Experiments and Performance Analysis of Path Planning Algorithms

5. IMPLEMENTATION AND EVALUATION OF CONTROLLERS

5.1. Experiments and Performance Analysis of Path Planning Algorithms

5. IMPLEMENTATION AND EVALUATION OF CONTROLLERS

 Path length: Path Length shows the length of the path taken between the start and the target while performing the robot's task. It determines the total working time required and the total energy consumption of the mobile robot. Therefore, if the path planning algorithm creates the shortest path, it is considered optimal, thus ensuring energy efficiency. That is why it is an essential parameter for real-world solutions.

 Execution Time: Describes the time required for application resolution for real-world applications. It is an important criterion, particularly in path planning applications.

 Total Number of Turns: The total number of vertices visited while performing the given task is directly related to the memory requirement. Further, the total number of corners, namely turning points, visited during the execution of the task becomes essential.

Taking the explained criterion into consideration, the implementation of the application on the developed simulation environment will be evaluated. In global path planning, the resulting route will be displayed on the robot motion area or on the robot map image.

In our experimental studies, various experiments have been conducted and the results of eight will be compared. The result of eight different application areas represented by nomenclatures ranging from Map1 to Map5 is illustrated in Figure 5.1.

These graphs show all the results (path coordinates) obtained from the algorithms used.

Figure 5.1. Comparison of planned paths for environment maps Map1 to Map 5B

The graphical representations of all the results obtained according to these criteria are shown in the following figures. Plots of the total number of nodes (vertices) in the final path are shown in Figure 5.2 for all grid-based approaches. Thus, it was observed that GA requires maximum memory to process more cells than other approaches.

The graphical results of path length and execution time for all approaches are shown in Figure 5.3 and Figure 5.4, together with the visual comparison. After this graphical representation, we have to evaluate and quantify these numerical values in order.

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Figure 5.2. A number of nodes (vertices) in a path for maps Map1 to Map5B.

Figure 5.3. A plot of computational time of all planners for all environment maps M1 to M5

Figure 5.4.A plot of path lengths of all planners for all environment maps M1 to M5

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The results obtained from the experiments carried out within the scope of this thesis were evaluated with two parameters that are the resulting path cost and execution time to obtain the appropriate path. To compare the methods in a robust approach, both the path costs and time Z-Scores (5.1) has been calculated according to the acquired results.

The Z-score indicates the number of standard deviations that a data set leaves above or below the average. The Z-score is also known as the standard score and can be placed on the normal distribution curve. Z-scores range from -3 to +3 standard deviation. A diagrammatic representation to show Z-scores on a normal standard normal distribution (SND) curve is given in Figure 5.5Figure 5.5. A standard normal distribution (SND)It is a standard normal distribution with a mean of 0 and a standard deviation of 1.

Figure 5.5. A standard normal distribution (SND)

𝑧 = 𝑥 − 𝜇

𝜎 (5.1)

In this equation, x represents the input data. The μ parameter corresponds to the average of the series. The σ data in the equation is the standard deviation of the series.

Before calculating the Z-score, the data must be normalized. This is the method used to standardize the property range of data. Therefore, the calculated Z-Scores were normalized and drawn to the 0-1 range. The following Equation (5.2) is used for normalization.

𝑧_𝑛 = 𝑧 − 𝑧_𝑚𝑖𝑛

𝑧_𝑚𝑎𝑥 − 𝑧_𝑚𝑖𝑛 (5.2)

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In the equation, 𝑧_𝑛 represents the normalized Z-Score (z) value to be calculated.

𝑧_𝑚𝑖𝑛 and 𝑧_𝑚𝑎𝑥 are the minimum and maximum Z-Score values in the series, respectively. In order to fuse the calculated Z-Scores, these values were multiplied by a pre-defined significance factor. The results of the Z-Scores multiplied by the factor of significance were given as input to the value calculation function in the multipurpose functions [146,147], and the final performance data was obtained. The equation of value calculation in multipurpose functions (5.3) is given below.

𝑓(𝑝, 𝑡) = 𝑠𝑓_𝑖(𝑧_𝑛𝑝) + 𝑠𝑓_𝑗(𝑧_𝑛𝑡) (5.3) This equation is calculated in the form of a function depending on the path cost (p) and elapsed time (t). The 𝑠𝑓_𝑖 and 𝑠𝑓_𝑗 parameters represent the significance factors;

their totals are always equal to 1 (5.4). The 𝑧_𝑛𝑝 and 𝑧_𝑛𝑡 parameters in the equation are the normalized Z-Score values for the path length and execution time, respectively.

∃(𝑠𝑓_𝑖, 𝑠𝑓_𝑗) ⇒ ∀(𝑠𝑓_𝑖 + 𝑠𝑓_𝑗) = 1 (5.4) All methods used in the thesis were tested in each configuration space. The tests were repeated five times, and the averaged results were evaluated. Table 5.1 shows the path plan costs obtained by the methods used for the different configuration spaces.

Table 5.1. Path Lengths (PL) obtained in different configuration spaces Maps A Star RRT RRT+