## 6 Discussion  
Based on the previous results, the applied algorithms are compared to select the most convenient path-planning technique for the 4 OWMR. A multi-criteria decision-making method named weighted sum [40] is chosen. The general formula for the weighted sum is shown in Equation (4).  
\[A^{*}_{WSM-score}=\text{max}\sum_{j=1}^{n}a_{ij}w_{j} \tag{4}\]  
where \(i=1,2,3...\), m  
\(A^{*}_{WSM-score}\) is the best choice score, \(n\) is the number of decision criteria, \(a_{ij}\) is the actual value of the \(i^{\text{th}}\) alternative in terms of the \(j^{\text{th}}\) criterion, and \(w_{j}\) is the ranking weight of the \(j^{\text{th}}\) criterion. The ranking is done on all results of all algorithms of all of the three available maps. The parameters that are ranked are the travel distance, average velocity, travel time, and absolute error in (x, y) coordinates. These parameters were given equal weights, and their ranking results for the three maps are displayed in Table 3.  
The main aim of this research is to present an experimental comparative study of different path-planning techniques for an indoor mobile robot. The results are ranked according to convergence rate, energy consumption and overall ranking. The convergence is represented by the absolute error in the x and y coordinates at the endpoint.  
This error is calculated using Middle Difference in Distance Driven (\(M_{DDD}\)) as shown in equation 5, which is the total distance of the planned path generated from the algorithms. Time is the total time for driving the mobile robot from the start point to the goal point in the real environment, and Maximum Deviation is the maximum absolute difference between the real and the actual path. \(M_{DDD}\) is calculated in all maps for all techniques and its results are ranked and presented in Table 3. The highest-ranking results in convergence are the RRT* technique followed by the Hybrid A*.  
\[M_{DDD}=\frac{\frac{\sum_{i=1}^{i}(dist_{actual}-dist_{planned})}{dist_{planned}}}{n} \tag{5}\]  
where the \(dist_{actual}\) is the distance between two consecutive points in the actual path, \(dist_{planned}\) is the distance between two consecutive points in the real path, and \(n\) is the number of distances in the real path.  
The energy consumption ranking is based on travel distance, average velocity and travel time. In the three maps, the Hybrid A* is ranked first in energy consumption parameters. Consequently, Hybrid A* has the lowest cost among the other techniques and relatively high convergence in the three maps (but not the best). In other words, if average  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Map Number**} & **Method of Path** & **Convergence** & \
\begin{tabular}{c} **Energy** \\ **Consumption** \\ **Ranking** \\ \end{tabular} &
\begin{tabular}{c} **Overall** \\ **Ranking** \\ \end{tabular} \\ \hline \multirow{3}{*}{Map1} & PRM & 2 & 4 & 4 \\  & Hybrid A* & 1 & 1 & 1 \\  & RRT & 4 & 3 & 2 \\  & RRT* & 3 & 2 & 3 \\ \hline \multirow{3}{*}{Map2} & PRM & 1 & 2 & 1 \\  & Hybrid A* & 4 & 1 & 2 \\  & RRT & 3 & 3 & 3 \\  & RRT* & 2 & 4 & 4 \\ \hline \multirow{3}{*}{Map3} & PRM & 4 & 2 & 2 \\  & Hybrid A* & 2 & 1 & 1 \\ \cline{1-1}  & RRT & 1 & 4 & 3 \\ \cline{1-1}  & RRT* & 3 & 3 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The ranking table of the applied algorithms on three indoor maps.  
velocity, travel time and travel distance are given higher weights in the ranking process, the Hybrid A* would be the best choice for the 4 OWM in indoor environments.  
Moreover, the Hybrid A* avoids complexity in computation during real-time deployment. Another observation is that Hybrid A* considers the robot's kinematics and geometry, so it doesn't require the addition of inflated maps during path planning generation.