I Introduction
Path planning algorithms are essential for the accomplishment of many activities in different areas, for example, robot navigation [10], path apps for locomotion in cities (for pedestrian and driver) [19], autonomousdriver cars [22]. These algorithms have different approaches to treat spatial information, the most used in the literature are, Gridbased search (which transforms the environment in a gridmesh) [21], Intervalbased search (similar to gridbased search it but uses space data instead of a grid) [7]
and Rewardbased (similar to a reinforcement learning in deep learning)
[9].Based on Gridbased search, the first path planning algorithm was proposed by Dijkstra in 1956. Although this solution is always able to find the shortest path between two points, Dijkstra’s algorithm has become obsolete because it has very high computational complexity. Considering the response time of the Dijkstra algorithm, it would be infeasible to be applied in many scenarios.
Given this problem, new algorithms with different approaches were created to improve performance in finding the shortest path between two points.
Since Dijkstra’s proposal, many algorithms have been created being able to find the shortest path with the lowest computational cost. A* [21], Bi A* [13], Breadthfirst [12], BestFirst [3] are a few of the search algorithms that exist for path planning. They have peculiarities that tackle different problems, and, therefore, are useful and important in many areas. These algorithms, however, become extremely costly when applied to large environments or environments with dynamic objects [18]. All these algorithms are detailed in the theoretical foundation section IIA.
The problem of the increased computational cost when increasing the amount of information is a problem that affects several fields of research, for example, pattern recognition
[20][1], text mining [11]. A very wellknown approach to avoid this problem is to reduce dimensionality by discarding irrelevant information to the task.Principal component analysis (PCA) is a mathematical procedure based on orthogonal transformation to convert data into a set of values of linearly unrelated variables called principal components. The number of principal components is always less than or equal to the number of original variables [5].
Truncated Singular value decomposition (TSVD) This algorithm use means of TSVD to performs linear dimensionality reduction. Differently of PCA, this solution does not center the data before computing the singular value decomposition
[4].Nonnegative matrix factorization (NMF) Creates two nonnegative matrices (W, H). The product of these matrices is an approximation of the nonnegative input data. This method is used for dimensionality reduction [15].
These solutions significantly reduce dimensionality, keeping enough information to accomplish some tasks. However, a limitation of these approaches is since they reduce dimensionality using only linear correlation [16]. Therefore, in [6]
, the authors built a deep learning model able to reduce dimensionality using nonlinearity correlation, named Convolutional Neuronal Network (CNN) Encoder. Their method removes mostly the useless information of the input data, including in dynamic environments. Eliminate useless information for path planning problem means to remove the paths which do not connect the start point and the goal point.
In this work, we perform an indepth evaluation of the application of their proposed CNN Encoder to decrease the time spent by different path planning algorithms, showing the efficiency of the proposal to improve various path planning solutions.
Ii Material and Methods
Iia Theoretical Foundation
IiA1 Dijkstra’s algorithm
The Dijkstra’s algorithm proposed in 1956 by Edsger W. Dijkstra [17] is a path planning algorithm based on graph search. It solves the singlesource shortest path problem for a graph with nonnegative edge path costs, producing a shortestpath tree, it can be defined as follows:
IiA2 A *
The A* algorithm [8]
was proposed to solve the limitations of Dijkstra’s algorithm, and to overcome it in the time spent to find the shortest path. This solution uses heuristics to be faster. It is defined as:
IiA3 Bi A*
Bidirectional A* search is a graph search algorithm that finds the shortest path from an initial vertex to a goal vertex in a directed graph running two simultaneous searches [13]. It can be described as:
IiA4 Breadthfirst
The Breadthfirst Search [12] is a classic graph search algorithm, and it works by expanding and systematically exploring a given node and progressively redoing the same procedure for all its neighbors. At each iteration, the last one explored, but not expanded, or visited, is selected. Also, this algorithm discovers all nodes that are a certain distance from the start.
IiA5 BestFirst
Based on the different strategies for solving search problems, the BestFirst [3] algorithm is one of the most popular in the literature. Given the heuristic function , which is applied equally throughout the search space, the algorithm aims to use this to quantify the value of each candidate exploited during the process and, thus, continue the exploration until reach the point of interest.
IiB Path Planning Database
Following the research of Janderson et al. previous work and thus demonstrating the efficiency of their proposal concerning the conventional approaches, we use the image database that was proposed by them, to expand previous results through the comparison with other solutions present in the literature. It contains various formats, distributed in five different scenarios. They have variations of start, goal points for each instance in the database; consequently, the possibilities of paths to be taken. In Figure 2, it is possible to see an instance of each scenario.
Using their database is possible to perform a more detailed analysis of the model’s ability to generalize its responses, as well as its level of efficiency when compared to other solutions in different scenario configurations. As mentioned before, their database contains five scenarios, where each one has a total of 10000 scenes, which are RGB images with a resolution of 60 x 60 pixels. The variation between them is due to the random positioning of obstacles; which simulates physical obstacles. Also, for each one of the images, there is a label, being a GrayScale 60 x 60 image, which contains the shortest path of the scene.
IiC The Convolutional Neural Networks Encoder
Autoencoders are being used to code data information in unsupervised learning [firstae]. They are trained to reconstruct the input data using fewer data than the original input; this way, many times, they can eliminate useless information. On the other hand, Convolutional Neural Networks has an excellent capability to extract highlevel features in tasks of deep learning and computational vision problems[14]. Trying to get the best of each model, Janderson et al. built a CNN Encoder to reduce the dimensionality of the data. This solution can eliminate useless routes from 2D maps [6].
IiC1 The model architecture
The architecture used was obtained through a testing process, where its construction took place through adjustments based on the results generated. Finally, the architecture reached can be analyzed in Table I.
Layer  Filters  Kernel Size  Activation  Batch Norm  Dropout  

1  Image           
2  Conv  64  3x3  ReLu  True   
3  Conv  128  3x3  ReLu  False  30% 
4  MaxPool    3x3       
5  Conv  256  3x3  ReLu  True   
6  Conv  512  3x3  ReLu  False  30% 
7  Dense  256    LeakyReLU  True  30% 
8  Dense  512    LeakyReLU  True  30% 
9  Dense  1024    LeakyReLU  True  30% 
10  Dense  3600    Tanh  False  30% 
IiD Experimental Setup
In this section, we describe the metrics used to evaluate the obtained results, how the database was manipulated, and the output processing. We also specify the hardware characteristics of the desktop computer used to perform the experiments; this is important because the hardware influences some experiments.
IiD1 Hardware Specification
The algorithms were written in python 3.7 and implemented in an Intel i58400 sixcore, with a base frequency of 2.80GHz and 8GB of RAM. More details are depicted in Table II.
Model  Intel(R) Core(TM) i58400GHz 

Number of Cores  6 
Number of Threads  6 
Base Frequency  2.80GHz 
Cache Size  9MB 
RAM  8GB 
IiD2 Metrics

Number of iterations. Represents the number of attempts until the algorithm found the shortest path.

The path planning algorithm time. Represents the time in seconds that the algorithm spent to find the shortest path.

CNN Encoder and preprocess output time. Represents the time in seconds that the CNN Encoder spent to predict the data input plus the time to preprocess it.

Total time.
IiD3 Database Division
Percentage Split

Train 80%

Validation 10%

Test 10%
Iii Experimental results
To evaluate this work, we applied the path planning algorithms mentioned in the theoretical foundation to the path planning database, and compare the average number of iterations when the CNN Encoder is combined or do not with these algorithms. Also, we compare the average of the time spent with and without using the proposal. The results were obtained using the test set (1000 images for each scene).
To facilitate the visualization of the results, they were compiled and divided into three tables. Table III shows the number of interactions of each algorithm for each scenario separately; this is important to analyze the model behaviour in different scenarios. Also, Table III shows the percentage of improvement between the algorithms when using or not using the model. On the other hand, Table IV shows the spent time of the algorithms to find the shortest path for each scenario. Also, the improvement time with and without the model was calculated.
In the conventional A* algorithm, we obtained an average improvement of 59.87% in terms of number of iterations. Looking at the execution time, with the application of the solution, we achieved an average improvement of 49.87%.
Going to the BestFirst search algorithm, we achieved an average improvement of 53.87% in terms of number of iterations, also, in execution time, an average improvement of 16.06%.
Using a variation of the first tested algorithm, Bi A*, an average improvement of 56.12% was presented in terms of number of iterations, in the execution time, an average improvement of 40.88%.
We also used the Breadthfirst algorithm, which is very widespread in the literature, we managed to achieve an average improvement of 83.77% in terms of number of iterations, in the execution time, an average improvement of 65.46%.
Finally, we applied the proposal to the Dijkstra algorithm, we obtained an average improvement of 84.12% in the number of iterations and looking at the execution time, there was an average improvement of 81.24%.
In Table V, it is possible to see a compilation of our results, containing a summary comparison between the standard execution of the search algorithms and their new results after the addition of our proposal. Also, it is possible to see some qualitative results in Figure 3.
Scene 1  Scene 2  Scene 3  Scene 4  Scene 5  
A*  910.95  623.33  449.56  616.71  584.32 
CNN Encoder + A*  301.42  246.70  221.70  254.06  254.07 
Improvement  66.91%  60.42%  50.68%  58.80%  56.52% 
Total Improvement  59.87%  
Bestfirst  263.07  86.01  119.24  162.42  174.1 
CNN Encoder + Bestfirst  93.45  75.64  63.15  67.69  71.34 
Improvement  64.48%  12.05%  47.04%  58.32%  59.03% 
Total Improvement  53.87%  
Bi A*  946.31  491.44  458.24  665.34  499.88 
CNN Encoder + Bi A*  341.61  254.85  227.30  272.18  247.39 
Improvement  63.90%  48.14%  50.40%  59.09%  50.51% 
Total Improvement  56.12%  
Breadthfirst  2268.59  2591.56  2188.41  2376.08  2286.77 
CNN Encoder + Breadthfirst  413.48  377.33  384.07  368.17  359.62 
Improvement  81.77%  85.44%  82.45%  84.51%  84.27% 
Total Improvement  83.75%  
Dijkstra  2284.51  2669.13  2285.65  2405.46  2343.36 
CNN Encoder + Dijkstra  413.82  377.70  384.33  368.38  359.83 
Improvement  81.89%  85.85%  83.18%  84.69%  84.64% 
Total Improvement  84.12% 
Scene 1  Scene 2  Scene 3  Scene 4  Scene 5  
A*  0.027  0.021  0.013  0.018  0.017 
CNN Encoder + A*  0.010  0.010  0.009  0.009  0.009 
Improvement  61.25%  51.61%  28.79%  49.60%  46.13% 
Total Improvement  49.87%  
Bestfirst  0.009  0.003  0.004  0.005  0.005 
CNN Encoder + Bestfirst  0.005  0.004  0.004  0.004  0.004 
Improvement  34.94%  50.54%  1.42%  26.42%  24.96% 
Total Improvement  16.06%  
Bi A*  0.024  0.013  0.011  0.017  0.012 
CNN Encoder + Bi A*  0.010  0.009  0.008  0.009  0.008 
Improvement  55.08%  30.37%  26.83%  45.76%  30.87% 
Total Improvement  40.88%  
Breadthfirst  0.013  0.015  0.013  0.014  0.013 
CNN Encoder + Breadthfirst  0.005  0.004  0.004  0.004  0.004 
Improvement  60.81%  69.08%  62.42%  67.51%  66.69% 
Total Improvement  65.46%  
Dijkstra  0.043  0.056  0.045  0.049  0.048 
CNN Encoder + Dijkstra  0.009  0.009  0.009  0.008  0.008 
Improvement  77.07%  83.73%  79.57%  82.33%  82.54% 
Total Improvement  81.24% 
Iterations  Time (s)  

A*  636.97  0.0194748744 
CNN Enconder + A*  255.59  0.0097622888 
Bestfirst  160.98  0.0056170788 
CNN Enconder + Bestfirst  74.25  0.00471486 
Bi A*  612.24  0.0158272148 
CNN Enconder + Bi A*  268.67  0.0093569152 
Breadthfirst  2342.28  0.0141633262 
CNN Enconder + Breadth first  380.53  0.0048917796 
Dijkstra  2397.62  0.0486876686 
CNN Enconder + Dijkstra  380.81  0.0091321876 
Iv Conclusion
This work aimed to show that it is possible to improve the performance of path planning algorithms using a CNN Encoder to eliminate useless routes.
From the results obtained, we can assume that it is more advantageous to apply the CNN encoder to the existing path planning techniques. That is, the proposal was able to reduce the time to find the shortest path with all analyzed algorithms. In fact that CNN Encoder can eliminate routes in scenarios with fixed and dynamic obstacles, which may help in research with robotic navigation. As such, our contribution is to validate the architecture’s efficiency with different solutions from the path planning literature.
As future work, we hope to check the proposed model for the creation of a socially aware motion planning algorithm [2]. Also, we intend to combine new Deep Learning features with improving the architecture, which may reduce the response time even further.
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