Manufacturing, development and control of a two-way 3D printed soft actuator actuated with SMAs

In this contribution, the development of a novel two-way 3D printed soft actuator actuated with shape memory alloys (SMAs) is presented, considering all the stages from the design, manufacturing, control, and implementation. The SMAs are integrated into the 3D printed composite using thermoplastic polyurethane (TPU). In order to measure the deflection of the soft actuator a computer vision system was implemented. With these measures and using system identification techniques, a mathematical model was developed, which describes the dynamics of the prototype and helps to design of a controller. However, precise control of deflection in systems actuated by SMAs is challenging due to their inherent nonlinearities and hysteretic behavior. To face this challenge, a proportional-integral (PI) controller was designed based on robust stability conditions. The effectiveness of the designed PI controller was validated through experimental results.


Introduction
Soft structures have been becoming relevant due to their ability to modify their properties in response to external stimuli, which makes them highly versatile in fields like aerospace, biomedicine, and robotics [1].Smart materials can work as sensors and actuators in order to drive, control, or support these structures [2].Shape memory alloys (SMAs) are one of the most popular smart materials used for developing soft actuators since they can change their properties when they are exposed to thermal stimuli, producing relatively large displacements and higher force-to-weight ratios compared to other smart materials that are used for actuation.By integrating smart materials into soft structures, it is possible to construct soft actuators that are lightweight and flexible.Heating SMAs can be achieved by passing electrical current or exposing them to thermal radiation [3][4][5][6].
There are many works about manufacturing active compliant parts, compared to the conventional molding process, 3D printing technology enables the customization of the design.A highly compliant structure gives us an advantage in high resolution, rapid prototyping, and lightweight construction.Additionally, the direct integration of wire-shaped SMAs into the structure results in a soft structure capable of active deformations [7].
The works in [8][9][10][11] the passive deformable parts and active parts were manufactured separately and then linked together through suitable mechanisms.Lohse et al. [12] and Mersch et al. [13] developed a novel type of actively deformable composites by knitting SMA wires into glass fiber fabrics and impregnating them with liquid silicone rubber.Instead of knitting SMA wire on a fiber fabric, Wang et al. [7] designed a cavity for SMA wire in the 3D printed matrix to give the SMA wire shape and integrate it into the matrix material and the experimental results illustrate the feasibility and reliability of this manufacturing approach.
SMA wires were fully integrated into the matrix material in [12,13], eliminating the need for subsequent installation of SMA wires and allowing for movements that are more complex by adjusting the configurations of different components within the composite material.However, the actuator prototypes in these studies could only deform in one direction.Therefore, the present study aims to create an actuator prototype that can deform in two directions and develop a control system to enable it to achieve a desired deflection.
In order to obtain a mathematical model of the actuator dynamics, system identification techniques can be used to obtain simplified equations.In [14][15][16], the relationship between the inputs and outputs of the system is studied using a rational transfer function that incorporates the system nonlinearities as unstructured uncertainty.
In this study, we present the manufacturing, development, and control of a 3D-printed soft actuator driven by two shape memory alloys (SMAs).In our design, the soft matrix of the actuator is created as a highly compliant structure and 3D-printed using thermoplastic polyurethane (TPU), with U-shaped SMA wires embedded during the 3D printing process.Benefiting from the symmetrical integration of two SMA wires inside the matrix material on both sides at out-of-neutral plane positions, the prototype can deform in both directions.Due to the hysteretic behaviour of SMAs and their inherent nonlinearities, controlling SMA-driven samples remains challenging.Therefore, we proposed a control technique that ensures robustness and precision to achieve a specific deflection.
This paper is organized into six sections.Section 2 describes the manufacturing process.Section 3 is dedicated to the experimental setup for the computer vision system used to measure the deflection.Section 4 discusses the identification of the model.Section 5 focuses on the control strategy to achieve the desired deflection.Finally, in Section 6, a brief summary of the conclusions is provided.

Actuator Manufacture
To enable automated manufacturing and rapid prototyping, 3D printing technology is utilized due to the advantages it offers, such as high resolution and custom design capabilities.This technology allows customization not only for the complex shape of the part but also for tailoring the stiffness distribution and creating anisotropic structures within the material.Additionally, 3D printed parts can reduce their mass by decreasing the percentage of infill, a feat difficult to achieve with traditional injection molding methods.
Two U-shaped SMA wires were integrated into the matrix symmetrically on both sides out of the neutral plane.By activating one of the two SMA wires, the soft actuator can be bent in the direction close to this SMA wire.The SMA wires used in this study are Nitinol SMA wires (SmartFlex® 300 µm) with a diameter of 0.3 mm, produced by SAES Getters (Lenarte, Milan, Italy, 20045), and pre-stretched to 4%-5% during the manufacturing process.The actuator matrix was 3D printed using thermoplastic polyurethane filament (TPU Flex Semisoft) with a hardness of A88, supplied by Filamentworld (89231 Neu-Ulm, Germany).The activation mechanism is similar to that of [7].
In Fig. 1, the fabrication of the actuator is shown.It consisted of two main steps: overbraiding the SMA wires and embedding the overbraided SMA wires into the TPU matrix.The SMA wires were first overbraided by copper wire and polypropylene fibers using a method similar to that of [13] it can be seen in Fig. 1 (left).Since the braided tube around the SMA wires is flexible, the SMA wires can slide inside the tube, ensuring that the shortening of the SMA does not disrupt the structure of the TPU matrix.For embedding the SMA wires, two cavities were cut out inside the matrix.A post-processing script called 'pause at height' was used in the slicing software CURA to temporarily stop the 3D printing process in the second last layer of the cavity, and then continue the printing after sequentially embedding the SMA wires, as shown in Fig. 1 (middle).Fig. 1 (right) illustrates the dimensions of the specimen.Additionally, we built a test bench and pre-stretching mechanism to properly stretch the SMA wires, in this way the pre-stretch force can be defined and the experimental results can be reproducible.The Fig. 2 shows a picture of the actuator prototype and the test bench setup.

Experimental setup for the computer vision system
In order to measure the deflection of the actuator an experimental setup for computer vision was implemented.This setup consists of a power supply, a light ring, a camera (Intel RealSense), a computer, a driver circuit, and an Arduino UNO as can be shown in Fig. 3.The deflection could be calculated using computer vision; for this purpose, we used three reference points with different colors.The blue and green points are on the actuator, and the red point is on the test bench.It is important to notice that the only mobile point is the green point.In Fig. 4, the actual actuator is on the left, and a sketch of the actuator with the variables used to calculate the deflection d is on the right.To calculate the deflection with the camera, we identify each of the circular areas that are red, green, and blue.Then, the centroid of each circle is calculated, allowing us to find the vectors ⃗ r BR and ⃗ r BG .Then we proceed to find the angle α in radians, using the equation 1.
Therefore α is calculated as Then we proceed to calculate the deflection d in pixels To obtain the deflection d in millimeters, it is necessary to know the distance between the blue and red points, in order to have the conversion factor that is | ⃗ r BR | [mm] = 125mm Then we can calculate the deflection d in mm In Fig. 5, the flow of all signals can be observed.Firstly, when the actuator undergoes deformation (step 1), a camera captures this change as an image (step 2).The captured image is then processed using MATLAB (step 3), where, through necessary calculations, the system determines both the angle and the deflection of the actuator.In this case, the deflection serves as the control variable and provides feedback for control.Additionally, within the MATLAB environment, the user configures the input signal and computes the control signal, which is subsequently transmitted to an Arduino.The Arduino, acting as the interpreter of the control signal, generates precise PWM (Pulse Width Modulation) signals (step 4).These PWM signals are then fed into the driver circuit (step 5).The primary function of the driver circuit is to receive digital signals from the Arduino and transform them into appropriate current levels needed to heat the SMA wires.Finally, the process starts again from step 1, closing in this way the loop.This closed loop is run in real time with a period of 0.025 [s].

Modeling
A mathematical model is used to provide a description of the dynamic behavior of a system, various approaches could be used such as the ones seen in [15,16].The approach followed in this contribution is system identification; it includes measuring the inputs and outputs that are involved in the systems and then constructing a model that closely matches with measured data.
The soft actuator can move in two directions for the purposes of the experiments when we activate the first SMA wire the actuator bends in clockwise direction it is taken as a negative deflection.Conversely, when the voltage is applied to the second SMA wire, the actuator bends in the opposite direction and the deflection measured will be taken as positive.
A process similar to the one used in [15,16] to obtain the model is followed.Firstly, in order to obtain the measurements for the input and the output, several actuation tests were performed.In Fig. 6, the input applied for the experiments and the outputs obtained can be observed.When the first SMA wire is heated up, the maximum deflection is 54 mm, and when the second SMA wire is heated up, the maximum deflection is also 54 mm.
Firstly we observe that the output obtained corresponds to the behavior of a first-order linear time-invariant system without overshoot.Therefore, the data measured of the input and output were utilized to obtain the parameters of the first-order transfer function by using the structure shown in (5) where K is the gain and it is in millimeters per volt [ mm V ] and T is the time constant in seconds [s].

Control
A crucial step in designing a robust controller involves the consideration of the potential uncertainties that could affect the behavior of the prototype.These uncertainties may include unknown nonlinearities, parametric variations, non-model dynamics, and more.Based on [17] and the research conducted in [15,16], we use a robust stability approach to achieve robust performance for the prototype, even in the presence of uncertainties.In this case, we utilized additive and multiplicative uncertainties models, assuming that the nominal transfer function of the plant is represented by G(s).The perturbed transfer function G(s) can be described for additive uncertainty as (6) and for the multiplicative as ( 7) In these formulas, W (s) represents a proper and stable weight function that characterizes the uncertainty dynamics, while ∆(s) contains the uncertainty itself, which can be any stable transfer function that satisfies the inequality ||∆|| ∞ ≤ 1.To satisfy these conditions, an appropriate weighting function W (s) and ∆(s) for additive uncertainty using the results in [15].Then, assuming an additive uncertainty, the closed loop system is according to [17] robustly stable if and only if ||W C S|| ∞ ≤ 1.And in the case of the multiplicative, the condition for robust stability is given by ||W T || ∞ ≤ 1.
To control the deflection of the soft actuator a proportional-integral (PI) controller is proposed specially because we are working with a first-order system.This controller is tuned based on the robust stability conditions where the proportional and integral actions, are the coefficients K p and K i , respectively.In ( 8) is shown the transfer function for the control.The (nominal) open-loop transfer function of the system with the controller is expressed as: The (nominal) corresponding complementary sensitivity functions are: By substituting the above equations into the robust stability condition for each uncertainty model, a range of valid combinations that guarantee the robust stability of the system is calculated.Fig. 7 shows the set of valid combinations of K p and K i for both additive and multiplicative uncertainties.The goal of the controller in the prototype is to achieve the desired The performance of the control can be seen in Fig. 8, and it can also be noticed that the system is capable of reaching the desired references.

Conclusions
This contribution helped us to generate invaluable insights for future advancements in our project.The use of 3D manufacturing techniques has empowered us to explore different structures and designs, opening the door for experimenting with diverse configurations and highcompliance structures in the future.Furthermore, employing the computer vision system has proven an excellent performance in obtaining highly accurate measurements of both deflection and angular deformations.This system has helped us enhance the mathematical model because we are obtaining more detailed and reliable data.These advancements such as the 3D manufacturing methods, sensing techniques, modeling methodologies, and robust controllers, will lead us to continue working on future designs, models, and controllers that help us to improve the creation of novel soft actuators.

Figure 2 .
Figure 2. Test bench and actual soft actuator.

Figure 3 .
Figure 3. Experimental setup for the computer vision system.

Figure 4 .
Figure 4. Actual actuator and sketch of the actuator and the variables used.

Figure 5 .
Figure 5. Flow diagram of the computer vision system.

Figure 6 .
Figure 6.Input and different measured outputs in different experiments.

Figure 7 .
Figure 7. Valid and invalid combinations for K p and K i to assure robust stability condition for additive and multiplicative uncertainty models.

Figure 8 .
Figure 8. Performance of the controller for the actuator deflection with different references in both directions. )