This work performs vibration suppression and trajectory tracking experiments on a 2-DOF serial flexible manipulator with three predefined motion profiles defined in polar coordinates $(r_d, \varphi_d)$, where $r_d$ represents the tip polar radius reference and $\varphi_d$ is the tip polar angle reference.
Video 1.1, 2.1 and 3.1 present the comparative experimental results between the proposed backstepping boundary control scheme and the conventional LQR + feedforward control strategy. Video 1.2, 2.2 and 3.2 supplement the experimental results of the backstepping boundary control via DeepONet approximation.
$r_d= r_1+ r_2\mathrm{sgn}(\cos(0.4\pi t)), \varphi_d=\frac{35\pi}{180}\mathrm{sgn}(\sin(0.2\pi t))$, where $\mathrm{sgn}(\cdot)$ is the sign function.
Video 1.1
Video 1.2
$r_d= r_1+ r_2(\lfloor 0.4t+0.5 \rfloor-0.4t), \varphi_d=\frac{35\pi}{180}(0.2t-\lfloor 0.2t+0.5 \rfloor)$, where $\lfloor \cdot \rfloor$ is the floor function.
Video 2.1
Video 2.2
$r_d= r_1+r_2\cos(1.2\pi t), \varphi_d=\frac{35\pi}{180}\sin(0.4\pi t)$
Video 3.1
Video 3.2