Sage Journals: Discover world-class research

Abstract

Modern industrial and medical applications require soft actuators with practical actuation methods, capable of precision control and high-speed performance. Within the realm of medical robotics, precision and speed imply less complications and reduced operational times. Soft fluidic actuators (SFAs) are promising candidates to replace the current rigid endoscopes due to their mechanical compliance, which offers safer human–robot interaction. However, the most common techniques used to operate SFAs, pneumatics, and hydraulics present limitations that affect their performance. To reduce manufacturing complexity, enhance response time, improve control precision, and augment the usability of SFAs, we propose a Pneudraulic Actuation (PHA) system that, for the first time, combines a pneumatic and hydraulic circuit in series. To examine this proposal, a comparative assessment of the proposed actuation technique with the common techniques was carried out, in terms of bending performance and generation of audible noise level during functioning. The analysis provides insights into the performance of various fluidic actuation methods for SFAs, highlighting significant effects related to fluid–structure interactions and the presence of trapped air. Thereafter, a comparative assessment of different fluidic circuits is performed, illustrating how tubing length, inner and outer diameter, as well as the amount of different fluidic medium impact the dynamic behavior of the system, amplifying the importance of fluid mechanics for design optimization. Furthermore, we propose a model-based control strategy that solely focuses on fluid dynamics, utilizing the hydraulic-electric analogy and the resistor–inductor–capacitor circuit theory. Our PID controller improved actuation speed by 52.63% and reduced audible noise by 17.17%.

Introduction

Soft robotics are making a positive impact in fields such as health care, agriculture, and industry due to their ability to safely handle delicate objects and morph around complex shapes.^1,2 They also provide cost-effective alternatives to rigid robots.³ To improve the precision, response, and usability of soft robots and to reduce complexity and maximize effectiveness, enhancing actuation performance is essential.^4,5

Actuation of soft robots is achieved by various methods, including tendons, shape memory alloys, and fluids.^6,7 However, soft fluidic actuators (SFAs), which consist of soft bodies with inflatable cavities and deform upon fluid injection, represent over 75% of these methods.⁸ This is due to its straightforward fabrication process and its high passive compliance and deformability⁹—qualities that are particularly advantageous for medical applications.¹⁰ Moreover, compatibility with lithographic processing makes them suitable for applications even at microscale.¹¹ Pneumatic soft actuators are the plurality¹²; however, hydraulic soft actuators are becoming increasingly popular for their enhanced actuation performance and efficiency.¹³

The performance of SFAs is coupled with the design of their inflatable cavities and the actuation strategy. Pneumatic systems rely on creating a controllable pressure difference between the source and the cavities. While different energy sources exist,¹⁴ pneumatic circuits frequently consist of an air compressor paired with pressure regulators and solenoid valves.¹⁵ Pneumatics offer fast pressure generation with low mechanical and fluid friction,¹⁶ enabling actuation speed to scale with pressure. This approach is practical and cost-effective,¹⁷ ensuring that SFA’s compliance remains unaffected by the actuation fluid.¹⁸ Additionally, compressed air is readily available in operating rooms, making pneumatics an ideal choice for medical applications. Albeit there are drawbacks, like limited force output and challenges in precise control due to the nonlinear behavior of elastomers and air compressibility, which requires adequate modeling.¹⁹ In contrast, hydraulic circuits offer higher actuation efficiency by using an incompressible fluid and typically regulate the amount of fluid infused or withdrawn from cavities through volume control. Multiple types of liquid-based pumps exist such as rotary diaphragm,²⁰ centrifugal,²¹ and peristaltic,²² but syringe pumps are favored,²³ for their model-based ability to control the fluid’s flow rate and volume.²⁴ Volume control can be deemed preferable for configuration control in soft robotics, as the relationship between volume, elongation, and motion is more direct, leading to greater precision and safety.^25,26 Nonetheless, hydraulics can affect the SFA’s mechanical compliance and may reduce response time, compared to pneumatics, due to greater mechanical and fluidic friction. Consequently, hybrid systems were developed to harness the strengths of different actuation methods.

A robotic arm was controlled using an air-hydraulic servo booster to increase payload and enable compliance and precision control in aquatic environments.²⁷ This complex system includes multiple pneumatic solenoid valves that activate separate hydraulic pistons antagonistically. Dynamic control focuses on mechanical and fluidic models of the pistons, arm, and fluidic flow within the booster’s orifice. However, fluid dynamics within the tubing are ignored. Additionally, a motor was powered by pressurized liquid, as compressing liquid rather than gas improves actuation efficiency.²⁸ In the same vein, various actuation techniques have been fused with soft robots (Summarized in Table 2 of Pagoli et al.²⁹) to improve aspects such as performance, stiffness, and workspace. Given the dominance of fluidic actuation, we focus on hybrid fluidic systems.

A hybrid actuation method using two syringe pumps operating in parallel, one with water and one with air, was introduced to modulate the stiffness and force output of a SFA.³⁰ Such systems are complex and expensive to manufacture, as multiple syringe pumps are required.³¹ Although hybrid systems with a single syringe pump can simplify manufacturing,³² viscous friction in the tubing and stiction and Coulomb friction from the O-ring seal³³ act on the syringe plunger. Accordingly, to increase response times, the motors must either be powerful and therefore bulky or be equipped with a high gear-ratio gearbox, which would significantly reduce the speed of the lead screw system. Recently, a hybrid system that omits the use of a syringe pump was suggested for amphibious applications.³⁴ The system relies on multiple diaphragm pumps and utilizes a representation-based learning controller on a three-port solenoid valve for pressure control. Diaphragm pumps can introduce pulsating flow requiring an air chamber (dumper) and have moving parts, generating noise and demanding periodic replacement.³⁵ Ultimately, the proposal of the study increases hardware requirements without providing insights into the factors influencing performance.

To analyze SFA’s performance and enhance dynamic controllability, fluid–structure interaction³⁶ and fluid mechanics³⁷ should be examined, as fluid energy distribution is neither immediate nor uniform due to fluid properties and viscous losses.³⁸ Pressure variations in air-filled cavities have been shown to cause localized stress concentrations and uneven deformations,³⁹ especially at high pressurization rates.⁴⁰ This, coupled with the inherent characteristics of the elastomer—including nonlinearity and hysteresis⁴¹—complicates their control when using a generally preferred model-based approach,⁴² which can require finite element analysis.⁴³ So far, the Lagrangian⁴⁴ or Cosserat Rod-Base⁴⁵ method has been primarily used to model SFA’s mechanical dynamics, neglecting fluid dynamics.⁴⁶ The trend toward smaller SFAs,^47–49 however, will inevitably increase the importance of fluid dynamics over solid mechanics. Accurately predicting 3D fluid flow requires solving computationally expensive differential equations (Navier–Stokes). To simplify this, prior studies have applied the hydraulic-electric analogy to derive governing differential equations for fluid flow in microfluidic chips^50–52 and the cardiovascular system.^53,54

In this article, we introduce a pneudraulic actuation (PHA) method and apply it to SFAs for the first time. This setup allows us to study the effects of fluid compressibility within elastic cavities and effectively model system dynamics using solely fluidic models. The main contributions of our study are: •

A unique PHA setup for SFAs that combines pneumatic and hydraulic circuits in series with a proportional pressure regulator, reducing hardware complexity and audible noise.

•

A comparison of fluidic elements influencing dynamic behavior, supporting design optimization of similar actuation systems.

•

A model-based controller that focuses solely on fluid dynamics, utilizing the hydraulic-electric analogy and resistor–inductor–capacitor (RLC) theory. The proposed setup and controller improves precision and actuation speed (by 52.60%).

Materials and Methods

Pneudraulic actuation method

The PHA has three identical channels (Fig. 1a). A single channel consists of a pneumatic- and hydraulic-analogue circuit connected in series and separated at Point A (Fig. 1c). Anything before Point A is called the “actuation circuit,” and thereafter, the “fluidic circuit.” The “actuation circuit” consists of an air compressor and an electronic proportional pressure regulator (Series K8P, Camozzi Automation). Hard polyvinyl chloride (PVC) tube with $l_{p}$ = 15 cm and $R_{i, p}$ = 1.25 mm connects the pressure regulators and water column. This defines the initial volume of air in the system ( $V_{o, P})$ . When pressurization occurs, part of the hydraulic fluid is diverted from the water column ( $V_{o, w}$ = 11 mL) into the cavities of the SFA via the interconnecting tubing of the “fluidic circuit.” During relaxation, the elastic energy of the SFA returns hydraulic fluid to the water column while releasing air into the atmosphere. To maintain water retention in the circuit, the water column is oriented vertically to utilize gravitational force. A pressure sensor (PX190, Omega Engineering) and a flow sensor (SLF3S-4000B, Sensirion) are used to provide feedback for pressure and/or volume control.

FIG. 1.

Elements of the pneudraulic actuation (PHA). (a) Real-life illustration of PHA, (b) cross-sectional anatomy of soft fluidic actuator, and (c) symbolic representation of components from a single channel of PHA.

Soft fluidic actuator

The SFA employed in this study (Fig. 1b) is part of the self-propelled MorphGI endoscope.⁵⁵ Its body is made from Shore A-20 silicone (RTV4420 Silbione) and measures 70 mm in length with a diameter of 17.5 mm. It features seven cavities: three for actuation and four working channels. The actuation cavities are cylindrical, with an inner diameter of 2 mm and an outer diameter of 6.5 mm. The outer diameter is defined by the polyethylene terephthalate (PET) woven mesh, which limits expansion and promotes bending and the reinforcement spring in the working channels to prevent radial collapse.

Fundamentals of hydraulic-electric analogy

Electric and fluidic circuits exhibit analogies defined by Hagen–Poiseuille law. Table 1 lists key microfluidic parameters and corresponding electronic components for assembling microfluidic circuits, from which the electric equivalent of a single actuation channel of PHA is composed (Fig. 2).

FIG. 2.

Hydraulic-electric analogy representation. The figure depicts the symbolic equivalent of fluidic components with the electric equivalent. Specifically, (a) air compressor and regulator with a voltage source, (b) pressure sensor with a voltmeter, (c) SFA with a capacitor due to radial expansion of the actuation chambers, (d) trapped air as a variable capacitor, (e) flow sensor as an ammeter and (f) tubing as a resistor and inductor connected in series. Analogies (a)–(f) are used to represent (g) the electric equivalent circuit of PHA. SFA, soft fluidic actuator.

Table 1.

Microfluidic and Electronic Components Analogy from Hagen–Poiseuille’s Law [Units]

Microfluidics	Electronics
Pressure, P [Nm⁻²]	Voltage, V [V]
Volumetric flow rate, Q [m³s⁻¹]	Current, I [A]
Fluidic resistance, Rh [Nsm⁻⁵]	Resistor, R [Ω]
Fluidic inductance, Lh [Nm⁻⁶]	Inductor, L [H]
Fluidic compliance, Ch [m⁵N⁻¹]	Capacitor, C [F]
Solenoid valve	Switch/transistor
Air compressor	Voltage source
Syringe pump	Current sourcev

The linear and proportional relationship between pressure difference ( $d P$ ), fluidic resistance ( $R_{h}$ ), and volumetric flow rate ( $Q$ ) in channels is analogous to Ohm’s law on electric circuits. This relationship holds for long, narrow channels with laminar flow. This is commonly the case in soft robotics, particularly in systems intended for endoscopic procedures.⁵⁶ Equation (1) illustrates the analogy mathematically as follows: $d P = R_{h} \cdot Q$ (1)

The $R_{h}$ of circular tubes can be calculated by the following equation: $R_{h} = \frac{8 \cdot μ \cdot l_{h}}{π R_{i}^{4}}$ (2)where $R_{i}$ and $l_{h}$ are the inner radius and length of the tube, respectively, and $μ$ the dynamic viscosity of the fluid. The pressure change caused by either the flexibility of the tube or the compressibility of fluid defines the fluidic capacitance ( $C_{h}$ ). It affects $Q$ as follows: $Q = \frac{d V}{d t} = \frac{d V}{d P} \cdot \frac{d P}{d t} = C_{h} \cdot \frac{d P}{d t}$ (3)

Circular elastic tubes can be approximated as thick-wall pressure vessels, whose fluidic capacitance ( $C_{t}$ ) is equal to⁵⁰: $C_{t} = \frac{2 \cdot π \cdot R_{i}^{2} \cdot l_{h} \cdot [(1 + v) \cdot R_{o}^{2} - (1 - 2 \cdot v) \cdot R_{i}^{2}]}{E \cdot (R_{o}^{2} - R_{i}^{2})}$ (4)where $R_{o}$ is the outer radius of the tube, $E$ is Young’s modulus, and $v$ is Poisson’s ratio. Furthermore, the compressibility of air inside the pneumatic supply lines introduces capacitance to the circuit. Assuming an isothermal process and using the ideal gas law, the fluidic capacitance of air ${(C}_{a})$ is as follows: $C_{a} = \frac{P_{atm} \cdot V_{o, P}}{{(P_{atm} + d P)}^{2}}$ (5)where $P_{atm}$ denotes atmospheric pressure. As such, $C_{a}$ varies according to the pressure difference in the system. Finally, the density ( $ρ)$ of the fluid, opposes sudden changes in flow that represent the fluidic inductance ( $L_{h})$ . For circular tubes, it can be estimated as follows: $L_{h} = \frac{ρ \cdot l_{h}}{π \cdot R_{i}^{2}} .$ (6)

Fundamental of RLC circuit theory

The three main circuit components, besides the voltage source, are the resistor (R), inductor (L), and capacitor (C). The equations following derivations are obtained online.⁵⁷ Using Kirchhoff’s voltage law, the differential equation between the voltage of the source, $V_{s}$ , and the capacitor, $V_{c}$ is as follows: $\frac{d^{2} V_{c}}{d t^{2}} + \frac{R}{L} \frac{d V_{c}}{d t} + \frac{V_{c}}{L C} = \frac{V_{s}}{L C}$ (7)

The characteristic equation in the Laplace domain of the serial RLC circuit is as follows: $S^{2} + 2 α S + ω_{ο}^{2} = 0$ (8)where $α$ is the damping factor and $ω_{o}$ the natural frequency is defined as follows: $α = \frac{R}{2 L}, ω_{o} = \frac{1}{\sqrt{L C}}$ (9)

The roots of (8) can be expressed as follows: $S_{1, 2} = - a \pm \sqrt{a^{2} - ω_{ο}^{2}}$ (10)

There are three possible time domain behaviors of voltage, $V_{c} (t)$ : (a) underdamped ( $a$ < $ω_{o}$ ), (b) critically damped ( $a$ = $ω_{o})$ and overdamped ( $a$ > $ω_{o}$ ). Critically damped systems are rare in practice, so the corresponding equation is ignored. An underdamped system has two complex conjugate roots and $V_{c} (t)$ is as follows: $V_{c} (t) = V_{c, 0} + d V + [(A_{1} \cos (ω_{d} t) + (A_{2} \sin (ω_{d} t)] e^{- a t}$ (11)where $V_{c, 0}$ is the initial voltage in the circuit, $A_{1}$ and $A_{2}$ are coefficients determined by circuits initial conditions and $ω_{d}$ is the damped frequency. Damped frequency is the coefficient of the imaginary part in (10). An overdamped system has two real distinct roots with $V_{c} (t)$ represented as follows: $V_{c} (t) = V_{c, 0} + d V + B_{1} e^{s_{1} t} + B_{2} e^{s_{2} t}$ (12)

Experiments

The bending performance of a single actuation cavity is analyzed based on the symmetrical cross-sectional area of the SFA. The experiments conducted are summarized below, with notations indicated in Figures 1 and 2.

Experiment 1 examined the fluid compressibility effects of SFA’s performance and audible noise levels of three “actuation circuits”: pneumatic, pneudraulic, and syringe pump. Although fluid–structure interaction is studied using commercial software such as COMSOL,⁵⁸ a real-life experiment was chosen for simplicity. The SFA was fixed vertically with four electromagnetic trackers (Aurora, NDI) positioned at the base and tip (two trackers at each location). We use a single channel of PHA for the Pneumatic circuit without hydraulic fluid. For the pneumatic and pneudraulic cases, pressure varied $P_{act} \in [0, 6]$ bar in 1 bar intervals. For the syringe-pump circuit, a commercially available pump was utilized (LSP02, LongerPump) to infuse $V_{w} \in [0, 3]$ mL at 0.5 mL intervals. Pressure (at Point A), bending angle, and noise (via a mobile app) were recorded. The “fluidic circuit” remained the same in all scenarios, and the experiment was repeated three times. In each trial, the SFA was disconnected and reconnected to introduce variability in the trapped air within the circuit.

Experiment 2 examined how pressure is transmitted from Point A to Point B for different “fluidic circuits,” by modifying four control variables. The control variables are: $V_{o, P}$ of the “actuation circuit,” $l_{h}$ , $R_{o}$ , and $R_{i}$ of the interconnecting tubing and the fluidic medium (air or water) present in the “fluidic circuit.” For two different combinations of these control variables (A and B), in each sub-experiment, the time-domain response of pressure was examined. Table 2 summarizes the examined “fluidic circuits” at each sub-experiment. Only polytetrafluoroethylene (PTFE) tubes, known for their high-pressure durability, were tested. Pressure transient behavior was recorded with a pressure sensor (PXM409, Omega Engineering) at Point B, sampled at 1 kHz. To exclude any SFA dynamics, the rear end of the fluidic circuit was blocked with a nonreturn valve. A single PHA channel was used for excitation $(P_{act}$ = 3 bar).

Table 2.

Summary of the Control Variables Used for the Different “Fluidic Circuits” of the Four Sub-Experiments of Experiment 2

	Control variables of “fluidic circuit”
	$V_{o, P}$ [ml]	$R_{i}$ [mm]	$R_{o}$ [mm]	$l_{h}$ [m]	Fluidic medium
Sub-experiment 1
A	0.08	0.50	0.80	2.40	Water
B	0.08	0.25	0.55	1.20	Water
Sub-experiment 2
A	0.08	0.50	0.80	2.40	Water
B	0.16	0.50	0.80	2.40	Water
Sub-experiment 3
A	0.08	0.25	0.55	1.20	Water
B	11.08	0.25	0.55	1.20	Air
Sub-experiment 4
A	0.08	0.50	0.80	1.00	Water
B	0.08	0.50	0.60	1.00	Water

Experiment 3 investigated the transient pressure behavior of the SFA to calibrate the $R_{h}$ , $L_{h}$ and $C_{h}$ values that are employed in (7)–(12). The system was excited for $P_{act} \in [0, 3]$ bar in 1 bar intervals while pressure was recorded, at Point B, using the PXM409 sensor at 1 kHz. The interconnecting tube used had $l_{h}$ = 2.40 m and $R_{i}$ = 0.50 ± 0.05 mm (TW19, Adtech Polymer Eng. Ltd). This tube is similar to that in our probe design.⁵⁵

Finally, Experiment 4 compared our model-based PID controller with the open-loop response in terms of actuation speed (settling time). The SFA was attached on the test rig from Experiment 1 and a single channel of PHA was employed for actuation. Using the interconnecting tubing and RLC values obtained from Experiment 3, a PID feedback loop was implemented. The segment was instructed to bend at θ = 90° $(P_{act}$ = 4.5 bar), an angle used for anchoring by self-propelling endoscopes.

Results

Experiment 1

Figure 3 illustrates the symbolic representation of the three actuation circuits and the experimental setup, while Figure 4a and b presents the results from the different repetitions alongside an empirical quadratic function. The segment shows good repeatability in terms of bending. The pressure regulator stabilizes the SFA at each actuation interval, whereas a syringe pump causes an exponential decay in the bending angle due to viscoelastic relaxation (Supplementary Data S1). The average root-mean-square error (RMSE) from each distinct repetition against the average of all repetitions is 0.61°, 1.89°, and 2.03° for the PHA, pneumatic, and syringe pump, respectively, and 2.80° for the model. Using an incompressible fluid, the segment reaches ≃132° at 6 bar. Examining Figure 4b, there is an interesting observation. When the actuation medium is incompressible and $P_{act} > 3$ bar, the SFA bends more for the same input pressure. To verify this observation, further tests were performed (Supplementary Data S2). The maximum noise recorded during actuation was 77, 80, and 69 dB for the PHA, pneumatic, and syringe pump, respectively. For the pneumatic pump and PHA, noise during deflation was measured at 105 and 87 dB, respectively (17.17% less).

FIG. 3.

“Actuation circuits” comparative assessment. (a) Symbolic representation of the three different “actuation” circuits used. Pneumatic, PHA, and syringe pump. (b) Experimental setup with electromagnetic tracker placement to measure (c) the bending angle of the SFA.

FIG. 4.

Results of Experiment 1. (a) depicts the results of bending angle ( $θ$ ) for the different “actuation circuits” across the three repetitions. (b) Average results of bending angle against pressure for the “actuation circuits” and the model prediction (with error bars).

Experiment 2

Sub-experiment 1 focused on investigating the impacts of $R_{i}$ and $l_{h}$ . Since the time constant can be approximated as τ = $R_{h} {\cdot C}_{h}$ , by reducing both $R_{i}$ and $l_{h}$ by 50%, according to (2), $τ_{2} = 8 \cdot τ_{1}$ . This is verified by our results since $τ_{1}$ = 0.21 s and $τ_{2}$ = 1.61 s (Fig. 5). An overshoot is observed for one of the pressure responses. The nonreturn valve (Fig. 5a) significantly increases the inertia of the system which drives it into an “underdamped state” for the given $R_{h}$ . Sub-experiment 2 was aimed at analyzing the effects of the initial volume of air ( $V_{o, P})$ present in the tubing of the “Actuation Circuit”. According to Equation (5), by doubling $V_{o, P}$ and keeping $d P$ constant, $C_{h}$ of the system should also double such as $τ_{3} = {2 \cdot τ}_{1}$ . This is verified by the experimental data with $τ_{3}$ = 0.43 s. Furthermore, the effects of the actuation medium were examined in sub-experiment 3. At room temperature, $R_{h, water} ≃ 55 {\cdot R}_{h, air}$ . If water is completely removed from the PHA and air is solely present, $V_{o, P} ≃ 139 {\cdot V}_{o, P - Hydro}$ . Combining these observations, $τ_{air} = \frac{55}{139} {\cdot τ}_{P - Hydro}$ . In Sub-experiment 4, the effect of $R_{o}$ is examined. It appears that by reducing $R_{o}$ of the tubes by 25%, subsequently reducing the wall thickness of the tube, $τ$ is increased by 70 ms.

FIG. 5.

Results of sub-experiments from Experiment 2. (a) depicts how the rare end of the fluidic circuit, Point B, was sealed using a nonreturn valve. The pressure sensor was used to measure the transient behavior of the pressure for (b) the different Sub-experiments 1–4. Sub-experiment 1 examined effects of $R_{i}$ and $l_{h}$ , Sub-experiment 2 the effect of volume of air $(V_{o, P})$ trapped in the system, Sub-experiment 3 the effect of the actuation medium, and Sub-experiment 4 the effect of $R_{o}$ .

Experiment 3

The $R_{h}$ and $L_{h}$ of the equivalent circuit are primarily influenced by $R_{i}$ of the interconnecting tube. PVC tube resistance is negligible. $C_{h}$ in the circuit arises from the radial expansion of actuation cavities and air compressibility. Radial expansion of PVC and PTFE is assumed negligible due to their stiffness. In a closed circuit, pressure equalizes uniformly as per Pascal’s law. Thus, the values of the variable and constant capacitor can be summed $(C_{h} = C_{t} + C_{a})$ .

Tolerance and fabrication imperfections (Fig. 6a) suggest that $R_{h}$ and $L_{h}$ fall within a range. Using (2) and (6), $R_{h}$ = 52.41–107.15 GΩ and $L_{h} = 2.09 - 3.00 GH .$ For the specified air volume and pressure range, (5) yields $C_{a}$ = [1.98, 0.84, 0.46] pF.

FIG. 6.

Results of Experiment 3. (a) microscopic images of PTFE tubes depicting manufacturing tolerance and geometric imperfections that affect $R_{h}$ and $L_{h}$ (b) water displaced from the water column (and into the SFA) postactuation affecting Ca and (c) the three different step responses of pressure used for calibrating $R_{h}$ , $L_{h}$ and $C_{h}$ . (D = data, M = model). PTFE, polytetrafluoroethylene.

However, postactuation water is displaced from the water column (Fig. 6b), which causes a discrepancy in the $C_{a}$ calculation. Additionally, the SFA’s nonlinear mechanical properties require empirical identification of $C_{t}$ .

Figure 6c shows experimental and predicted pressure curves using the RLC model ( $R_{h} = 61.05 G Ω & L_{h} = 2.47 GH, C_{t} = 6 p F)$ . Experimental curves display a sigmoidal rise, typical for the step response of a second-order system.⁵⁹ Time constants vary almost linearly and are found to be: $τ_{1 b a r} = 0.59$ s, $τ_{2 b a r} = 0.52$ s, and $τ_{3 b a r} = 0.48$ s. As expected, settling time decreases as excitation pressure increases, since τ = $R_{h} {\cdot C}_{h}$ . Steady-state error is observed, stemming from open-loop inaccuracy of the pressure regulator. RMSE of the RLC model prediction for the three-step responses, presented in a matrix form, is [0.023, 0.051, 0.059] bar.

Experiment 4

The control strategy of our PID loop is visualized in Figure 7a. In a real-life application, the pressure sensor used at Point B for feedback will not be present. Thus, depending on the desired pressure ( $P_{des})$ , the RLC model provides the feedback without the presence of any sensory unit. The results of the bending are shown in Figure 7b. ${(P}_{des} = 4.5 bar)$ . For the open-loop response, the input pressure (measured with PX190 at Point A) has, as expected, the common step-input profile. However, the input pressure of the PID controller initially overshoots, but the controller gradually adjusts the input pressure to $P_{des}$ as SFA reacts. This makes the SFA reach the desired bending angle at $t_{PID}$ = 1.81 s instead of $t_{Open}$ = 3.80 s, resulting in a 52.63% improvement in the actuation speed (Video S1). Steady-state error is also eliminated.

FIG. 7.

Results of Experiment 4. (a) Block diagram of model-based PID controller indicating how the feedback loop is implemented using the RLC circuit theory model and (b) comparison of pressure (red) and bending (blue) behavior when the SFA was commanded to trace $θ$ = 90, ( $P_{des}$ = 4.5 bar) with the PID active or disabled (open loop). RLC, resistor–inductor–capacitor.

Discussion

Actuation circuit

To our knowledge, this is the first comparative assessment of actuation methods with a focus on fluid–structure interactions and audible noise. Enhanced workspace with an incompressible fluid and stiff segment likely relates to the fluid’s bulk modulus (β). β, the ratio of dP to relative volume change (ΔV/V), is $β_{air} =$ 1.05 bar and $β_{water} =$ 21.5 kBar for the two fluids. In air-filled chambers, pressure may not be distributed uniformly,³⁹ whereas in water-filled chambers, pressure distribution can be more uniform. Additionally, as actuation chambers collapse radially with elongation (Poisson’s ratio), a higher β resists collapse, pushing fluid towards the tip, increasing output force and elongation.^60,61 This insight could benefit soft prosthetics⁶² and exoskeletons,⁶³ which are often pneumatically actuated.⁶⁴

Pneumatic and PHA systems provide consistent bending due to regulated pressure, unlike syringe pumps, which depend on volume control and are affected by trapped air.⁶⁵ This variability causes differences in bending angle for the same injected volume. Additionally, the exponential decay in bending angle results from the viscoelastic relaxation of silicone,⁶⁶ as syringe pumps are inactive postactuation. Conversely, the pressure regulator, being constantly energized, can maintain a constant bending angle. A normally open solenoid valve could help our PHA maintain system pressure and enable intrinsic force sensing using the hydraulic fluid.⁶⁷ Finally, a hydrophobic membrane improves viability and safety by retaining water without relying solely on gravity.

Research shows that noise levels in operating rooms (OR), which can range from 51 to 79 dB, negatively impact surgical team performance.⁶⁸ The maximum noise using a pressure regulator during actuation and deflation is 80 and 105 dB, respectively. Although the deflation noise is high, it could be managed by using a pneumatic exhaust and placing the regulator within a soundproof enclosure. This highlights the need to consider aeroacoustics⁶⁹ or electric motor noise⁷⁰ in future medical actuation mechanisms. Pneumatic devices release compressed air in high-speed jets, allowing the noise level near the source to be calculated as follows (assuming adiabatic conditions): $L (d B) = 10 \log (\frac{π K_{a} ρ u^{3} R_{i}^{2}}{32}) + 120$ (13)where $K_{a}$ = 5x $10^{- 5}$ is the acoustical power coefficient and u the fluid’s speed. Water in the PHA setup slows deflation speed (higher viscous fiction), reducing audible noise compared to the pneumatic circuit.

Bending speed is affected by the dynamic response of any syringe pump and its ability to overcome mechanical and fluidic friction. This depends on the choice of the DC motor and the design of the lead screw system. The torque $(T)$ required to generate a given force $(F)$ can be determined by equating the rotational work done by the DC motor to the translational work done by the leadscrew, expressed by the following equation: $F δx = ηTδθ$ (14)where, δθ denotes the angular displacement, η the leadscrew efficiency, and δx represents the translational displacement. F can be expressed as the product of the pressure (p) and the area of the syringe plunger (A) (i.e., F = P A). Nonetheless, pressure is influenced by two primary factors (a) the stiffness of the SFA and (b) $d P$ across the tubing, as indicated in (1). The latter factor will dominate the speed ( $δ x / δ θ)$ as we move towards miniature SFA. Table 3 summarizes the findings on the actuation circuits.

Table 3.

Summary of Key Performance Observations from Experiments 1 and 2 and Literature on Different Fluidic Actuation Methods

	Control		Speed	Setup complexity	Noise (dB)	Pressure distribution in actuation chamber	Effect from
	Variable	Complexity	Speed	Setup complexity	Noise (dB)	Pressure distribution in actuation chamber	Viscoelastic relaxation	Trapped air in fluidic circuit	Fluid on SFA’s compliance
Pneumatics	Pressure^a	High	High^b	Low	80–105	Nonuniform^39,40	Low^d	Low^d	Low¹⁸
Syringe pump	Volume	Low	Low^c	High³¹	69^c	Uniform	High	High	High¹⁸
Pneudraulic	Pressure^a + volume	Medium	Medium^b	Medium	77–87	Uniform	Low^d	Low^d	Medium

Compressed air is readily available in operating rooms.

Scales with pressure difference.

Depends on motor design and power.

Selectable pressure levels prevent issues with viscoelastic relaxation and trapped air in fluid lines.

SFA, soft fluidic actuator.

Fluidic circuit

Comparing τ from Experiment 2 highlights the importance of fluid mechanics in microscale actuators. As shown in Fig. 5a, a 50% reduction in interconnecting tube’s $R_{i}$ and $l$ results in an 800% increase in the system’s open-loop response speed. The wall thickness of PTFE tubes does not significantly affect pressure transient behavior; however, thinner walls can snap, altering geometry and $R_{h} .$ This probably explains the slight difference in transient behavior in sub-experiment 4. Sub-experiment 2 indicates that constant $V_{o, w}$ with increased $V_{o, P}$ slows response, while sub-experiment 3 shows that air improves it. This demonstrates that $V_{o, w}$ and $V_{o, P}$ should be tailored to specific applications. As the SFA requires $V_{w}$ =3 mL per chamber, $V_{o, w} \approx V_{w}$ should be true and be placed near the pressure regulator. The change of $V_{o, P}$ postactuation due to pressure-induced water displacement will be reduced if PHA is used for SFA actuated by microvolume fluid.⁷¹

Results from Experiment 3 indicate that the hydraulic-electric analogy and the RLC approximation can effectively predict transient pressure behavior. Nonetheless, inaccuracies ascribed to material nonlinearity, hysteresis, and geometric nonuniformities of the device can affect its accuracy.⁵⁰

Enhancement of bending speed

The result of Experiment 4, which implemented a PID controller using a regulator and air compressor with a broader operating range (0–7 bar) than that of the system (0–6 bar), showed that response times (or bending speed) can be improved by 52.6% if there is “excess” supply pressure. This should not create a problem, as compressed air (>13.79 bar) is present in OR to operate pneumatic surgical instruments.⁷² Such control approach suits SFAs with predefined motions, like self-propelling soft endoscopes.⁷³ Potentially though, excessive pressure may cause the SFA to fail. Additionally, since only positive pressure inputs can be applied by the regulator, relaxation speeds cannot be enhanced. The dynamic nature of $C_{a}$ , suggests that the gains of the PID controller must be adjusted online,⁷⁴ or interpolated for each target point. Although not tested here, different fabrication materials⁷⁵ are likely to influence transient response for SFAs.

For our SFA, dynamics of mechanics slightly dominate the bending response and should be considered in the future.⁷⁶ The open-loop time constant of bending from Experiment 4 is 0.53 s. However, based on the results from Experiment 3, it should be 0.48 s. Although small, this dominance is expected to diminish as SFA gets smaller and requires less volume for actuation, an element which will also increase the rate of actuation.⁴⁰

Conclusion

Our proof-of-concept and setup characterization of the PHA contributes to advancing SFAs usability and enhancing controllability. Comparing three actuation setups shows that stiff segments at high pressures achieve better bending performance with an incompressible fluid, likely due to factors related to fluid–structure interaction. PHA is simple to manufacture and can maintain a stable bending angle, compared to syringe pumps. It also offers greater consistency and is quieter during operation compared to a pneumatic pump. Key design choices impacting PHA response time include: the air and water volume in the “actuation circuit,” the smallest inner radius of the tubes in the “fluidic circuit” and the flexibility of the actuation cavities. Using the hydraulic-electric analogy and RLC circuit theory, we developed a model-based PID controller, which can improve bending speed by 52.63%.

Footnotes

Authors’ Contributions

D.M.: Conceptualization, methodology, software, formal analysis, investigation, data curation, writing—original draft, and visualization. S.W.: Methodology, investigation, and resources. W.H.: Investigation and resources. L.L.: Conceptualization, writing—review and editing, and supervision. W.X.: Writing—review and editing and supervision. H.L.: Conceptualization, writing—review and editing, supervision, project administration, and funding acquisition.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This research is funded by an internal King’s College London (KCL) grant from CDT in Surgical & Interventional Engineering and the InnoHK program.

Supplementary Material

References

Banerjee

. The impact of soft robotics in today’s world: Applications, challenges faced, and future outlook. In: 2022 International Conference on Smart Generation Computing, Communication and Networking (SMART GENCON). Bangalore, India; 2022, pp. 1–6.

Wang

, Xie

, Huang

, et al. Pioneering healthcare with soft robotic devices: A review. Smart Med, 2024; 3(1):e20230045; doi: 10.1002/SMMD.20230045

Franco

, Ayatullah

, Sugiharto

, et al. Nonlinear energy-based control of soft continuum pneumatic manipulators. Nonlinear Dyn, 2021; 106(1):229–253; doi: 10.1007/s11071-021-06817-1

Tang

, Chi

, Sun

, et al. Leveraging elastic instabilities for amplified performance: Spine-inspired high-speed and high-force soft robots. Sci Adv, 2020; 6(19):eaaz6912; doi: 10.1126/sciadv.aaz6912

Xiong

, Su

, Lipson

. Fast Untethered Soft Robotic Crawler with Elastic Instability. In: 2023 IEEE International Conference on Robotics and Automation (ICRA). IEEE: London, UK; 2023, pp. 2606–2612.

El-Atab

, Mishra

, Al-Modaf

, et al. Soft actuators for soft robotic applications: A review. Advanced Intelligent Systems, 2020; 2(10):2000128; doi: 10.1002/aisy.202000128

Boyraz

, Runge

, Raatz

. An overview of novel actuators for soft robotics. Actuators, 2018; 7(3):48; doi: 10.3390/act7030048

Hasanshahi

, Cao

, Song

K-Y

, et al. Design of soft robots: A review of methods and future opportunities for research. Machines, 2024; 12(8):527.

, Pal

, Aghakhani

, et al. Soft actuators for real-world applications. Nat Rev Mater, 2022; 7:235–249; doi: 10.1038/s41578-021-00389-7

10.

Decroly

, Mertens

, Lambert

, et al. Design, characterization and optimization of a soft fluidic actuator for minimally invasive surgery. Int J Comput Assist Radiol Surg, 2020; 15(2):333–340; doi: 10.1007/s11548-019-02081-2

11.

De Volder

, Reynaerts

. Pneumatic and hydraulic microactuators: A review. J Micromech Microeng, 2010; 20(4):e043001; doi: 10.1088/0960-1317/20/4/043001

12.

, Hou

, Zhang

, et al. Pneumatic soft robots: Challenges and benefits. Actuators, 2022; 11(3):92; doi: 10.3390/act11030092

13.

Shi

, Tan

, Zhang

, et al. Review on research progress of hydraulic powered soft actuators. Energies, 2022; 15(23):9048.

14.

Wehner

, Tolley

, Mengüç

, et al. Pneumatic energy sources for autonomous and wearable soft robotics. Soft Robotics, 2014; 1(4):263–274; doi: 10.1089/soro.2014.0018

15.

Joshi

, Paik

. Pneumatic supply system parameter optimization for soft actuators. Soft Robot, 2021; 8(2):152–163; doi: 10.1089/soro.2019.0134

16.

Shi

, Xu

, Sun

, et al. Research on the pressure regulator effect on a pneumatic vibration isolation system. Chin J Mech Eng, 2022; 35(1); doi: 10.1186/s10033-022-00799-w

17.

Bell

, Gorissen

, Bertoldi

, et al. A modular and self-contained fluidic engine for soft actuators. Advanced Intelligent Systems, 2022; 4(1):2100094; doi: 10.1002/aisy.202100094

18.

Focchi

, Guglielmino

, Semini

, et al. Water/air performance analysis of a fluidic muscle. In: 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE: Taipei, Taiwan; 2010, pp. 2194–2199.

19.

Xavier

, Fleming

, Yong

. Design and control of pneumatic systems for soft robotics: A simulation approach. IEEE Robot Autom Lett, 2021; 6(3):5800–5807; doi: 10.1109/LRA.2021.3086425

20.

Hepp

, Alexander

. A novel spider-inspired rotary-rolling diaphragm actuator with linear torque characteristic and high mechanical efficiency. Soft Robot, 2022; 9(2):364–375; doi: 10.1089/soro.2020.0108

21.

Katzschmann

, Maille

, Dorhout

, et al. Cyclic hydraulic actuation for soft robotic devices. In: 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE: Daejeon, Korea (South); 2016, pp. 3048–3055.

22.

, Nunez

, Souri

, et al. A compact DEA-based soft peristaltic pump for power and control of fluidic robots. Sci Robot, 2023; 8(79):eadd4649; doi: 10.1126/scirobotics.add4649

23.

Kalisky

, Wang

, Shih

, et al. Differential pressure control of 3D printed soft fluidic actuators. In: 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE: Vancouver, Canada; 2017, pp. 6207–6213.

24.

Xavier

, Fleming

, Yong

. Modelling and simulation of pneumatic sources for soft robotic applications. In: 2020 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM). IEEE: Boston, MA; 2020, pp. 916–921.

25.

Rus

, Tolley

. Design, fabrication and control of soft robots. Nature, 2015; 521(7553):467–475; doi: 10.1038/nature14543

26.

Wang

, Chortos

. Control strategies for soft robot systems. Advanced Intelligent Systems, 2022; 4(5):2100165; doi: 10.1002/aisy.202100165

27.

Hyon

S-H

, Akama

. Air-hydraulic servo booster toward submersible water-driven robots. IEEE Robot Autom Lett, 2021; 6(2):1966–1972; doi: 10.1109/lra.2021.3061068

28.

Shaw

, Yu

J-J

, Chieh

. Design of a hydraulic motor system driven by compressed air. Energies, 2013; 6(7):3149–3166.

29.

Pagoli

, Chapelle

, Corrales-Ramon

J-A

, et al. Review of soft fluidic actuators: Classification and materials modeling analysis. Smart Mater Struct, 2022; 31(1):e013001; doi: 10.1088/1361-665x/ac383a

30.

Peters

, Anvari

, Chen

, et al. Hybrid fluidic actuation for a foam-based soft actuator. In: 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE: Las Vegas, Nevada; 2020, pp. 8701–8708.

31.

Lake

, Heyde

, Ruder

. Low-cost feedback-controlled syringe pressure pumps for microfluidics applications. PLoS One, 2017; 12(4):e0175089; doi: 10.1371/journal.pone.0175089

32.

Choi

, Park

, Yang

G-H

, et al. A series elastic actuator using air and water and its force control. J Mech Sci Technol, 2023; 37(9):4825–4835; doi: 10.1007/s12206-023-0835-5

33.

Capes

, Herring

, Sunderland

, et al. The effect on syringe performance of fluid storage and repeated use: Implications for syringe pumps. PDA J Pharm Sci Technol, 1996; 50(1):40–50.

34.

Sugiyama

, Kutsuzawa

, Owaki

, et al. Latent representation-based learning controller for pneumatic and hydraulic dual actuation of pressure-driven soft actuators. Soft Robot, 2024; 11(1):105–117; doi: 10.1089/soro.2022.0224

35.

Zhao

, Lou

, Peng

, et al. A review of the development and research status of symmetrical diaphragm pumps. Symmetry, 2023; 15(11):2091.

36.

Bungartz

H-J

, Schäfer

. Fluid-Structure Interaction: Modelling, Simulation, Optimisation. Springer: Ghent, Belgium; 2006.

37.

Çengel

, Cimbala

. Fluid Mechanics: Fundamentals and Applications, 3rd ed. McGraw-Hill Education: New York, NY; 2019.

38.

Breitman

, Matia

, Gat

. Fluid mechanics of pneumatic soft robots. Soft Robot, 2021; 8(5):519–530; doi: 10.1089/soro.2020.0037

39.

Maruthavanan

, Seibel

, Schlattmann

. Fluid-structure interaction modelling of a soft pneumatic actuator. Actuators, 2021; 10(7):163.

40.

Mosadegh

, Polygerinos

, Keplinger

, et al. Pneumatic networks for soft robotics that actuate rapidly. Adv Funct Materials, 2014; 24(15):2163–2170; doi: 10.1002/adfm.201303288

41.

Hosovsky

, Pitel

, Zidek

. Analysis of hysteretic behavior of two-DOF soft robotic arm. MM Sj, 2016; 2016(03):935–941; doi: 10.17973/MMSJ.2016_09_201625

42.

Della Santina

, Duriez

, Rus

. Model-based control of soft robots: A survey of the state of the art and open challenges. IEEE Control Syst, 2023; 43(3):30–65; doi: 10.1109/mcs.2023.3253419

43.

Xavier

, Fleming

, Yong

. Finite element modeling of soft fluidic actuators: Overview and recent developments. Advanced Intelligent Systems, 2021; 3(2):2000187; doi: 10.1002/aisy.202000187

44.

Shariati

, Shi

, Spurgeon

, et al. Dynamic modelling and visco-elastic parameter identification of a fibre-reinforced soft fluidic elastomer manipulator. In: 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE/RSJ: Prague, Czech Republic; 2021, pp. 661–667.

45.

Roshanfar

, Dargahi

, Hooshiar

. Cosserat rod-based dynamic modeling of a hybrid-actuated soft robot for robot-assisted cardiac ablation. Actuators, 2023; 13(1):8; doi: 10.3390/act13010008

46.

Stölzle

, Santina

. Piston-driven pneumatically-actuated soft robots: Modeling and backstepping control. IEEE Control Syst Lett, 2022; 6:1837–1842; doi: 10.1109/LCSYS.2021.3134165

47.

Shi

, Abad

, Menciassi

, et al. Miniaturised soft manipulators with reinforced actuation chambers on the sub-centimetre scale. In: 2024 IEEE 7th International Conference on Soft Robotics (RoboSoft). IEEE: San Diego, CA; 2024, pp. 157–164.

48.

Sun

, Song

, Liang

, et al. A miniature soft robotic manipulator based on novel fabrication methods. IEEE Robot Autom Lett, 2016; 1(2):617–623; doi: 10.1109/LRA.2016.2521889

49.

Chi

, Zhao

, Hong

, et al. A perspective on miniature soft robotics: Actuation, fabrication, control, and applications. Advanced Intelligent Systems, 2024; 6(2); doi: 10.1002/aisy.202300063

50.

Kalantarifard

, Alizadeh Haghighi

, Elbuken

. Damping hydrodynamic fluctuations in microfluidic systems. Chemical Engineering Science, 2018; 178:238–247; doi: 10.1016/j.ces.2017.12.045

51.

, Liu

, Sun

. Hydraulic–electric analogy for design and operation of microfluidic systems. Lab Chip, 2023; 23(15):3311–3327; doi: 10.1039/d3lc00265a

52.

Kim

, Chesler

, Beebe

. A method for dynamic system characterization using hydraulic series resistance. Lab Chip, 2006; 6(5):639–644; doi: 10.1039/b517054k

53.

Mynard

, Davidson

, Penny

, et al. A simple, versatile valve model for use in lumped parameter and one-dimensional cardiovascular models. Int J Numer Method Biomed Eng, 2012; 28(6–7):626–641; doi: 10.1002/cnm.1466

54.

Canuto

, Chong

, Bowles

, et al. A regulated multiscale closed-loop cardiovascular model, with applications to hemorrhage and hypertension. Int J Numer Method Biomed Eng, 2018; 34(6):e2975; doi: 10.1002/cnm.2975

55.

Bernth

, Zhang

, Malas

, et al. MorphGI: A self-propelling soft robotic endoscope through morphing shape. Soft Robot, 2024; 11(4):670–683; doi: 10.1089/soro.2023.0096

56.

Gifari

, Naghibi

, Stramigioli

, et al. A review on recent advances in soft surgical robots for endoscopic applications. Int J Med Robot, 2019; 15(5):e2010; doi: 10.1002/rcs.2010

57.

Elton

, University of South Florida. Analyzation of the resistor-inductor-capacitor circuit. Ujmm, 2017; 7(2); doi: 10.5038/2326-3652.7.2.4876

58.

COMSOL Multiphysics® v. 6.2. COMSOL AB: Stockholm, Sweden: 2023. Available from: www.comsol.com

59.

Shin

Y-J

, Bleris

. Linear control theory for gene network modeling. PLoS One, 2010; 5(9):e12785; doi: 10.1371/journal.pone.0012785

60.

Silvia Filogna

, Vecchi

, Musco

, et al. A bioinspired fluid-filled soft linear actuator. Soft Robot, 2023; 10(3):454–466; doi: 10.1089/soro.2021.0091

61.

Xie

, Wang

, Yao

, et al. Design and modeling of a hydraulic soft actuator with three degrees of freedom. Smart Mater Struct, 2020; 29(12):125017; doi: 10.1088/1361-665X/abc26e

62.

Jyothish

, Mishra

. A survey on robotic prosthetics: Neuroprosthetics, soft actuators, and control strategies. ACM Comput Surv, 2024; 56(8):1–44; doi: 10.1145/3648355

63.

Morris

, Diteesawat

, Rahman

, et al. The-state-of-the-art of soft robotics to assist mobility: A review of physiotherapist and patient identified limitations of current lower-limb exoskeletons and the potential soft-robotic solutions. J Neuroeng Rehabil, 2023; 20(1):18; doi: 10.1186/s12984-022-01122-3

64.

Saldarriaga

, Gutierrez-Velasquez

, Colorado

. Soft hand exoskeletons for rehabilitation: Approaches to design, manufacturing methods, and future prospects. Robotics, 2024; 13(3):50; doi: 10.3390/robotics13030050

65.

Huang

, Wippold

, Stratis-Cullum

, et al. Eliminating air bubble in microfluidic systems utilizing integrated in-line sloped microstructures. Biomed Microdevices, 2020; 22(4):76; doi: 10.1007/s10544-020-00529-w

66.

Yenigun

, Gkouti

, Jankowski

, et al. Numerical validation of the influence of temperature on viscoelastic behavior of silicone rubber at low temperatures. In: Proceedings of the Canadian Society for Mechanical Engineering International Congress 2020. Charlottetown, PE; 2020.

67.

Malas

, Zhang

, Wang

, et al. Fluidic multichambered actuator and multiaxis intrinsic force sensing. Soft Robot, 2024; doi: 10.1089/soro.2023.0242

68.

McLeod

, Myint-Wilks

, Davies

, et al. The impact of noise in the operating theatre: A review of the evidence. Ann R Coll Surg Engl, 2021; 103(2):83–87; doi: 10.1308/rcsann.2020.7001

69.

Hansen DABaCH. Engineering Noise Control: Theory and Practice. Spon Press: Milton Park, Abingdon; 2009.

70.

Gonzalez

, Buigues

, Mazon

. Noise in electric motors: A comprehensive review. Energies, 2023; 16(14):5311; doi: 10.3390/en16145311

71.

Fang

, Chow

MCK

, Ho

JDL

, et al. Soft robotic manipulator for intraoperative MRI-guided transoral laser microsurgery. Sci Robot, 2021; 6(57):eabg5575; doi: 10.1126/scirobotics.abg5575

72.

National Fire Protection Association. NFPA 99: Health Care Facilities Code (Chapter 5). NFPA: Quincy, MA; 2012.

73.

Winters

, Subramanian

, Valdastri

. Robotic, self-propelled, self-steerable, and disposable colonoscopes: Reality or pipe dream? A state of the art review. World J Gastroenterol, 2022; 28(35):5093–5110; doi: 10.3748/wjg.v28.i35.5093

74.

Halim

, Ismail

. Online PID controller tuning using tree physiology optimization. In: International Conference on Intelligent and Advanced Systems, ICIAS. IEEE: Kuala Lumpur, Malaysia; 2016, pp. 1–5.

75.

Marechal

, Balland

, Lindenroth

, et al. Toward a common framework and database of materials for soft robotics. Soft Robot, 2021; 8(3):284–297; doi: 10.1089/soro.2019.0115

76.

Wang

, Zhang

, Zhu

, et al. A computationally efficient dynamical model of fluidic soft actuators and its experimental verification. Mechatronics, 2019; 58:1–8; doi: 10.1016/j.mechatronics.2018.11.012

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.15 MB

2.80 MB

0.06 MB

0.00 MB

A Novel Pneudraulic Actuation Method to Enhance Soft Robot Control

Abstract

Introduction

Materials and Methods

Pneudraulic actuation method

Soft fluidic actuator

Fundamentals of hydraulic-electric analogy

Fundamental of RLC circuit theory

Experiments

Results

Experiment 1

Experiment 2

Experiment 3

Experiment 4

Discussion

Actuation circuit

Fluidic circuit

Enhancement of bending speed

Conclusion

Footnotes

Authors’ Contributions

Author Disclosure Statement

Funding Information

Supplementary Material

References

Supplementary Material