**3. Experimental results**

Numerous experiments were carried out with the intention of validating the accuracy and consistency of the proposal made in this investigation; in addition, typical quantitative variables used in the field of exploration methods were analyzed, such as exploration time, distance traveled, and total environmental coverage, which were compared with data obtained by other methods such as SRT [11], SRG [6], and REG [12], which allows us to explain the efficiency of our method.

With respect to the integrated exploration paradigm, our exploration approach was designed to operate under the general concept of any SLAM method; however, for the tests performed, it was determined to use the method presented in [13] given the integral way of exploiting data from the work environment.

The tests were conducted using simulated information from a pioneer P3DX differential robot, which was equipped with a Hokuyo URG-04LX range sensor with a maximum detection range of 4 meters, an angular resolution of 0.360°, and a scanning angle of 240°. The environment used for the experiments is a modified version of the corridors of the Montpellier Computer, Robotics and Micro-electronics laboratory (LIRMM) (see **Figure 8**).

**Figure 9** shows the exploration structure generated by the extended REG method after its application in the LIRMM environment; in it, the edges represent routes that the robot can navigate without the risk of colliding with obstacles in the environment.

**Figure 8.** *The LIRMM environment.*

**71**

**Table 1.**

*on the basis of 30 tests*

*Extending the Limits of the Random Exploration Graph for Efficient Autonomous Exploration…*

**Tables 1** and **2** show the comparative results of the time and distance variables traveled by the robot using the SRT, SRG, REG, and Extended REG exploration methods; the results were obtained on the basis of 30 tests. In these tables, it is easy

*Time needed for the Extended REG, REG, SRT, and SRG exploration methods to explore the LIRMM environment* 

*DOI: http://dx.doi.org/10.5772/intechopen.84821*

**Figure 9.** *Generated graph structure by the proposed exploration approach.*

*Extending the Limits of the Random Exploration Graph for Efficient Autonomous Exploration… DOI: http://dx.doi.org/10.5772/intechopen.84821*

**Tables 1** and **2** show the comparative results of the time and distance variables traveled by the robot using the SRT, SRG, REG, and Extended REG exploration methods; the results were obtained on the basis of 30 tests. In these tables, it is easy


#### **Table 1.**

*Time needed for the Extended REG, REG, SRT, and SRG exploration methods to explore the LIRMM environment on the basis of 30 tests*

*Path Planning for Autonomous Vehicles - Ensuring Reliable Driverless Navigation...*

**3. Experimental results**

laboratory (LIRMM) (see **Figure 8**).

The MOVE\_TO function will then use the path P obtained in the previous step to take the robot to the node from where scanning will continue. In this way, the method will continue executing the described process, until there are no more free frontiers in the current node, and the frontier control list is empty; at this point, the robot will look for a path to return to the initial node from where the exploration process starts. **Figure 7** shows the flow diagram of the extended REG algorithm.

Numerous experiments were carried out with the intention of validating the accuracy and consistency of the proposal made in this investigation; in addition, typical quantitative variables used in the field of exploration methods were analyzed, such as exploration time, distance traveled, and total environmental coverage, which were compared with data obtained by other methods such as SRT [11], SRG [6], and REG [12], which allows us to explain the efficiency of our method. With respect to the integrated exploration paradigm, our exploration approach was designed to operate under the general concept of any SLAM method; however, for the tests performed, it was determined to use the method presented in [13] given

The tests were conducted using simulated information from a pioneer P3DX differential robot, which was equipped with a Hokuyo URG-04LX range sensor with a maximum detection range of 4 meters, an angular resolution of 0.360°, and a scanning angle of 240°. The environment used for the experiments is a modified version of the corridors of the Montpellier Computer, Robotics and Micro-electronics

**Figure 9** shows the exploration structure generated by the extended REG method after its application in the LIRMM environment; in it, the edges represent routes that the robot can navigate without the risk of colliding with obstacles in the environment.

the integral way of exploiting data from the work environment.

**70**

**Figure 9.**

**Figure 8.**

*The LIRMM environment.*

*Generated graph structure by the proposed exploration approach.*


#### **Table 2.**

*Distance traveled for the Extended REG, REG, SRT, and SRG exploration methods to cover the LIRMM environment on the basis of 30 tests*

to observe that the Extended REG requires approximately 25% less time than the best average time of the other three methods, and about 16% in the best average distance was reported by the other three methods. In addition, it is possible to observe that

**73**

**Table 3.**

*methods on the basis of 30 tests*

*Extending the Limits of the Random Exploration Graph for Efficient Autonomous Exploration…*

the standard deviation in both variables is very low compared to the other methods due to the deterministic way of choosing the next position to explore, which allows sustaining the affirmation that the method will always obtain the same results.

*Surface covered of the LIRMM environment for the Extended REG, REG, SRT, and SRG exploration* 

*DOI: http://dx.doi.org/10.5772/intechopen.84821*

*Extending the Limits of the Random Exploration Graph for Efficient Autonomous Exploration… DOI: http://dx.doi.org/10.5772/intechopen.84821*


#### **Table 3.**

*Path Planning for Autonomous Vehicles - Ensuring Reliable Driverless Navigation...*

to observe that the Extended REG requires approximately 25% less time than the best average time of the other three methods, and about 16% in the best average distance was reported by the other three methods. In addition, it is possible to observe that

*Distance traveled for the Extended REG, REG, SRT, and SRG exploration methods to cover the LIRMM* 

**72**

**Table 2.**

*environment on the basis of 30 tests*

*Surface covered of the LIRMM environment for the Extended REG, REG, SRT, and SRG exploration methods on the basis of 30 tests*

the standard deviation in both variables is very low compared to the other methods due to the deterministic way of choosing the next position to explore, which allows sustaining the affirmation that the method will always obtain the same results.

**Figure 10.**

*Consistency test of the Extended REG method applied to the SLAM problem.*

**Figure 11.** *Map obtained with the Extended REG method applied to the SLAM problem.*

Moreover, since our proposal is based on the REG algorithm, one of the main benefits contained in the extension presented in this paper is the guarantee with a high degree of confidence that the environment will be fully covered in most cases, because it is possible to have a constant knowledge of the state of unexplored areas of the environment thanks to frontier control. Thus, to evaluate the coverage of the environment by the exploration method, this was divided into grids, which served to determine which of them had been explored (**Table 3**).

Finally, the algorithm of path planning for unknown environments presented in this article was developed with the intention of being integrated to SLAM algorithms to obtain an integral tool for the construction of autonomous maps. Although the Extended REG method could be used as a control module with any SLAM algorithm, for the tests performed, it was decided to use the method developed by Pedraza et al. [13] given the similarity of approaches when applying the methods in unstructured environments. The tests and results obtained are shown in **Figures 10** and **11**.

## **4. Conclusions**

In this work, a strategy was presented for the problem of exploration of environments for SLAM; the approach presented is based on the REG algorithm introduced in [12], which builds a graph-like data structure that integrally exploits the experience acquired during the exploration process to perform this task efficiently. The main contribution of the exploration proposal made in this article is the use of a simplified criterion to find the next position to explore based on the hierarchy of free borders detected in an instant of time, which allows the elimination of unnecessary movements of the robot, increasing its efficiency. The main advantage of this

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**Author details**

Alfredo Toriz Palacios1

provided the original work is properly cited.

2 Autonomous University of Puebla, Puebla, Mexico

\*Address all correspondence to: alfredo.toriz@upaep.mx

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\* and Abraham Sánchez López2

1 Popular Autonomous University of the State of Puebla, Puebla, Mexico

*Extending the Limits of the Random Exploration Graph for Efficient Autonomous Exploration…*

choice criterion is that the robot will travel short distances to the position closest to being explored, reducing the amount of time needed to reach them, which can be

Also the Extended REG method is designed to be integrated in the context of a SLAM method, which facilitates the construction of environment maps simplifying the task of planning paths in unknown environments, which allows giving true autonomy to the robot responsible for obtaining the environment map eliminating the dependence on decision-making by a human operator. Finally, a series of simulations of the proposed integrated exploration strategy were carried out, which

*DOI: http://dx.doi.org/10.5772/intechopen.84821*

allowed us to validate our approach.

verified in the results of the tests performed to the method.
