# Control-Based 4D Printing: Adaptive 4D-Printed Systems
## 4 Adaptive 4D-Printed Systems Design  
The synergic integration of the main components to develop adaptive 4D-printed systems are explained in this section (Figure 3). In addition to the incorporation of 3D-printed sensors and 4D printing, controller units are required to command the necessary input to the 4D-printed system based on the acquired information. The 4D-printed systems developed so far are mainly reliant on the morphology of soft materials rather than the sophisticated control methods. However, considering the potential exposure to a wide range of dynamic environments, 4D-printed systems demand more robust controllers, particularly in highly sensitive tasks. A closed-loop controller for the 4D-printed soft robots was recently introduced in order to improve the performance of the soft robots [112]. The active control of 4D prints was achieved by combining the 3D-printed shape-memory polymer composites with a controller that regulated power input to the composite in order to manipulate the material's heating behavior, considering the variations in resistance caused by the changes in strain or temperature [113]. However, the dynamic modeling of such systems was not simply due to their non-linear behavior, infinite degrees of freedom, hyperelasticity, heterogeneous materials properties and hysteresis [114]. In other words, predicting the motion of the actuators based on the input-stimuli could not readily be calculated via the inverse kinematics equations used in the rigid bodies such as the Cosserat rod theory [115] beam theory [116] and constant curvature model [117] methods, because of the computational expenses and steady state assumptions [118]. Therefore, machine-learning methods could be an appropriate choice to realise adaptive 4D-printed systems [119]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Proprioceptive** & & & & & \\
**Feedback** & **Sensors Type** & **Mechanisms** & **3D Printers** & **Materials** & **Applications** \\ \hline \multirow{8}{*}{_Mechanical_ _Motions and Deformations_ _Measurements_} & \multirow{3}{*}{Stress} & Capacitive [99] & Extrusion & Ionic gel & \\  & & Optical FBG [82] & FDM & ABS & \\  & & Piezoelectric [80] & EPAM & PVDF & \\ \cline{2-6}  & \multirow{3}{*}{Strain} & Capacitive [100] & Extrusion & Silicone & \\  & & Optical waveguide [101] & FDM & OrmOClear & \\  & & Resistive [102] & FDM & TPU & \\ \cline{2-6}  & \multirow{3}{*}{Displacement} & Eddy current [103; 104; 105] & FDM & ABS/Copper & \\  & & Hall effect [72] & FDM & ABS/Magnetite & \\  & & Optical waveguide [106] & Inkjet & InkEpo/InOrmO & \\ \cline{2-6}  & \multirow{3}{*}{Tactile} & Piezo-resistive [68] & FDM & TPU/CNT & \\  & & Capacitive [107] & FDM & TPU & \\ \hline \multirow{8}{*}{_Environment Measurements_} & \multirow{3}{*}{Bio} & Bioluminescence [94] & FDM & ABS/PLA & \\  & & Electrochemical [108] & SLA & PEGDA & \\  & & Vibratory [109] & DLP & Bisphenol & \\ \cline{2-6}  & \multirow{3}{*}{Chemical} & Chemoresistive [92] & FDM & PVDF/MWCNT & \\  & & Electrochemical [91] & FDM & PLA/Graphene & \\ \cline{1-1}  & & Optical waveguide [110] & SLA & Accura®60 & \\ \cline{1-1} \cline{2-6}  & Humidity & Solvatochromic [88] & Extrusion & Cu(II)-Thymine & \\ \cline{1-1} \cline{2-6}  & Temperature & Capacitive [111] & DLW & Nanocrystals & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sensors integration into 4D printing. To equip the 4D-printed systems with adaptive controllability required for real-world dynamic variations, ML algorithms are suitable solutions due to recent advancements in nonlinear systems modeling [120; 121; 122]. The finite element model (FEM) is employed to train the ML algorithm to effectively calculate volumetric properties such as spatially heterogeneous mechanical strengths, variable stiffness and the targeted anisotropy during the 4D-printing process. Further, the control algorithms will be developed and incorporated into the 4D-printing platform to compute the precise actuation signal to adapt to the uncertain and dynamic environments [123; 124; 125; 126].