Closed-loop control of a 3D printed soft actuator with integrated flex sensors and SMA wires

This article presents a soft SMA-driven actuator capable of achieving desired bending angles. To create the actuator, flex sensors and Shape memory alloy (SMA) wires were embedded into the thermoplastic polyurethane (TPU) matrix of the sample during the 3D printing process. By deactivating and activating the two SMA wires according to sensing signals from the flex sensors, the actuator sample can track the input bending angle. This approach enabled closed-loop control and improved the overall efficiency of the system. Additionally, the proposed manufacturing process provides a simple and cost-effective solution for the rapid prototyping and custom design of smart materials with complex structures and high resolutions.


Introduction
Smart materials have become increasingly popular due to their unique ability to sense and respond to stimuli, making them valuable for a wide range of applications.The integration of smart sensing and actuating materials into soft matrices allows for the fabrication of soft actuators, that can be closed-loop controlled.Such multi-functional active soft parts are lightweight, compact, highly deformable and adaptable to a wide range of conditions, allow for seamless movement and precise control to achieve specific movements or adjustments required for a mission.As such, they show great potential for aerospace and space applications in aircraft wing morphing, satellite attitude control, robotic in space missions and deployable structures, such as solar panels or antennas [1].
One of the most commonly used smart actuator materials is shape memory alloy (SMA), which can provide a high level of active force and deformation that other materials cannot achieve [2].SMA wires can be given different complex shapes integrated into flexible matrix by sewing on fiber fabrics using tailored fiber placement (TFP) technology (cf.[2,3]) or embedding into cavities during 3D printing (cf.[4]) to achieve variant and even spatial movement effects.In the TFP sewing process due to the uneven tautness of the fiber fabric, the damage left by the sewing thread on the fiber fabric and the twisting of the SMA wires, the sewing trajectory tends to be shifted, resulting in a undesired deformation, so the method of 3D printing can provide a higher degree of manufacturing precision as well as more repeatable experimental results compared to TFP.In addition, SMA wires are available in a wide range of commercial varieties, making it an easily accessible material.
Flex sensor changes its electrical resistance when bent and offer great advantages for integration into soft actuators due to their large deformation capacity, compactness, versatility, reliability, real-time detection, cost-effectiveness, customizability and ease of use.Giada et al. integrated two flex sensors in opposite direction into a flexible fluid actuators to measure the bending angle in both directions and achieved a closed-loop control [5].
There are mainly four approaches for integrating sensors in soft structures to achieve closedloop control: using self-sensing soft materials, fabricating soft composite materials with sensing components by 2D/3D printing or resin molding process, placing commercial sensors or sensing components into soft matrix and post-installing sensors.Dielectric elastomer actuators (DEAs) have great potential for self-sensing capabilities.Zhang et al. proposed a self-sensing mechanism that utilizes capacitive sensing to detect force actuation in DEA [6].Using special printing materials with sensing properties, custom sensors can directly produced by 2D or 3D printing.Leigh et al. present a formulation of a conductive composite material that can be used for 3D printing and demonstrate how its piezoresistive properties can be utilized to sense mechanical bending and how the material can be used to create capacitive sensing devices [7].Correia et al. presents strain sensors with different configurations developed by 2D inkjet printing technology and tested their performance [8].In some cases, soft structure of the actuator or the actuator itself can be 3D printed.Combined with 2D/3D printing of sensors, composites with sensing and actuation functions can be rapid manufactured and customized to enable closed-loop control of the component.However, 3D printing of such smart materials often requires relatively expensive multi-material 3D printers with high print accuracy.Mersch et al. created a soft actuator by braiding copper wire around a SMA wire and subsequently injecting it with silicone [3].They monitored the temperature on the SMA wire's surface by assessing the alterations in the copper wire's resistance.Resin molded soft sensing composites require more complex fabrication steps than 3D-printed ones.Lehmann et al. attached commercial sensing components to the semifinished non-woven product using polyurethane adhesive at specific fixing points to manufacture a ePreform, which was placed between two glass fiber fabrics and embedded in a wet pressing process [9].Integration of commercial sensors or sensing components also involves complex manufacturing processes and even expensive machinery but does not require sensing material development costs.Walters et al. installed a pair of resistive flex sensors inside a 3D printed soft actuator to sense the actuator deformation [10].Post-installation integration methods involve specialized design of the flexible structure to make it suitable for sensor installation and circuit connections.
The Manufacturing and closed-loop control of soft actuators still remains a significant challenge primarily due to the absence of sensors that are robust and reliable, and cost-effective enough to be integrated into highly deformable actuator structures [5].This requirement is further complicated by the need for sensors that can be incorporated using low-cost materials and manufacturing processes.This work is an extension of [4] to develop a cost-effective approach for manufacturing and closed-loop controlling soft SMA-driven actuators integrated with commercial flex sensors and capable of bi-directional bending and achieving desired bending angles.
The remaining parts of this article are organized as follows.Section 2 describes the materials used, the specimen design and manufacturing process.Section 3 presents the flex sensor calibration, mathematical model and controller design of the actuator.Section 4 shows experimental results and discussions.Section 5 proposes conclusions and suggestions for future work.1, two SMA wires are placed outside the neutral plane within the compliant matrix of the actuator sample.These SMA wires possess a partial two-way shape memory effect, allowing them to alter their length in response to temperature changes.When an electric current is applied to one of the SMA wires, it undergoes a reduction in length, inducing mechanical strain within the layer where they are located and causing the sample to bend in the direction of the activated SMA wire.Conversely, activating the other SMA wire leads to bending in the opposite direction.As the temperature of the SMA wire decreases, it reverts to their original length, causing the sample from bent to straight.By controlling which SMA wire is activated, the duration of activation, and the applied voltage, it enables fast reversible bending in the actuator sample and precise control of the bend angle.

Manufacturing process of the actuator sample
The presented work employed identical manufacturing method and materials as described in [4], as shown in Figure 2. To enhance the sample's flexibility in the axial direction, a prismatic structure was incorporated into the matrix design.Furthermore, for precise control, two flex sensors (model FS-L-0095-103-ST by Spectrasymbol, Salt Lake City, UT 84119, USA) were positioned adjacent to each other in the neutral plane of the sample.These sensors were oriented in opposite directions and were used to measure the bending angle of the sample in both clockwise and counterclockwise directions for closed-loop control.Input is the target bending angle that we want the system to achieve or maintain.It serves as a reference for the control system.The controller continuously adjusts the actuator's output based on the feedback from the flex sensors to maintain the actual sample deformation as close as possible to the input, effectively regulating the system's behavior.In order to calibrate the flex sensors, several tests were conducted to establish the correlation between the output response and the bending angle of the sample.The experimental results, as depicted in Figure 5, demonstrate significant linearity as well as repeatability.A line graph is drawn as a calibration curve based on the green data that highly overlaps with the other measurements.The calibration curve was used to convert raw sensor readings into angle measurements.

Modeling of the sample deformation behavior
The dynamic deformation behavior of the actuator sample was modeled using system identification, which involves creating mathematical models of dynamic systems based on experimental data.In a process similar to the one described in [11], actuation tests were carried out using a step signal as the input.The displacement at the tip of the actuator sample was measured by optical method.As shown in Figure 6a, the dynamic deformation behavior aligns with the characteristics of a first-order linear time-invariant system without overshoot, allowing  for the implementation of a PI (Proportional-Integral) controller to achieve precise control and model the sample using a first-order transfer function, as depicted in Equation 1, where K represents the gain and t is the time constant.
Based on the test results, the parameter ranges of gain and time constant were determined: The nominal transfer function G(s) of the system is calculated by averaging the values of the parameters.

Controller Design
In order to determine the setting parameters K i and K p of the PI controller, a robust stability analysis was performed based on the variation of the parameters K and T in the mathematical model, see and K p is in the blue area, the control system can still maintain stability and reliable operation even if it is affected by changes or uncertainties.After several tests, the combination of K p = 50 and K i = 2.5 is finally selected as the setting parameter of PI controller.Figure 8 shows the PI controller created in Matlab.

Set up of the control system
Figure 9a is a photo of the test bench.Figure 9b shows the setup and data stream of the control system.In the presented control system, the PI controller in Matlab regulates the voltage supplied to the sample via the Arduino and driver circuit.As the sample undergoes deformation, the resistance of the flex sensor changes accordingly.The measurement circuit conditions this signal and relays it back to the controller through the Arduino.The controller calculates the necessary adjustments to achieve the desired set point and repeats these steps continuously, thereby achieving closed-loop control.

Experimental Results and discussions
The response of the actuator sample when subjected to a typical step reference signal is illustrated in Figure 10.The real system response is measured by a optical method.In order to evaluate the performance of the actuator sample, 40 tests as shown in Figure 10 above were performed.The error in the measured bending angle using flex sensors compared to the actual angle was −0.01 • ± 1.42 • (mean ± standard deviation (SD)).Figure 11a illustrates how these errors relate to different bending angles, with a notable trend: flex sensors are more precise at smaller angles.The average bending angle overshoot after reaching the target steps was 0.41 • ± 0.60 • (mean ± SD). Figure 11b

Conclusions and future works
In conclusion, our work has explored a promising approach for manufacturing and controlling SMA-driven elastomeric composites with self-deformation sensing capabilities.A actuator sample was 3D printed with integrated SMA-wires and flex sensors, which allow the actuator to bend in two directions and demonstrate promising closed-loop-controllability.A mathematical model was established to describe how the actuator sample responds to constant voltage stimuli

EASN-2023
Journal of Physics: Conference Series 2716 (2024) 012050 using system identification method.A control system was developed in Matlab.Moreover, the controller parameters was optimized using robust stability methods, leading to satisfactory control accuracy.
Looking ahead, there are several avenues for further research and improvement.Using low-friction PTFE tube instead of braided tube improves the accuracy, response time and overshoot of the actuator sample.Continuous improvement of controller parameters is essential to achieve higher levels of control accuracy and system responsiveness.To ensure the robustness of the proposed controller system, there is a need of on its anti-interference capability.The proposed manufacturing and controlling approach can be applied to different actuator configurations, extended to 2.5D deformations and achieve adaptability to diverse scenarios.

Figure 1 .
Figure 1.Deformation mechanism of the actuator sample.

Figure 5 .Figure 6 .
Figure 5. Output signal of the measurement circuit under varying sample bending angles.

Figure 7 .Figure 7 .
Figure 7. Diagram of K p and K i combinations for robust stability analysis.

Figure 9 .
Figure 9. a) Photo of the test bench.b) Setup and data stream of the control system.

Figure 10 .
Figure 10.Closed-loop response of the actuator sample when subjected to a step reference signal.

Figure 11 .
Figure 11.a) Average measurement error of the flex sensors calculated during 40 tests.b) Average bending angle overshoot after reaching the target steps during 40 tests.c) Average response time for 10 s during 40 tests, which is the time taken to reach the next step for the first time.
Design and manufacturing process of the actuator sample 2.1.Deformation mechanism of the actuator sample As shown in Figure 3 2.