Table A1.

Definition and explanation of variables.

Variable	Definition	Variable	Definition
R	Bending radius of PAM	$e_1$	Eccentricity of cavity A
$e_2$	Eccentricity of cavity B	$\theta$	Bending angle of PAM
$r_{10}$	Original radius of cavity A	$r_{20}$	Original radius of cavity B
$L_1$	Length of the central axe of cavity A	$L_2$	length of the central axe of cavity B
$C_{i0}$	Yeoh model material parameter.	${\lambda }_1$	Axial stretch ratios
${\lambda }_2$	Radial stretch ratios	${\lambda }_3$	Circumferential stretch ratios
$L_0$	Initial length of the central axis	$R_0$	Initial radius of the PAM
$t_{10}$ $/t_{30}$	The thickness of the front and rear sides of cavity A
$t_{20}$ $/t_{40}$	Thickness of the left and right sides of cavity A
$t_1$ $/t_2$ $/t_3$ $/t_4$	$t_{10}$$/t_{20}$$/t_{30}$$/t_{40}$ after inflating	$\beta$	The variation of the thickness along the bottom to the top
${\rho }_w$	Strain energy density	$E_g$	Gravitational potential energy
$m$	PAM mass	$g$	Gravitational acceleration
$E_w$	Strain energy	$E_k$	Kinetic energy
$s$	The arc length between the point on the PAM and the origin
$f_p$	Generalized force	$V_h\left(\theta \right)$	Volume of the cavity A
$u$	Air pressure	$L_f$	Lagrangian function
$k_1$ $/k_2$ $/k_3$ $/k_p$	Coefficients used to simplify equations	$\xi$	The coefficient for the damping characteristics and resistance
$h_j\left(t\right)$	Gaussian kernel function	$x\left(t\right)$	Input of RBFNN
$c_j\left(t\right)$	The center of the kernel function	$b_j$	The width of the kernel function
W	Weight of RBFNN	$\widehat{W}$	Estimated value of W
$D$	Sample set	${\mu }_i$	Clustering center
$x_j$	A sample in D	$C_i$	$\mathrm{Cluster}\mathrm{belong}\mathrm{to}{\mu }_i$
$d_{ji}$	$\mathrm{Distance}\mathrm{from}{x}_j$ $\mathrm{To}{\mu }_i$	$S_j$	The variance
${\epsilon }_j$	Scaling factor	y	Actual trajectory
$y_d$	Desired trajectory	$\stackrel{̑}{f}\left(x\right)$	Estimated value of f(x)