What Happens When Pneu-Net Soft Robotic Actuators Get Fatigued?

With an aging worldwide population [1], the demand for accessible rehabilitation and physical therapy is increasing rapidly. The intensity, duration, frequency, and timing of rehabilitative exercises are critical to recovery [2], [3], [4]. For stroke patients, this therapy should be delivered in a timely manner since rehabilitation is most effective in the acute stages [5], [6]. These factors put a high strain on our healthcare system, which calls for the development of in-home therapeutic systems. During the COVID-19 pandemic, the need became pronounced due to concerns of infection spread. In-home rehabilitative robotic devices that can physically interact with patients in an intelligent and safe manner have the potential to address the aforementioned challenges [7], [8], [9].

Rehabilitative technologies such as smart exercise machines and robotic exoskeletons are intended to help improve patient mobility, motor control, and strength by either assisting a patient through different rehabilitative motions or providing appropriate resistance during an exercise [10], [11]. In-home robotic rehabilitation devices can help address the labor demand and allow for improved recovery [12]. For patients to use rehabilitative technology in their homes, it should be safe, comfortable, and economically accessible, which soft robotics affords [13]. The inherent compliance of soft robots makes them safer for independent in-home use by patients in assistive and rehabilitative applications [14], [15]. Made out of relatively inexpensive materials, soft robots are also more affordable when compared with rigid-body systems.

One of the fundamental research challenges in soft robotics is that soft materials change in behavior over time due to fatigue [16], [17]. In this work, we characterize fatigue for one of the most common types of soft actuators: the pneu-net. Pneu-nets are pneumatically-operated soft actuators made from elastomeric materials with a network of air chambers. They actuate in a bending motion due to the embedding of a strain-limiting layer. The actuation will result in a rotation-like deformation, in a direction toward the strain-limiting layer and away from the regions of high strain. The regions of highest stress/strain will undergo the most fatigue [18], which can result in micro-fractures (changing the behavior) or macro-fractures (breaking of the walls and leading to failure of the robot). In the case of a pneu-net, these highest levels of fatigue occur in the upper regions of the interior walls between air chambers (see Fig. 5). Some have tried to optimize the design by discarding material from these high-stress/strain regions. In [19], the fast pneu-net (fPN) design was introduced as an improvement to reduce fatigue. The fPN design involves cutting out the interior walls from the outside, creating a ridged external surface. As another alteration, described in [20], the interior walls are cut out from the inside by creating trapezoidal-shaped air chambers, allowing the design to maintain an almost continuous external surface. Whether or not the design is optimized or constrained for a specific application, the elastomeric material of a soft actuator will still undergo strain, which will eventually lead to fatigue. In this paper, we analyze this fatigue behavior, which is a necessary consideration for any soft robotics application, and show how it causes deviation from the FEM model.

It should be highlighted that the high strain within the interior walls of the sPN not only leads to fatigue but it also makes finite element modeling (FEM) a challenge. Most FEM techniques have been developed for analyzing solid structures, such as metals with much less deformation than hyperelastic silicone, a common material used for soft actuators. Thus, studies of soft actuators with high strain rates such as sPNs do not quantitatively compare FEM and experimental data. These studies either: (a) only present experimental data with no FEM modeling [20], [21], or (b) only present FEM modeling with no experimental data [22], [23], [24], or (c) only qualitatively compare the FEM and experimental data, and so the accuracy of their FEM models is not validated [19], [25], [26].

In this work, for the first time, we present a comparison of FEM vs. experimental data for the sPN past 90^∘; furthermore, we present this comparison over several cycles of bending. We perform this comparison up to $\sim$170^∘, and we demonstrate 96% accuracy in the first trial (before fatigue accumulation). Using this accurate model, we then analyze fatigue in a systematic manner. For this, the paper leverages the use of a 3rd-order Yeoh model for Finite Element Analysis with coefficients determined by stress-strain experiments conducted up to 800% strain [27]. We will then show that fatigue will result in a 20% deviation from the ideal FEM behavior. This observation highlights the importance and significance of considering fatigue in modeling soft robots and in the future for the control of such systems.

The rest of this paper is organized as follows. In Section II, we present the end-to-end fabrication of the actuator, the FEM model, the pneumatic control of the actuator, and our automated data collection methods. In Section III, we compare the simulated and experimental data, validating the 96% accuracy of the FEM. We then use this model to demonstrate and analyze the effect of fatigue in a targeted, precise manner. In Section IV, we suggest how future researchers can use these results to conduct more informed analysis of soft actuator design and behavior.

In this section, a brief overview of the fabrication of a soft actuator is given, followed by FEM modeling, pneumatic control, and data collection methods. As discussed in the introduction, soft fluidic actuators made of elastomeric materials function by applying pneumatic or hydraulic pressure to the internal surface of a hyperelastic body. The key is that the body is constrained on one or more surfaces by a flexible but inextensible strain-limiting layer. When pressure is applied, the actuator only expands in the areas that are extensible. The strain-limiting surfaces will bend but not elongate. In the case of a pneu-net, the strain-limiting layer spans the entire base. As the air chambers above the base expand, the limiting layer stops the actuator from elongating, which in turn causes bending. Fig. 2 shows a fabricated sPN embedded into a wrist sleeve. This is an early conceptual prototype to show how such an actuator could be used for wrist rehabilitation (flexion and extension).

In this section, we conduct experiments (static analysis) on bending angle response to pressure, compared to the behavior of the FEM, in order to: (a) validate the accuracy of our FEM model, and (b) analyze fatigue in the experimental data over repeated bending. Fig. 7 qualitatively depicts the ability of the simulation to correctly model the actuator’s shape. The left, middle, and right views show side-by-side comparisons of the FEM model and the pressurized actuator at angles of 73^∘, 125^∘, and 212^∘, respectively.

In order to quantitatively analyze the performance of the system with that of the simulation, a series of fixed pressures were applied to the actuator, and the resulting error was examined at steady-state. Each step of the staircase pressure function holds the pressure constant for 16 seconds. Successive steps increment by 5 kPa, ranging from 0 to 45 kPa. The purpose of the staircase function is to allow the actuator to reach a steady state at each pressure so that the measurements can be compared to the static FEM model. Fig. 8 shows data collected from an actuator on its first trial after fabrication. Fig. 8(a) shows a Y-Y plot of the time series data. The blue data points are the readings from a pressure sensor located at the air inlet to the actuator. The resulting bending angle measurements from the markerless computer vision system are shown in orange. We observe that the actuator is able to fully respond to the pressure increment and reach a steady state in most cases within 2.5 seconds past the start of the pressure steps. This 2.5-second mark is shown with black points overlaid on the orange curve. We repeated this staircase experiment for ten trials (each with ten steps from 0 to 45 kPa for 16 seconds) to induce fatigue.

In Fig. 8(b), we compare our experimental data from trial one to the simulated data from our FEM model. The angle measurements from each 5kPa step in the staircase are displayed here in orange as a distribution from 2.5 seconds and after. The bottom of the orange distribution is the angle at the 2.5-second mark corresponding to the black point in Fig. 8(a). The top of the orange distribution is the end of the corresponding pressure step (at 16 seconds when the angle is also the highest). For lower pressures where the angle plateaus, the bottom and top angles are the same; thus, the distribution appears as a flat line. The distribution becomes wide at the higher-pressure steps that do not plateau. No matter the size of the distribution, the bottom (the 2.5-second mark) is very close to the FEM data for all pressure steps, demonstrating the ability of the simulation to accurately model the actuator.

Fig. 9 shows subsequent data collection trials with the same staircase reference signal. Fig. 9(a) is the trial directly after the first one, and we see that for the two highest pressures, the bottom of the distribution is no longer close to the simulation, and we also see that the third highest pressure is starting to show non-plateau behavior. This is caused by the micro-fractures in the body of the system due to fatigue, which changes the behavior of the system and causes the system to deviate from the ideal FEM model. Fig. 9(b) is after ten trials. We see that the three highest pressures have risen above the simulation with non-plateau behavior, while the lower pressures continue to match the simulation and reach steady-state behavior.

Fig. 10 shows the normalized RMSE (NRMSE), highlighting the deviation (the error) from the FEM model. Each bar is for a corresponding trial. Computing the NRMSE allows us to compare experimental and simulated data. It can be seen that the error for trial one is 4%, and for trial 10 it goes up to 20% as a result of fatigue. This highlights the major effect of fatigue on the behavior of the system.

Fig. 11 characterizes the error for each pressure step. Each bar in the bar plot is for one 5 kPa step and one trial. The height of the bar is the error, which is the absolute value of the difference between the angle predicted by the simulation at that pressure and the actual angle at that pressure after it has been at that pressure step for 2.5 seconds. Each pressure step is shown as a main group of bars on the x-axis, and each trial is a different color within each main group.

Fig. 12 shows the same organization of steps and trials as in Fig. 11, but now includes the distribution of angle values after 2.5 seconds. The colored bars from Fig. 11 are now simplified to be all in black, and the distribution from 2.5 seconds to 16 seconds is plotted above each bar in orange. The orange portion of the bar corresponds to the orange distributions in the previous Angle vs. Pressure graphs.

In Fig. 10, we observe that the first trial exhibits a very low NRMSE error of 4% with respect to the simulated model, but then the error increases significantly. Investigating further into subsequent trials, we observe in Fig. 11 that for all but the three highest pressures, the error stays very low for all ten trials. In Fig. 11, we observe that for the highest two pressures, the error significantly jumps up after the first trial. Looking at this trend in Fig. 12, we notice that there is a clear correlation between the presence of error from the simulation and non-steady state behavior. This non-steady state behavior is due to the forming of microtears in the silicone, resulting in fatigue. This fatigue then changes the actuator’s behavior, making it deviate from the simulated model.

Pneumatic soft actuators undergo high deformation, making them hard to model even without fatigue. To the best of the authors’ knowledge, this work is the first to show an FEM vs. experimental comparison for an sPN with angles exceeding 90^∘. We have shown that our FEM model can predict the bending angle of a newly-fabricated sPN up to 167^∘; furthermore, this prediction has a very low error of 4% before repeated use. Capitalizing on the accuracy of the FEM model, this paper focuses on the effect of fatigue over repeated use of the actuator. We have shown that fatigue can cause significant errors in the behavior of the actuator deviating from the ideal (FEM-based) prediction. Using computer vision, the bending angle was captured with fine temporal resolution, demystifying the dynamic step response, which allowed the observation of a correlated pattern between deviation from the FEM model and the non-steady-state behavior.

This paper highlights the importance and significance of taking into account the fatigue behavior caused by micro-fractures, which can later result in macro-fractures and actuator failure. In the future, the outcomes from this study can be used to (a) select more durable materials with lower fatigue, (b) optimize geometrical designs to minimize fatigue, (c) guide the bending angle thresholds given fatigue provocation, and (d) oversee seamless soft-robot control through objective time-variable fatigue monitoring.