In order to effectively improve the efficiency of surface garbage cleaning robot, an intelligent control algorithm was applied to plan the robot path. To do so, an improved immune particle swarm algorithm was developed based on the robot model. This algorithm introduced the adaptive information dynamic adjustment strategy to dynamically adjust the main link indices, which improved the global searchability and convergence of particles and facilitated the quick identification of the optimal path by the robot. Through comparative simulation experiments with the particle swarm optimization algorithm, genetic algorithm, and immune particle swarm optimization algorithm, it was found that the robot based on the Adaptive Immune Particle Swarm Optimization (AIPSO) algorithm had the shortest planning path and search time, the lowest energy consumption, and the highest efficiency. A robot prototype platform was built. Compared to other algorithms, the efficiency of the robot space search based on the AIPSO algorithm was the highest, the search time was the shortest, and the energy consumption was also the lowest. Especially in the complex level 4 wave water environment, the AIPSO algorithm had the best adaptability and robustness, and the robot had the highest working efficiency and comprehensive performance. The experimental results revealed that the AIPSO algorithm effectively improved the path search and garbage cleaning efficiency of the robots and reduced the working time, which further verified the reliability and accuracy of the designed algorithm.

## I. INTRODUCTION

With the development of marine resources in different countries, marine pollution has become an increasing problem. Protecting marine environments has attracted great attention all around the world. Particularly, cleaning marine floating objects in a timely and effective manner has become an important goal in the protection of marine environments. Surface garbage cleaning ships have become important tools for cleaning up marine debris.^{1} With the development of electronic and artificial intelligence technologies, a great number of robots are being applied to deal with marine garbage. Quick and efficient planning of reasonable paths to make the robot capable of completing the garbage cleaning task in a short time has become a research hot topic.^{2–4} Shi *et al.*^{5} applied the bidirectional ant colony algorithm to plan mobile robot path, which improved the efficiency of the path search. Zhu *et al.*^{6} applied the improved particle swarm algorithm to plan the trajectory of an unmanned aerial vehicle, developed a coordination function, and obtained ideal results. Shi J *et al.*^{7} used an improved A* algorithm to plan and track the path of picking robot, to improve control accuracy, and to shorten the search path. Zan *et al.*^{8} used the Bezier curve to optimize robot path and improved the efficiency and accuracy of path planning. Li *et al.*^{9} employed a Python visual recognition system to test and improve the garbage cleaning efficiency of surface robots. Kiani *et al.*^{10} proposed the Ex-GWO (Expanded Gray Wolf Optimization) algorithm to plan robot path and found that the robot effectively avoided obstacles to reach the determined destination. Abgenah *et al.*^{11} applied the enhanced Dijkstra algorithm to synthesize robot path with multiple objectives to find the most feasible path. Zagradjanin *et al.*^{12} developed a fuzzy inference system and a learning algorithm to optimize robot path in a dynamic environment and reduced the length and planning risk of path. Sharma *et al.*^{13} used an improved cuckoo search algorithm to search path and obtained better optimization results. Wei *et al.*^{14} developed a method by integrating chaos and Particle Swarm Optimization (PSO) and Immune Particle Swarm Optimization (IPSO) algorithms to plan the path and improve the search speed of the robot.

In the current work, a robotic device was designed for surface garbage cleaning, which was equipped with a visual sensor for automatic identification of surface garbage. Solar panels were installed on the device to provide electricity, which contributed to energy saving and environmental protection. To improve the working efficiency and reduce the search path of the robot, this paper applied an improved IPSO algorithm for path planning. AIPSO had better global solving ability and convergence and effectively avoided the “premature” problem of traditional PSO.^{15–17} The AIPSO algorithm was designed to optimize the searching path and reduce the garbage searching time of the robot. Furthermore, while shortening the path, the energy consumed when robots searched for garbage was reduced, resulting in energy saving and emission reduction.

The water surface environment was a key factor affecting the robot’s navigation, and it was necessary to consider the current speed, wind direction, and waves. When planning water surface paths, it was necessary to fully understand the current information on the water surface environment and make decisions based on the actual situation. In the meantime, many factors had to be taken into account, such as sailing time, fuel consumption, and vessel load.

As a typical Traveling Salesman Problem (TSP), the path planning problem of surface robots had always attracted researchers. The optimization effectiveness of traditional controlled algorithms in improving robot search efficiency and reducing energy consumption needs to be further improved. The AIPSO algorithm proposed in the current work could help robots find the optimal path more effectively and significantly improve search efficiency, which was of great application and promotion value.

In this study, a surface robot model was built to analyze the path planning problem. The AIPSO algorithm was developed to optimize the robot’s path in different water environments. Verification experiments were carried out by constructing a test platform. Finally, more accurate control rules of the AIPSO algorithm for robots were obtained.

## II. PATH PLANNING PROBLEM DESCRIPTION

Assuming a stationary lake, the robot was not affected by waves and currents during its function. Assuming the existence of several garbage pieces in a certain water area, the robot actively detected the water area through the visual sensor and cleaned the garbage pieces one by one following a certain path. To improve the efficiency of the garbage cleaning robot, the optimal path had to be as short as possible, which was a typical solution for the TSP.^{18} The target was selected as a random combination. As there were several sampling targets, finding the shortest path took a long time. It was seen that a reasonable optimization algorithm could effectively accelerate the path optimization process of the robot.

*n*garbage pieces in the water area, and the surface garbage cleaning robot collected the garbage pieces one by one. The robot used an integrated network camera for the detection of a certain range of water surface garbage and calculated the optimal path using an intelligent algorithm. The device started to drive to the target water area and cleaned the garbage. When the garbage in that area was cleaned up, the robot scanned and detected other garbage pieces in other areas. When the

*n*th garbage was cleaned up, the robot returned to the starting point. The objective function that defined the planned path was considered as

*J*, and the mathematical model of TSP with

*n*garbage is expressed as

^{19}

*i*and

*i*+ 1 garbage pieces.

^{4}

*F*is the water resistance experienced by the robot,

*C*is the resistance coefficient,

*ρ*is the water density,

*v*is the robot sailing speed, and

*S*is the cross-sectional area of the robot hull.

*L*is the sailing distance of the robot and

*η*is the mechanical efficiency.

It was seen from Eq. (4) that the robot energy consumption during the navigation process was proportional to its navigation speed and traveled distance.

## III. MODELING OF WATER SURFACE GARBAGE CLEANING ROBOT PROTOTYPE

### A. Operating principle

The water surface garbage cleaning robot controlled the machine’s working path using visual sensors. When the visual sensor detected garbage on the water surface, the device would start driving toward the garbage water area and automatically clean up the garbage. The garbage was collected by the collection device and transported to the storage box by the conveyor belt. To ensure the continuous and stable operation of the machine, an induction solar panel was installed on the top of the storage box to provide continuous kinetic energy. The electrical signal returned by the transmission image was transmitted to the staff, and the staff generally controlled the cleaning device so that it cleaned the garbage quickly. The working flow of the water surface garbage cleaning robot is shown in Fig. 1.

This device adopted computer remote control, which could achieve the function of remote, real-time, and efficient collection of water surface garbage. Two mutually compatible propellers were installed on the left and right sides behind the equipment storage box to provide power for the device. The device used a conveyor belt to transport the garbage into the storage box. A solar panel was designed on the top of the machine to improve the device’s endurance. When the garbage collection is finished and the visual sensor detects that there is no garbage on the water surface, the robot would automatically return.

### B. Prototype modeling

To effectively clean up water surface garbage, a robot model was constructed for water surface garbage cleaning as shown in Fig. 2. The device mainly consists of a floating body, a photosensitive solar panel, a conveyor belt, a garbage basket, a visual sensor, a conveyor belt beam, a pair of balanced polished rods, a push rod, a U-shaped bottom plate, and a collection device. When the vision sensor detects a garbage piece on water surface, the device starts to drive to the target location and automatically collects the garbage. The push rod set moves the collection device up to reduce water resistance during sailing. When the hull reached the working area, the collection device was driven down by the push rod again, in a way that the lowest end of the conveyor belt was submerged into the water. The collection device gathered the garbage to the hull front and transported it through the conveyor belt into the garbage basket of collection box. For continuous operation of the machine, the device was equipped with photosensitive solar panels on the top of the storage box, which constantly provided electric energy.

The floating body of the robot prototype was compression-molded from Expandable Polystyrene (EPS) foam, and its outer layer was fully coated and hardened. The conveyor belt was made of Polyvinyl Chloride (PVC). The weight of the water surface garbage cleaning robot prototype was 75 Kg, which was increased to 95 Kg when it was fully loaded with garbage. The center of mass of the robot prototype coincided with the center of trash basket.

In order to more clearly observe the structure of the robot, Fig. 3 shows the front and rear views of the robot.

## IV. DESIGN OF AIPSO ALGORITHM

### A. Particle swarm algorithm

PSO was a commonly used biological heuristic method in the field of computational intelligence.^{20–22} It was widely applied in TSP path optimization problems to find the optimal solution by simulating the feeding of birds.

*n*particles in a D-dimensional space, the spatial position of the

*i*th particle was $Xi=Xi1,Xi2,\u2026,Xin$, and its velocity was $vi=vi1,vi2,\u2026,vin$. Through iterative optimization to obtain the local (

*Pbest*) and the global (

*Gbest*) optimal solutions of the particle, the updated velocity

*v*

_{id}(

*t*) and position

*x*

_{id}(

*t*) of the particle are, respectively,

^{23}

*v*

_{id}(

*t*) represents the particle velocity at time

*t*,

*x*

_{id}(

*t*) is the particle position at time

*t*,

*ω*is the inertia weight, and

*c*

_{1}and

*c*

_{2}are the acceleration factors.

Although PSO was extensively applied in finding the optimal path of TSP, it was easy for particles to fall into local optimums in the iterative process, resulting in a “premature” phenomenon and inaccurate optimization results. To address the above-mentioned issues, an improved algorithm based on immune particle swarm was developed to solve the shortest path problem of the robot.

### B. AIPSO algorithm

Immune algorithm depended on the theory of biological immune system and obtained the optimal result through antigen recognition, cell differentiation, memory, and self-regulation functions. While solving the problem, the artificial immune algorithm not only retained the performance of the optimal individual of the previous generation, but also searched for the global optimal solution. It was a swarm intelligence search algorithm.

In the current study, PSO and immune algorithms were integrated. Taking the advantages of immune algorithm in global search and population diversity maintenance, the self-adaptive recognition and self-adjustment performance of immune system were introduced into the optimization process of PSO, to improve the global convergence of particles and effectively avoid the traditional algorithm from falling into local optimum during the solution process.

In addition, in order to solve the problem of robot path planning in complex environments and improve the efficiency of robot path optimization, the adaptive algorithm was introduced to help the robot adapt to the changing environment and task requirements.^{24} The adaptive algorithm could automatically adjust path planning parameters and strategies according to the robot’s historical path data and environmental information to adapt to different environments and tasks. In a complex environment, robot path planning had to take into account many factors, such as terrains, obstacles, and dynamic changes. The adaptive algorithm could help the robot automatically adjust its path planning strategy according to the actual situation, such as adjusting speed, direction, and step size, in order to achieve the optimal path planning and task completion. The adaptive algorithms could learn optimal path planning strategies by allowing the robot to self-explore and trial and error in the environment. The AIPSO algorithm could predict environmental information and the optimal path around the robot by training the fitness of the particles, thereby achieving fast and accurate path planning.

In order to improve the working efficiency of the robot in complex environments, the adaptive algorithm was used to dynamically adjust the key indices, such as inertia weight, acceleration factor, crossover probability, mutation probability, and antibody fitness, of the IPSO algorithm. While optimizing the robot’s optimal path, it also considered reducing the energy consumption during the robot’s navigation, which was equivalent to the multi-objective optimization problem in the traditional mathematical model optimization solution. In other words, when designing an IPSO algorithm, not only objective function *J* was optimized, but also energy consumption *E* was taken into account.

### C. Adaptive dynamic inertia weight adjustment

The search accuracy of the particle swarm algorithm depended on the magnitude of inertia weight *ω*. Based on the classification of inertia weight, it mainly included constant inertia weight,^{25} linear decreasing inertia weight,^{26} nonlinear inertia weight,^{27} random inertia weight,^{28} fuzzy inertia weight,^{29} etc. For small values of *ω*, the particle search precision was high, making it more suitable for local search. However, when *ω* was large, the global search efficiency of particles was high, which made it suitable for global search.

*ω*will reduce to enhance the particle’s local optimization ability. If the fitness of the particle is lower than the average, the size of

*ω*will increase to enhance the particle’s global search ability. When particles were disturbed by external factors,

*ω*was adaptively adjusted with the objective function of the particles, thus improving the particle search ability. To improve the rapidity of convergence,

*ω*was adaptively regulated.

^{24}The dynamic adjustment formula of

*ω*is shown as follows:

*k*th time,

*ω*

_{max}and

*ω*

_{min}are the maximum and minimum values of inertia weight, respectively,

*x*

_{i}represents the

*i*th antibody, $fxi$ represents the antibody fitness,

*f*

_{avg}represents the average antibody fitness, and

*f*

_{max}represents the maximum antibody fitness.

### D. Adaptive dynamic acceleration factor adjustment

The acceleration factors included constant acceleration coefficient,^{25} nonlinear acceleration coefficient,^{30} sine–cosine acceleration coefficient,^{31} sigmoid-based acceleration coefficient,^{32} etc. *c*_{1} indicates that the following action of the particle came from the weight occupied by its own experience and the acceleration weight that pushed the particle to the local optimal solution *Pbest*. *c*_{2} indicates that the following action of the particle came from the weight occupied by the experience part of other particles and pushed the particle to the acceleration weight of the global optimal solution *Gbest*.

*c*

_{1}would be set to a larger value in the pre-iteration period and

*c*

_{2}would be set to a larger value in the late iteration period.

^{33}The value range of the improved adaptive dynamic acceleration factor is shown as follows:

*c*

_{1}(

*k*) and

*c*

_{2}(

*k*) are the values of

*c*

_{1}and

*c*

_{2}iterated to the

*k*th time; $c1max$, $c1min$, $c2max$, and $c2min$ are the maximum and minimum values of

*c*

_{1}and

*c*

_{2}, respectively; and

*D*

_{max}is the maximum number of iterations.

### E. Adaptive dynamic cross-probability and mutation probability adjustment

In the iterative process of IPSO, crossover and mutation operations were introduced. The main function of the crossover operation was to produce new particles. By combining genes, new particles could effectively avoid the shortcomings of the parent particles and inherit the advantages of the parent particles. The IPSO algorithm was able to gradually search for the optimum solution through the continuous crossover operation. The main function of the mutation operation was to increase the diversity of individuals and to prevent the algorithm from settling on local optimal solutions too early.

Compared with Genetic Algorithm (GA), the IPSO algorithm realized the search of target diversity, and the search targets it faces had a certain degree of dispersion and independence. GA is mainly applied to obtain the global optimal solution, and the search target it faces is single and exclusive. Both algorithms had crossover and mutation operations, but GA took crossover and mutation operations as the main methods to solve the target and auxiliary operations, respectively. Meanwhile, to maintain group diversity and achieve multi-peak convergence, the IPSO algorithm mainly operated on mutation, supplemented by crossover.

*p*

_{c}and the mutation probability

*p*

_{m}of immune particle swarm optimization were fixed values. When the environment in which the particles were located was more complex, the convergence speed of the population would be greatly reduced, and it was very easy to fall into the dilemma of local optimality. This was because with the continuous renewal of the population, the quality of the population was also declining. Adaptive adjustment of the crossover probability and mutation probability could effectively improve the fitness and diversity of the second and third generation populations, thus improving the convergence speed and solution accuracy of the particles.

^{33}The formulas of the adaptive crossover probability and mutation probability are shown as follows:

*f*

_{min}represents the minimum antibody fitness, $pmmax$ is the maximum mutation probability, and $pmmin$ is the minimum mutation probability.

### F. Adaptive dynamic antibody fitness adjustment

*x*

_{j}is the

*j*th antibody, $fxj$ is the antibody fitness, and

*N*is the population size.

### G. Algorithm step

The implementation steps of the robot path planning problem of the AIPSO algorithm are as follows:

Step 1: Parameter setting. Parameters such as the maximum number of particle iterations

*D*_{max}, particle population size*N*, inertia weight*ω*, and learning factors*c*_{1}and*c*_{2}were set.Step 2: Particle initialization. Based on the initial velocity and position of the particle, the particle fitness $fxi$ was calculated.

Step 3: Population evaluation. Based on the current fitness of the particle, the local optimal solution

*Pbest*and global optimal solution*Gbest*were updated.Step 4: The improved inertia weight and acceleration factor were calculated by Eqs. (7) and (8), respectively, and new particles were updated and evolved. New particles were then generated through adaptive crossover and mutation operations.

Step 5: Filtration of new particles. The concentration of new particles was adaptively adjusted, and the new population was determined according to the concentration. During the calculation process, “premature” antibody particles as well as memory particles with low fitness were adopted for cross-mutation processing to improve the fitness of new particles.

Step 6: Selection of the target particle. The particle fitness value of new population was calculated. If the fitness value of the new particle was greater than that of the parent particle, the particle was retained; otherwise, it was eliminated. By selecting new particles with high concentration and high fitness in step 5, the problem of “premature” particles was effectively solved. The cross-mutation process effectively maintained the particle diversity.

Step 7: Termination of the operation. When the maximum number of iterations was reached, the operation was terminated; otherwise, the process was returned to step 3 to repeat the operation. It was seen that only the best antibody appeared in the current antibody group, that is, antibody having the greatest affinity to the antigen, and the calculation was immediately stopped to give antibody solution. Otherwise, the calculation and solution steps were repeated.

The specific operation process of the IPSO algorithm is shown in Fig. 4.

The AIPSO algorithm was written using the MATLAB 7.0 software through the algorithm steps shown in Fig. 3. The robot path optimization process was simulated by the MATLAB software. The MATLAB software is commonly used in data analysis, wireless communication, deep learning, signal processing, robot control system, etc. This software has the advantages of simple operation, good interactivity, and high programming efficiency. Some pseudo-codes controlling the robot movement are as follows:^{34}

while the path list is not empty:

value = Get the current robot head direction information |

if value = = 0: %% If the robot head direction is consistent with the current |

forward() %% Robot moving forward |

if value in [-1,1]: %% If the current robot head is opposite to the selected direction |

overturn() %% Robot turns around |

if value in [-1,2]: %% If the forward direction is on the right side of the robot |

right() %% Robot turns right |

if value in [-2,1]: %% If the forward direction is on the left side of the robot |

left() %% Robot turns left |

now_value = next_value %% Get the current robot direction |

next_value = save_path.pop() %% Get the robot status of the next node |

value = Get the current robot head direction information |

if value = = 0: %% If the robot head direction is consistent with the current |

forward() %% Robot moving forward |

if value in [-1,1]: %% If the current robot head is opposite to the selected direction |

overturn() %% Robot turns around |

if value in [-1,2]: %% If the forward direction is on the right side of the robot |

right() %% Robot turns right |

if value in [-2,1]: %% If the forward direction is on the left side of the robot |

left() %% Robot turns left |

now_value = next_value %% Get the current robot direction |

next_value = save_path.pop() %% Get the robot status of the next node |

## V. PATH PLANNING SIMULATION EXPERIMENT

### A. Parameter determination

To obtain the path planning efficiency of IPSO algorithm on robot cleaning garbage, a mathematical model of the robot was developed and a numerical simulation was performed. Forty sampling points were set in the water area of 120 × 120 m^{2}; the population number was set to 1500; the maximum number of iterations was set to 350; *c*_{1} = *c*_{2} = 2 and *ω* = 0.9; the crossover probability was considered as *p*_{c} = 0.1; and mutation probability was assumed to be *p*_{m} = 0.8.

It should be noted that, for large values of *c*_{1}, particles wandered locally, and when the value of *c*_{2} was large, the particles prematurely converged to the local maximum. Considering comprehensively, *C*_{1} and *C*_{2} are both set to 2.^{35}

The inertia weights of the AIPSO algorithm were considered as *ω*_{max} = 0.9 and *ω*_{min} = 0.3; the acceleration factors were considered as $c1max=2$, $c1min=1$, $c2max=2$, and $c2min=1$; the crossover probability was assumed to be $pcmax=0.9$ and $pcmin=0.1$; and the mutation probability was assumed to be $pmmax=0.9$ and $pmmin=0.1$.

### B. Path planning analysis

To verify the superiority of the designed algorithm, the PSO,^{19} GA,^{36} IPSO, and AIPSO algorithms were applied to plan and design robot path. The iterative solution process of fitness and the simulation results of path planning are shown in Figs. 5 and 6, respectively.

Path planning algorithm . | Path length (m) . | Path optimization (%) . | Average search time (s) . | Time optimization (%) . |
---|---|---|---|---|

PSO | 1113.12 | ⋯ | 120.64 | ⋯ |

GA | 901.82 | 18.98 | 98.58 | 18.29 |

IPSO | 589.18 | 47.07 | 62.72 | 48.01 |

AIPSO | 542.69 | 51.25 | 58.37 | 51.62 |

Path planning algorithm . | Path length (m) . | Path optimization (%) . | Average search time (s) . | Time optimization (%) . |
---|---|---|---|---|

PSO | 1113.12 | ⋯ | 120.64 | ⋯ |

GA | 901.82 | 18.98 | 98.58 | 18.29 |

IPSO | 589.18 | 47.07 | 62.72 | 48.01 |

AIPSO | 542.69 | 51.25 | 58.37 | 51.62 |

The path planning simulation results showed that the planned path lengths of the four algorithms were 1113.12, 901.82, 589.18, and 542.69 m, respectively. The average search time was 120.64, 98.58, 62.72, and 58.37 s, respectively. It was seen that the AIPSO algorithm had the shortest path length and the shortest average search time. Compared with PSO, the robot optimization path was shortened by 51.25% and the average search time was reduced by 51.62%. The AIPSO algorithm presented a stronger solving ability, and the probability of obtaining the global optimal solution with this algorithm was higher. In the path planning process, due to the “prematurity” phenomenon, PSO had weak adaptive recognition and poor problem-solving abilities, resulting in the longest search path length. Compared with PSO, the solving ability of GA was significantly improved, the path was shortened by 18.98%, and the average search time was reduced by 18.29%, but its solving efficiency was still lower than that of IPSO, leading to the low accuracy of solving the global optimal solution. Compared with PSO and GA, the traditional IPSO algorithm had significantly improved the optimization results, but it was still lower than the AIPSO algorithm. It was seen that the AIPSO algorithm could quickly and efficiently obtain the optimal path to meet the requirements of robots to quickly identify and clean surface garbage.

### C. Energy consumption analysis

To analyze robot energy consumption when searching for a path and cleaning up garbage, the energy consumption of each algorithm was determined separately. Figure 7 illustrates the convergence process.

It was seen from the iterative process of energy consumption that due to optimization path shortening, the overall energy convergence process was continuously decreased. This echoes the energy calculation formula (4), which verified the accuracy of the developed path planning algorithm. However, fluctuations were observed in the convergence process, which also showed that the energy consumption of the robot during the navigation process was not only proportional to path length but also related to factors such as the turning amplitude of robot hull and water flow.

The relevant data were extracted from the diagram. The energy consumption based on PSO, GA, IPSO, and AIPSO is shown in Table II.

Path planning algorithm . | Maximum energy consumption (kJ) . | Minimum energy consumption (kJ) . | Average energy consumption/kJ . | Energy consumption optimization (%) . |
---|---|---|---|---|

PSO | 58.53 | 31.64 | 45.34 | ⋯ |

GA | 42.37 | 29.89 | 36.74 | 18.97 |

IPSO | 31.06 | 16.22 | 24.36 | 46.27 |

AIPSO | 27.45 | 15.98 | 22.48 | 50.42 |

Path planning algorithm . | Maximum energy consumption (kJ) . | Minimum energy consumption (kJ) . | Average energy consumption/kJ . | Energy consumption optimization (%) . |
---|---|---|---|---|

PSO | 58.53 | 31.64 | 45.34 | ⋯ |

GA | 42.37 | 29.89 | 36.74 | 18.97 |

IPSO | 31.06 | 16.22 | 24.36 | 46.27 |

AIPSO | 27.45 | 15.98 | 22.48 | 50.42 |

As can be seen from this table, compared with PSO, the energy consumptions of robots based on GA IPSO, and AIPSO were significantly improved presenting 18.97%, 46.27%, and 50.42% reduction, respectively. It was found that the AIPSO algorithm improved the accuracy and efficiency of particle search, accelerated the convergence speed of the algorithm, improved the quality of the global optimal solution, and finally planned the shortest path by dynamically adjusting the main index parameters. Since the robot moved at a constant speed during the navigation process, the AIPSO algorithm gave the shortest path, thus the least energy consumption, which played a role in energy saving and emission reduction.

## VI. EXPERIMENTAL VERIFICATION

In order to verify the superiority of AIPSO algorithm and improve the garbage cleaning efficiency of the robot, a prototype of surface garbage cleaning robot was built according to the design model, as illustrated in Fig. 8. The prototype was equipped with a 32-bit MCF51QE128CLH microcontroller, and an immune particle swarm control algorithm was developed based on the PLC software and imported into the controller. The workflow of robot path optimization and garbage cleaning is presented in Fig. 9.

It was seen from this figure that, due to the installation of different controllers on the floating bodies on the left and right sides, hull force was unbalanced. To ensure the successful completion of test experiments, stones were temporarily configured. In order to solve the above-mentioned problems, the following step was the addition of counterweights at the bottom of the hull to ensure hull stability.

In order to test the search efficiency of the robots in different water environments, tests were carried out on water surfaces with different wave levels. The level of the water surface waves consisted of ten levels, ranging from 0 to 9. Due to the influence of the local climate and environment, test experiments were conducted in wave level environments of level 1 and level 4, respectively. Under a level 1 wave condition, there were tiny waves on the water surface and the wind force was level 1. Under a level 4 wave condition, the waves on the water surface had obvious shapes, and groups of white waves appeared due to the rupture of the peaks, and the wind force was level 5.

### A. Level 1 wave test

In the actual experiment process, the algorithm was imported into a robot controller and the robot performed path planning and garbage cleaning work by area. Due to the high actual area of the lake, it was impossible for the integrated webcam of the robot to search for all lake information at one time and then calculate the path. Instead, the area was cleaned up one by one, which was equivalent to dividing the lake surface into several area blocks. In the actual search process, the path of each area block was optimized, and the obtained results were relatively good.

Multiple garbage pieces were set on a selected water surface area, and the robot set its own search path and cleaned up the garbage one by one. As the wave level was 1, the wind on the water surface was low and there were tiny waves. The robot was less disturbed by the outside world, and path planning and garbage collection went relatively smoothly. Figures 10 and 11 illustrate the spatial search ratio and search running time of the robot, respectively. Figure 10 shows the spatial search of the robot in the same area. Figure 11 shows the search time required by the robot in the same area.

According to Fig. 10, robots based on different algorithms finished cleaning the garbage in the specified area. This showed that the designed intelligent algorithms were applicable to robot systems and played an important role in garbage identification. Figure 11 shows that, at the same search path, the AIPSO algorithm effectively shortened the search time and achieved the desired goal.

As shown in Fig. 10, in a given area, the spatial search ratios of the robot based on IPSO and AIPSO reached 26.65% and 22.38%, respectively, i.e., all target garbage was cleaned up. PSO and GA needed to search 51.36% and 35.64%, respectively, to complete the task. Since the robot search spaces of PSO and GA were large, their search times were also increased, reaching 635.78 and 472.34 s, respectively. However, the robot search time of IPSO and AIPSO was 306.12 and 262.89 s, respectively, which was 51.85% and 58.65% lower than that of the PSO algorithm. In summary, the AIPSO algorithm effectively shortened the planned path of the robot and improved its garbage cleaning efficiency, which verified the accuracy and superiority of the designed algorithm.

### B. Level 4 wave test

The wave level of the tested water surface was 4, with obvious waves and strong wind. The garbage placed on the water surface drifted slowly with the wind direction, which caused a significant interference with the robot’s search and clean-up operations. At the same time, the speed of the robot was also affected by the headwind, which increased the search time.

To solve the TSP in a complex environment, in order to obtain the optimal solution in the shortest time, heuristic algorithms have usually been used to obtain the optimal solution. Commonly used heuristic algorithms include particle swarm optimization, genetic algorithm, immune algorithm, simulated annealing algorithm, and ant colony algorithm.^{37} The traditional ant colony algorithm had the problems of slow convergence, weak optimization ability, and easy to fall into local optimization when solving the optimal path in complex environments.^{38} In particular, when the convergence speed of the algorithm was accelerated, the population diversity would be reduced, which was not conducive to improving the global optimization ability of the algorithm. The introduction of Simulated Annealing (SA) algorithm into Ant Colony (AC) algorithm could effectively avoid the above-mentioned problems.^{39} The Simulated Annealing Ant Colony (SAAC) algorithm had strong optimization ability and robustness, which could solve the problems of difficult convergence and poor convergence results in complex environments.^{40} The SAAC algorithm was widely used to solve the robot path planning problem.

In order to further test the effectiveness and reliability of the AIPSO algorithm in complex environments, robot path optimization and garbage collection experiments were conducted on the level 4 wave water surface. Meanwhile, SAAC was introduced for path planning in complex environments. The experimental results were compared with those of the AIPSO algorithm in order to judge the superiority of the designed optimization algorithm.

Considering the complex water surface environment, in order to improve the accuracy of the experimental results, each algorithm underwent ten repeated experiments, and ten sets of path planning results were statistically analyzed. The statistical data of test results are given in Table III.

Path planning algorithm . | Longest path (m) . | Optimal path (m) . | Average value (m) . | Standard deviation . | Average time (s) . | Average energy consumption (kJ) . |
---|---|---|---|---|---|---|

PSO | 1345.28 | 1287.52 | 1310.25 | 20.64 | 1121.88 | 423.58 |

GA | 1054.87 | 997.59 | 1025.58 | 16.86 | 853.72 | 319.24 |

IPSO | 684.27 | 641.25 | 664.38 | 15.47 | 556.51 | 227.26 |

SAAC | 631.52 | 594.51 | 617.91 | 13.35 | 522.19 | 213.86 |

AIPSO | 586.34 | 549.72 | 567.43 | 12.64 | 477.91 | 192.67 |

Path planning algorithm . | Longest path (m) . | Optimal path (m) . | Average value (m) . | Standard deviation . | Average time (s) . | Average energy consumption (kJ) . |
---|---|---|---|---|---|---|

PSO | 1345.28 | 1287.52 | 1310.25 | 20.64 | 1121.88 | 423.58 |

GA | 1054.87 | 997.59 | 1025.58 | 16.86 | 853.72 | 319.24 |

IPSO | 684.27 | 641.25 | 664.38 | 15.47 | 556.51 | 227.26 |

SAAC | 631.52 | 594.51 | 617.91 | 13.35 | 522.19 | 213.86 |

AIPSO | 586.34 | 549.72 | 567.43 | 12.64 | 477.91 | 192.67 |

Table III shows that robots based on PSO and GA had the longest average optimization path, more time, and higher average energy consumption. The optimization results of robots based on IPSO, SAAC, and AIPSO in complex water surface environments were significantly improved, and all showed good robustness. The convergence speed and optimization efficiency of the SAAC algorithm were significantly better than those of the IPSO algorithm. In addition, the IPSO algorithm introducing the adaptive information dynamic adjustment strategy had better adaptability and robustness, as well as faster convergence speed and better optimization results. At the same time, it was found that the standard deviation of several algorithms gradually decreased, which also confirmed the accuracy of the experimental scheme. The experimental results further proved the reliability and superiority of the AIPSO algorithm, which provided an important solution to the problem of surface debris cleaning in complex environments and had a strong engineering application value.

## VII. CONCLUSION

To improve the cleaning efficiency of water surface garbage cleaning robots, a robot model was constructed for surface garbage cleaning.

An improved IPSO algorithm was developed for the path planning problem of surface robots. An adaptive control strategy was introduced into the algorithm, which dynamically adjusted the key link indices, such as inertia weight, acceleration factor, crossover probability, mutation probability, and antibody fitness, thus improving the accuracy and efficiency of path solving. The simulation results showed that the robot using AIPSO had the shortest optimization path and the lowest energy consumption compared with PSO, GA, and IPSO.

To verify the accuracy of the AIPSO algorithm, a prototype of a surface trash cleaning robot was constructed. In a level 1 wave water surface environment, the experimental results showed that within the same area, the robot space search ratio based on the AIPSO algorithm was the lowest and the time consumed was the shortest. The AIPSO algorithm had better adaptability and robustness, the fastest convergence speed, and the best overall performance in the complex level 4 wave water environment. This provided strong technical support for the surface robots to quickly and efficiently clean up garbage.

It was seen that AIPSO was an excellent iterative optimization algorithm. It had a strong solving ability and was easy to use. At the same time, it avoided the dilemma of falling into the local optimal solution. Especially when solving complex, constrained, and nonlinear problems, the AIPSO algorithm showed excellent robustness and reliability, and the stability of the solution was high, which had a strong engineering practicality. The next step will be to continue in-depth research on the path-seeking problem of robots in complex water environments, especially when disturbed by external factors, such as water currents and wind direction. In addition, the accuracy of different algorithms for path solving will be considered in many aspects, such as seagull optimization algorithm, expert algorithm, quantum evolution algorithm, and robust optimization algorithm.

## ACKNOWLEDGMENTS

This project was funded by the Anhui Province University Discipline (Professional) Top Talent Academic Funding Project (Grant No. gxbjZD2021076), the Key Project of Natural Science Research in Colleges and Universities of Anhui Province (Grant No. KJ2021A1026), and the National College Student Innovation and Entrepreneurship Training Program Project (Grant No. 202310380020).

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

Y.W. was mainly engaged in algorithm design, model establishment, and prototype testing. H.A. was mainly engaged in structural design work. L.S. was mainly engaged in data processing. H.Z. was mainly engaged in prototype design and production. All authors reviewed the manuscript.

**Yuqin Wang**: Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Writing – original draft (equal). **Alexander Hernandez**: Formal analysis (equal). **Lixiang Shen**: Data curation (equal). **Haodong Zhang**: Resources (equal).

## DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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