## 3 Methodology
### Dynamic Task Allocation
Agents can aggregate as a compact group afterwards and fly to the destination as shown in Figure 5. We run the simulation many times with random distribution of obstacles to evaluate the robustness of path planning. Obstacle avoidance and all results turn out to be able to find a satisfactory trajectory to reach the static single goal. Each agent only needs to exchange information with its neighbor teammate because we design the algorithm in a distributed method in computing the path for each agent during the movement. Figure 6 shows the simulation of multiple static targets. The purpose of this simulation is to evaluate the effectiveness of our algorithm in the case of multiple targets and obstacles. In the experiments, we adopted nine agents that were randomly placed around the starting position and took off at the same time to approach four goal targets which are indicated by triangular symbols with a different color in a 2D space. Obstacles were placed randomly between the starting positions of agents and the targets with varying sizes, as shown in Figure 6,b shows the result of the simulation using the proposed method. Agents were grouped into four subgroups and planned the trajectories autonomously. The trajectory and formation are based on minimum costs which include the distance, the compactness of the group without the inter-collision among agents and the collision with obstacles. Figure 5: Simulation of static single target. (**a**) Original toward to the target. (**b**) Finally stop at the target. #### 4.2.3 Dynamic Target

Since in a dynamic situation, the targets can appear and disappear, in order to evaluate the difference of the effects on our methods, we separate the experiments into two aspects, dynamically increasing the targets versus decreasing the targets. Figure 7 shows the simulation of increasing targets. The original targets are denoted by red, yellow and blue triangles. Nine agents launch from the starting positions and are demanded to approach the targets as groups Figure 7a. After 40 iterations of time steps, a new target (indicated as a purple triangle) was added and it turns out that the two subgroups in blue and yellow were reconfigured into three subgroups. We assume the newly added target has the same priority as the original blue and yellow targets. Moreover, the subgroup targets in red did not change their path Figure 7b. Figure 8 target disappeared during the movement after 40 iterations of time steps. It turned out that the red group was split shows the simulation in decreasing a target. Four targets in terms of red, yellow, blue and purple colors and denoted with triangle symbols that appeared initially. A fleet of nine agent launched from the starting position and was demanded to move toward targets as four subgroups as shown in Figure 8a. We tentatively set that the red and joint to other groups that were approaching to the blue and yellow targets, respectively, as shown in Figure 8b. Figure 6: Simulation of static multi target. (**a**) Original toward to the target. (**b**) Finally stop at the target. Figure 7: Simulation of increasing target. (**a**) Original toward to the target. (**b**) Finally stop at the each target. #### 4.2.4 Comparison with the Previous Method CBAA

In this section, we compared the performance between the CBAA and the proposed C-CBAA algorithm when the number of targets varies from one to three. Obstacles are also randomly distributed in the testing scenarios and the target(s) are randomly appeared and disappeared during the movement in the scenarios. The efficiency is based on the average number of iteration steps needed to finish re-allocation task due to the change of targets. We simulated the same scenarios with different number of agents (3, 6, 9, 12 and 15, respectively) and the results are as shown in Table 2 to compare the efficiency at situations with different agent complexity. Figure 9a shows the result of increasing targets while Figure 9b shows the result of decreasing targets.