A hybrid air-sea cooperative approach combined with a swarm trajectory planning method

3.5.1 Phase 1: monitoring setup

The monitoring step is performed, for example, twice a week in the maritime region to be monitored. The general coordinator General_crd prepares the monitoring drones according to the region numbers, allocating a UAV_mr for each region. In addition, General_crd checks periodically the maritime space statistics that are saved in the database. If it finds a statistic region that contains a high percentage of dirty zones in a certain period, it launches a UAV_mr for a full day to monitor this dirty zone.

3.5.2 Phase 2: monitoring execution

General_crd triggers the monitoring step according to the following actions:

1. Prepare each UAV_mr with startup parameters Parameters_startup(_M) (Id_region, Position_region, Path_region), the atmosphere map explored, the energy (battery charged) and the associated speed before starting.

2. Each UAV_mr is launched from the base of life to the end position according to the assigned Path_region. It follows this path with a rectilinear movement [16] to reach its region. When UAV_mr arrives at its region, using the explored map (a discrete grid 2D) of the atmospheric part of the region, it moves, captures and records the data of maritime sub-space in List_zone(List_Degree_cell, List_Position_cell, Position_zone) following a swipe movement [16]. The collection of data is based on a discretized map (grid 2D) by the UAV_mr using its sensor (a camera and an ultrasonic).

3. Once the maritime level data collection is complete, UAV_mr sorts the collected list and saves it in a List_zoneS. Then, it compares the List_Degree_cell of List_zoneS with a fixed threshold. After the comparison, it saves the result in List_threshold__degreeZ and sends it to General_crd.

3.6.1 Phase 1: cleaning setup

The two proposed solutions (modified-GA and modified-AA) are applied exactly in this phase. In addition, they guide the USV_cz swarm to execute the moving phase to dirty zones. Before applying the two solutions, General_crd analyzes the received data (List_threshold_degreeZ) from each UAV_mr. Then, it determines the USV_cz number containing the swarm for each dirty zone. This action is described by Algorithm 1. Then, the main phases of the two proposed solutions are presented so that the USV_cz swarm can plan its way to its dirty zone.

3.6.1.1 Solution 1: modified-GA trajectory planning

This phase is presented as the first solution modified to the trajectory planning problem. Different actions of this solution are mentioned so that the USV_cz swarm selected can build its trajectory towards its dirty zone.

1. Genetic algorithm setup: the proposed GA is inspired by the algorithm presented in [24]. In this GA, the USV_cz swarm must search for an optimal trajectory between the starting position (the base of life) and the goal (the dirty zone). Table 2 presents a comparative table of the proposed approach with the work of [24] in [16].

   1. Environment modeling: the environment modeling depends on the map of the discretized region (metric map) by Sup_mr. The workspace is discretized by a square grid G which is composed of square cells. A node is located inside each cell to facilitate the movement of USV_cz. These nodes build a dynamic graph where the arcs are presented by R_ij connection links. R_ij between two neighboring cell-nodes represents the distance between two positions (Figure 3). This distance is represented by the energy value E_ij that USV_cz can consume in the displacement. Each cell-node i_th represents a free / occupied position by a position or a non-solid obstacle in the environment. These positions are identified by Cartesian coordinates (x,y) in a 2D plane. These positions have a maximum of eight links (R_ij) with the neighboring positions j_th.

   2. Trajectory planning method: General_crd assigns a Pos_Start(x,y) and the list of end positions ListPos_End(x,y) to each USV_cz. This list sets the positions to arrive at the dirty zone. Then, the trajectory, traveled by USV_cz from a Pos_Start(x,y) to a Pos_End(x,y) passing through all accessible positions and avoiding obstacles, is called the global trajectory planning. To obtain this global trajectory, it should be divided into a mini-trajectory; the latter must not exceed the sensor range of USV_cz (an ultrasonic sensor), as shown in Figure 4. The range of the sensor represents a detection of the region Rs of s * s boxes that allows USV_cz to capture its neighboring positions relative to its current position. A USV_cz can move by one step between cells. The mini-trajectory contains Pos_Start(x,y) and Pos_Gol(x,y). If Pos_Gol(x,y) is equal to one of ListPos_End(x,y), then USV_cz has arrived in the dirty zone. The mini-trajectory contains Pos_Gol(x,y) which are occupied by USV_cz when it is moved. The others remain un-browsed until they are taken into account during the next planning. The aim is to obtain an efficient global trajectory. To this end, the mini-trajectory should be effective and with a short distance, less obstacle and a minimum of energy consumed.

   3. Evolutionary approach: an evolutionary approach based on GA is proposed to minimize the energy consumption, obstacle and trajectory distance. GA helps the USV_cz find an efficient trajectory from the Pos_Start(x,y) to Pos_End(x,y) (further details in [16]).

   4. Encoding and generation of initial population: after the environment modeling is finished, each node has its own number. The gene is made of one part which represents the number nodes. This gene corresponds to a position of USV_cz. The chromosome represents a mini-trajectory which contains a number of genes, the latter should belong to the rayon of the sensors. The population has a fixed length of individuals and each individual has a sequence of initial positions (cell-node). The mini-trajectory planning is random by choosing neighboring positions in the known environment. As a result, individuals have their sequences of positions (mini trajectory), where a mini trajectory is chosen to execute it by USV_cz (more clarification found in [16]).

   5. Fitness Function and Selection: fitness function is necessary to know the details and solution of the problem. Two parameters are taken into consideration to evaluate the fitness of the mini-trajectories: the total distance of mini-trajectory and the direction cost for each USV_cz. An appropriate fitness function of mini-trajectory (i) is constructed as follows:

      (1)Fi=A∗DistTrajectory(i)+B∗∑CostDir(i)

      (2)CostDir(i)=Directcost+Leftcost+Rightcost

      where, A and B are two equilibrium parameters (constant numbers) and Dist_{Trajectory(i)} and Cost_Dir(i) are the distance of the mini-trajectory (i) and the direction cost for each USV_cz respectively. Dist_{Trajectory(i)} is calculated by the sum of each distance between two cell-nodes in which this distance is represented by a value of energy. Cost_Dir(i) is calculated according to the direction of USV_cz when it moves to another node. It has three directions: direct direction (Direct_cost) where USV_cz moves to another position in the same direction; right/left direction (Right_cost/Left_cost) where it turns to the right/left of its position to get to another position.

   6. Genetic operators: new position sequences (new individuals) are created by applying crossover and mutation operators. Crossover is a performed positions sequence provided by two parents. These parents (two mini-trajectories) are selected by the tournament, where they (the individuals) are chosen at random and who with a low fitness value becomes a parent. A one-point crossover technique was chosen for this approach; two children are then added to the population. Figure 5 shows an example of a crossover operator, where the crossover point is the middle of the trajectory of parent 1. Then, child 1 takes the first part of the parent 1 chromosomes plus the second part of the parent 2 from the crossover point. Thus, child 2 takes the first part of parent 2 and the second part of parent 1. Therefore, two new mini-trajectories are provided. The mutation defines a quantity of genes that build a problem in the trajectory. The gene is replaced by one of the neighbor genes of its previous gene that are also randomly selected. Figure 6 shows the mutation operation on child 1 of the previous example. At each generation, applied elitism can be created by new individuals (children) of length l who have a low fitness to replace previous individuals (parents). Each new position sequence is executed by an associated USV_cz, so that the fitness value of each new individual is calculated.

2. Modified-GA based trigger process: when General_crd chooses USV_cz swarm, it sends the List_{idu sv}(Id_USVCZ) to their Sup_mr. In return, Sup_mr sends its discrete maritime exploration map. General_crd broadcasts a set of parameters to the selected swarm, as shown in the sequence diagram of Figure 7.

Table 2

Displacement-cleaning energy consumption for a zone with a strong degrees of dirt.

Numbers of USVcz	CEC_GA	CEC_AA
3	292,25	289,75
4	347,15	344,65
5	331,15	451,7
6	353,9	354,2
7	404,3	409,6
Average gain: 0.4%	Minimum gain: 0.5%	Maximum gain: 1.2%

Figure 3

Environment modeling of the modified-GA.

Figure 4

Trajectory planning method.

Figure 5

Crossover operator.

Figure 6

Mutation operator.

Figure 7

Sequence diagram of the ’modified-GA based trigger process for USV_cz swarm’.

After, General_crd launches the execution of GA and each USV_cz of the swarm plans to move from the above mentioned steps of GA to the dirty zone.

3.6.1.2 Solution 2: modified-AA trajectory planning

This phase is presented as the second suitable solution for the trajectory planning problem.

Different actions of this solution are mentioned so that the USV_cz swarm selected can build its trajectory towards its dirty zone.

1. Ant algorithm setup: this solution is based on an ant algorithm proposed in [6, 25]. These algorithms show the steps of modeling ants’ behavior in the environment. To this end, the proposed modified-AA can model the behavior of a USV_cz swarm to find an optimal trajectory between the base of life and the dirty zone. In addition, the discretized grid G is composed of cells that contain positions. These positions are presented as cities. Each city i_th represents a free / occupied position by a USV_cz agent. These cities are identified by Cartesian coordinates (x,y) in a 2D plane. Cities i_th can have connection links (edges) R_ij between neighboring positions j_th. R_ij represents the distance between cities (Figure 8). This distance is represented by an energy cost E_ij that a USV_cz agent will consume in the displacement between the cities.

   Based on the proposed algorithm, named ‘Modified-Ant Algorithm’, each agent USV_cz is placed in a starting city. USV_cz moves from one city to another using the connection links between cities towards the goal. u_i(t) is the vehicle number in city i at time t and U=∑i=0mui(t)the total number of vehicles. The cities have three positions known by the USV_cz: starting city Pos_Start(x,y), goal city Pos_Gol(x,y) and final city Pos_End(x,y). If the end city Pos_End(x,y) equals the goal position Pos_Gol(x,y), then the USV_cz has arrived at the dirty zone. Each USV_cz agent has the following characteristics:

   1. It deposits a pheromone trace on R_ij when it moves from city i to city j;

   2. It chooses the destination city according to a probability that depends on the distance between this city and its position and the amount of pheromones present on the edge (transition rule);

   3. To pass only once through each city, USV_cz cannot go to a city that has already been crossed, that’s why USV_cz must have a memory ‘List_tabooPos(Id_USV, Pos_Gol(x,y))’.

Figure 8

Environment modeling of the modified-AA.

The traces of pheromones are modeled by the variables τ_ij(t) which give the intensity of the trace on the trajectory (i, j) at time t. The transition probability from city i to city j by the agent u_i(t) is given by:

(3)Pij=[τij(t)]α.[Vij(t)]β∑l∉Lu(i)[τil(t)]α.[Vil(t)]β,ifj∉Lu(i)0,else

where, L_u(i) represents the List_tabooPos of u_i(t) located on the vertex i and V_ij represents a measure of visibility that corresponds to the inverse of the distance between cities i and j. This list is represented by:

(4)Vij←∑1jdij

where, d_ij is the distance between the city i and j, which is presented by the E_ij in the array List_Cost. Then α and β are two parameters for modulating the relative importance of pheromones and visibility. The update of the pheromones is done once all the ants have passed through all the cities:

(5)τij←(1−ρ)τij+∑u=1mΔτiju

where ρ is a coefficient the evaporation of traces of pheromones. Then Δτijurepresents the link reinforcement (i, j) for u_i(t):

(6)Δτiju=QLu,if USV passed through the arc (i, j)0,else

where Q is a constant and L_u is the length of the trajectory traveled by u_i(t) (the sum of the energy costs consumed during the travel between cities).

2. Running of ‘Modified-AA’ algorithm:

   General_crd prepares a virtual list of List_virtualPos(List_PosS(x,y), Pos_End(x,y)). This list is constructed by a starting position list List_PosS(x,y) and an ending position Pos_End(x,y) (the arrival at the dirty zone). General_crd assigns a Pos_Start(x,y) for each agent USV_cz of the selected swarm, and the Pos_End(x,y) is shared in this swarm. General_crd launches Algorithm 2 to find the best trajectory that will apply to the swarm. The flow is started by initializing the transition trace τ_ij(t) (3). An interval of time is proposed to assess the improvement of the trajectories built. Each u_i(t) will build its trajectory (Path^u(t)) from its Pos_Start(x,y) to the Pos_End(x,y). This construction is made based on the transition rule (3). The agent u_i(t) detects its detection region via its ultrasonic sensor to identify its neighboring cities. From the maximum transition probability P_ij(t) that was computed, its next destination city is known. When the trajectory is complete, its length L^u(t) is calculated. This trajectory is saved in a ListPath_UT list. At each end of the time lapse, the τ_ij(t) (rule (5)) is updated. After, the best trajectory found in ListPath_UT is selected based on the maximum value of P_ij(t). The best trajectory of t is saved in a list PathFinal_UT. When t = tmax, the best trajectory Best_path_u is selected of all t turns among the trajectories found in PathFinal_UT. This trajectory is selected based on its maximum value of P_ij(t).

3. Modified-AA based trigger process: when

   General_crd chooses the USV_cz swarm, it sends the List_{idu sv}(Id_USVCZ) to its Sup_mr. In return, Sup_mr sends its discrete maritime exploration map. General_crd broadcasts a set of parameters to the selected swarm, as shown in the sequence diagram of Figure 9. After, General_crd sends Best_path^u to the swarm after changing the starting position of each USV_cz. The latter moves together in the grid following the Best_path^u. Then, the first USV_cz is started from the Pos_Start(x,y) of the trajectory, then the second starts from the first position of the first USV_cz, and so on. Each USV_cz follows its neighbor USV_cz. When the first USV_cz arrives at Pos_End(x,y), every USV_cz except the first one checks its position to see if it is one of the positions found in List_PosE(x,y) except the Pos_End(x,y) of the first USV_cz. Otherwise, each of these USV_cz performs a small function to arrive at one of the end positions (Algorithm 3). When all USV_cz are found in their end positions, General_crd changes the Pos_End(x,y) of each USV_cz in the startup parameters.

Figure 9

Sequence diagram of the ‘modified-AA based trigger process for USV_cz swarm’.

Algorithm 2: Modified - Ant Algorithm

Inputs

List_{ID_USV} [u]: list which contains the ID of USV, where U represente the length of List_{ID_USV} [].

L^u(t): length of path.

P_{_}ij(t): transition probability.

t₀: initial time.

t_max : maximal time.

n: numbers of cities (positions).

m: numbers of USV.

Outputs

Path^u(t): path built by USV.

ListPath_UT: list of Path^u(t).

Best_path^u: best path found in ListPath_UT.

PathFinal_UT: list of Best_path^u.

Best_pathT^u: best path selected.

begin

(double) T_ij = (double)T_0 ∀(i, j) ∈ 1,...,n

for (T_0 to t_max) do

for all ((int) u ∈ List_{ID_USV} ) do

build Path^u(t) with the transition rule (2.1)

calculate the length L^u(t) of this path

save Path^u(t) in ListPath_UT with corresponding P_ij(t).

end for

for all (Path^u(t) ∈ ListPath_UT) do

find Best_path^u with a maximum (double) P_ij(t). save Best_pathT^u in ListPath_U T with corresponding P_ij(t). update τ_ij (t) with the rule (2.2).

end for

end for

for all (Best_pathT^u ∈ ListPath_UT) do

find Best_path^u with a maximum P_ij(t).

end for

Algorithm 3: Position adjustment of USV

for ((int) u ∈ List_{ID_USV} ) do

while ((int) Pos_End^u ∉ List_PosE) do

search if Pos_End^u != occupied by another u;

search nearest Pos_Gol in neighboring positions;

if ((int) Pos_Gol == Pos_End^u) then

Pos_End^u Pos_Gol;

end if

end while

end for

3.6.2 Phase 2: cleaning operation

This phase allows the USV_cz swarm to move into the dirty zone and clean it. The maritime space is discretized in square grid (G). Each box of G can contain an object (a dirty cell / a clean cell). Objects are points in a numerical space with M dimensions; these objects to be partitioned are positioned. USV_cz can move in G and perceive a detection region Rs in their neighborhood (Figure 4). These USV_cz can clean the dirty cell type objects. To this end, Algorithm 4 applies the proposed approach with the two solutions. Using this algorithm, the swarm can move in the dirty zone and clean its dirty objects. This phase is started when the swarm arrives at its dirty zone. General_crd stops the execution of modified-GA and modified-AA. Subsequently, General_crd selects a Leader_cz from the USV_cz composing the swarm, and at the same time shares this information with the other USV_cz. This leader has a very high energy capacity compared to other USV_cz. After, General_crd launches Algorithm 4 on the swarm and at the same time Leader_cz launches the recording of the characteristics of himself and its followers. The USV_cz of the swarm follow the algorithm so that they can properly position and move between the clean cells, select the cells to be cleaned after-wards, and share their positions between them.

3.6.3 Phase 3: cleaning finalization

This phase identifies the end of the cleaning step and collects the current characteristics of USV_cz for each proposed solution, and has three cases:

1. Case 1: The cleaning task is completed. When the USV_cz finishes its cleaning task, it returns to the base of life with a message of acceptance received by its Leader_cz (further details in [16]).

2. Case 2: The cleaning task is not complete and Energy_capCZ is average. In this case, two situations are available:

   1. The first situation: if Energy_capCZ of USV_cz is greater than a Threshold_average__energycap, i.e. its energy capacity is average. So, its Sup_mr finds a USV_cz(free) in the swarm of the same zone (further details in [16]).

      Algorithm 4 Cleaning Operation

      Inputs

      List_{Crd_USV} [sizeU]: list which contains the cartesian coordinate of each USV (u_x , u_y ), where sizeU represente the length of List_{Crd_USV} [sizeU].

      ListCrd_{threshold−degreeZ}[sizeD]: list which contains the cartesian coordinates of the dirty cells of zone (d_x , d_y ), where sizeD represente the lenght of this list.

      Outputs

      (NewU_x , NewU_y ): cartesian coordinate pair that represents the new position of each USV.

      List_TabooCelU[sizeC]: list which represent the memory of dirty cells that are already cleaned by USV.

      List_NearbyCrdU[sizeN]: list which contains the neighboring coordinates (v_x , v_y ) of USV (u_x , u_y ), where sizeN represente the length of

      List_NearbyCrdU[sizeN].

      List_{Crd_USV} [sizeU].

      begin

      while ((int) u < sizeU && (int) d < sizeD) do

      for all ((int) d ∈ ListCrd_{threshold−degreeZ}[sizeD]) do

      calculate the distance between (u_x , u_y ) and (d_x , d_y );

      end for

      select couple (d_x , d_y ) which it has a minimal distance with (u_x , u_y );

      if ((u_x − d_x==0) && (u_y − d_y==0)) then

      NewU_x = d_x; A

      NewU_y = d_y; B

      update((NewU_x , NewU_y),List_{Crd_USV}[sizeU]); C

      delete((d_x , d_y);ListCrd_{threshold−degreeZ}[sizeD]); D save((NewU_x , NewU_y),List_TabooCelU[sizeC]); E

      else if ((u_x − d_x==0) && (u_y − d_y==1)) then execute A, B, C, D and E instructions;

      else if ((u_x − d_x==1) && (u_y − d_y==0)) then

      execute A, B, C, D and E instructions;

      else

      find nearby positions((u_x , u_y ); List_NearbyCrdU[sizeN]);

      for all ((v_x , v_y ) && List_NearbyCrdU[sizeN]) do

      if ((v_x , v_y)!= occupied_another (u_x , u_y ) && (v_x , v_y)!= dirty) then calculate the distance between (u_x , u_y ) and (v_x , v_y );

      end if

      end for

      select couple (v_x , v_y ) which it has a maximal distance with (u_x , u_y );

      NewU_x = v_x ;

      NewU_y = v_y ;

      update((NewU_x , NewU_y ), List_{Crd_USV} [sizeU]);

      end if

      u++;

      if ((u==sizeU) && (d!=sizeD)) then

      u=0;

      end if

      end while

   2. The second situation shows the case where there is not a USV_cz(free) in the same zone. So, USV_cz(discharge) informs its Leader_cz by its List − energy_usv(Id_USVCZ, Energy_capCZ). Leader_cz(USV_cz_discharge) sends List − energy_usv and Parameters_cleaning(PosUSV, Cell_cz, Id_region, Id_zone, Position_zone, Trajectory_zone, Id_UAVMR) to its Sup_mr. After a waiting deadline, if Sup_mr does not receive another message (a detection message of USV_cz(free) in the other zone in the same region by Leader_cz(USV_cz_free)) before exceeding this deadline, then it passes to the third situation. Otherwise, Leader_cz(USV_cz_free) sends List_{characteristicsu svs} with List − energy_usv of their USV_cz(free) to Sup_mr. Sup_mr processes the received message and selects USV_cz(free) that has a higher energy capacity. So, if it does not find any competent USV_cz then it passes to the third situation. Otherwise, Sup_mr informs its Leader_cz(USV_cz_free) by USV_cz(free) with the complete cleanup parameters (Sup_mr changes the new position of USV_cz(free), Id_zone and new cell that USV_cz(free) will clean it with the same parameters Id_region, Position_zone, Trajectory_zone, Id_UAVMR). Leader_cz(USV_cz_free) returns the received message to its USV_cz(free). Leader_cz(USV_cz_free) waits until the power capacity of USV_cz(discharge) becomes low to launch the USV_cz(free).

   3. The third situation is illustrated by Algorithm 5. This situation shows the case where Sup_mr finds a USV_cz(free) that is assigned to dirty zones in the other region.

   4. The fourth situation is presented where there is not a free and competent USV_cz to complete the task of USV_cz in discharge state. So, Sup_mr(USV_cz_discharge) sends a message to the General_crd to inform / require it of the need for a USV_cz with Parameters_cleaning. It prepares a USV_cz in the base of life with the filled Parameters_cleaning. After, it sends the identifier of USV_cz(prepared) with the cleaning parameters to Sup_mr (USV_cz_discharge). This latter sends this identifier to Leader_cz(USV_cz_discharge) expecting the message of the energy capacity of USV_cz(discharge) becomes low.

3. Case 3: The cleaning task is not complete and Energy_capCZ is low. This case is realized when the energy of USV_cz(discharge) becomes low; that is, the energetic capacity (Energy_capCZ) of USV_cz is greater than a Threshold_low__energycap (following the situations mentioned above). USV_cz(discharge) sends this information to its supervisor through its leader (all situations except the first situation: USV_cz(discharge) sends this information right to its leader and the leader informs it to return to the base of life). Then, Sup_mr(USV_cz_discharge) sends a message (Inform launch):

   1. Directly to Leader_cz(USV_cz_free) to USV_cz(free): if this vehicle is owned in another zone in the same region (second situation);

   2. General_crd to another Sup_mr(USV_cz_free): run the USV_cz(free) and prepare it with the cleaning parameters to calculate its trajectory and swim to its new dirty zone and clean it; General_crd broadcasts this information to other Sup_mr (third situation);

      Algorithm 5: Third Situation (3)

      for all ((int)USV ∈ swarm) do

      if CleaningTask_USV =6nul and ErgyCap_USV ≥ Threshold_Average then

      send(USV_discharge ), (int) Leader(USV_discharge ), ’ErgyCap_USV and

      Parameters_cleaning’);

      save(Leader(USV_discharge ), ’ErgyCap_USV and

      Parameters_cleaning’);

      send(Leader(USV_discharge ), (int) Sup(USV_discharge ), ’ErgyCap_USV and Parameters_cleaning’);

      save(Sup(USV_discharge ), ’ErgyCap_USV and Parameters_cleaning’); send(Sup(USV_discharge ), (int) General_Crd, ’Need a USV(free) and

      Parameters_cleaning’);

      broadcast(General_Crd, Sup_mr,’Need a USV(free)’);

      while (time != nul) do

      for all ((int) USV ∈ AllDirtyZone(others regions)) do

      if (USV == free) then

      inform(USV (free), (int) Leader(USV_free ),

      ’CleaningTask_USV = nul’);

      save(Leader(USV_free ), USV(free), ’List_USV(free)’);

      end if

      end for

      for all ((int) Leader(USV_free ) ∈ AllDirtyZone(same region)) do

      send(LeaderUSV_free ), (int) Sup(USV_free ), ’List_USV(free) and

      ListCharacteristics_usvs’);

      save(Sup(USV_free ), ’List_USV(free) and

      ListCharacteristics_usvs’);

      end for

      for all ((int) Sup(USV_free ) ∈ others regions) do

      send(Sup(USV_free ), General_Crd, ’List_USV(free) and

      ListCharacteristics_usvs’);

      end for

      send(General_Crd, Sup(USV_discharge ), ’List_USV(free) and

      ListCharacteristics_usvs’);

      analyze(Sup(USV_discharge ), ’List_USV(free) and

      ListCharacteristics_usvs’);

      if (List_USV(free) =6nul) then

      select(Sup(USV_discharge ), USV_Competent);

      requestfill(Sup(USV_discharge ), (int) General_Crd,

      ’Parameters_cleaning’);

      fill(General_Crd, ’Parameters_cleaning’);

      send(General_Crd, Sup(USV_discharge ), ’Parameters_cleaning’);

      broadcast(General_Crd, Sup(USV_free ), ’USV_Competent and Parameters_cleaning’);

      send(Sup(USV_free ), Leader(USV_free ), ’Parameters_cleaning’);

      inform(Leader(USV_free ), USV_Competent, ’Wait’);

      else

      pass(Sup(USV_discharge ), Situation4);

      end if

      end while

      pass(Sup(USV_discharge ), Situation4);

      end if

      end for

   3. General_crd to USV_cz(prepared): launch USV_cz(prepared) which is in the base of life and to prepare it with the cleaning parameters; it can calculate its trajectory and swim to its new dirty zone and clean the remaining cells (fourth situation); Sup_mr(USV_cz_discharge) informs USV_cz(discharge) through its Leader_cz(USV_cz_discharge) to return so that it can swim from its zone to the base of life (and to charge) (all situations except the first situation). Leader_cz(USV_cz_discharge) sends List_{characteristics}__usvs of USV_cz(discharge) to its supervisor and to General_crd for the record. Sup_mr(USV_cz_discharge) informs the Leader_cz(USV_cz_free) to modify List_{characteristics_usvs} (second and third situations) or prepare it for USVcz(prepared) (fourth situation). Finally, Leader_cz(USV_cz_free) informs its USV_cz(free) to start the cleanup and modifies at the same time the List_{characteristics_usvs} of USV_cz(free) (first situation).

4.1.1 A running example of ’ UAV-M ’, ’ SUSV-C ’ & ’ USVS-C ’

The planning procedures and techniques are illustrated in an example of simple nontrivial execution that include three domains, namely UAV-M, SUSV-C and USVS-C. These domains complement each other. An abstract version of these domains can be defined from ten complete sets of constant symbols [16], namely a set of: regions (R_r), locations for each region (L_lr), base of life (B_br), dirty zones (Z_zl), monitoring vehicle (UAV_mr), cleaning vehicle swarm (USV_cz), cleaning vehicle in discharge state (USVD_cz), cleaning vehicle in free state (USVF_cz), cleaning vehicle in prepared state (USVP_cz) and a set of cranes (C_nb).

Thus, the topology of these domains is noted using the instances of predicates [16]: adjacent(E, E’) where localization E = {L_lr, R_r} is adjacent to E = {L_′lr, R_′r}, belong (C, L) where crane C = C_nb belongs to location L and belong (B, R) where a base of life B = B_br belongs to region R=R_r. Also, the current configuration of the domains is denoted using instances of the following predicates, which represents the relationships that change over time [16], namely at(NAME, E) where NAME = NAME1{UAV_mr, USV_cz} and NAME2{USVF_cz, USVP_cz, USVD_cz, SUSV_cz}, occupied(L), start-clean (NAME, Z), end-clean(NAME, Z), start-monitor(NAME, R), end-monitor(NAME, R), replace(NAME, NAME) notreplace (NAME, NAME), discover(NAME, Z), undiscover(NAME, Z), supervise(NAME,NAME), notsupervise(NAME, NAME), holding(C, NAME), stayinbase(NAME, B), flapoutbase(NAME, B). Possible actions for this domains [16] can be: start-clean(NAME, Z), end-clean(NAME, Z), start-monitor(NAME, R), end-monitor(NAME, R), discover(NAME, R, Z), undiscover(NAME, R, Z), stayinbase(NAME, B), flapout-base(NAME, B), move(NAME, E1, E2), moveD(NAME, E1, E2), take(NAME, C, R), takeD(NAME, C, R). The action ‘moveD’ is executed in parallel with the action ‘start-clean’, ‘end-clean’ and ‘move’. The actions ‘takeD’ and ‘putD’ are executed in parallel with the action ‘move’.

4.1.2 Representations for classical planning

The classical planning problems are presented in three differentways [26], namely: i) Set theoretic representation, ii) Classical representation, iii) State-Variable representation. This work focuses on the second representation (classical) to apply its planning on the proposed approach.

Example 2. This example illustrates a classical representation of the scenario ‘UAV -M domain’ and ‘SUSV-C domain combined with USVS-C domain’ which are described in Example 1:

1. For the UAV-M domain: a UAV-M planning domain is formulated with a drone (UAV₁₁), a region (R₁), a base of life (B₁₁), three locations (L₁₁, L₂₁, L₃₁), six dirty zones (Z₁₁, Z₄₂, Z₆₃, Z₂₂, Z₃₂, Z₅₃) and five vehicles (USV₁₁, USV₃₁„ USV₂₆, USV₄₆, USV₆₆). The set of constant symbols is given by {UAV₁₁, R₁, L₁₁, L₂₁, L₃₁, B₁₁, USV₁₁, USV₃₁, USV₂₆, USV₄₆, USV₆₆}. One of the states is the state 3 illustrated in Figure 13.

   S3 = belong(B₁₁,R₁), flapoutbase(UAV₁₁, B₁₁), start-monitor(UAV₁₁, R₁), discover(UAV₁₁, Z₁₁), discover(UAV₁₁, Z₂₂), discover(UAV₁₁, Z₆₃), undiscover(UAV₁₁, Z₃₂), undiscover(UAV₁₁, Z₄₂), undiscover(UAV₁₁, Z₅₃), supervise(UAV₁₁, E₁₁), supervise(UAV₁₁, E₃₁), adjacent(L₁₁, L₂₁), adjacent(L₂₁, L₁₁), adjacent(L₂₁, L₃₁), adjacent(L₃₁, L₂₁), occupied(L₁₁), occupied (L₂₁), occupied(L₃₁).

Figure 13

UAV-M planning domain.

1. For the SUSV-C domain combined with USVS-C domain: an SUSV-C domain is illustrated with the USVS-C domain including a region (R₁), three locations(L₁₁, L₂₁, L₃₁), eleven cleaning vehicles (USVR₃₄, USV₂₂, USV₅₂, USVR₆₂, USV₇₄, USV₄₄, USV₂₅, USV₅₅, USV₈₅, USV₆₆, USV₇₆), a crane (C₁₁) and five dirty zones (Z₁₂, Z₄₂, Z₆₃, Z₂₂, Z₅₃). The set of constant symbols is {R₁, L₁₁, L₂₁, L₃₁, USVR₃4, USV₂₂, USV₅₂, USVR₆₂, USV₇₄, USV₄₄, USV₂₅, USV₅₅, USV₈₅, USV₆₆, USV₇₆}. Figure 14 illustrates a state of this domain.

   S3 = belong(C₁₁, L₁₁), holding(C₁₁, USVR₃₄), end-clean(USV₅₂, USV₆₂, USV₂₂, Z₂₄₂), start-clean(USV₇₄, USV₄₄, Z₄₂), start-clean(USV₅₅, USV₂₅, USV₈₅, Z₅₃), start-clean (USV₆₆, USV₆₇, Z₆₃), at(USV₂₂, USV₅₂, USV₆₂, L₂₁), replace(USVR₃₄, USVD₄₄), replace(USVR₃₄, USVD₄₄), at(USV₃₄, L₁₁), adjacent(L₁₁, L₂₁), adjacent(L₂₁, L₁₁), adjacent(L₂₁, L₃₁), adjacent(L₃₁, L₂₁), occupied(L₁₁), occupied(L₂₁), occupied(L₃₁).

Figure 14

SUSV-C planning domain combined with USVS-C planning domain.

5.2.1 Scenario 1: Zone with a strong degrees of dirt

This first scenario shows the simulation results of a dirty zone with strong degrees of dirt. These results give the curves of DEC1 (or DEC), DCEC and TEC of USV_cz swarm for the two proposed solutions:

1. Result of displacement Energy Consumption (DEC1): Figure 18 shows the results of the displacement energy consumption of each USV_cz swarm from the base of life to its dirty zone. The modified-GA was compared with the modified-AA in terms of energy consumption (DEC1). It can be noted that the DEC curve of the modified-AA is less than the DEC curve of the modified-GA with a minimum gain of 1.01% and a maximum gain of 3.51%. Therefore, USV_cz consumes less energy to plant its trajectory using the modified-AAalgorithm compared to the modified-GAwith an average gain of 2.62%.

2. Result of displacement-cleaning energy consumption (DCEC): Figure 19 shows a simulation to evaluate the USV_cz swarm behavior by its energy consumption for displacement and cleaning its dirty zone. Table 2 shows that the DCEC of the modified-AA decreases when the swarm is composed of 3, 4, 6 and 7 USV_cz compared to the second DCEC with a low minimum gain of 0.5%. On the other hand, it increases rapidly when the swarm contains 5 USV_cz with a maximum gain of 1.20%. Thus, the modified-GA is generally better than the modified-AA to move and clean with a USV_cz swarm in a zone with strong degrees of dirt. Therefore, an average gain of 0.4% is obtained.

3. Result of total energy consumption (TEC): the two previous results were combined to calculate the total energy consumption based on the two proposed algorithms. Figure 20 shows that the TEC curve of the modified-AA is below the TEC curve of the modified-GA with a minimum gain of 1.13% and a maximum gain of 3.5%. Therefore, the proposed modified-AA proposal consumes less energy than the modified GA with an average gain of 2.4% in a zone with a strong degrees of dirt.

Figure 18

Displacement – energy consumption in a zone with a strong degrees of dirt.

Figure 19

Displacement – cleaning energy consumption in a zone with a strong degrees of dirt.

Figure 20

Total energy consumption in a zone with a strong degrees of dirt.

5.2.2 Scenario 2: Zone with a low degree of dirt

The second scenario shows the simulation results for a zone with a low degrees of dirt. These results give the curves of DEC1 (or DEC), DCEC and TEC of USV_cz swarm for the two proposed solutions.

1. Result of displacement energy consumption (DEC1): Figure 21 shows the results of DEC1 of each USV_cz swarm from the base of life to its dirty zone. The modified-GAwas compared with the modified-AAwith respect to DEC1. It can be noted that the DEC1 curve of the modified-AA is less than the DEC1 curve of the modified-GA with a minimum gain of 0.63% and a maximum gain of 3.4%. Therefore, the USV_cz swarm consumes less energy to plan its trajectory using the modified AA algorithm compared to the modified-GA with an average gain of 1.71%.

2. Result of displacement - cleaning energy consumption (DCEC): Figure 22 presents a simulation that evaluated the USV_cz swarm behavior in DCEC in a zone with a low degree of dirt. Table 3 shows that the swarms of 3, 4, 5 and 7 USV_cz consume almost the same displacement energy and clean-up by applying the modified-AA and modified-GA with a minimum gain of 0.01%. In addition, the amount of energy consumed by a swarm of 5 USV_cz using the modified-AA increases rapidly with a maximum gain of 0.4% compared to the modified-GA. Thus, the modified-GA is generally better than the modified AA in moving and cleaning for the USV_cz swarms in this dirty zone with an average gain of 0.4%.

Figure 21

Displacement energy consumption in a zone with a low degrees of dirt.

Figure 22

Displacement – cleaning energy consumption in a zone with a low degrees of dirt.

1. Result of total energy consumption (TEC): the two previous results were used to calculate TEC based on the two proposed algorithms. Figure 23 shows that the TEC curve of the modified-AA is below the TEC curve of the modified-GA with a minimum gain of 0.63% and a maximum gain of 3.4%. Therefore, the proposed modified-AA consumes less energy than the modified-GA with an average gain of 1.64% in a zone with a low degree of dirt.

Figure 23

DTotal energy consumption in a zone with a low degrees of dirt.

5.2.3 Discussions

The USV_cz swarm trajectory planning applied in this approach is based on two modifiable meta-heuristic methods: modified-AA and modified-GA. The implementation of these algorithms shows that the modified-GA takes a lot of computation time in the execution of its steps compared to the modified-AA. Thus, the convergence of its best solution reached a number of strong iterations compared to the modified-AA. In addition, a single path obtained / generated by the modified-AA is applied to a USV_cz swarm in a sequential manner to arrive at its zone. However, the modified-GA generates a trajectory for each USV_cz of a swarm while respecting the shape of a swarm. Therefore, the results of the simulation show that the USV_cz swarm consumes less displacement and cleaning energy using the modified-AA compared to the modified-GA in zones with different degrees of dirt.

5.2.4 Positioning of the approach

This section positions the proposed approach in relation to the related works cited in Section 2. Each study mentioned has the characteristics / parameters that differentiate it from the others. Table 4 shows a comparison study of these studies and the advantage of the proposed approach. In this hybrid approach, a method of cooperation and coordination between a General_crd, a semi-autonomous UAV_mr, and a USV_cz swarm was proposed to accomplish the cleaning missions of dirty oceanic regions contrary to the work of [17]. In [17], the authors developed a complete frame-work for the design and control of swarms of autonomous collaborative robots, with particular emphasis on quad-copters collaborating with each other to perform space tasks.

Furthermore, the work in [13] proposed a trajectory planning guidance system based on a USV_cz swarm. In addition, the article of [3] enhanced the first system for an ASVs, an AUV and a guide. The UAV_mr of this approach locates and detects the dirty zone on the basis of its sensors like the developed USV [19], which enables the location of the gas source in the sea by two gas sensors. In [21], it extracts a sample of the surface water and runs an image-based detection algorithm to confirm the presence of oil. Depending on the data received and the map being explored by the UAV_mr, the general coordinator can send a swarm of USV_cz to each dirty zone by executing Algorithm 1.

Thus, in this paper two solutions were proposed for the trajectory planning from the base of life to the dirty zone for each USV_cz swarm. The first solution is based on a modified-GA compared to the GA proposed in [24]. While the second modified solution is inspired by the ant algorithms proposed in [6, 25]. The swarm is moved in a square grid (space 2 D) discretized by UAV_mr (Sup_mr). The cells are marked based on the degrees of dirt that the UAV_mr processes according to the colors captured. On the other hand, the work of [5] used a grid that is modeled by black (obstacles) and white (clean) cells. In addition, a Voronoi free space scheme for modeling the work environment used in [12]. The swarm applies both solutions to find its trajectory with less distance. The fitness function of the modified-GA is calculated in relation to the energy consumed between the positions traveled and the energy consumed by all the actions performed (turn left / right or continue directly) by USV_cz.

On the other hand, the fitness of [9, 12, 22] is based on the distance traveled and the Euclidean distance of the goal. The tournament selection method was applied in the modified AA while the roulette method was applied in [9, 11]. The USV_cz swarm trajectory planning problem was managed to find its shortest trajectory. During simulation, it was noticed that the proposed algorithm MMAS [11] offers very good performances for the optimal path compared to a GA and an algorithm A*. Thus, the GA of [9] has a higher average performance than the one proposed by A* and C*. For this purpose, a dirty zone cleaning algorithm was applied to the USV_cz swarm where each swarm can at the same time move and clean its dirty cells without specifying how to remove the dirt (the oil spill). On the other hand, the swarms of labor robots [20] can place the barge with oil suction equipment and move it to another location to remove the oil more safely.

The two proposed solutions were also compared with respect to the two different scenarios, namely a zone with a homogeneous degree of dirt and a zone with a strong degree of dirt. These scenarios were simulated according to three metrics: energy consumption of displacement of the base of life towards the dirty zone, energy consumption of displacement and cleaning in the dirty zone, and total energy consumption. The simulation results obtained confirmed the choice to use both solutions. Thus, the modified-AA algorithm gives encouraging results compared to the modified-GA algorithm.