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This work investigates the possibility of using a novel evolutionary based technique as a solution for the navigation problem of a mobile robot in a strange environment which is based on Teaching-Learning-Based Optimization. TLBO is employed to train the parameters of ANFIS structure for optimal trajectory and minimum travelling time to reach the goal. The obtained results using the suggested algorithm are validated by comparison with different results from other intelligent algorithms such as particle swarm optimization (PSO), invasive weed optimization (IWO), and biogeography-based optimization (BBO). At the end, the quality of the obtained results extracted from simulations affirms TLBO-based ANFIS as an efficient alternative method for solving the navigation problem of the mobile robot.

The use of mobile robots in many applications such as security, medicine, industry, space exploration, and many other fields is growing day by day. This autonomous agent must be able to navigate in the strange environment with the aim to accomplish these applications. Therefore, robot navigation is one of the essential problems in the robotics fields which can be categorized into local and global path planning.

In the global path planning, the environment is completely known to the robot. Various techniques have been suggested for global navigation, that is, Voronoi graph [

The complexity of the fuzzy logic system is found in the partition of the membership functions and the number of the rules. However, the complexity of the neural network systems is the selection of the optimal architecture and the synaptic weight. To overcome these problems, neurofuzzy models for robot navigation are developed [

The adaptive neurofuzzy system combines the automatic adjusting of the fuzzy parameters and the adaptability of the neural networks. Robot navigation using adaptive neurofuzzy system has been developed by Pothal and Parhi [

Deshpande and Bhosale [

In [

Two of the most important problems are the training and updating of the different parameters in the adaptive neurofuzzy inference system. The antecedent parameters of the fuzzy membership functions are usually determined by the gradient descent algorithm, but the calculation of the gradients is complicate and can lead to the local minimum. As a result, the precision can be affected.

To get over this problem, a method benefiting from the combination of ANFIS and Teaching-Learning-Based Optimization (TLBO) algorithm is suggested to solve the navigation task of the mobile robot. Different optimization algorithms demand different parameters that affect the response of the algorithm. Unlike these intelligent optimization techniques, TLBO does not demand any parameters to be adjusted.

Wu et al. have [

In [

A navigation problem approach based on TLBO was developed by Ansari and Katiyar [

In [

TLBO is introduced in this work in order to improve the performance of the ANFIS by training the parameters of the membership functions and thereafter reducing the root mean square error.

This paper is organized into six sections. Section

In this work, we employed a differential mobile robot called Khepera III [

Figure

The kinematic model of Khepera III.

The mathematical kinematic model is made through the link between the derivate of the position and orientation of the mobile robot and its linear (

The PSO technique is a swarm intelligence method member of a large category for solving the optimization problems. It is a population-based search algorithm, where each individual is referred to as particle and represents a candidate solution.

The notion of the PSO algorithm is that particles just move around multidimensional search space to approach the optima. Initially, a population is randomly created and set into movement. Each particle adjusts its position based on both its own experience and the neighboring particles’ experience. At the end of each iteration, all particles value the fitness and move toward better positions. The velocity of each individual is a stochastic variable and can vary with respect to the distance from its best position. For the standard algorithm, the velocity

The parameters

Biogeography-based optimization is a novel evolutionary algorithm and metaheuristic, which is inspired by the biogeography concepts: speciation (the evolution of new species), the migration of species between islands, and the extinction of species. The algorithm was originally proposed by Simon in 2008 [

In biogeography-based optimization, every habitat is considered as an individual and every individual has its habitat suitability index (HSI) with the aim to evince its goodness. Habitat that has high HSI represents the good solution and habitat that has the low HSI represents the poor solution.

Through the process of immigration, a lot of novel features will be transmitted from high-HSI habitats to low-HSI habitats. Thus, emigration and immigration are two operators that are used to optimize a solution for the optimization problem.

The invasive weed optimization (IWO) is a nature-inspired metaheuristic algorithm. It was developed for the first time by Mehrabian and Lucas in 2006 [

The novel generated seeds grow and produce plants. They are classified together with their parents on the basis of fitness values. The plants that have the lower value of fitness are remote to attain the maximum number of admissible plants in the colony

Teaching-Learning-Based Optimization algorithm was proposed for the first time by Rao et al. in 2011 [

Like other evolutionary algorithms, TLBO is also based on population method, which employs a population of solution to proceed for the search of the optimum solution. The population of solution is considered as a class of students.

In the optimization algorithm, the population of solutions contains many different design variables. In Teaching-Learning-Based Optimization, different variables correspond to different subjects given to students and student’s result corresponds to the “fitness” function as in other optimization methods based on population. So far, teacher is the best obtained solution.

The working procedure of TLBO consists of two phases. The first part is the “Teacher Phase.” In this phase, students learn from teacher. The second part is the “Learner Phase.” In this phase, students learn via the interaction between learners.

The principal purpose of this paper is to predict the optimized angular velocity for Khepera III using TLBO-based ANFIS controller.

The optimization of the different parameters of the fuzzy system is achieved when the error between the target and the actual output is minimized.

The most important step in implementing optimization algorithms is to choose the appropriate objective function. In this work, the objective function of all considered algorithms, PSO, IWO, BBO, and TLBO, is the root mean square error (RMSE). It is defined as follows:

For PSO, inertia weight

Table

Some training and testing dataset.

Angle_gtg_ao | Angular velocity |
---|---|

0.04575968951088669 | −0.5136580646789393 |

0.05161782158495741 | 0.21358442837709696 |

0.05028751858455458 | 0.20346639427862612 |

0.04892471599559453 | 0.1967326390214124 |

0.04322374721979803 | 0.19129939110585853 |

0.035830613708575966 | 0.16764949463891513 |

0.043838843149825314 | 0.13775644295379605 |

0.039227218313333735 | 0.17289155273086265 |

0.03454703339172103 | 0.1519406961385048 |

0.029562255127593785 | 0.13322351795172563 |

0.024763088824827337 | 0.11323826735427753 |

0.02009879569488924 | 0.09409110607989632 |

0.015529357393452271 | 0.07547095759255704 |

0.011702662987861356 | 0.05721994003120612 |

0.008353106242134456 | 0.0420675625195056 |

0.005261204814970032 | 0.02876893962169187 |

0.002237266274856186 | 0.016455495579154156 |

A database of 310 input-output pairs is prepared based on knowledge of Khepera III. 217 datasets are randomly chosen as training patterns and the remaining 93 datasets are employed as testing patterns to confirm the efficiency of the suggested ANFIS structure. Figures

Training data of go to goal and avoidance obstacle behavior using PSO.

Testing data of go to goal and avoidance obstacle behavior using PSO.

Training data of go to goal and avoidance obstacle behavior using IWO.

Testing data of go to goal and avoidance obstacle behavior using IWO.

Training data of go to goal and avoidance obstacle behavior using BBO.

Testing data of go to goal and avoidance obstacle behavior using BBO.

Training data of go to goal and avoidance obstacle behavior using TLBO.

Testing data of go to goal and avoidance obstacle behavior using TLBO.

The TLBO method gives the outputs with small errors.

MSE, RMSE, mean error, and std. dev. of the training and testing data using PSO, IWO, BBO, and TLBO algorithms are summarized in Table

Comparison of performances of PSO-ANFIS, IWO-ANFIS, BBO-ANFIS, and TLBO-ANFIS models.

Optimization algorithms | Training data | Test data | ||||||
---|---|---|---|---|---|---|---|---|

MSE | RMSE | Mean error | Std. dev. | MSE | RMSE | Mean error | Std. dev. | |

PSO | 0.11254 | 0.33547 | 0.0044081 | 0.33622 | 0.097484 | 0.31222 | 0.00022889 | 0.31392 |

IWO | 0.018774 | 0.13702 | 0.0088525 | 0.13705 | 0.014758 | 0.12148 | −0.016566 | 0.121 |

BBO | 0.0038922 | 0.062388 | 0.0061697 | 0.062225 | 0.0072857 | 0.085536 | 0.00007763 | 0.085819 |

TLBO | 0.00062319 | 0.024964 | −0.0011524 | 0.024995 | 0.00066108 | 0.025691 | −0.0028541 | 0.025691 |

When they are compared with each other, it can be clearly observed that the best outcomes are obtained from the ANFIS trained with the Teaching-Learning-Based Optimization (TLBO) algorithm.

The convergence of the algorithm plays an essential role in the optimization algorithm. The convergence of best cost averaged for 15 independent runs of all considered algorithms is illustrated in Figure

Convergence of the different optimization algorithms.

In this section, a comparative study has been made of the suggested evolutionary trained ANFIS controller (TLBO-based ANFIS) and the other intelligent navigational controllers using the PSO, IWO, and BBO algorithms in the graphical mode. We have presented simulations to prove the ability of the developed path planner to lead the navigation of the mobile robot in various situations. All simulations are performed using Matlab environment using sim.I.am simulator which is developed by GRITS Laboratory of Georgia Tech University.

Figures

Motion of the mobile robot in the first strange environment.

Motion of the mobile robot in the second strange environment.

To evince the efficiency and the power of the developed navigational controller, two significant criteria based on path length and travelling time are measured and given in Table

Comparison of simulation results between the TLBO-based ANFIS controller and other techniques.

Methods | Path length (m) | Travelling time (s) | ||
---|---|---|---|---|

Scenario 1 | Scenario 2 | Scenario 1 | Scenario 2 | |

PSO-based ANFIS | 4.17 | 6.23 | 20.85 | 31.15 |

IWO-based ANFIS | 3.61 | 5.46 | 18.05 | 27.3 |

BBO-based ANFIS | 3.36 | 4.92 | 16.8 | 24.6 |

TLBO-based ANFIS | 3,04 | 4.28 | 15.2 | 21.4 |

Four different evolutionary algorithms have been used to train an ANFIS controller for the navigation problem of mobile robot in a strange cluttered environment. These algorithms are PSO, IWO, BBO, and TLBO algorithms. Two main objectives are considered to minimize joint travelling time and total path length at the same time. Compared with the three other intelligent algorithms, TLBO-based ANFIS has performed very well for the studied navigational problem, while PSO algorithm performed poorly for the same problem. Real implementation of the announced approach will be developed in our future work. More intelligent evolutionary algorithms may be used.

The authors declare that they have no conflicts of interest.