Soft pneumatic actuators (SPAs) have been extensively researched due to their flexible motions with simple morphological structures and versatility. To improve the functionality of SPAs, various sensors have been integrated for training data obtained from soft pneumatic actuators. Given that the solid-state sensors traditionally used in rigid robots may limit the flexible movements of SPAs, soft and flexible sensors have frequently been integrated to obtain contacts or bending motions of SPAs. In addition, the simple internal pressure sensor data of the SPA was used to improve the functionality of the soft gripper [82]. RNNs were employed for the SPAs, which were integrated with soft resistive sensors to obtain the contact forces and the bending motions [10]. Instead of embedding the sensors into the SPAs, a camera sensor was used to obtain the states of the actuators. To track the 3D trajectories of the SPA, an inverse model was also employed for training, as the application of the nonparametric and online learning of locally-weighted projection regression for endoscopy applications [83]. Jung et al. developed a proprioceptive sensing method of a soft pneumatic actuator based on the GP regression by incorporating with an extended Kalman filtering for state estimation and sliding mode control for the feedback control strategy [84].

Obtaining a kinematic or dynamic model of a soft robot has been a challenge in model-based control strategies. To overcome such limitation, learning algorithms have been applied to acquire the kinematic or dynamic model of soft robots based on SPAs [8588]. An FNN and radial basis function (RBF) neural networks were applied to the inverse or forward kinematic modeling of a soft continuum robot based on SPAs including 3-Dimensional motions [85, 86]. M. Gillespie et al. and P. Hyatt et al. proposed a predictive model based on the neural networks, and a learning method for the linearized discrete state space representation of soft robots [87, 88]. G. Fang et al. developed a learning method based on the local Gaussian Process Regression (GPR) to estimate the motion of SPAs using the kinematic model from the control inputs to the manipulator configurations based on the sequential camera images [89]. Instead of the inverse, or forward kinematic modeling, an asymmetric hysteresis of a pneumatic artificial muscle was modeled by integrating the Convolutional Neural Network and an existing extended up-parallel Prandtl-Ishlinskii model. J. Kim used a Gaussian Process Regression to learn control policy for a simple tripod mobile robot based on membrane vibration actuators [90].

M. Rolf et al. developed learning strategies to obtain an inverse model, which indicates the relationship between the target position and the required control inputs [91]. Instead of modeling the dynamics of a soft robot itself, hysteresis was also predicted for a pneumatic artificial muscle over a wide range of input by combining conventional hysteresis model and the CNN [92]. M. Wiese et al. studied hyperparameter optimizations to model SPAs using a simple FNN [93].

Another approach for controlling the pneumatically actuated soft robot is a model-free learning algorithm, which is a learning method to calculate the control policy without an analytical model. Reinforced learning algorithms such as Q-learning have been usually used for the model-free approaches [94]. In general, the objective of reinforcement learning is to find the control policy that maximizes the expected discount return, which is the weighted sum of rewards received by the agent for the system [95]. X. You et al. and S. Satheeshbabu et al. developed and implemented a multi-segment soft manipulator for planar motions using the Q-learning algorithm [96, 97]. J. Kim et al. used a model-free reinforcement learning algorithm to control a pneumatic actuated tripod mobile robot. They used an adaptive soft actor-critic (ASAC) algorithm and a reinforcement algorithm to obtain an accurate dynamic model of the robot [98].

Commercially available sensors, like depth cameras, film-based flex sensors, and potentiometers, are generally used to estimate the configurations of SPAs with machine learning techniques [85, 88, 89, 91]. On the other hand, as the traditional sensors can be relatively too rigid to be compatible with SPAs that are highly deformable, soft sensors have often been integrated with SPAs to estimate the configurations of soft robots. However, the non-linear behaviors of the soft sensors may cause delays when estimating states of soft robots. For example, T. Thuruthel et al. suggested SPAs integrated with a soft sensor using cPDMS (carbon-polydimethylsiloxane) and film-based flex sensors to estimate contact forces or configurations; they reported that the proposed learning-based model showed longer delays when using the soft sensors compared to the film-based flex sensors due to the high-dimensional deformability of soft sensors [10]. Based on this perspective, it would be an open issue for the future direction to develop soft sensors with fast responses. For instance, the development of three-dimensional printing-based fabrication of soft sensors would be a possible solution to estimate the configurations of SPAs in that it tends to have consistent and fast responses [99]. At the same time, machine learning algorithms need to be developed to overcome the nonlinear dynamic responses of soft sensors when integrated with SPAs. Although [92] showed potentials in that the large hysteresis of the SPAs could be reduced via machine learning algorithms, it was limited to simple linear motions of Pneumatic Artificial Muscles (PAMs). Thus, it is necessary to develop algorithms that deal with the non-linear and hysteresis behaviors of soft sensor-embedded systems with fast responses, as a future goal.

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