Fig.1

Voronoi tessellation and centroidal Voronoi tessellation

Tab.1

Relationship between density function and Voronoi diagram

ρ(q)	密度分布	维诺图	队形
$\mathrm{e}^{-\sigma(a x+b y+c)^{2}}$			直线形
$\mathrm{e}^{-\sigma\left[a\left|x-x_{\mathrm{c}}\right|+b\left(y-y_{\mathrm{c}}\right)+c\right]^{2}}$			V形
$\mathrm{e}^{-\sigma\left[a\left(x-x_{\mathrm{c}}\right)^{2}+b\left(y-y_{\mathrm{c}}\right)^{2}-r^{2}\right]^{2}}$			环形

Fig.2

Switching ring formation

Fig.3

Shape interpolation of density function

Fig.4

Dynamic transition from linear density distribution to annular density distribution

Fig.5

Dynamic density guided formation switching process of Simulation 1

Fig.6

Formation switching directly guided by linear density function

Fig.7

Dynamic transition from annular density distribution to linear density distribution

Fig.8

Dynamic density guided formation switching process of Simulation 2

Fig.9

Robot position error in formation switching process of Simulation 2

Fig.10

Robot cost function of formation switching process in Simulation 2

Fig.11

Desired density directly guided formation splitting

Fig.12

Dynamic transition from linear density distribution to expected density distribution

Fig.13

Dynamic density guided formation splitting process

Fig.14

Direct formation merging guided by annular density function

Fig.15

Dynamic transition from initial formation density distribution to annular density distribution

Fig.16

Dynamic density guided formation merging process

Fig.17

Position error of robot in formation merging process of Simulation 4

Fig.18

Robot cost function of formation merging process of Simulation 4

Tab.2

Average position error and iteration times of formation switching process

Fig.19

Experimental environment

Fig.20

Switching from linear formation to circular formation

Fig.21

Switching from circular formation to linear formation