynamically adjust the values of \(\alpha\) and \(\beta\). The fuzzy control is a digital control system based on the fuzzy set theory, the fuzzy language variables and the fuzzy logic inference. The fuzzy controller consists of four parts:  
1. _Fuzzification._ The main function is to select the input quantity of the fuzzy controller and convert it into the fuzzy quantity that the system can recognize. The input quantity is processed to meet the requirements of fuzzy control. The input quantity is scaled to determine the fuzzy language value of each input quantity and the corresponding membership function. 2. _Rule base._ The fuzzy rule base is established based on the experience of human experts. The fuzzy rule library contains many control rules. It is a key step in the transition from actual control experience to fuzzy controller. 3. _Fuzzy reasoning._ This part mainly implements knowledge-based reasoning decision. 4. _Defuzzification._ The main function of this part is to convert the control quantity obtained by reasoning into control output. To satisfy the fuzzy control algorithm, the following variables are defined:  
**Definition 1**. : _Quality of paths solved by ant colony._  
\[ \begin{array}{l}Value=L_{best}(n)-\min\{L_{best}(n-1),L_{best}(n-2),\ldots,L_ {best}(1)\},\\ Value\in[-6,6]\end{array}  \tag{7}\]  
**Definition 2**. : _Evolution of ant colony._  
\[Iter=\frac{n}{N},Iter\in(0,1] \tag{8}\]  
where \(L_{best}\) is the best path in contemporary ant colony, \(n\) is the current iteration times, and \(N\) is the total iteration times. In Equation (7), \(Value\in[-6,6]\) is derived from a large number of experimental effect comparisons and selections. In this paper, the fuzzy controller contains two input variables and two output variables. The input variables are \(Value\) and \(Iter\). The output variables are \(\alpha\) and \(\beta\). The values of \(\alpha\) and \(\beta\) are controlled by the convergence state of ant colony in different stages. It can improve the pre-convergence speed and avoid falling into local solution of the algorithm. The whole fuzzy control algorithm includes three stages. In the early stage of the algorithm, pheromone accumulates insufficiently on each path. At this time, the ant colony for selecting the route is related to the expectation heuristic factor \(\beta\). Then, \(\beta\) should be larger and \(\alpha\) should be smaller. With the iteration, the pheromone concentration on the shortest path is gradually higher than other paths. In this case, \(\alpha\) should increase and \(\beta\) should decrease accordingly to enhance the positive feedback effect of pheromone. In the later stage of the algorithm, the pheromone concentration in some paths is much higher than in other paths. The algorithm has the highest risk trapped in the local optimum. In order to increase the randomness of the algorithm, the influence of the pheromone for selecting a path should be reduced. The value of \(\alpha\) decreases and the value of \(\beta\) shouldfurther decrease. In the fuzzy algorithm, the value shows the ant colony's searchability. It can accurately control the parameters according to each optimal path. The values of \(\alpha\) and \(\beta\) are usually taken from [1; 9] in traditional ACO.