Recently, the path planning problem may be considered one of the most interesting researched topics in autonomous robotics. That is why finding a safe path in a cluttered environment for a mobile robot is a significant requisite. A promising route planning for mobile robots on one side saves time and, on the other side, reduces the wear and tear on the robot, saving the capital investment. Numerous route planning methods for the mobile robot have been developed and applied. According to our best knowledge, no method offers an optimum solution among the existing methods. Particle Swarm Optimization (PSO), a numerical optimization method based on the mobility of virtual particles in a multidimensional space, is considered one of the best algorithms for route planning under constantly changing environmental circumstances. Among the researchers, reactive methods are increasingly common and extensively used for the training of neural networks in order to have efficient route planning for mobile robots. This paper proposes a PSO Weighted Grey Wolf Optimization (PSOWGWO) algorithm. PSOWGWO is a hybrid algorithm based on enhanced Grey Wolf Optimization (GWO) with weights. In order to measure the statistical efficiency of the proposed algorithm, Wilcoxon rank-sum and ANOVA statistical tests are applied. The experimental results demonstrate a 25% to 45% enhancement in terms of Area Under Curve (AUC). Moreover, superior performance in terms of data size, path planning time, and accuracy is demonstrated over other state-of-the-art techniques.

Mobile robots are used in different fields to carry out critical unmanned tasks, including military operations, industrial automation and rescue operations [

Mobile robots are necessary to respond under real-time constraints, which cannot be realized by hardware with restricted computational power. Moreover, mobile robots are essential to be controlled simultaneously by single or multiple users. Nonexistence of scalability, absent real-time performance, and allowing one mobile robot to be controlled at a time reflect challenging concerns in the literature of finding the best route of mobile robots. While designing a mobile robot route, three requirements are generally considered. Firstly, environment modeling is performed. In environment modeling, a natural map in which a mobile robot must operate is translated to a map features format that can easily be stored. The second requirement is the need for optimization criteria, while the third requirement is the path discovery algorithm [

Efficiency and accuracy in route planning can be achieved firstly by designing an environment model that will better understand the environmental factors. Environmental modeling will significantly reduce the complexity involved in route planning. Different approaches can be used as techniques for environment modeling, including the framework space approach, the free space approach, the cell decomposition approach, the topological approach, and the probabilistic roadmap approach [

An optimization criterion must be set in the route planning process. Several variables can play an important role and can be included in the criteria for optimization inside the rote planning for mobile robots. Three often used optimization criteria are path length, smoothness, and degree of safety. Heuristic approaches and artificial intelligence algorithms are the two broad types of methods used to design route planning or optimization algorithms. Metaheuristic algorithms solve unexpected issues because of having intelligence and prior knowledge of random search the two elements of population-based heuristic algorithms [

This paper proposes the PSOWGWO algorithm to combine the hunting behavior of Grey Wolf Optimization (GWO) and the social behavior of Particle Swarm Optimization (PSO) to have efficient route planning for mobile robots. The optimization procedure begins with a random set of agents in the proposed optimizer. To measure the statistical efficiency of the proposed algorithm, Wilcoxon rank-sum and ANOVA statistical tests are applied. Moreover, the algorithm’s superior performance in data size, path planning time, and accuracy is tested over other state-of-the-art techniques.

To organize this paper, related work is presented in Section 2. The proposed model is explained in Section 3, while results are shown and discussed in Section 4. Finally, the conclusion and future directions are discussed in Section 5.

Map facilities have interested extensive studies on the fast computation of driving directions in road networks. Finding the best route amongst two points can be modeled as the shortest path problem on weighted graphs. The field of mobile robots is continuously gaining popularity among the research community. To solve the issues of identification, and categorization Dynamic Neural Networks (DNNs) have previously shown a significant degree of proficiency [

The development of low-cost sensing technology has benefited robots by delivering an abundance of potentially rich and multimodal data. However, the concerned issue still is the techniques for deriving meaningful and usable state representations from such data. To solve this issue, numerous machine learning techniques and algorithms exist, including Artificial Neural Network (ANN), Support Vector Machine (SVM), K-Nearest Neighbor (KNN) and Decision Tree (DT) [

Metaheuristic algorithms solve unexpected issues because of having intelligence and prior knowledge of random search [

The Differential Evaluation (DE) optimizer is based on the concept of survival of the fittest. DE starts with a random population, and a new candidate is created by mixing old candidates with mutant solutions. This optimizer’s strong convergence promotes population variety and adaptation in the context of changing conditions. It takes a long time to converge, and it is also hard to determine the parameters [

Sundran proposed genetic optimization technique with B Spline deals with the static environment for global route planning [

The mobile robot path planning challenge is typically conveyed as follows: for an assumed mobile robot and a depiction of an environment, it is required to find a path among two stated locations, a start point and an endpoint. The path should be free of collision and satisfies certain optimization criteria. According to this definition, a path planning problem is considered an optimization problem. Most of the recent methods stated above and in the recent literature used to solve the path planning problem are according to two factors, (i) the path planning algorithms (local or global) (ii) the environment type (dynamic or static).

Overcoming the problem depicted above requires considering the following three objectives to obtain accurate and efficient solutions, (i) path safety, path length, and path smoothness (related to the energy consumption). (ii) test the proposed PSOWGWO; realistic scenarios for the path’s calculation have been used. (iii) comparison of the proposal with other state-of-the-art approaches, showing the advantages of PSOWGWO. In particular, to evaluate the obtained results, we applied specific quality metrics. Moreover, a statistical analysis is also performed to demonstrate the statistical evidence of the obtained results.

Due to efficient computing and capacity to cope with an unpredictable environment, it is noticed that smart strategies for robot navigation problems are gaining much attraction from the research community. In this paper, an algorithm PSOWGWO, based on PSO and an enhanced weighted GWO based algorithm, is designed and applied in order to provide an efficient solution for route planning of mobile robots. The proposed model mainly consists of 4 main steps, as shown in

The first step is the preprocessing step that includes configuration parameters for the proposed optimization and population for search space. The second step is about training deep neural network parameters in order to choose the best path, while the third step selects the best navigation path planning. The fourth and final step statistically evaluates the quality of proposed algorithms.

PSOWGWO combines the social behavior of PSO with the hunting behavior of GWO. In the proposed hybrid optimizer, the optimization procedure begins with a random set of agents. The set actively suppressed potential solutions, and following that, the fitness function for each person’s iteration is computed, and the top three leaders are designated as alpha, beta, and delta. The population is then split into two equal groups. The proposed hybrid method divides the population into two groups where the first group adheres to PSO procedures and the second group adheres to GWO processes. The first group follows the PSO procedure strictly, while the second group adheres to GWO processes.

Fitness functions are used to determine each PSOWGWO solution’s quality. Classification error rate and the number of chosen features are the two main variables that affects the fitness function. A satisfactory solution is to select a subset of features with a minimum classification error rate and a smaller number of selected features. The following equation is used to determine the quality of each solution for

The presented PSOWGWO algorithm is shown in Algorithm 1 step by step. In this way, the search area is thoroughly searched for potential locations, those are then exploited with the help of PSO and weighted GWO. As shown in

The PSOWGWO algorithm complexity analysis can be explained as follows.

Step 1: initialize PSOWGWO population: O (1).

Step 2: initialize PSOWGWO parameters: O (1).

Step 3: initialize iteration counter: O (1).

Step 4: evaluate fitness function evaluation: O (

Step 5: find the three best solutions: O (

Step 9: update first fitness: O (Max_{iter} ×

Step 10: update second fitness: O (Max_{iter} ×

Step 11: update third fitness: O (Max_{iter} ×

Step 16: update positions by WGWO: O (Max_{iter} ×

Step 19: update positions by PSO: O (Max_{iter} ×

Step 21: evaluate fitness function evaluation: O (Max_{iter} ×

Step 22: find the three best solutions: O (Max_{iter} ×

Step 23: update PSOWGWO parameters: O (Max_{iter}).

Step 24: find the best solution: O (Max_{iter}).

Step 25: increase iteration counter: O (Max_{iter}).

Thus, from the above analysis, the complexity of the PSOWGWO algorithm is O (Max_{iter} × _{iter} ×

Path planning for mobile robots’ results in quick and fast responses, as well as it also minimizes the wear and tears on the robot that then results in saving the cost. For the route planning of mobile robots, several approaches have been suggested and documented in the scientific literature. In the heuristic technique, sub-targets are determined at each phase of the rolling calculation. These sub-targets are then implemented using real-time planning in the current PSOWGWO algorithm. When the suggested algorithm (PSOWGWO) is started, the sub-targets are updated with the new information gleaned from the move, which continues until the planning job is done.

Experimental configurations of the PSOWGWO algorithm those are used to determine the fitness function for a specific solution are shown in

Parameter | Value |
---|---|

#Agents | 30 |

#Iterations | 100 |

Inertia |
[0.9, 0.6] |

[2, 2] | |

2 to 0 | |

0.99 | |

0.01 | |

Search Domain | [0, 1] |

#Runs | 20 |

Dynamic Neural Networks (DNNs) may be considered as an extension of unidirectional recurrent neural networks, with an addition of a second hidden layer and the reversal of the direction of the connections between the hidden layers. As a consequence, this model is capable of incorporating information from both the past and the future. The output

A DNN employs weights to perform two essential functions: the first is to determine the rate of output impacted by the input, and the second is to govern the learning rate of the hidden layer. The result is created by multiplying the weights assigned to the inputs and then adding them together like linear regression. Weights are the numerical values which describe the number of neurons involved in a specific interaction. If the inputs are

There are many potential paths to pick from but finding the ideal one (the one that would need the least amount of travel or cost) is something that mathematicians and computer scientists have been attempting to solve for years and years. The proposed model divides the issue into smaller sub-problems that may be tackled individually. There are multiple potential answers to each sub-problem, and the solution chosen for one point may impact the possible solutions of future sub-problems. It is a system for addressing a sequence of subproblems, each with several alternative solutions. In the scenario of selecting the best path, the main two issues include the selection of start point and the next step. In order to determine the overall performance of the proposed model; it is evaluated using a series of simulated situations, such as the one shown in

Automatic navigation is a fundamental problem in robotics, and numerous alternative algorithms are developed to provide courses those are either length or time optimum. The social navigation architecture output results using the proposed and state of the art algorithms are shown in

Optimization | Distance (M) | Total time (S) |
---|---|---|

PSOWGWO | ||

PSO | 20.8 | 140 |

GWO | 21.9 | 150 |

GA | 23.6 | 230 |

WOA | 26.8 | 280 |

FA | 25.3 | 270 |

PSOWGWO | PSO | GWO | GA | WOA | FA | |
---|---|---|---|---|---|---|

Number of values | 10 | 10 | 10 | 10 | 10 | 10 |

Minimum | 108.0 | 140.0 | 150.0 | 230.0 | 275.0 | 270.0 |

25% Percentile | 111.5 | 140.0 | 150.0 | 230.0 | 280.0 | 270.0 |

Median | 112.0 | 140.0 | 152.5 | 235.0 | 285.0 | 272.5 |

75% Percentile | 112.0 | 146.3 | 160.0 | 255.0 | 291.3 | 276.3 |

Maximum | 112.0 | 160.0 | 160.0 | 260.0 | 295.0 | 285.0 |

Range | 4.000 | 20.00 | 10.00 | 30.00 | 20.00 | 15.00 |

10% Percentile | 108.2 | 140.0 | 150.0 | 230.0 | 275.5 | 270.0 |

90% Percentile | 112.0 | 159.0 | 160.0 | 259.5 | 295.0 | 284.5 |

Mean | 111.4 | 143.5 | 154.2 | 241.0 | 285.5 | 274.0 |

Std. Deviation | 1.350 | 6.687 | 4.686 | 12.65 | 7.246 | 5.164 |

Std. Error of Mean | 0.4269 | 2.115 | 1.482 | 4.000 | 2.291 | 1.633 |

Coefficient of variation | 1.212% | 4.660% | 3.039% | 5.249% | 2.538% | 1.885% |

Geometric mean | 111.4 | 143.4 | 154.1 | 240.7 | 285.4 | 274.0 |

Geometric SD factor | 1.012 | 1.046 | 1.031 | 1.053 | 1.026 | 1.019 |

Harmonic mean | 111.4 | 143.2 | 154.1 | 240.4 | 285.3 | 273.9 |

Quadratic mean | 111.4 | 143.6 | 154.3 | 241.3 | 285.6 | 274.0 |

Skewness | −2.277 | 2.076 | 0.3204 | 0.4406 | 0.06024 | 1.241 |

Kurtosis | 4.765 | 4.059 | −2.070 | −1.893 | −1.700 | 0.9459 |

Sum | 1114 | 1435 | 1542 | 2410 | 2855 | 2740 |

The ANOVA and Wilcoxon Signed Rank Test statistical methodologies are used to compare the populations in order to establish the efficiency of the proposed solution over the other available solutions. The results of the ANOVA and two-way tests are shown in

The null hypothesis (H0) states that there is no statistically significant difference between the groups.

The alternative hypothesis (H1) states a statistically significant difference between the means of two populations, which is the distinction.

SS | DF | MS | F (DFn, DFd) | ||
---|---|---|---|---|---|

Treatment (between columns) | 275917 | 5 | 55183 | F (5, 54) = 1076 | |

Residual (within columns) | 2769 | 54 | 51.28 | - | - |

Total | 278686 | 59 | - | - | - |

PSOWGWO | PSO | GWO | GA | WOA | FA | |
---|---|---|---|---|---|---|

Theoretical median | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

Actual median | 112.0 | 140.0 | 152.5 | 235.0 | 285.0 | 272.5 |

Number of values | 10 | 10 | 10 | 10 | 10 | 10 |

Wilcoxon Signed-Rank Test | ||||||

Sum of signed ranks (W) | 55.00 | 55.00 | 55.00 | 55.00 | 55.00 | 55.00 |

Sum of positive ranks | 55.00 | 55.00 | 55.00 | 55.00 | 55.00 | 55.00 |

Sum of negative ranks | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

0.0020 | 0.0020 | 0.0020 | 0.0020 | 0.0020 | 0.0020 | |

Exact or estimate? | Exact | Exact | Exact | Exact | Exact | Exact |

** | ** | ** | ** | ** | ** | |

Significant (alpha = 0.05)? | Yes | Yes | Yes | Yes | Yes | Yes |

How significant is the discrepancy? | ||||||

Discrepancy | 112.0 | 140.0 | 152.5 | 235.0 | 285.0 | 272.5 |

Additionally, the ROC analysis is performed on a standard of ranking and findings from continuous diagnostic tests. The accuracy indices derived from classification, notably the area under the curve (AUC) that provide a meaningful comprehension of the variety.

In an environment with obstacles, finding a plausible route for a mobile robot is one among the popular research areas. The goal of a route planning algorithm is to move from a given start state to goal state within minimum time and cost. Our proposed PSOWGWO algorithms utilized the benefit of both, PSO procedure and enhanced GWO process. The algorithm has a preprocessing phase and the deep learning phase along with selection of best route planning. The results demonstrate the efficiency and superiority of the PSOWGWO algorithm in terms of AUC and other performance measures. Furthermore, The ANOVA and Wilcoxon Signed Rank Test statistical methodologies are also used to compare the populations in order to establish the efficiency of the proposed solution over the other available solutions.

The researcher(s) would like to thank the Deanship of Scientific Research, Qassim University for funding the publication of this project.