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Kulkarni et al. Soft Sci. 2025, 5, 12 https://dx.doi.org/10.20517/ss.2023.51 Page 21 of 35

Many of these control strategies also require models of the soft robotic device to analyze the material
dynamics of the device in response to the actuation mode. However, due to the nonlinear structure of soft
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robots, it can be difficult to develop mathematical models that accurately represent device deformation .
Finite input, output, and disturbance parameters of the control system can be set to describe actuation.
Additionally, internal memory variables of the soft robot are set using state variables to control the motion
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of the robot across time . Control systems, generally classified as open-loop (OL) and closed-loop (CL)
systems , have utility for different soft devices in various environments.
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Runciman et al. developed soft hydraulic actuators for minimally invasive surgery using an OL position
control system . The actuator contracts by changing the volume of the actuator without feedback from the
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environment. Open loop control systems for fluid-driven assistive robots can be achieved by cycling
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pressure to the actuators . CL feedback control systems have been used for many biomedical applications.
Beatty et al. developed a drug delivery device that uses CL control to change its actuation regimen to
dispense the precise amount of the drug . The device, composed of thermoplastic polyurethane, can
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monitor foreign body response by changes in the electrical impedance to determine the actuation regimen
and efficiently deliver therapeutics.

Model-based (MB) controls use kinematic or dynamic modeling strategies to develop efficient control
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systems for the device . The piecewise constant curvature model is a popular model that divides the soft
robot into sections with constant curvature . FEM methods divide a soft robotic structure into discrete
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elements to obtain a set of partial differential equations to solve at each degree of freedom . In this case,
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FEM can efficiently evaluate the structure and model material deformations once actuated . Model-free
(MF) control systems rely only on feedback data from sensors . MF control systems may be implemented
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for device applications in environments that cannot be accurately described by mathematical tools .
Proportional-integral-derivative (PID) control systems use a signal that consists of the sum of adjustable
proportional, integral, and derivative constant factors multiplied by the error . Therefore, these systems
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help reduce the error between the output and desired signals .
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Adaptive control (AC) systems can be implemented as MB or MF systems and allow for changes in the
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control signal using real-time data collected from the current conditions of the system and the environment.
These control systems make changes to the control signal depending on the known parameter
disturbances . The AC signal allows for the desired performance index to be achieved using a feedback
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loop and an adaptation system which helps reduce errors in the performance of the system . Model
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reference adaptive control (MRAC) systems use a system model to determine the error between the outputs
of the actual system and the model, allowing adjustments to the control signal .
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Reinforcement learning (RL) control systems can be implemented as MF or MB systems . They are based
on action and reward paradigms . The system uses evaluated feedback to determine whether the behavior
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of the robot has improved to achieve the desired action. It also tries to maximize the reward from the
evaluated feedback by implementing different actions. Li et al. developed a deep RL framework for motion
control of an underwater soft robot . The robot could efficiently travel through the environment by
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training a neural network developed using a deep RL algorithm called soft actor-critic. The soft robot was
trained to move in a straight line starting from a random initial position to later learn how to travel through
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the unpredictable environment . Table 3 displays the various control systems that can be used for soft
robots.