Fig.1

Schematic diagram of virtual leader and reference trajectory

Fig.2

Schematic diagram of multi-stage safe formation transformation method for UAVs formation

Table 1

Key symbols and meanings

Fig.3

Schematic diagram of a virtual leader passing through a narrow corridor

Fig.4

Schematic diagram of formation transformation for passing through a narrow corridor

Fig.5

Schematic diagram of safe configuration solving for each trajectory point

Fig.6

Schematic diagram of chromosome encoding method in genetic algorithm

Fig.7

Schematic diagram for deriving relationship between two Euclidean distance multiples

Fig.8

Schematic diagram of maximum multiple of distance change from a point to a distorted curve

Fig.9

3D schematic diagram of virtual leader trajectory

Fig.10

Comparison of trajectories projected onto xy-plane between unimproved MILP and improved MILP algorithms

Fig.11

Velocity and acceleration magnitude curves of virtual leader trajectory generated by improved MILP

Fig.12

Velocity and acceleration magnitude curves of virtual leader trajectory generated by unimproved MILP

Fig.13

di and di,safe for each trajectory point

Fig.14

Schematic diagram of safe configuration at narrowest position solved by genetic algorithm

Table 2

Genetic algorithm parameters setting and experiment results

Fig.15

Computed trajectory results of UAVs

Fig.16

UAVs velocity optimization results

Fig.17

UAVs acceleration optimization results

Table 3

Nonlinear optimization parameters setting and experiment results

Fig.18

Time reallocation results of UAVs velocities

Fig.19

Time reallocation results of UAVs accelerations

Fig.20

Trajectories of UAV swarm generated by vector potential field method

Fig.21

Relative initial configuration differences between vector potential field method and multi-stage safe formation transformation method for UAVs formation

Table 4

Comparison of multi-stage safe formation transformation method for UAVs formation and distributed model predictive control method