Optimal trajectory planning algorithm for autonomous flight of multiple UAVs in small areas

Abstract

The development of science and technology requires UAV to improve the accuracy of path planning to better apply in the military field and serve the people. The research proposes to use the social spider algorithm to optimize the ant colony algorithm, and jointly build an IACA to deal with the optimal selection problem of UAV path planning. Firstly, the swarm spider algorithm is used to make a reasonable division and planning of the UAV’s flight field. Secondly, the AC is used to adjust and control the UAV’s state and path. Then, the IACA is formed to carry out performance simulation and comparison experiments on the optimal path planning of the UAV to verify the superiority of the research algorithm. The results show that the maximum number of iterations of the original AC and the IACA is 100, but the IACA under the route planning optimization reaches the convergence state in 32 generations; Moreover, when the number of iterations is about 20 generations, there will be a stable fitness value, which saves time for the experiment to find the optimal path. In the simulation experiment, it is assumed that three UAVs will form a formation to conduct the experiment, and the multiple UAVs will be subject to global track planning and repeated rolling time domain track planning. The autonomous operation time of multiple UAVs through the assembly point is (5.30 s, 5.79 s, 9.29 s). The distance between UAVs during flight is predicted. It is found that the nearest distance is 2.3309 m near $t=$ 6.65 s, which is in line with the safety distance standard. Under the improved algorithm, the speed in all directions is also relatively gentle. All the above results show that the improved algorithm can effectively improve the iteration speed and save time.

Keywords

Multi-UAV autonomy trajectory IACA

1. Introduction

With the continuous reform and development of aviation technology, more and more UAVs are used in high-risk, high-intensity search and rescue missions or patrol tasks. Therefore, UAV is gradually becoming an important pillar in China’s aviation field [1]. In fact, the path planning of UAV is to plan the best path with the help of its own system and external conditions under the premise of comprehensive consideration of UAV’s flight time, fuel consumption and threats, so as to better complete the task. However, at present, the search and inspection of airspace requires that UAVs can complete tasks efficiently and quickly in a short time, which undoubtedly increases the difficulty in the forward development of aviation technology [2]. How to innovate on the existing aviation path planning technology and expand the application field at the same time, so as to realize the autonomous flight of multiple UAVs in a small area is still the focus of researchers and scholars [3]. In order to solve this kind of problem, the research proposes to integrate the swarm spider optimization algorithm and the ACO to build an improved algorithm, which can be applied to the track and path optimization problem to improve the search ability and task completion efficiency of multiple UAVs. The two algorithms integrate with each other and introduce guidance factors, which can speed up the search to a certain extent and has high feasibility [4, 5].

2. Related works

The prosperity of a country is inseparable from the aviation technology of each country. Lin et al. [6] proposed an error resistant track association algorithm based on distance hierarchical clustering for the problem of track association of aircraft platforms under complex conditions of different targets. Monte Carlo simulation shows that, compared with the classical algorithm based on reference topology feature (RET), this algorithm has significantly improved the correlation accuracy and adaptability to complex conditions. Zhou et al. [7] proposed the VIKOR method based on flight parameters to evaluate the landing quality of UAVs. During the experiment, several flight parameters were used to evaluate the landing quality, and the absolute standard was determined using the ranking obtained. The comparison results show that there is a high similarity between the two, with a correlation coefficient as high as 0.917, which is better in quality assessment. In order to improve the aerial spraying efficiency of helicopters, Liu et al. [8] proposed the optimal full coverage path planning method and developed the corresponding device. The longer the spraying path is, the larger the spraying area is, and the greater the pesticide consumption is. Under the premise of full coverage, the shortest spraying route distance can ensure the most accurate coverage. Xia et al. [9] proposed a global path planning algorithm based on improved quantum ant colony algorithm to improve the ability of Unmanned Surface Vehicles (USVs) to carry out underwater tasks. The simulation results show that the algorithm requires the lowest number of iterations to converge to the minimum value, and can effectively obtain the optimal path of USV. Nguyen et al. [10] proposed an online path planning algorithm for joint detection and tracking, which also uses null probability constraints to maintain a safe distance between UAVs and interested targets. It has been proved through practice that the algorithm is capable of being subjected to multiple unmanned electrically labeled objects.

Wang and Liu [11] established a multi-target detection method based on virtual reality technology by comparing the advantages and disadvantages of multi-target tracking algorithm, ant colony algorithm and hybrid particle swarm optimization algorithm. The results show that compared with previous models, the overall optimization efficiency of UAV route is improved by 15%, which is more practical. Warner and Rogers [12] proposed an algorithm to determine flight performance by estimating aircraft attachment position and payload weight. Simulation results illustrate the performance of the algorithm for various modular aircraft configurations. Zhao et al. [13] proposed a model called YOLO Expressway, which uses an improved YOLO model to enhance the real-time detection of expressway marking problems. The experimental results show that the proposed YOLO road model can accurately detect the road centerline in real time, and has high robustness to changes in different environmental conditions. Miao et al. [14] proposed a new position based lightweight beamforming technology. During the experiment, in order to overcome the inherent position error, a new position correction method was designed, which combined the position information of 5G system. The simulation results show that the algorithm proposed in the study has higher advantages. Wang et al. [15] proposed a Gaussian process unscented Kalman filter (GP-UKF) hybrid method based on UAV flight pattern recognition (FMR) to deal with UAV flight data estimation and prediction. The model has good effectiveness and practical application potential.

It can be seen from the research on the free planning algorithm of UAV and track by domestic and foreign scholars that there are many researches applied to UAV path planning and UAV driving control. There are fewer trajectory planning algorithms for autonomous flight. For this reason, the research mainly discusses the trajectory planning algorithm applied in the field of multi-UAV flight.

3. IACA for optimal track planning and construction of multi-UAV autonomous flight model

3.1 Experimental design of social spider algorithm in the field of multi UAV flight

The gregarious spider optimization algorithm is a heuristic algorithm, the specific idea is to imitate the behavior of gregarious spiders, such as predation, web weaving and reproduction. The SSO algorithm regards the spider as a search space, and the position of the spider in the space is a solution to the problem. And in the SSO algorithm, the spider is assigned a weight value by calculation, and this value represents the size or quality of the spider [16, 17]. The determination of the population size and the proportion of male and female spider population in the optimization algorithm of social spiders is shown in Eq. (1).

$\displaystyle\left\{{{\begin{array}[]{l}{N_{f}=[{({0.9-\textit{rand}\times 0.2% 5})\times N}]}\\ {N_{m}=N-N_{f}}\\ \end{array}}}\right.$ (1)

In Eq. (1), it $N$ represents the total number of spiders; it represents $N_{f}$ the number of female spiders; $N_{m}$ it represents the number of male spiders; it can be found from the equation that among the total number of spiders, the female spiders are about 65–90%, and the male spiders are about 65–90%. Between 10% and 35%. The female spider $F$ and the male spider collection $M$ are generated by randomness. The expression for the mating radius $r$ of the spider population is shown in Eq. (2).

$\displaystyle r=\sum\limits_{j=1}^{N}{\frac{P_{j}^{\textit{high}}-P_{j}^{% \textit{low}}}{2N}}$ (2)

In Eq. (2), it $P_{j}^{\textit{high}}$ represents the upper limit of the first $j$ dimension variable; $P_{j}^{\textit{low}}$ it represents the lower limit. Then, the individual weight of the spider is solved, as shown in Eq. (3).

$\displaystyle Wi=1-\frac{J({Si})-\textit{worst}}{\textit{best}-\textit{worst}}$ (3)

In Eq. (3), $W_{i}$ represents $i$ the weight of the numbered spider individual; $J({S_{i}})$ then represents $i$ the fitness value of the numbered spider individual; best represents the fitness value of the best individual; worst represents the fitness value of the worst individual. The moving methods of spiders are different. For female spiders, they approach the spider with the larger weight according to the weight of the individual occupied, as shown in Eq. (4).

$\displaystyle\left\{{{\begin{array}[]{l}{F_{i}^{k+1}=F_{i}^{k}+\alpha\textit{% Vib}_{ci}({S_{c}-F_{i}^{k}})+\beta\textit{Vib}_{bi}({S_{b}-F_{i}^{k}})+\delta(% {\textit{rand}-0.5}),\textit{rand}\leqslant PF}\\ {F_{i}^{k+1}=F_{i}^{k}+\alpha\textit{Vib}_{ci}({S_{c}-F_{i}^{k}})-\beta\textit% {Vib}_{bi}({S_{b}-F_{i}^{k}})+\delta({\textit{rand}-0.5}),\textit{otherwise}}% \\ {\textit{Vib}_{ij}=w_{j}e^{-d_{ij}^{2}}}\\ \end{array}}}\right.$ (4)

In Eq. (4), it $\textit{Vib}_{ci}$ represents the perception ability of the spider $i$ to the female individual with the largest weight $c$ ; $\textit{Vib}_{bi}$ it represents the perception ability of the female spider to the spider that is $i$ closest to the female spider and whose proportion is larger than $i$ that $i$ of the spider; it represents $b$ the perception ability $\textit{Vib}_{ij}$ of the female spider $i$ to all spiders; $\alpha,\beta,\delta$ it is [0, 1] constant coefficients in the interval. It $S_{c}$ represents the position of the female spider $c$ in space; $S_{b}$ it represents the position of the spider with a greater weight than the female spider $i$ and $i$ the closest spider to the female spider [18, 19]. The male spiders are arranged in descending order according to the weight value, and the middle weight value is obtained by calculation. The weight value in the middle is called the middle male spider, and the middle male spider is used to update the position of other male spiders.

$\displaystyle M=\left\{{{\begin{array}[]{l}{M_{i}^{k}+\alpha\times\textit{Vib}% _{fi}({S_{f}-M_{i}^{k}})+\delta({\textit{rand}-0.5}),W_{Nf+1}\geqslant W_{Nf+m% }}\\ {M_{i}^{k}+\alpha_{i}\left({\frac{\sum\limits_{h=1}^{N_{m}}{M_{h}^{k}W_{Nf+h}}% }{\sum\limits_{h=1}^{N_{m}}{W_{Nf+h}}}}\right),\text{otherwise}}\\ \end{array}}}\right.$ (5)

In Eq. (5), it $W_{Nf+h}$ represents the weight of the middle male spider; $S_{f}$ it represents $i$ the position of the closest spider with a weight greater than that of the male spider. Female spiders select male spiders for mating within their notification range, and the expression of the new spider population after mating is shown in Eq. (6).

$\displaystyle P({S_{k}})=\left({w_{k}\left/\sum\limits_{g\in T_{G}}{w_{g}}% \right.}\right),k\in T_{G}$ (6)

In Eq. (6), $T_{G}$ represents a new spider population. Iteratively update the group according to the above equation steps. When the number of iterations does not meet the preset maximum value, repeat the steps; if the maximum value is reached, stop the iteration and output the position of the optimal spider at this time, which is obtained. global optimal solution. Then, the weight of the spider is determined according to the comprehensive cost of the UAV’s trajectory planning path. Among them, fuel consumption cost, threat cost, etc. are all influencing factors [20, 21, 22]. One of the goals of trajectory planning is to minimize the comprehensive cost, and the total cost of the trajectory can be expressed as Eq. (7).

$\displaystyle\left\{{{\begin{array}[]{l}{W=\int_{0}^{L}{\left[{\sum{\delta w(s% )ds}}\right]}}\\ {\sum{\delta w(s)ds}=\delta_{O}w_{O}(s)+\delta_{M}w_{M}(s)+\delta_{A}w_{A}(s)+% \delta_{T}w_{T}(s)}\\ \end{array}}}\right.$ (7)

In Eq. (7), it $L$ represents the flight path of $W$ the UAV; it represents the comprehensive cost consumed during the flight of the $w_{L}(s)$ UAV; the fuel consumption cost of the UAV; the $w_{M}(s)$ missile threat cost; the $\delta_{A}w_{A}(s)$ antiaircraft artillery position threat cost; the $w_{T}(s)$ mountain threat The cost of; $\delta_{O},\delta_{M},\delta_{A},\delta_{T}$ is the threat weight factor that adds up to 1. The threat cost is shown in Fig. 1.

Figure 1.

Schematic diagram of UAV threatened by a single missile position.

It can be found from Fig. 1 that the threats received by the UAV come from all directions during the mission. Therefore, in order to minimize the threat cost, each factor needs to be solved, as shown in Eq. (8).

$\displaystyle L=\sum\limits_{i=1}^{n-1}{L_{i}},w_{O}=c_{1}*L=c_{1}*\sum\limits% _{i=1}^{n-1}{L_{i}}$ (8)

In Eq. (8), the number of nodes in the UAV path is assumed to be $n$ ; $c_{1}$ it represents a constant, which is the proportional coefficient of fuel consumption and path length. Adding the calculation of the threat cost can synthesize the function of the threat cost $W$ , in which the weight of the spider is set as the reciprocal of the threat cost, see Eq. (9).

$\displaystyle W_{\textit{spider}}=\frac{1}{W}$ (9)

The smaller the weight of the corresponding spider in Eq. (9), the least threat to the UAV path, which is the optimal solution.

3.2 Construction of the path planning algorithm model for multi-UAV autonomous flight

During the autonomous flight of UAVs, the connections between UAVs are connected through communication topology, and the process is also limited by the random occurrence of various tasks and the distance between UAVs. For the performance of the conflict suffered by the UAV, see Fig. 2 for details.

Figure 2.

Schematic diagram of UAV collision detection.

In Fig. 2, the multi-UAV often needs to maintain the flight distance during the flight and ensure that it is greater than the safe distance $R_{\textit{safe}}$ . However, the communication distance in the actual flight of the UAV $R_{c}$ is limited by the range. When the operating position of the UAV changes, no The communication topology of man-machine also changes dynamically. Then, the algorithm is used to adjust and control the state of the UAV. In the IACA (Improved Ant Colony Algorithm), a guiding factor that can change dynamically with the number of iterations is designed, which is convenient to deal with the fact that the ant colony algorithm cannot quickly select the next node to pass through due to the joint influence of pheromone and heuristic factors when selecting different paths. The guiding factor of the $\lambda_{iE}$ node is shown $i$ in Eq. (10).

$\displaystyle\lambda_{iE}=\frac{m-k}{m}*\frac{N_{\max}-N}{N_{\max}}*\frac{1}{d% _{iE}}$ (10)

In Eq. (10), $m$ represents the number of ants; $k$ represents the current number of ants; represents the current number $N$ of iterations; $N_{\max}$ represents the maximum number of iterations; $d_{iE}$ represents the distance from the node $i$ to the destination node $E$ . After introducing the guiding factor, $i$ the probability of selecting a node to move from a node is shown in Eq. (11).

$\displaystyle p_{ij}^{k}(t)=\left\{{{\begin{array}[]{l}{\frac{\tau_{ij}^{% \alpha}(t)\eta_{ij}^{\beta}(t)\lambda_{jE}^{\gamma}(t)}{\sum\limits_{s\in% \textit{allowed}_{k}}{\tau_{is}^{\alpha}(t)\eta_{is}^{\beta}(t)\lambda_{iE}^{% \gamma}(t)}}}\\ {0,\text{otherwise}}\\ \end{array}}}\right.,j\in\textit{allowed}_{k}$ (11)

In Eq. (11), it $\lambda_{jE}^{\gamma}$ represents the guiding factor; $\lambda_{iE}^{\gamma}$ it represents the guiding function of the current node; $\gamma$ it represents the guiding function of the next node selected by the algorithm. Adding the guiding factor into the ant colony algorithm, when the initial pheromone is similar, can guide the ants to move towards the better path. And as the ant jumps from the destination, the number of iterations and transition probability continue to increase, which strengthens the purpose of the ant’s search activity, so as to better find a feasible solution. There are three models of pheromone increase in traditional ant colony algorithm: ant cycle, ant amount and ant density, as shown in the following Equations [23, 24].

$\displaystyle\Delta\tau_{ij}^{k}=\left\{{{\begin{array}[]{ll}\frac{Q}{L_{k}},&% \text{If UAV }k\text{ passes through side }({i,j})\\ 0,&\text{Otherwise}\\ \end{array}}}\right.$ (12) $\displaystyle\Delta\tau_{ij}^{k}=\left\{{{\begin{array}[]{ll}\frac{Q}{d_{ij}},% &\text{If UAV }k\text{ passes through side }({i,j})\\ 0,&\text{Otherwise}\\ \end{array}}}\right.$ (13) $\displaystyle\Delta\tau_{ij}^{k}=\left\{{{\begin{array}[]{ll}Q,&\text{If UAV }% k\text{ passes through side }({i,j})\\ 0,&\text{Otherwise}\\ \end{array}}}\right.$ (14)

Equations (12) and (14) represent the ant circle model and the ant dense model respectively, which are the reciprocal of the UAV total track path length; Eq. (13) represents the ant volume model, which uses the reciprocal of the local track path length. $Q$ is a constant that has been set, representing the amount of information; $L_{k}$ it represents $k$ the total track path length of the first UAV; $d_{ij}$ it represents the length of the track path $({i,j})$ . After the UAV completes the selection of the path from the starting point to the target point, the track path is updated according to Eq. (15). At this time, the pheromone concentration on the track path will also decrease correspondingly with time.

$\displaystyle\left\{{{\begin{array}[]{l}{\tau({t+n})=({1-\rho})*\tau_{ij}(t)+% \Delta\tau_{ij}(t)}\hfill\\ {\Delta\tau_{ij}(t)=\sum{\Delta\tau_{ij}^{k}(t)}}\hfill\\ \end{array}}}\right.$ (15)

Equation (15) represents $\Delta\tau({t+n})$ the increment of the pheromone left by $\rho$ the $k$ -th UAV between the track paths after $n$ seconds after time $t$ ; $({i,j})$ it represents the volatility factor, which takes a value in the interval [0, 1]. and is satisfied at the beginning of the algorithm run $\tau_{ij}(0)=0$ , $\Delta\tau_{ij}(0)=0$ . However, the above three pheromone update methods cannot satisfy the evaluation of solutions in complex environments. Therefore, after comprehensive consideration, it is combined with the swarming spider algorithm, and the spider is used as the solution, and the weight of the spider represents the pros and cons of the solution. And the weight of the new spider group is used as the new value of the pheromone to update the pheromone of each track path in the ant colony algorithm [25, 26]. The IACA has a long search time and a fast convergence speed, and can find a suitable solution value in a relatively short time. The selection of nodes follows the calculation of Eq. (11).

Figure 3.

Flow chart of IACA.

It can be found in Fig. 3 that after the parameters are initialized, the number of iterations is set to 0, that is $N=$ 0, the maximum number of iterations is $N_{\max}$ , and the UAV $m$ racks are allocated to each initial node. Then judge whether it is satisfied $N<N_{\max}$ . If it is satisfied, the search ends, and the next search is continued; if it is not satisfied, it returns to step 2 to reassign the ants.

4. Performance comparison and simulation experiment of the improved algorithm under optimal trajectory planning

In order to prove that the proposed algorithm can have the best planning effect for multi-UAV track paths. The experiment was set up in the following environment: the memory was 8 GB, the hard disk was 500 GB, the processor CPU was Intel (R) Core (TM) i5-8300 H, and the process software was MATLABR2018b. Assuming that the experimental flight area is within 20 km*20 km, the comprehensive cost function of the threat to the UAV is set to be 0.3, 0.2, 0.3, and 0.2 $\sum\delta_{w}(s)ds=\delta_{O}w_{O}(s)+\delta_{M}w_{M}(s)+\delta_{A}w_{A}(s)+% \delta_{r}w_{r}(s)$ , $\delta_{O},\delta_{M},\delta_{A},\delta_{r}$ respectively. The algorithm is used to plan the track path. The number of UAVs is assumed to be $m=$ 50, and the maximum number of iterations $N_{\max}=$ 100 represents the information heuristic factor $\alpha=$ 1, the expected heuristic factor $\beta=$ 3, and the guidance factor $\gamma=$ 4. And compare the traditional ant colony algorithm with the ant colony algorithm that introduces the guiding factor, as shown in Fig. 4.

Figure 4.

Effect Comparison of weighted path length between the improved algorithm and the original algorithm.

In Fig. 4, it can be found that the maximum number of iterations of the original ant colony algorithm is 100 generations, and it starts to converge at about 62 generations; while under the IACA, although the maximum number of iterations is also 100 generations, it starts at about 32 generations. convergence. Based on the above results, the optimal planning ant colony algorithm for the track path proposed by the research has high convergence, that is to say, the algorithm has high computational efficiency in the optimization process of the UAV track path planning, and has a high computational efficiency for the data. The set is highly inclusive and has high universality. The performance of the original ant colony algorithm and the IACA with the introduction of the guiding factor and the colony spider algorithm are compared, as shown in Fig. 5.

Figure 5.

Effect Comparison of fitness value between the improved algorithm and the original algorithm.

In Fig. 5, it can be found that the fitness value of the original ant colony algorithm is also changing rapidly in the process of gradually increasing the number of iterations. Before about 30 generations, the fitness value changes greatly, but after 80 generations, the fitness value is stable. at 120. This is because the original ant colony algorithm does not plan the UAV’s trajectory comprehensively, and the search time is too long. The IACA can effectively reduce the sensitivity of the initial state during the experiment, and the fitness value can be stabilized at 118 when the number of iterations is about 20 generations, which effectively saves time for the ants to find the optimal path. This also shows that adding a guiding factor and using the colony spider algorithm to optimize the information update pheromone can make the ant colony algorithm converge faster, shorten the search time, and speed up the algorithm process. Then the simulation experiment is carried out on the planning of the UAV track path under the research algorithm. In the process, the fitness value of the UAV is first converged in the process of assembling, and the fitness value required for the experiment is determined, as shown in Fig. 6.

Figure 6.

Objective function convergence curve of UAV assembly section.

In Fig. 6, it can be found that when the number of iterations of the objective function in the UAV assembly stage reaches 10, the fitness value reaches 154; then continue to operate, when the number of iterations reaches about 50, the fitness value reaches 153. At this time, the convergence speed of the multi-UAV during the flight is the best, and the search ability is the best, and it is used in the subsequent experiments. The trajectory planning routes of multiple UAVs are different in different situations, as shown in Fig. 7.

Figure 7.

Track planning route of multiple UAVs under different conditions.

In Fig. 7, (a) is the track path of the three UAVs in the global planning, and (b) is the track re-planning of the three UAVs in the rolling time domain. In Figure (a), it can be found that the trajectory obtained in the global planning will conflict with the UAV near the rendezvous. This is because the communication topology and the state of the UAV when passing through the rendezvous point are not considered during the experiment. situation that arises. Therefore, the operation of Figure (b) is added for optimization. In (b), the flight missions are classified into two parts: formation assembly and formation composition. All pass through the rendezvous point at the desired speed. During the mission, the optimized autonomous running times of multiple UAVs passing through the rendezvous point are (5.30 s, 5.79 s, 9.29 s) respectively. This means that the UAV can adjust the remaining tasks within the experimental time, and reach their respective positions according to the total expected time and preparation speed, and achieve the same frequency resonance of speed, time and position. The main coordinated flight tasks for trajectory planning are shown in Table 1.

Table 1

Display of main flight tasks of track planning

Time/S	Main collaborative tasks
0–5.30	Uav1 arrived at the rendezvous point according to the track path designed in the experiment, but 2 and 3 did not
5.30–5.79	Uav1 left the assembly point and flew to the team formation point. No. 2 arrived at the assembly point according
	to the speed set in the process, and No. 3 did not
5.79–9.29	Uav1 and uav2 fly to the formation point of the team respectively, and 3 arrive at the assembly point according
	to the experimental design speed
9.29–15	Uav1, uav2 and uav3 all reach the team formation point and match the speed with the team
15–30	The three UAVs continue to fly and perform missions after forming a team

Figure 8.

Distance between multiple UAVs in track reprogramming.

Figure 9.

Velocity performance diagram of UAV in all directions in track planning.

In Table 1, it can be clearly found that during the flight of the multi-UAV, the task events can be completed according to the experimental time regulations. And continue to fly after forming a team to perform tasks. Since UAVs are easily affected by the surrounding environment during flight, especially the conflicts between their flying fixed wings, it is necessary to consider the dynamic conflicts between UAVs, so it is necessary to consider the dynamic conflicts between UAVs in the trajectory planning. The distance is reasonably preset, and the specific effect is shown in Fig. 8.

As shown in Fig. 8, the minimum value of the distance between the drones is around $t=$ 6.65 s, and this is the closest distance between the second drone and the third drone, $x=$ 2.3309 m, which is larger than the safe distance, and the drone can fly safely in this state. During the UAV flight, the speed in all directions needs to be paid special attention. Therefore, the study monitors the flight speed of UAV No. 1. The specific effect is shown in Fig. 9.

Figure 9 shows the speed of UAV No. 1 in all directions in the track planning. It can be seen that under different calculation methods, the speed of the UAV’s track planning in the three directions of X, Y, and Z is the trend of flight time. A steady state is reached in about 15 s. However, before 15 s, it can be seen in Figure (a) that the flight speed intervals of the UAV in the X, Y, and Z directions of the original algorithm are [ $-$ 6 $\sim$ 12], [ $-$ 5 $\sim$ 8], [ $-$ 6 $\sim$ 12] respectively, the flight speed changes in a large range, and the flight speed slope changes steeply in a short time. In the UAV track under the IACA, the flight speed intervals in each direction of X, Y, and Z are [ $-$ 6 $\sim$ 6], [ $-$ 10 $\sim$ 5], [ $-$ 12 $\sim$ 6], and the speed intervals in each direction are becomes smaller and becomes smoother. This has better control over the UAV’s attitude, lift force and track in motion, and better flightability for multi-UAV track planning.

5. Conclusion

The increasing progress of aviation has brought great attention to UAVs in both military and civilian fields. However, the current UAV trajectory planning technology still has many problems such as blind path selection and slow calculation speed. In view of this, the research proposes to apply the ant colony algorithm based on the swarm spider optimization algorithm to the trajectory planning. The optimality of the algorithm is proved by the comparison of algorithm performance and simulation experiments. In the process, the guidance factor is set, and the colony spider algorithm is integrated into the ant colony algorithm. The research results show that the maximum number of iterations of the original ant colony algorithm and the IACA are both 100, but the former begins to converge in the 62nd generation; It can effectively improve the convergence speed of the algorithm and enhance the inclusiveness of the data set; the fitness value of the IACA stabilizes at 118 when the number of iterations reaches about 20 generations, which can effectively reduce the sensitive problem of the initial state in the process. The simulation results show that the autonomous running time of the UAV through the rendezvous point in the trajectory planning of the UAV under the IACA is (5.30 s, 5.79 s, 9.29 s), and the minimum distance between multiple UAVs is at $t=$ 6.65 s, the closest distance between UAV2 and UAV3 is $x=$ 2.3309 m, the distance is included in the safe range, so the drone can fly safely. The speed intervals of X, Y, and Z directions under the IACA are [ $-$ 6 $\sim$ 6], [ $-$ 10 $\sim$ 5], [ $-$ 12 $\sim$ 6] respectively, which are smaller than the original ant colony algorithm, is also more gradual. The above results all prove that the ant colony algorithm based on the swarm spider optimization algorithm proposed by the research can effectively optimize the UAV track, and provide new ideas for the progress of aviation industry.

Footnotes

Funding

The research is supported by: Hunan Natural Science Foundation Project, Development of multi-rotor uav platform based on CORS system (2019JJ70029).

References

Seraj

Silva

Gombolay

. Multi-UAV planning for cooperative wildfire coverage and tracking with quality-of-service guarantees. Auton Agent Multi-Ag. 2022; 36(2): 1-39.

Nguyen

Chesser

Koh

Rezatofighi

Ranasinghe

. TrackerBots: Autonomous unmanned aerial vehicle for real-time localization and tracking of multiple radio-tagged animals. J Field Robot. 2019; 36(3): 617-635.

Wang

Zhao

. Based on robust sliding mode and linear active disturbance rejection control for attitude of quadrotor load UAV. Nonlinear Dynam. 2022; 108(4): 3485-3503.

Bordbar

Basiry

Yahaghi

. Design and equivalent circuit model extraction of a broadband graphene metasurface absorber based on a hexagonal spider web structure in the terahertz band. Appl Opt. 2020; 59(7): 2165-2172.

Nagendranth

MVSS

Khanna

Krishnaraj

Sikkandar

Aboamer

Surendran

. Type II fuzzy-based clustering with improved ant colony optimization-based routing (t2fcatr) protocol for secured data transmission in manet. J Supercomput. 2022; 78(7): 9102-9120.

Lin

Wei

You

. Anti-bias track-to-track association algorithm for aircraft platforms based on distance hierarchical clustering. Tien Tzu Hsueh Pao/Acta Electron Sin. 2018; 46(6): 1475-1481.

Zhou

Qian

Qiao

Chang

Cao

. The UAV landing quality evaluation research based on combined weight and VIKOR algorithm. Wireless Pers Commun. 2019; 2018; 102(2): 2047-2062.

Liu

Chen

. Algorithm for planning full coverage route for helicopter aerial spray. Trans Chin Soc Agr Eng. 2020; 36(17): 73-80.

Xia

Han

Zhao

Liu

Wang

. Global path planning for unmanned surface vehicle based on improved quantum ant colony algorithm. Math Probl Eng. 2019; 2019: 2902170.

10.

Nguyen

Rezatofighi

Ranasinghe

. Online UAV path planning for joint detection and tracking of multiple radio-tagged objects. IEEE Trans Signal Proc. 2019; 67(20): 5365-5379.

11.

Wang

Liu

. Virtual reality technology of multi UAVEarthquake disaster path optimization. Math Probl Eng. 2021; 2021: 5525560.

12.

Warner

Rogers

. Autonomous flightworthiness determination for modular vertical lift vehicles. J Aircraft. 2018; 55(5): 1955-1969.

13.

Zhao

Han

Song

. YOLO-highway: An improved highway center marking detection model for unmanned aerial vehicle autonomous flight. Math Probl Eng. 2021; 2021: 1205153.

14.

Miao

Luo

Min

Zhao

. Lightweight 3-D beamforming design in 5G UAV broadcasting communications. IEEE Trans Broadcast. 2020; 66(2): 515-524.

15.

Wang

Liu

Wang

Peng

. A hybrid approach for UAV flight data estimation and prediction based on flight mode recognition. Microelectron Reliab. 2018; 84(5): 253-262.

16.

Bakshi

Chowdhury

Maulik

. Energy-efficient cluster head selection algorithm for IoT using modified glow-worm swarm optimization. J Supercomput. 2021; 77(7): 6457-6475.

17.

Shirjini

Farzi

Nikanjam

. MDPCIuster: A swarm-based community detection algorithm in large-scale graphs. Comput. 2020; 102(4): 893-922.

18.

Kanso

Kansou

Yassine

. Open capacitated ARC routing problem by hybridized ant colony algorithm. RAIRO-Oper Res. 2021; 55(2): 639-652.

19.

Zhao

. Parameters’ identification of vessel based on ant colony optimization algorithm. Math Probl Eng. 2021; 2021: 6256785.

20.

Saleh

Elkasas

Hamza

. Ant colony prediction by using sectorized diurnal mobility model for handover management in PCS networks. Wirel Netw. 2019; 25(2): 765-775.

21.

Gao

. Multi-UAV reconnaissance task allocation for heterogeneous targets using grouping ant colony optimization algorithm. Soft Comput. 2021; 25(10): 7155-7167.

22.

Peng

Bingyu

. Safety route planning of UAV based on improved ant colony algorithm. China Safety Sci J. 2021; 31(1): 24.

23.

Sun

Dai

Zhang

Chang

. RSOD: Real-time small object detection algorithm in UAV-based traffic monitoring. Appl Intell. 2022; 52(8): 8448-8463.

24.

Tang

Huang

Zhang

. Multi-objective optimization for UAV-assisted wireless powered IoT networks based on extended DDPG algorithm. IEEE Trans Commun. 2021; 69(9): 6361-6374.

25.

Asim

Mashwani

Shah

Belhaouari

. An evolutionary trajectory planning algorithm for multi-UAV-assisted MEC system. Soft Comput. 2022; 26(16): 7479-7492.

26.

Bai

Fan

Niu

Cui

. Multi-UAV cooperative trajectory planning based on many-objective evolutionary algorithm. Complex Syst Model Simul. 2022; 2(2): 130-141.