1. Introduction
Drones are becoming increasingly popular in several application areas, such as education [
1], topography [
2], inspection tasks [
3], rescue operations [
4], and military applications [
5]. The multirotor is the most common type of drone; it employes multiple rotors that enable it to fly. A vital challenge for successful drone operations is path planning. The purpose of path planning algorithms is to find a sequence of points that lead from a starting to an ending position while avoiding obstacles in the drone’s flight environment. The importance of path planning is relevant to several areas, such as road network development policy in cities [
6], unmanned aerial vehicles (UAVs) [
7], the problem of the optimization of delivery vehicle routing [
8], mobile robot navigation in environments with obstacles [
9], automated guided vehicles (AGVs) [
10], and dynamic building fire rescue operations [
11]. The path planning process is executed separately from the drone’s control loop and is conducted online or offline, depending on whether the environment and obstacles are known in advance or not. The process of solving the path planning problem consists of two major steps: modeling the real environment to a virtual environment and searching for the optimal path [
12].
Drones can easily navigate in three directions in outdoor environments and adjust their orientation by modifying the three Euler angles. In addition, spatial obstacles, such as trees and human-made structures, are encountered during outdoor drone navigation. In this paper, for effective drone path planning and detailed simulation of the physical environment, the problem of finding the optimal path is solved by adopting a 3D environment approach. The use of a 2D environment would be equally effective in cases where the drone navigates at a constant altitude. The proposed methodology for finding the optimal path in a 3D environment can also solve these cases by appropriately modifying the input data. Finding the 2D path is a sub-case of the 3D path finding process.
One of the main issues preventing the widespread use of drones is their limited flight time due to battery depletion. Li et al. mentioned that energy consumption can be reduced by decreasing the number of turns in a flight path [
13]. For a given fixed distance, a drone’s flight time increases when the path contains turns instead of straight lines. The flight time increases because the drone has to stop completely in order to change the yaw angle and continue its course while maintaining a constant aircraft orientation. Furthermore, to stop and change its orientation and direction, the drone needs to slow down and then speed up. Unlike ground vehicles, drones do not use a mechanical brake system to slow down; rather, a drone’s speed is controlled by increasing or decreasing the rotational speed of its propellers and by its aerodynamic drag. Multirotor drones are able to move in any 3D direction. Thus, they can change direction without changing the heading orientation. However, during the path planning process, it is important to avoid zig-zag movements and keep the course as straight as possible in order to reduce the time and energy spent on every turn.
Alongside drones, similar challenges in the path planning process are also encountered by other robotic systems with identical motion capabilities but different sizes or mechanical parts, such as industrial robots and coordinate measuring machines (CMMs). The main challenge is to develop an autonomous path planning procedure that allows robots to operate independently of any external human interaction and aligns with the mobility of the robotic system. CMMs and industrial robotic arms can navigate in 3D space and also change the orientation of their end effector. It is noteworthy that criteria such as the speed of task execution, obstacle avoidance, and energy saving are common to drones.
The path planning problem, due to its multiple applications and importance, has attracted the interest of several researchers. Ning et al. proposed an improved mutation operator genetic algorithm in a 3D environment to improve the accuracy and efficiency of a sediment sampling process in oceans [
14]. Wang et al. proposed an improved rapidly exploring random tree (RRT) algorithm for welding industrial robotic arm path planning [
15]. Sathiya et al. proposed a fuzzy enhanced improved multi-objective particle swarm algorithm to solve path planning problems faced by ground vehicles [
16]. Liang et al. suggested an efficient artificial bee colony algorithm to solve the online path planning of multiple mobile robots while avoiding obstacles and other robots in an experimental environment [
17]. Xie et al. used an improved ant colony optimization algorithm to solve the multi-objective inspection path planning problem in radioactive environments so that professionals working in these environments receive the lowest possible radiation dose during the overhauling of nuclear power plants [
18]. Chen et al. introduced a framework of trajectory planning for UAVs with two parallel planners. The map planner finds the shortest path in limited computational time using an improved jump point search (JPS) method; then, the point cloud planner is activated when the point cloud near the drone differs from the 3D map to avoid any potential collision [
19]. Liu et al. presented a multi-objective optimization model for bus route optimization using a pareto artificial fish swarm algorithm combined with a crossover and mutation operators [
20].
The Artificial Fish Swarm Algorithm (AFSA) is a type of swarm intelligence optimization algorithm that belongs to the continuous solution domain optimization category [
21]. Zhang et al. proposed a hybrid algorithm combining the A* and an improved artificial fish swarm algorithm to solve the 2D path planning problem [
22]. Li et al. applied a combination of artificial fish swarm algorithms and the artificial bee colony swarm algorithm [
23]. Fang et al. combined a real coded genetic algorithm (RCGA) and AFSA for the short-term hydrothermal scheduling of a complicated nonlinear optimization problem with a series of hydraulic and electric system constraints [
24]. Peng et al. proposed artificial fish swarm optimization to improve foraging behavior in order to enable the artificial fish to perceive more information about their surroundings, to obtain an optimal state, and to select the most beneficial movement direction [
25]. Qi et al. used an AFSA to optimize the battery capacity, charging current, and discharge current of a three-lithium battery-powered system to extend its lifetime [
26].
During the evolution of research in this field, several researchers have proposed new modifications and variations of traditional AFSA. Multi-objective optimization problems (MOOP) have more than one objective function to satisfy. Traditional AFSA was designed to execute global optimization in single-objective optimization problems. Thus, to solve MOOP, several researchers have adjusted the algorithm to satisfy the requirements of these problems. Xu et al. nominated an iterative deletion artificial fish swarm algorithm that integrates the global optimal solution into the AFSA’s behaviors in order to find the appropriate parameters for suspension and a mechanical elastic wheel [
27]. AFSA has also been used to solve optimization problems in dynamic environments. In this kind of problem, the search space modifies over time because of the changes in constraints or the objective function [
28]. Yazdani et al. suggested an AFSA for optimization in dynamic environments in which changes in the problem space occur in discrete intervals. Their method categorizes swarms into three main types and configures them in a way that they can demonstrate high efficiency in terms of performing their assigned tasks [
29]. Many researchers have proposed hybrid AFSA models to leverage their strengths and counter their imperfections. Yaseen et al. combined the follow and the swarm behavior of AFSA with particle swarm optimization (PSO) to optimize a dam reservoir, increase energy production, and minimize downstream water shortages [
30]. Zhang et al. used AFSA’s crowding factor to prevent an artificial bee colony from falling into local optimal solutions [
31]. Zheng et al. integrated the AFSA’s follow and swarm behavior with the bacterial foraging algorithm in order to overcome the poor convergence speed and the local optima drop of the bacteria foraging algorithm [
32]. Fang et al. applied a combination of AFSA and PSO to detect the onset of ultrasonic signals [
33]. Guo et al. proposed a hybrid model combing AFSA with an ant colony algorithm-based backpropagation neural network to compensate for the thermal error during a precision machining process using a computer numerical control (CNC) machine [
34]. Zhuang et al. combined a multi-strategy artificial fish swarm algorithm with support vector regression to determine the mechanical parameters of surrounding rock masses in tunnel engineering [
35]. Zhou et al. suggested a chaotic parallel artificial fish swarm algorithm to optimize water quality monitoring sensor networks [
36].
Path planning in 3D environments needs to overcome several challenges in order to be successful. The existence of static obstacles increases the complexity and demands of the path planning process. Important factors are the density of obstacles and their positions in the environment. Finally, a path planning process needs to take into consideration obstacle avoidance, flight time minimization, and the robot’s movement capabilities, which can sometimes conflict.
Collision detection and path planning strategies need to be implemented in order to generate optimal motion paths for automatic navigation in a 3D environment [
37]. Path planning can be achieved using two different types of methodologies. Offline path planning finds and optimizes the trajectory before a drone’s flight. On the other hand, online path planning generates trajectories during flight. Tan et al. combined the Nash equilibrium algorithm with particle swarm optimization to solve the UAV path planning problem in complex 3D environments with obstacles [
38]. Zhang et al. proposed a collision free path planning algorithm that takes into account the static obstacles and dynamic threats that are typical of urban airspace environment operations [
39]. Colas et al. suggested a real-time point cloud-based system and lazy tensor voting to navigate in a 3D environment [
40]. Wang et al. proposed a framework based on deep learning path planning and tracking control for obstacle avoidance and real time navigation of a fixed-wing UAV in a 3D environment with obstacles [
41].
In robotics, the accurate simulation of a real environment through a digital model is vital. The evaluation of the quality of the formed digital paths is directly related to the accuracy of the 3D model and the requirements of the performed task due to the fact that the formed path will be executed in real-world conditions. Although the accurate digitization of the real world is an open research field, there have been several proposals for the implementation of path planning algorithms using different 3D modeling methodologies [
42,
43,
44]. An effective and popular 3D modeling method is the grid environment methodology [
45,
46]. The grid method simulates a real-world environment using a set of feasible discrete points for the areas in which robots can move freely and infeasible discrete points to simulate obstacles or restricted areas.
Comparatively, with other swarm intelligence algorithms like particle swarm optimization or ant colony optimization, AFSA does not keep any previous information about the quality of the selected positions in a memory structure. As a result, a path that consists of several points and approaches a high percentage but is not completely the optimal path is not optimized further during the algorithm’s execution in order to completely examine its potential to become the optimal path; rather, it is completely discarded if a shorter path is created. This trait can be a disadvantage in the path planning problem, especially in cases where a route with a large number of intermediate points needs to be formed. On the other hand, it significantly reduces the required execution time for path formation.
Researchers have made significant efforts to expand the scope of application of the AFSA and optimize its performance and the quality of the provided solutions. However, the lack of some form of memory is regarded as a disadvantage that arises from the algorithm’s structure, and no solution has yet been proposed to deal with it. Moreover, researchers have successfully implemented several algorithmic methods to solve the path planning problem in a 3D grid environment with obstacles. Nevertheless, due to the large number of the next possible movement points and the increased complexity of the 3D environment, restricted 3D applications of the 4 or 8 possible movement point models for agent navigation have been adopted. On the one hand, the implementation of these navigation models leads to optimal solutions successfully, but on the other, the length of the formed paths can be reduced even further by using a model with 24 possible movement points [
47]. Another challenge faced by path formation algorithms is that increasing the accuracy of a natural environment’s representation prolongs their execution duration. As a result, the significance of algorithms with a fast convergence rate in such conditions is further emphasized.
This paper presents solutions to the problems described above. The AFSA is used with a 3D model of 24 possible movement points model in a dense grid environment that can accurately represent the real-world environment in which the robots are operating. A technique for solving the AFSA’s lack of a memory structure in the path planning problem is presented.
In this paper, the incorporation of an improved AFSA with a ray casting algorithm is proposed in order to solve the offline path planning problem in a 3D environment with obstacles. The improved AFSA proposed in [
47] is implemented in 3D path planning and further enhanced. An appropriate enhancement of AFSA is presented and applied on a modified navigation model of 24 possible movement points in order to more thoroughly explore the attainable alternative paths and to more realistically simulate the motion capabilities of robotics systems. Moreover, the next movement point selection process is improved by a simple and advanced 3D point elimination procedure. In this procedure, the points whose selection significantly excludes the optimal path are deleted from the set of possible movement points, and the agent is limited to choosing points that can lead it effectively to the end point. An advancement of the obstacles heatmap presented in [
47] is also introduced to improve the agent’s navigation in a 3D environment, and the effectiveness of the heatmap in 3D dimensions is examined. The use of the safety value factor and the total movement point factor in the objective function is proposed to optimize the fish navigation in a 3D environment and to find the shortest 3D path that successfully connects a start to an end point in dense environments. Finally, a multiple laser activation method is proposed to mitigate the main disadvantage of AFSA, i.e., the lack of a memory structure, in the path planning problem. The multiple laser activation method also further optimizes the optimal path and overcomes the limitation of the finite number of possible movement points encountered when applying bio-inspired algorithms in a grid environment to solve the path planning problem. A comparison of the results of the proposed algorithm with those of some state of the art path planning algorithms is presented. The introduced methodologies and algorithms were subjected to a variety of 3D environments with obstacles. They performed successfully on real-world tasks, such as quadcopter drone navigation in urban ecosystems, object transportation using a 6-degree-of-freedom industrial robotic arm, and performing measurements using a CMM in an environment with multiple components.
The main contribution of the presented methodologies compared to other state of the art path planning algorithms can be summarized as follows:
An enhanced AFSA that implements a 3D model of 24 possible movement points to solve the path planning problem;
The application of an obstacle heatmap navigation model to a 3D environment with obstacles;
A multiple laser activation methodology that can provide a solution to the AFSA’s problem, i.e., the lack of a memory structure in path planning, enables AFSA and other bio-inspired algorithms that address the problem of finding the optimal path in a grid environment to select the next possible movement point beyond the models of 4, 8, or 24 possible movement points and reduce the number of points in the optimal path.
3. Results
Multiple experiments were conducted to evaluate the performance and the efficiency of solving the path planning problem using the proposed methods. The experiments for our comparison between the proposed methods were performed in the same 3D environment to optimally reflect the response of the algorithm and assess the contribution of each technique. The final algorithm was tested in various environments and applied to real case scenarios for the planning of the path of a quadcopter drone, a CMM, and an industrial robotic arm. The experiments were carried out in a space with 507 points, 13 along the x axis, 13 along the y axis, and 3 along the z axis. In addition, 2 rows of obstacles were placed starting from the 9th row. The end point is located after the obstacle so that the optimal path is forced to pass over the obstacle. An environment with fewer obstacles contains more possible points due to the fact that they are not eliminated by obstacles and the algorithm’s overall behavior can be carefully analyzed.
The exhibited tests are intended to compare the methodologies. Thus, the environmental conditions and parameters were kept the same, namely, MaxIt = 90, MaxStepsNum = 40, numFish = 150, fishTryNum = 15, and δ = 0.2 Regarding the creation of the obstacle heatmap, obsHeatVal = 150, heatIncrCoef = 0.4, obsNearHeatVal = 90, obsNearHeatVal2 = 40. The distribution of bonuses was carried out according to the following method. Initially, the heatmap values, hv, were examined in relation to average value mh and distance df of the examined point from the position where the fish is located. If , for the objective function’s value of points, their is multiplied by bh = 1.35 da; this represents the length of the elementary squared parallelepiped. If and for the district points with or , bh = 1.25. If and for the district points with , bh = 0.82. If for the district points with or , bh = 0.82.
The response of each algorithm and its impact on shaping the optimal path are reported in detail. The objective function used for the results reported was Equation (17), without including the proposed safety value factor and the total movement point factor. The contribution of these terms to the path’s formation and the algorithm’s convergence is presented in separate experiments.
Figure 10a depicts the outcome of using the improved AFSA behaviors proposed in [
47], here applied to a 3D environment.
Figure 10,c show the route resulting from the implementation of the proposed 3D simple and advanced elimination techniques.
Figure 11a–c show in diagrams the arithmetic value of the path length for each algorithm’s iterations. The route depicted in
Figure 10a shows several unnecessary changes in direction along the
z axis. These oscillations caused an increase in the length of the found path. As shown in
Figure 10b,c, the 3D elimination of possible movement points led to a reduction of these oscillations and a partial stabilization of the course when the fish were located in an area with few or without obstacles. Oscillations did not disappear completely; however, their amplitude was reduced, as was their influence on the length of the paths that were designed. Using the advanced point elimination method appears to further reduce the length of the path and encourages the selection of points closer to the ending point. Using the simple elimination method compared to AFSA yielded an 8.91% reduction in the total length of the found path, while using the advanced method decreased it by a further 6.68%. Moreover, comparing the results of AFSA and the 3D point elimination methods, a significant reduction in the variation of the formed path length was observed; see
Figure 11a–c. Without using the 3D point eliminations, several paths with increased length were formed. Nevertheless, paths of varying lengths were formed closer to the optimal route by using eliminations, which indicates that not only one fixed path was formed but also alternative paths in the surrounding space were explored. The lengths of the generated paths for each methodology are summarized in
Table 1.
Figure 12a shows the results of the formed path by additionally using the heatmap, and
Figure 12b shows the results of randomly activating the heat map.
Figure 12c,d show the diagrams for each process, respectively. Using the obstacle’s heatmap reduced the oscillations even more and stabilized the path’s course. This benefited the formation of the path, reducing its length by 2.29%, while random activation reduced it by a further 3.82%. Another important advantage of its use, as seen in
Figure 12c, was that it enabled the determination of the movement policy of the fish, taking into account the conditions of the environment based on its location in order to optimally enhance the exploration of the possible routes and find the optimal path. Also, in the case of random activation, it was observed that more paths ended up in deadlock and were rejected, but the optimal path was shorter than those in the previous cases.
Figure 13a,b depict the resulting combination of all the above techniques, adding separately to the objective function the proposed safety value factor and the total movement point factor, respectively. Coefficients w1 and w2 were 1.2 and 0.2, respectively.
Figure 13c shows the results of using the entire objective function of Equation (17) with coefficients w1 = 1.8 and w2 = 0.3.
Figure 14a–c show the diagrams for each case, respectively. The use of the safety value factor seemed to stabilize the course of the path in the XY plane and reduce its unnecessary oscillations while the obstacles were successfully overcome. The use of the total movement point factor seemed to stabilize the 3D course of the path and diminish the unnecessary oscillations, enabling the fish to maintain a stable course. Both factors appeared to have a similar effect on the length of the formed path, reducing it by about 0.7%, while their simultaneous use led to finding the optimal solution.
Table 3 summarizes the results for the described cases.
Figure 15a,b show the results of combining the artificial fish swarm algorithm enhanced with the ray casting algorithm and the multiple laser method, respectively.
Figure 15c,d show the lengths of the formed paths during the execution of the algorithm for both cases, respectively. The integration of the laser in this example did not affect the formation of the optimal path because the ending point was very close to the obstacle and the laser was activated from a point that was located within the range of possible movement points of the fish for its movement to the end point. However, the laser activation point favored the model of multiple laser activation in terms of the examined points. Multiple laser activation found an even shorter path, with a length 0.93% shorter than the optimal one. Also important is the fact that the path it found consisted of only three points, which is the minimum number of possible points that can form a path within a 3D grid environment and effectively overcome the obstacles. Furthermore, the final path overcame the limitation set by the model of 24 possible movement points and chose a point that was far away from the original. At the same time, it more realistically simulated the flexibility and movement capabilities of the drones by overcoming the computational limitations posed when solving the optimal path planning problem in a 3D grid environment. Finally, the weaknesses of the effective application of bio-inspired algorithms such as AFSA to choose the next point of movement from among a large number of possible points were overcome. In this example, in order for the fish to be moved from the starting point to a selected intermediate point, if the proposed methodology was not applied, it would have to choose it from among 390 possible movement points. The results are summarized in
Table 4.
Figure 16a,b show the results of the proposed algorithm using the multiple laser beam technique in different 3D environments with predefined obstacles.
Figure 16c,d show the path length diagram for each environment, respectively. The 3D environments depicted in
Figure 16a,b consist of 900 discrete points, of which 127 and 156 are obstacles. In both cases, the algorithm efficiently found the optimal 3D path using the multiple laser method.
Figure 17a shows the results of the path formation of a state of the art (SOTA) methodology in path planning, the ant colony optimization algorithm, presented in [
48].
Figure 17b–d show the final path from the proposed AFSA, the proposed AFSA integrated with the laser beam, and the multiple laser beam algorithm, respectively. The experiments were executed in 14 × 14 × 4 3D grid environment with obstacles.
Table 5 summarizes the lengths and the required time of execution of the resulting path for each algorithm. The algorithms in
Figure 17a,b used the eight possible movement point model to accomplish the agent’s navigation, whereas those in
Figure 17c,d employed the 24 possible movement point model. The comparison was performed using common parameters across all AFSAs, i.e., the same as those described in the Results section. For the proposed AFSA + Multiple Laser Beam algorithm, LMaxIt = 5. The presented time describes the time that the algorithms required without including collective activities such as environmental set up. The reason these procedures are not included is to translate the comparison into straightforward and accurate data. The ant colony optimization algorithm successfully formed a final path, but it was not the optimal one. This was attributed to the fact that there were multiple movement points, the existence of several potential paths that connected the start to the end point, and the fact that the algorithm fell into a locally optimal solution. Also, its execution time was considerably longer than those of the other algorithms. On the other hand, the proposed AFSA found the optimal path, which was 8.05% shorter than the path created by the ant colony optimization algorithm, while its execution time was 57% faster. The integration of laser with the AFSA and the 24 possible movement points further reduced the length of the formed path by 22.18% compared to the ant colony optimization and by 15.36% compared to the proposed AFSA with the 8 possible movement points model, while its execution time was shorter by 80% and 53.96%, respectively. The shorter path was created by the multiple laser beam algorithm, i.e., 23.45% shorter than the ant colony optimization and 16.74% shorter than AFSA with the 8 possible movement points model. Its execution time was reduced by 59.09% and 3.01% compared to the two algorithms, respectively.
The path length results generated by the ant colony optimization method and proposed AFSA can be considered as an equivalent example of the SOTA algorithm’s results that may fall into a local optimum path solution or successfully find the optimal path in a 3D grid environment [
49,
50,
51]. Thus, as seen by the above comparison of results, the combination of the ray casting algorithm and the multiple laser activation method with the 24 possible movement points model can significantly reduce the length of the optimal path obtained from the SOTA methods. SOTA methods need to be modified appropriately so that they can find the optimal path in a 3D environment using the 24 possible movement point model and the ray casting algorithm integration presented in this paper in order to compare the proposed methodologies more precisely and comprehensively.
Several experiments were conducted in a
3D grid environment with several obstacles in order to compare the four algorithms, i.e., traditional AFSA, named 3D tr-AFSA; the proposed AFSA, 3D pr-AFSA; the proposed AFSA integrated with the ray casting algorithm, 3D laser-AFSA; and the multiple laser beam AFSA, 3D multi-AFSA. In all algorithms, the model of 24 possible movement points was used with common parameter values, i.e., identical to those presented in this section. For the 3D multi-AFSA algorithm, LMaxIt = 5. In
Figure 18a–d, the results of the formed paths for 3D tr-AFSA, 3D pr-AFSA, 3D laser-AFSA, and 3D multi-AFSA are presented, respectively. The starting point is shown in green.
Table 6 summarizes the results of the maximum acceptable, minimum acceptable, and average lengths of the generated paths during the execution of the algorithms for each method. The lengths of the paths that were not successful and were rejected are excluded from the minimum length recording. The column of percentage reduction contains the reduction percentage of the path length from each algorithm in relation to the most extensive path, i.e., that of 3D tr-AFSA. The values of the maximum, minimum, and average number of nodes from the formed path during the execution of the algorithms are presented in
Table 7.
Table 6 shows that 3D tr-AFSA formed paths with much higher maximum, minimum, and average lengths than the other algorithms. This implies that due to the high number of possible movement points, the fish unsuccessfully meandered in the 3D environment, forming paths that connected the start to the end point, but they were not optimal.
Figure 19 also indicates that the dropout number of 3D tr-AFSA was low. These indications, combined with the high average path length, suggest that during the formation of the paths, several oscillations were encountered, and the fish had difficulty in the selection process of their next movement point. Comparing
Figure 18a and
Figure 18b, it is observed that 3D tr-AFSA tended to select more points from the 8 possible movement points than the 24, and the point selection of the 24 point model was not always the most beneficial.
Table 6 shows that the maximum length of 3D pr-AFSA was reduced by 81% compared to 3D tr-AFSA, and the numerical values of the maximum and minimum path lengths were closest to the average. Moreover, the lower disparity between the minimum and the maximal values of the lengths implies that attempts at route formation were focused on the optimal path. As a result, the employed methodologies favored the choice of the next movement point and helped the swarm to reach its final destination. The 3D pr-AFSA could find the optimal path in a 3D environment. The behavior of 3D laser-AFSA was identical to 3D pr-AFSA, achieving lower values for the maximum, the minimum, and average lengths of the formed paths. The additional reduction was due to the combination of the ray casting algorithm, which formed slightly shorter paths throughout the algorithm’s execution. The 3D multi-AFSA algorithm also exhibited similar behavior to 3D laser-AFSA. Its average value in
Table 6 was higher because it included the arithmetic values of multiple repetitions, even from the paths that were rejected. It is noteworthy that the difference between 3D laser-AFSA and 3D multi-AFSA is captured in
Table 7 through the arithmetic value of the minimum node number, which was further decreased for the case of 3D multi-AFSA.
Figure 19 shows that the proposed methodologies adopted in 3D pr-AFSA significantly reduced the execution time of the algorithm in comparison with 3D tr-AFSA, and that the integration of the ray casting algorithm reduced it even further. Although the proposed methodologies required the execution of more calculations, their contribution seemed to importantly affect the algorithm’s convergence speed. The 3D multi-AFSA needed more time to achieve completion compared to 3D pr-AFSA and 3D laser-AFSA. This was due to the fact that it examined more alternative routes and explored the environment more thoroughly, eliminating the memory disadvantage of AFSA, which is particularly profitable in larger environments where 3D laser-AFSA, in some part of the formed path, may not choose the optimal possible solution and may be corrected by the 3D multi-AFSA. Also, as shown in
Figure 19, the 3D multi-AFSA displayed the largest number of drop out points. This was due to the fact that the number of additional formed paths was included. If they were not included, its value would have been identical to 3D laser-AFSA.
Figure 19 shows a reduction in the infection points of the path as the proposed methodologies were included in the traditional AFSA, which would be particularly important when the formed paths are executed by the robots.
The proposed methodologies were implemented to solve some real-world challenges in robotics. They have been successfully applied to solve a drone path planning problem in real-world conditions, finding the safe, optimal path for conducting measurements by a CMM machine in an environment with multiple components and generating the path for the precise transfer of objects by an industrial robotic arm in an environment with obstacles. A Dji Mavic Air 2 drone (Shenzhen, China) was used for the experiment.
Figure 20a shows the environment where the experiment was conducted. The green point shows the drone’s take off location. The drone had to navigate to an end point, shown in orange, without colliding with obstacles such as buildings or trees.
Figure 20b shows the modeling of the 3D environment and the results after running the algorithm using multiple laser activation.
Figure 20c shows the path length diagram and
Figure 20d depicts the drone implemented for this scenario.
It is a common occurrence in the manufacturing production process to increase the efficiency of CMM to have more than one piece in a machine’s operating area during the measurement process. CMMs are highly sensitive, and any contact with an object during the relocation of their probe from one component to another may cause damage to the machine or require a mandatory restart and remeasuring procedure. This kind of error can significantly slow down the execution of the process and the production cycle.
Figure 21a–l exhibits the outcomes of utilizing the suggested methodologies to solve the 3D path planning problem for the safe navigation of a CMM probe to components where the measurements were to be conducted.
Figure 21a shows the CMM used for the experiments.
Figure 21b illustrates the arrangement of the objects, the components that the measuring procedure would interact with, and the collision free path that the machine would follow. The parts to be measured were numbered and the sequence in which the measurements were performed was predetermined. Letters A and B were used for parts that were not measured in the current research but which were located in the operation space. The different colors of the path indicate the individual parts of the path during the transfer from one target area to the next.
Figure 21c–k show the CMM probe position during the execution of the path.
Figure 21l shows the path formed by the proposed methodology. It is worth noting that during the environment modeling to ensure that the formed path could be executed without any part of the CMM colliding with the obstacles, the components were represented as solid volumes. A characteristic example of this process is part A, where if it was modeled exactly as it is in the real world, the generated optimal path would pass underneath and not above it, resulting in the parts colliding with the section of CMM that moves the probe vertically.
Industrial robotic arms are extensively used in factories for transferring items from one location to another. A key aspect of successfully and optimally accomplishing this task is the path planning of the end effector on the robotic arm. In this experiment, the proposed algorithm was used to determine the sequence of points from a start to an end position in a 3D environment with obstacles. The simulation was performed in order to examine if the proposed methodology could be obtained to solve real-world manufacturing problems. The experiments were conducted using an industrial robotic arm with 6 degrees of freedom, i.e., the Kawasaki RS010N (Minato, Tokyo, Japan).
Figure 22a shows the general experimental setup, the robotic arm, the obstacles, the and the start and end positions. The optimal path to be executed by the robot is shown in magenta. The purpose of this task was to safely navigate the robot’s end effector while simultaneously carrying a small object. A pneumatic gripper was used on the robot’s end effector in order to manipulate the small object. The operation space consisted of two obstacles while the end position was located slightly higher in elevation than the start position.
Figure 22b–d shows the robotic arm reaching an intermediate location in the path.
Figure 22e exhibits the results of the multiple laser beam algorithm execution. The thickness of the obstacles was considerably less than the rest of the operation area, so a dense mesh was used. The proposed algorithm successfully coped with this task, while the number of points given to the robotic arm for its execution was the minimum possible.
4. Discussion
Searching for the optimal path in a 3D complex environment with obstacles is an intertemporal challenge for the effective navigation of mechatronic systems and especially for drones. The application of the artificial fish swarm algorithm using the model of 24 possible nearby movement points in a 3D grid environment with obstacles was the main research concern of the present study. Finding the optimal path was achieved taking into account the drone’s movement capabilities and flexibility.
A number of methodologies were developed and tested to achieve this endeavor. The simple and the advanced 3D elimination of possible movement points during the process of selecting the next movement point, as described in this paper, was shown to be highly effective. Their combination was able to reduce the length of the formed path by 15% and focus the search of the fish on routes that were close to the optimal path, thereby reducing unnecessary wandering in the environment.
The 3D implementation of the obstacle heatmap stabilized the course of the fish during the execution of the algorithm, reduced unnecessary oscillations, and provided the possibility of creating navigation policies on a map based on the density, size, and position of obstacles in the environment. In this way, alternative routes can be explored in the different areas of the map and the exploring capabilities of the fish are increased.
The proposed safety value factor and the total movement point factor contributed to obstacle avoidance, reduced unnecessary oscillations, maintained the direction of the fish, and led to the finding of the optimal path.
The combination of the artificial fish swarm algorithm with the ray casting algorithm reduced the length of the optimal path. The reduction rate depended on the location of the end point and its proximity to obstacles. It also played an important role in the creation of the proposed methodology of multiple laser activations. The methods of multiple laser activation solved one of the main issues of the utilization of the artificial fish swarm algorithm in the path planning problem, i.e., the lack of a memory structure. Moreover, it reduced the number of points and the length of the optimal path. Its reduction rate depended on the location of the start and end points, as well as the shape and the obstacles of the 3D environment. Finally, it solved the problem of the artificial fish swarm algorithm and other bio-inspired algorithms to navigate successfully and select their next point of movement among a larger number of points. Without increasing the number of possible points, it provided the capability of selecting as the next point in the path, i.e., one that may have been located far away from the current location of the fish.
The proposed approach can successfully found the optimal path in a 3D environment with obstacles. Nevertheless, there are some restrictions, which are specified below:
The parameters and strategies for distributing the bonuses and penalties in the heatmap methodology are not tuned by any intelligent algorithmic method. Therefore, erroneous actions may impact the algorithm’s convergence.
The provided methodologies can be utilized for the enhancement of other path planning algorithms and could be further extended to positively enrich existing scientific knowledge. Suggestions for future research may include addressing the limitations and the application of the algorithm to online path planning cases.