A Fuzzy GainBased Dynamic Ant Colony Optimization for Path Planning in Dynamic Environments
Abstract
:1. Introduction
 In the case of dynamic scenarios, there tends to be more uncertainty. Metaheuristic approaches tend to converge more slowly to avoid a collision. Faster convergence of approximate algorithms while handling dynamic scenarios is a significant challenge.
 Maintaining the consistency of the algorithm when dealing with dynamic scenarios is another challenge to be addressed. The algorithms must be robust and stable in the unknown scenario.
 Though there are many algorithms in the literature for finding the collisionfree shortest path, there is still a need for more intelligent algorithms with clear approximate and syllogistic reasoning.
 A fuzzy gain based dynamic ant colony optimization (FGDACO) for collisionfree path planning in dynamic scenarios is proposed. The improved pheromone enhancement in the ant system will curtail unwanted traversals during the search.
 A fuzzy logicbased collision avoidance strategy based on approximate reasoning is proposed, in addition to the pheromone enhancement. This collision avoidance strategy is combined with gain enhanced ant colony optimization for safe path planning.
 The proposed algorithm was observed to converge faster with the improved pheromone enhancement and no local optima trap.
 The proposed algorithm was observed to be stable in all the scenarios with a lower deviation among the independent runs.
2. Preliminaries
2.1. Fuzzy Logic and Definitions
 (i).
 Fuzzification: the process of transforming a crisp value to a fuzzy value is called fuzzification. This transformation is realized using the membership function. As shown in Figure 1, triangular membership functions are used in this work. Each linguistic variable will have its fuzzy variable values defined in its universe of discourse. The fuzzy variables are characterized by the membership function, with their values in (0,1). In this work, the linguistic variables are relative distance to the target, angle towards the target, and distance towards the nearest obstacle. The fuzzy variable set for each linguistic variable is (low, medium, and high).
 (ii).
 Fuzzy Inference Engine: this is the critical unit of a fuzzy logic controller. The role of the fuzzy inference engine is to make decisions using the IF…THEN rules. The rules are represented as given below:$$\begin{array}{c}RULE\text{}I:\text{}if\text{}D\text{}is\text{}{a}_{1}\text{}and\text{}E\text{}is\text{}{b}_{1},\text{}then\text{}F\text{}is\text{}{c}_{1}\text{}\\ RULE\text{}II:\text{}if\text{}D\text{}is\text{}{a}_{2}\text{}and\text{}E\text{}is\text{}{b}_{2},\text{}then\text{}F\text{}is\text{}{c}_{2}\\ \vdots \\ RULE\text{}N:\text{}if\text{}D\text{}is\text{}{a}_{i}\text{}and\text{}E\text{}is\text{}{b}_{i},\text{}then\text{}F\text{}is\text{}{c}_{i}\end{array}$$
 (iii).
 Defuzzification: the fuzzy variables are converted to crisp outputs using the defuzzification phase. In this work, the centroid method is used for defuzzification. The defuzzified output x* obtained from the centroid method can be represented as the Equation (2)
2.2. Ant Colony Algorithm
3. Materials and Methods
3.1. Problem Definition and Formulation
3.2. Fuzzy LogicBased Obstacle Avoidance
3.3. Gain Based Path Planning
Calculating Gain
3.4. Proposed FGDACO for Target Seeking and Obstacle Avoidance
3.4.1. Environment Perception
3.4.2. Ant Colony Parameters Initialization
3.4.3. Node Transition and Cost Calculation
 Distance to target
 2.
 Nearest obstacle distance
 3.
 Angle to be turned
3.4.4. Path Selection
Algorithm 1 Framework for fuzzy gainbased dynamic ant colony optimization (FGDACO) 
Input: G, N, S, D, $\alpha ,\text{}\beta ,\text{}\rho $ 
Output: best_path 




























4. Experimental Results and Discussion
4.1. Experimental Setup and Dataset Description
 The start and destinations were considered to be the same during the whole process of path planning, but they differed with each scenario.
 The speed of the moving obstacles was considered as random between 0.5–1.5 m/s.
4.2. Performance Measures:
 Standard Deviation: The consistency of the proposed method was verified using standard deviation. The method was stable when there was less variation in the performance between independent runs.
 Median of path length and computation time: The median of the computational time and the length of path computed for 30 independent runs were compared and analyzed.
4.3. Parameter Setting:
4.4. Performance Evaluation
4.5. Discussion
 The proposed FGDACO outperformed COA, FuzzyGA, and FLACO by 6%, 11%, and 3%, respectively, in terms of length in scenario 1.
 The proposed FGDACO outperformed COA, FuzzyGA, and FLACO by 15%, 10%, and 4%, respectively, in terms of length in scenario 2.
 The proposed FGDACO outperformed COA, FuzzyGA, and FLACO by 8%, 10%, and 2%, respectively, in terms of length in scenario 3.
 With regard to consistency, FGDACO exhibited higher consistency, with a deviation of 2% on average among its independent runs.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
 Yang, X.S. NatureInspired Algorithms and Applied Optimization; Springer: Berlin/Heidelberg, Germany, 2017; Volume 744. [Google Scholar]
 Boussaïd, I.; Lepagnot, J.; Siarry, P. A survey on optimization metaheuristics. Inf. Sci. 2013, 237, 82–117. [Google Scholar] [CrossRef]
 Tuncer, A.; Yildirim, M. Dynamic path planning of mobile robots with improved genetic algorithm. Comput. Electr. Eng. 2012, 38, 1564–1572. [Google Scholar] [CrossRef]
 Son, C. Intelligent rulebased sequence planning algorithm with fuzzy optimization for robot manipulation tasks in partially dynamic environments. Inf. Sci. 2016, 342, 209–221. [Google Scholar] [CrossRef]
 Bakdi, A.; Hentout, A.; Boutami, H.; Maoudj, A.; Hachour, O.; Bouzouia, B. Optimal path planning and execution for mobile robots using genetic algorithm and adaptive fuzzylogic control. Robot. Auton. Syst. 2017, 89, 95–109. [Google Scholar] [CrossRef]
 Pandey, A.; Parhi, D.R. Optimum path planning of mobile robot in unknown static and dynamic environments using FuzzyWind Driven Optimization algorithm. Def. Technol. 2017, 13, 47–58. [Google Scholar] [CrossRef]
 Hu, X.; Chen, L.; Tang, B.; Cao, D.; He, H. Dynamic path planning for autonomous driving on various roads with avoidance of static and moving obstacles. Mech. Syst. Signal. Process. 2018, 100, 482–500. [Google Scholar] [CrossRef]
 Chen, P.; Zhang, X.; Chen, X.; Liu, M. Path planning strategy for vehicle navigation based on user habits. Appl. Sci. 2018, 8, 407. [Google Scholar] [CrossRef] [Green Version]
 Wei, K.; Ren, B. A method on dynamic path planning for robotic manipulator autonomous obstacle avoidance based on an improved RRT algorithm. Sensors 2018, 18, 571. [Google Scholar] [CrossRef] [PubMed] [Green Version]
 Wang, M.; Liu, J.N. Fuzzy logicbased realtime robot navigation in unknown environment with dead ends. Robot. Auton. Syst. 2008, 56, 625–643. [Google Scholar] [CrossRef]
 Wu, Q.; Chen, Z.; Wang, L.; Lin, H.; Jiang, Z.; Li, S.; Chen, D. RealTime Dynamic Path Planning of Mobile Robots: A Novel Hybrid Heuristic Optimization Algorithm. Sensors 2020, 20, 188. [Google Scholar] [CrossRef] [Green Version]
 Alomari, A.; Phillips, W.; Aslam, N.; Comeau, F. Dynamic fuzzylogic based path planning for mobilityassisted localization in wireless sensor networks. Sensors 2017, 17, 1904. [Google Scholar] [CrossRef] [PubMed] [Green Version]
 Salehinejad, H.; Talebi, S. Dynamic fuzzy logicant colony systembased route selection system. Appl. Comput. Intell. Soft Comput. 2010, 2010, 1–13. [Google Scholar] [CrossRef] [Green Version]
 Purian, F.K.; Sadeghian, E. Mobile robots path planning using ant colony optimization and Fuzzy Logic algorithms in unknown dynamic environments. In Proceedings of the 2013 International Conference on Control, Automation, Robotics and Embedded Systems (CARE), Jabalpur, India, 16–18 December 2013; pp. 1–6. [Google Scholar]
 Song, Q.; Zhao, Q.; Wang, S.; Liu, Q.; Chen, X. Dynamic Path Planning for Unmanned Vehicles Based on Fuzzy Logic and Improved Ant Colony Optimization. IEEE Access 2020, 8, 62107–62115. [Google Scholar] [CrossRef]
 Hosseininejad, S.; Dadkhah, C. Mobile robot path planning in dynamic environment based on cuckoo optimization algorithm. Int. J. Adv. Robot. Syst. 2019, 16, 1729881419839575. [Google Scholar] [CrossRef]
 Bai, X.; Wen, W.; Hsu, L.T. Robust VisualInertial Integrated Navigation System Aided by Online Sensor Model Adaption for Autonomous Ground Vehicles in Urban Areas. Remote Sens. 2020, 12, 1686. [Google Scholar] [CrossRef]
 Singh, S.J.; Roy, S.; Singh, K.M.; Khelchandra, T. Motion planning of mobile robot using FuzzyGA method along with three path concept in dynamic environment. J. Intell. Fuzzy Syst. 2018, 35, 1445–1457. [Google Scholar] [CrossRef]
 Das, P.K.; Behera, H.S.; Jena, P.K.; Panigrahi, B.K. Multirobot path planning in a dynamic environment using improved gravitational search algorithm. J. Electr. Syst. Inf. Technol. 2016, 3, 295–313. [Google Scholar] [CrossRef] [Green Version]
 Solak, S.; Yakut, Ö.; Dogru Bolat, E. Design and Implementation of WebBased Virtual Mobile Robot Laboratory for Engineering Education. Symmetry 2020, 12, 906. [Google Scholar] [CrossRef]
 Bi, M. Control of Robot Arm Motion Using Trapezoid Fuzzy TwoDegreeofFreedom PID Algorithm. Symmetry 2020, 12, 665. [Google Scholar] [CrossRef] [Green Version]
 Li, S.; Xie, J.; Wang, X.; Ren, F.; Zhang, X.; Bao, Q. Path Planning of Hydraulic Support Pushing Mechanism Based on Extreme Learning Machine and Descartes Path Planning. Symmetry 2021, 13, 97. [Google Scholar] [CrossRef]
 Zagradjanin, N.; Pamucar, D.; Jovanovic, K. CloudBased MultiRobot Path Planning in Complex and Crowded Environment with MultiCriteria Decision Making Using Full Consistency Method. Symmetry 2019, 11, 1241. [Google Scholar] [CrossRef] [Green Version]
 Sangeetha, V.; Krishankumar, R.; Ravichandran, K.S.; Kar, S. Energyefficient green ant colony optimization for path planning in dynamic 3D environments. Soft Comput. 2021, 1, 21. [Google Scholar]
 Zhang, H.Y.; Lin, W.M.; Chen, A.X. Path Planning for the Mobile Robot: A Review. Symmetry 2018, 10, 450. [Google Scholar] [CrossRef] [Green Version]
 Mac, T.T.; Copot, C.; Tran, D.T.; De Keyser, R. A hierarchical global path planning approach for mobile robots based on multiobjective particle swarm optimization. Appl. Soft Comput. 2017, 59, 68–76. [Google Scholar] [CrossRef]
 Liang, J.H.; Lee, C.H. Efficient collisionfree pathplanning of multiple mobile robots system using efficient artificial bee colony algorithm. Adv. Eng. Softw. 2015, 79, 47–56. [Google Scholar] [CrossRef]
 Fakoor, M.; Kosari, A.; Jafarzadeh, M. Humanoid robot path planning with fuzzy Markov decision processes. J. Appl. Res. Technol. 2016, 14, 300–310. [Google Scholar] [CrossRef] [Green Version]
 Das, P.K.; Behera, H.S.; Panigrahi, B.K. A hybridization of an improved particle swarm optimization and gravitational search algorithm for multirobot path planning. Swarm Evol. Comput. 2016, 28, 14–28. [Google Scholar] [CrossRef]
 Zadeh, L.A. Fuzzy sets (PDF). Inf. Control 1965, 8, 338–353. [Google Scholar] [CrossRef] [Green Version]
 Mamdani, E.H. Application of fuzzy algorithms for control of simple dynamic plant. Proc. Inst. Electr. Eng. 1974, 121, 1585–1588. [Google Scholar] [CrossRef]
 Dorigo, M.; Maniezzo, V.; Colorni, A. Ant system: Optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. Part B 1996, 26, 29–41. [Google Scholar] [CrossRef] [Green Version]
 Sangeetha, V.; Ravichandran, K.S.; Shekhar, S.; Tapas, A.M. An Intelligent Gainbased Ant Colony Optimisation Method for Path Planning of Unmanned Ground Vehicles. Def. Sci. J. 2019, 69, 167–172. [Google Scholar]
 Padhy, N.P. Artificial Intelligence and Intelligent Systems; Oxford University Press: Oxford, UK, 2005. [Google Scholar]
 Ravankar, A.; Ravankar, A.A.; Kobayashi, Y.; Hoshino, Y.; Peng, C.C. Path smoothing techniques in robot navigation: Stateoftheart, current and future challenges. Sensors 2018, 18, 3170. [Google Scholar] [CrossRef] [PubMed] [Green Version]
 MATLAB^{®} (2019). 9.7.0.1261785 (R2019b); The MathWorks Inc.: Natick, MA, USA.
Ref #  Method  Dataset  Optimality Achieved 

[4]  Rulebased sequence planning algorithm with fuzzy optimization  Simulated scenarios  Flexibility and adaptability 
[5]  Genetic algorithm and adaptive fuzzy logic control  RobuTER robot  Smooth collisionfree path 
[6]  Fuzzy winddriven optimization  Realtime navigation using Khepera III mobile robot  Collision free path 
[7]  Dynamic path planner  Simulated single and multilane roads  Static and dynamic safety, comfortability, appropriate acceleration and speed for the vehicle 
[8]  Personalized path planner with fuzzy cmeans clustering  Simulated grids, road simulation model in Changsha  Improved personalization of existing path planning 
[9]  Improved rapidly exploring random tree (RRT) algorithm  Simulated and realtime implementation using MATLAB and robot operating system(ROS)  Correctness, effectiveness, and practicability 
[10]  Fuzzy logic  Realtime navigation using mobile robot on long u shape, large concave, cluttered, mazelike dynamic environments  Minimum risk and global convergence 
[11]  Hybrid heuristic optimization algorithm (Beetle antennae search)  Virtual map and the real map  Accelerated convergence speed 
[12]  Dynamic Fuzzy logic based path planning  Wireless sensor networks in MATLAB  Localization ratio and localization accuracy 
[13]  Dynamic fuzzylogicant colony system  Regions of London, United Kingdom  Efficient route selection 
[14]  Ant colony and fuzzy logic  Simulated maps in MATLAB  Shortest path in minimum time 
[15]  Fuzzy logic ant colony optimization  Simulated road networks  Shortest path length 
[16]  Cuckoo optimization algorithm  Simulated scenarios of size 20 × 20, 100 × 100 and 200 × 200  Safe, smooth, and collisionfree path 
[17]  A visualinertial navigation system  Urban areas of Hong Kong  Effective mitigation of dynamic objects and improved accuracy 
[18]  Fuzzy genetic algorithm (GA) with three path concept  Simulated maps  Computationally efficient 
[19]  Improved gravitational search  Realtime navigation using Khepera III mobile robot  The safe and shortest path 
[20]  Genetic algorithm  Web based virtual mobile robot laboratory  Usability of remote controlled robot laboratory 
[21]  Trapezoid fuzzy 2 DOF algorithm  Simulated proportional integral derivative (PID) control system  Faster response with low position tracking error 
[22]  Extreme Learning Machine and Descartes  Virtual simulation in Unity3D  Reduced local error and correction error 
[23]  Full Consistency method with D* Lite  Simulated occupancy maps  Consistent determination of weight factors for effective risk management during motion 
[24]  Improved Ant colony optimization  Elevation data from international society for photogrammetry and remote sensing (ISPRS) and United States geological survey (USGS)  Faster convergence 
Parameter  Description 

N  Number of ants 
${\tau}_{o}$  Initial pheromone 
${\tau}_{ij}$  Quantity of pheromone deposited while traversing from i to j 
${\eta}_{ij}$  Heuristic function indicating the visibility of route between i and j; 
${d}_{ij}^{k}$  Cost of the route (i,j) obtained by kth ant 
α  Impact of pheromone on the choice of next node 
β  Impact of heuristic function on the selection of next node 
$\rho $  Rate of pheromone evaporation; 0 < $\rho $ < 1 
$visi{t}_{k}$  A table containing nodes that are feasible to be visited by kth ant 
Q  Constant related to the pheromone increment 
Linguistic Variable  ${\mathit{U}}_{\mathit{l}\mathit{o}\mathit{w}}$  ${\mathit{U}}_{\mathit{m}\mathit{e}\mathit{d}\mathit{i}\mathit{u}\mathit{m}}$  ${\mathit{U}}_{\mathit{h}\mathit{i}\mathit{g}\mathit{h}}$ 

relative distance to the target  (0,0.4)  (0.3,0.7)  (0.6,1) 
angle towards the target  (0,0.4)  (0.3,0.7)  (0.6,1) 
distance towards the nearest obstacle  (0,0.3)  (0.2,0.7)  (0.6,1) 
IF  IF  IF  Then 

Relative distance to the target  Angle to be turned  Distance to the nearest obstacle  The priority of the node during next node selection in ant colony 
Medium  High  low  Low 
Low  Medium  Low  Low 
Low  High  Low  Low 
Low  Low  Medium  High 
Low  Medium  Medium  Medium 
High  Medium  Medium  Low 
Low  Low  High  High 
Low  Medium  High  High 
High  Medium  High  Medium 
Medium  Medium  Low  Low 
High  High  High  Medium 
High  Low  Medium  Low 
Scenario  Static Obstacle  Moving Obstacle 

1  3  3 
2  4  3 
3  2  3 
Parameter  Value 

α  0.5 
β  0.5 
ρ  0.5 
Time interval  3 ∆t 
Sampling interval  10 s 
Number of iterations  100 
Number of independent runs of the algorithm  30 
Number of ants (N)  20 
Scenario #  Algorithm  Time (s)  Length (m)  

Median  SD  Median  SD  
1  Proposed FGDACO  28.97  2.24  126.65  1.37 
COA  37.94  4.35  134.57  3.48  
FuzzyGA  41.79  4.58  141.24  5.69  
FLACO  31.47  3.77  129.64  2.78  
2  Proposed FGDACO  38.74  1.97  135.96  2.37 
COA  51.76  4.69  158.96  4.99  
FuzzyGA  48.61  3.47  149.67  6.35  
FLACO  43.78  2.07  141.27  3.78  
3  Proposed FGDACO  74.33  2.54  197.69  2.77 
COA  84.95  4.77  214.68  5.78  
FuzzyGA  81.31  3.18  219.96  6.35  
FLACO  77.12  2.11  201.43  4.69 
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. 
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Sangeetha, V.; Krishankumar, R.; Ravichandran, K.S.; Cavallaro, F.; Kar, S.; Pamucar, D.; Mardani, A. A Fuzzy GainBased Dynamic Ant Colony Optimization for Path Planning in Dynamic Environments. Symmetry 2021, 13, 280. https://doi.org/10.3390/sym13020280
Sangeetha V, Krishankumar R, Ravichandran KS, Cavallaro F, Kar S, Pamucar D, Mardani A. A Fuzzy GainBased Dynamic Ant Colony Optimization for Path Planning in Dynamic Environments. Symmetry. 2021; 13(2):280. https://doi.org/10.3390/sym13020280
Chicago/Turabian StyleSangeetha, Viswanathan, Raghunathan Krishankumar, Kattur Soundarapandian Ravichandran, Fausto Cavallaro, Samarjit Kar, Dragan Pamucar, and Abbas Mardani. 2021. "A Fuzzy GainBased Dynamic Ant Colony Optimization for Path Planning in Dynamic Environments" Symmetry 13, no. 2: 280. https://doi.org/10.3390/sym13020280