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Hindawi Journal of Robotics Volume 2022, Article ID 2168964, 9 pages https://doi.org/10.1155/2022/2168964 Research Article Path Planning of Multirotor UAV Based on the Improved Ant Colony Algorithm 1,2 1,2 3 Duo Qi , Zhihao Zhang , and Qirui Zhang Aviation Swarm Technology and Operational Application Laboratory, Air Trac Control and Navigation College, Air Force Engineering University, Xi’an, China Shaanxi Province Laboratory of Meta-Synthesis for Electronic and Information System, Xi’an, China Unit 93525 of PLA, Rikaze City, Xizang Province, China Correspondence should be addressed to Zhihao Zhang; 408691252@qq.com Received 29 November 2021; Revised 18 April 2022; Accepted 23 May 2022; Published 9 June 2022 Academic Editor: Ruthber Rodriguez Serrezuela Copyright © 2022 Duo Qi et al. ƒis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Path planning is an important part of the unmanned aerial vehicle (UAV) to realize its autonomous capabilities. Aiming at the shortcomings of the traditional ant colony algorithm-based trajectory planning method, which has slow convergence speed and easy to fall into the local optimum, a path planning method based on the improved ant colony algorithm is proposed. First, a dynamic adjusting factor is added into the heuristic function to improve the directivity of path selection and search speed. ƒen, the state transition strategy is improved to solve the problem of slow convergence in the initial stage and easy to fall into local optimum in the later stage. Finally, the path in•ection point is smoothly optimized through the cubic B-spline curve. Simulation results show that the improved ant colony algorithm can quickly converge to the optimal path and well adapt to the •ight requirements of multirotor UAV. optimal control method [5, 6], as well as intelligent algo- 1. Introduction rithms such as the genetic algorithm [7, 8], ant colony al- With the continuous progress of science and technology, gorithm [9, 10], and particle swarm optimization algorithm especially the continuous development of microelectronic [11]. technology and microelectromechanical technology, UAV ƒe classical algorithm is generally only suitable for has been widely used in military and civil ˜elds. Compared simple spatial path planning. In the face of complex with large UAVs, small UAVs have a broader application problems, the di™culty of solving them increases expo- space in the ˜elds of police, rescue and disaster relief, tra™c nentially with the increase of dimension, which has certain management, news media, aerial photography, geological limitations. With the development of computer and big data survey, environmental evaluation, pipeline inspection, and technology, intelligent algorithms have more and more so on. Among them, the multirotor small UAV, as a typical obvious advantages of good robustness, positive feedback representative, has developed particularly rapidly in recent mechanism, and self-organization. Taking the ant colony years and received the focus of researchers. algorithm as an example, theoretically, it can ˜nd the op- Path planning is one of the key technologies for UAV to timal solution of the path, which is suitable for path planning realize autonomous •ight. A large number of scholars have in complex environment. However, in practice, we must done research on it and achieved a lot of results. In fact, path consider the problems of how to shorten search time, speed planning is to ˜nd an optimal •ight path from initial point to up convergence, and jump out of local optimal. Li et al. [12] target point under certain constraints. Common planning introduced a weight factor into the probability transfer methods include classical algorithms such as the A (A-star) function and improved the updating way of information. algorithm [1, 2], arti˜cial potential ˜eld method [3, 4], and ƒe simulation results showed that the convergence speed of 2 Journal of Robotics the improved algorithm is improved, and the optimal path is electronic map are shown in Figure 1. .e map is numbered shorter, but the search results are not stable. Wu et al. [13] from left to right and top to bottom. .e grid serial number adopted the method of integrating the current optimal track corresponds to coordinates one by one, and the expression pheromone and the historical optimal track update, intro- of the relationship between them is shown in equation (1). duced the pheromone rollback clearing mechanism, and .e result obtained is the center point of the grid. carried out oﬄine calculation, which improved the search x � r × mod(i, R) − 0.5, eﬃciency, but did not signiﬁcantly reduce the number of (1) y � r × (R + 0.5 − ceil(i, R)) − 0.5, iterations. Wang et al. [14] used the artiﬁcial potential ﬁeld method to improve the heuristic function of the ant colony where r is the grid size, i represents the number of the grid, R algorithm, allocated pheromones reasonably when the al- is the number of rows of the grid matrix, mod () is the gorithm is not running, and improved the volatilization remainder operation function, and ceil () is the rounding up coeﬃcient to ﬁnd the optimal path of the algorithm. operation function. It can be seen that many research studies are all based on In order to prevent the collision between UAV and the traditional ant colony algorithm and have achieved obstacles, when the obstacle is less than one grid, it is ﬁlled certain results. However, the traditional ant colony algo- into a complete grid. At this time, the UAV is treated as a rithm has the shortcomings of slow convergence speed and particle. easy to fall into local optimum, which is not applicable to the .e ﬂight rules of UAV are as follows: it can only appear real ﬂight environment. Aiming at the defects of the basic ant in the white grid and cannot pass through the black grid, but colony algorithm, an improved ant colony algorithm is it can pass through the four corners of the black grid; it is proposed in this study to make it suitable for path planning forbidden to repeat the same grid; and in unit time, it can of multirotor UAV. First, a dynamic adjusting factor is only move between two adjacent grids. We use Euclidean added into the heuristic function to improve the directivity distance to measure the length of the ﬂight path. For ex- of path selection and search speed. .en, the state transition ample, if moving up, down, left, and right, the path length is strategy is improved to solve the problem of slow conver- 1 unit and if moving to the four corners of the grid, the path gence in the initial stage and easy to fall into local optimum length is 1.41 units. in the later stage. At the same time, combined with the existing pheromone volatilization factor update strategy, the overall performance of the algorithm is improved. Finally, 3. Basic Ant Colony Algorithm the path inﬂection point is smoothly optimized through the cubic B-spline curve, so that the path planning of multirotor Ant colony algorithms are inspired by the foraging behavior UAV is more in line with the ﬂight reality. of ant populations, in which each ant in the colony leaves .e study is organized as follows: Section 2 describes the pheromones in its movement path to communicate infor- environment in which the UAV performs its mission. mation to the colony. .e shorter the moving path is, the Section 3 introduces the basic principle and deﬁciency of the higher the pheromone concentration is, and the probability ant colony algorithm. Section 4 improves the shortcomings that the path is selected by ants, which forms the positive of the ant colony algorithm and proposes the UAV track feedback mechanism for ants to ﬁnd the shortest path. .e planning method and smoothing method. In Section 5, the basic principle of the ant colony algorithm is as follows. proposed algorithm is simulated and analyzed, which ver- Ants select paths according to pheromone concentration iﬁes the eﬀectiveness of the proposed algorithm. Finally, the and heuristic function, and the probability of ant k moving full text work is summarized and the next research direction from grid i to grid j can be expressed as is pointed out. ⎧ ⎪ α β α β ⎪ ⎝ ⎠ ⎛ ⎞ τ (t)η (t)/ τ (t)η (t) , s ∈ A , k ij ij is is k 2. Environmental Model P � (2) ij ⎪ s∈A In order to accurately describe the path planning process of 0, s ∉ A UAV, its two-dimensional environment map [15, 16] needs where α is the pheromone heuristic factor and β is the to be modeled. .e conventional environment modeling distance expectation function factor, which aﬀect the im- methods include the grid method [17, 18], geometric in- portance of pheromone and distance heuristic function, formation method, and view method. Considering that the respectively, A indicates the next destinations ants can grid method has the advantages of simple drawing, clear data reach, τ (t) is the pheromone concentration on the moving ij structure, and easy implementation, we select the grid path at time t, and η (t) represents the distance heuristic ij method to complete the UAV ﬂight environment modeling. function. Here, .e grid method decomposes the plane map into a series of grids to facilitate the analysis of map information. .e grid map is composed of 0 and 1 matrices with binary values. In η (t) � , ij ij the matrix, 0 stands for free grid, in which the UAV can enter (3) and exit freely, represented by white grid, and 1 stands for ����������������� obstacle grid, in which the UAV needs to move around, and 2 d � x − x + y − y . ij i j i j represented by black grid. .e grid environment and the Journal of Robotics 3 02468 10 Figure 1: Grid map and electronic map. Each ant will leave a certain amount of pheromone when where d is the Euclidean distance between j and the target jE moving. .erefore, when the algorithm iterates continu- point, iter is the current number of iterations, and iter is max ously, the pheromone content in the path gradually accu- maximum number of iterations. mulates and volatilizes at the same time. When all ants in the population complete each round of iteration, the pheromone content on the path will be updated according to the fol- 4.2. 8e Improved State Transition Rule. In the basic ant lowing rules: colony algorithm, ants mainly rely on the probability function to select the next node. However, in the early stage τ (t + 1) � (1 − ρ)τ (t) + Δτ (t), ij ij ij of the algorithm, the diﬀerence between the pheromone concentrations of the path is very small, which cannot ef- τ (t) � Δτ (t), ij ij fectively guide the ant to choose the path. Based on the initial (4) k�1 transition probability, the convergence speed of the algo- Q/L , k rithm is guaranteed by introducing pseudorandom rules. Δτ � ij .e ant will select the next node j according to the following 0, formula. where ρ is the pheromone volatilization coeﬃcient, Δτ represents the sum of pheromones released on the path ij ⎧ ⎪ max τ ∗ η β, q< q , ⎨ is jE 0 between the two nodes, Δτ denotes the pheromone in- ij P (t) � (6) ij ⎪ crement, L is the path length of ant k, and Q is the P , q≥ q , ij 0 pheromone enhancement coeﬃcient. where q represents a random number between (0, 1), and q is a design parameter, which is usually determined by 4. The Improved Ant Colony Algorithm previous experience and repeated experiments. Its value determines the path selection mode. If the value of q is too 4.1. 8e Improved Heuristic Function. When using the basic large, the path shift is more likely to be a deterministic algorithm to plan the path, the ant colony has not left pattern, and the convergence speed is faster, but the global pheromone in the initial stage. At this time, the pheromone search capability is reduced. On the contrary, if the value of on the path is scarce. .e ant cannot select the next grid q is very small, the path shift is more inclined to the roulette according to the pheromone concentration. .e search has mode, which not only increases the randomness of the global no purpose and cannot quickly search the feasible path. On search but also reduces the convergence speed. .erefore, the basis of the heuristic function in [19], we add a dynamic setting a reasonable value of q has an important inﬂuence regulation factor ξ. .e new expressions of heuristic func- on the convergence process. In order to better improve the tion and ξ are shown as problem of slow convergence in the initial stage and easy to fall into local optimization in the later stage, we designed it as n � ∗ ξ, ij a dynamical parameter adjusted with the number of itera- d + d ij jE tions. .e details expression is as follows: (5) ⎧ ⎪ exp −5∗ iter/iter , iter≠ iter , max max −1 ξ � ⎪ (7) q � 0.25∗ exp− . 1/iter , iter � iter , iter max max 4 Journal of Robotics 0.9 2.5 0.8 0.7 1.5 0.6 0.5 0.5 0.4 0.3 -0.5 0.2 -4 -3 -2 -1 01234 020 40 60 80 100 Figure 3: Simulation of local path smoothing results. Figure 2: Changing curve of ρ. .e basis function in cubic B-spline curve equation is 4.3. Pheromone Volatilization Factor Update Strategy. Due to the particularity of path planning, diﬀerent volatil- k−i m m k ⎝ ⎠ ⎛ ⎞ ization coeﬃcients are required in diﬀerent stages: if ρ is too F (t) � (−1) (t + k − m − j) . (10) i,k k! large, ants cannot complete path search according to the m�0 k + 1 pheromone information, resulting in slow convergence Furthermore, the mathematical expression of the basis speed; if ρ is too small, the pheromone will accumulate function of cubic B-spline curve is excessively, easily make the path search fall into local op- timization. Referring to the research ideas of [19], the ⎧ 3 F (t) � (1 − t) , adaptive updating strategies of pheromone volatile factors 0,3 ⎪ 6 are designed as follows: iter 1 ⎪ max ⎪ 3 2 ρ(t + 1) � ∗ . (8) F (t) � 3t − 6t + 4, 1,3 iter + iter exp(1 − ρ(t)) ⎪ 6 max (11) In order to search as many paths as possible, the ⎪ 3 2 pheromone content should be controlled at a low level at the F (t) � −3t + 3t − 3t + 1 , 2,3 initial stage of algorithm optimization. .erefore, the value ⎪ of the initial volatile factor ρ should not be too small. At this ⎪ 1 time, pheromone concentration has little interference in the ⎪ F (t) � t . 3,3 process of path exploration, and ants can search more possible paths. With algorithm iteration step by step, the .e cubic B-spline curve equation can be converted by value of ρ gradually decreases, and the negative feedback bringing the basis function into the general equation: eﬀect is weakened. .e pheromone content on the moving path is increased, and the guiding eﬀect of pheromone P(t) � P ∗ F (t) + P ∗ F (t) + P ∗ F (t) + P ∗ F (t). 0 0,3 1 1,3 2 2,3 3 3,3 concentration on ant colony is enhanced. When the number (12) of iterations increases to a certain number, ant colony will Based on the above cubic B-spline curve equation, the converge to the path with a higher pheromone content. ﬂight path can be smoothed. Figure 3 shows the simulation .erefore, the improved algorithm can expand the searching of local path smoothing results. .e red line is the path to be range of ant colony and improve the convergence speed. .e smoothed, and the blue dotted line is the smoothing result. changing curve of ρ is shown in Figure 2 (initial ρ � 0.8). .e goal of this strategy is to replace the broken line with a curve near the inﬂection point, so that the obtained path is smoother and more in line with the reality of UAV ﬂight. 4.4. Path Smoothing Method. .e optimal path generated by the improved ant colony algorithm is not smooth enough .e ﬂow of the improved ant colony algorithm is shown in Figure 4. and has sharp inﬂection point. .erefore, cubic B-spline smoothing is introduced to optimize the path at the in- ﬂection point. .e total equation of the B-spline curve is 5. Simulation Analysis [20, 21] .e simulation hardware environment is the Huawei MateBook Pro laptop equipped with Intel Core I7-8565U P(t) � P F (t). (9) i i,k processor. Software environment is the Win10 operating i�0 Journal of Robotics 5 Start Environmental model Set the starting point, target point and algorithm parameters Save the path length, select the current optimal path, and update the global optimal path Put the ant colony at the starting point and start to search the path Whether the maximum number of iterations is reache Select the next node according to the probability formula of heuristic factor Perform smoothing on the optimal path Whether to reach the target Output the Y results Adjust volatile factors and update pheromones according End to rule Figure 4: Improved ant colony algorithm ﬂow. Table 1: Basic parameter settings of BACA and IACA. Parameter name Number of ants (m) Pheromone heuristic factor (α) Expectation function factor (β) Strength of the pheromone (Q) Value 50 1 7 1 Table 2: Basic parameter settings of GA. Parameter name Number of swarms Crossover probability Variation probability Number of terminative iterations Value 50 0.6 0.001 100 system, installed with MATLAB 2017B simulation test en- achievable minimum value of both functions is 0. .e two vironment. BACA, GA (genetic algorithm), and IACA al- function expressions are as follows, respectively: gorithms are implemented in the simulation tests. .e basic parameter settings of three algorithms are given in Tables 1 f (x) � x , 1 i and 2. i�1 (13) f (x) � x sin x + 0.1x . 2 i i i 5.1. Performance Test. In order to verify the optimization i�1 ability of the improved ant colony algorithm in this study, ﬁrst, the typical single-mode test function Sphere and .e basic ant colony algorithm (BACA) and the im- proved ant colony algorithm (IACA) are independently run multimode test function Alpine are used for the optimiza- tion comparison test. .e dimension value of the two for 20 times on each test function, and the common pa- rameters of the algorithm remained consistent. .e results functions is 30, the value range of Sphere is [−100, 100], the value range of Alpine is [−10, 10], and the theoretically are given in Table 3. 6 Journal of Robotics Table 3: Comparison of test functions for optimization results. Function name Algorithm name Average value Worst value Best value BACA 2.43E − 6 2.98E − 5 7.92E − 14 Sphere IACA 7.64E − 82 6.49E − 69 0 BACA 5.43E − 2 1.21E − 1 9.84E − 3 Alpine IACA 6.99E − 79 2.14E − 66 0 Flight path Convergence curve y 10 0 5 10 15 20 0 20406080 100 e number of iterations (a) (b) Figure 5: Path planning of BACA. (a) Optimal path. (b) Convergence curve. Table 4: Comparison tests of 20 × 20 simulation environment. Algorithm name Length of the path Time consuming Number of path grid Number of convergent iterations BACA 36.04 4.62 32 62 GA 39.45 4.65 30 70 IACA 30.47 3.97 26 46 Table 5: Comparison tests of 30 × 30 simulation environment. Algorithm name Length of the path Time consuming Number of path grid Number of convergent iterations BACA 53.19 64.15 43 211 GA 51.94 62.31 46 161 IACA 45.62 58.59 38 170 According to the test results in the above table, the IACA study are used to plan the ﬂight path of UAV, respectively, algorithm proposed in this study has a good optimization with the maximum iteration times of 100. Path planning eﬀect. .e theoretical global optimal value can be obtained diagram and iterative convergence curve are shown in by searching for Sphere function and Alpine function. Figures 5–7. .e experimental results are given in Table 4. It can be seen from the above table that the shortest path length obtained by applying the IACA algorithm proposed 5.2. Comparison Test of Path Planning. In order to verify the in this study is 15.4% shorter than that obtained by applying eﬀectiveness of IACA in UAV path planning, BACA and GA the BACA algorithm, and the running time is reduced by (genetic algorithm) are used as a comparison to conduct 14.1%. Compared with GA, IACA is 22.8% shorter, and the simulation comparison tests in 20 × 20 and 30 × 30 envi- running time is reduced by 14.6%. ronment maps. 5.2.1. 20 × 20 Simulation Environment. .e simulation test is 5.2.2. 30 × 30 Simulation Environment. When the ﬂight ﬁrst carried out in a 20 × 20 grid map, with the starting point environment is large and obstacles are densely distributed, at the upper left corner of the map and the target point at the the 100 iteration times of 20 × 20 map cannot be eﬀectively lower right corner. BACA, GA, and IACA proposed in this converged to the shortest path. We increase the maximum Minimum path length Journal of Robotics 7 Flight path Convergence curve 20 60 y 10 30 0 0 0 2 4 6 8 10 12 14 16 18 20 0 102030405060708090 100 The number of iterations (a) (b) Figure 6: Path planning of GA. (a) Optimal path. (b) Convergence curve. Filght path Convergence curve 20 45 y 10 05 10 15 20 0 20406080 100 The number of iterations (a) (b) Figure 7: Path planning of IACA. (a) Optimal path. (b) Convergence curve. Filght path Convergence curve 30 90 20 60 y 15 10 30 0 0 0 5 10 15 20 25 30 0 50 100 150 200 250 300 The number of iterations (a) (b) Figure 8: Path planning of BACA. (a) Optimal path. (b) Convergence curve. Minimum path length Minimum path length Minimum path length 8 Journal of Robotics Flight path Convergence curve y 15 0 5 10 15 20 25 30 0 20 40 60 80 100 120 140 160 180 200 The number of iterations (a) (b) Figure 9: Path planning of GA. (a) Optimal path. (b) Convergence curve. Flight path Convergence curve y 15 0 5 10 15 20 25 30 0 50 100 150 200 250 300 The number of iterations (a) (b) Figure 10: Path planning of IACA. (a) Optimal path. (b) Convergence curve. iteration times to 300. Path planning diagram and iterative .rough the comparison of MATLAB simulation convergence curve are shown in Figures 8–10. As given in experiments, it can be seen that the improved Table 5, the shortest path obtained by IACA is 14.2% algorithm has more advantages than the basic algorithm shorter than that obtained by BACA, and the system in the optimization eﬀect and reﬂects the eﬀectiveness running time is reduced by 8.7%, respectively. Compared of the algorithm in the operation time and the shortest with GA, though the system running time is added by 6.4%, path. the shortest path obtained by IACA is 13.8% shorter than In practical applications, UAVs usually perform tasks in that obtained by GA. a swarm. .erefore, how to complete the coordinated tra- jectory planning of UAV swarms on the basis of this study will become the focus of our next research. 6. Conclusion In this study, we proposed an improved ant colony al- Data Availability gorithm for multirotor UAV path planning. By rede- signing the heuristic function of the ant colony algorithm .e data used to support the ﬁndings of this study are and improving the state transition matrix, the running available from the corresponding author upon request. time of the algorithm and the distance of the optimal moving path are eﬀectively shortened. 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Journal of Robotics – Hindawi Publishing Corporation
Published: Jun 9, 2022
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