Grasping Profile Control of a Soft Pneumatic Robotic Gripper for Delicate Gripping

Abstract

Soft pneumatic grippers (SPGs) have garnered significant attention and recognition in various industries owing to their remarkable flexibility, safety, and adaptability. They excel in manipulating delicate, irregularly shaped, and soft objects, surpassing the limitations of conventional grippers. However, effective control techniques for managing the grasping profile of SPGs are still under development. Simple on–off pressure control using a regulator valve is inadequate for delicate gripping with pneumatic robot grippers. To address this, a synergy pressure control system was implemented. In addition, a proportional–integral–derivative control technique, complemented by an unknown input observer, was devised to control the volume of the soft pneumatic robotic gripper, ensuring its alignment with the desired volume level. The simulation and experimental results provide substantial evidence of the effectiveness of the developed control technique and the unknown input observer in managing the volume and pressure of the gripper. Consequently, this breakthrough empowers precise and delicate gripping actions, enabling the handling of delicate objects such as tofu.

1. Introduction

Robotic grippers are essential components in robotics and automation because they serve as a crucial link between robots and the objects they handle. They perform various operations such as grasping, storing, transferring, and releasing objects [1,2]. They are known for their precision, consistency, versatility, and ability to operate in harsh environments, making them an essential component in modern manufacturing and assembly processes. These grippers, which are at the core of industrial automation, establish a vital physical link between robotic arms and the objects they manipulate. They are good at tasks such as lifting, transporting, moving, and releasing items, surpassing human capabilities in efficiency and consistency. Robotic grippers are indispensable, making robotic automation impossible without them [3,4]. The Industry 4.0 era will continue to enhance productivity, reduce labor costs, and improve safety in various sectors using robotic grippers [5,6].

Different industries rely on diverse ranges of robotic grippers tailored to their specific needs. Mechanical grippers, which are driven by pneumatic or electric actuators with mechanical linkages, excel in performing precise and repetitive tasks in manufacturing and assembly lines [7,8,9]. Vacuum grippers play a crucial role in packaging, as they securely grip delicate or irregularly shaped items by using suction to preserve their integrity [10,11]. Magnetic and electromagnetic grippers are primary choices in metal industries, offering reliable lifting and manipulation of ferrous materials, and enhancing productivity and safety [12,13]. Adaptive grippers are valued for their versatility in conforming to various object shapes, and are ideal for handling diverse objects in different environments [14,15,16]. Adhesive grippers securely grip objects using adhesion, and they provide stability and flexibility in handling irregular shapes, delicate surfaces, or complex textures [17]. These grippers are used in applications where other types of grippers may not be suitable or efficient. Overall, the selection of robotic grippers depends on the application and operational environment, enabling industries to optimize their processes [18,19].

Recently, soft grippers have gained significant attention and recognition in various industries owing to their exceptional flexibility, safety, and adaptability [20,21,22]. These grippers, which are made with compliant materials, can deform and conform to the shapes of the handled objects, providing a distinct advantage in managing various items. Soft grippers excel in manipulating delicate, irregularly shaped, and soft objects, overcoming the limitations of conventional grippers. Industries such as food processing rely on soft grippers to handle items without causing damage to them [23,24]. Furthermore, in environments requiring close human interaction, soft grippers significantly reduce the risk of injuries. Their versatility and gentle gripping ability make them a vital robotic tool for effectively and safely handling delicate objects. Researchers are actively developing and refining soft grippers, recognizing their potential to revolutionize various applications across industries. Continuous improvement unlocks new possibilities and expands the range of tasks that soft grippers can undertake.

Soft pneumatic grippers (SPGs) are a common type of soft gripper (Figure 1). They are widely used soft grippers, which are composed of two or more soft pneumatic actuators (SPAs). The main advantage of SPAs is their inherent flexibility, providing excellent compliance that allows for SPGs to grip diverse objects with simple control [25,26]. However, because of their infinite number of degrees of freedom and nonlinear characteristics, the operation of SPAs poses a significant challenge, necessitating the development of control techniques for the effective modeling and control of SPAs and SPG grasping [27,28]. Various control techniques have been devised specifically for these actuators, allowing for the efficient control of SPGs in delicate grasping applications.

Researchers have made significant progress in developing models for SPGs, including empirical models of SPAs [29], analytical SPA models of variable length [30], analytical models and feedback control [31,32], analytical models of amphibious SPAs [33], analytical models of SPAs with parametric identification [34], and analytical models and observer-based feedback control of SPAs [35]. However, the development of control techniques to effectively manage the grasping profile of SPGs is still underway.

An air pump with a digital regulator is a common actuator used to control the grasping profile of an SPG. Because of its low cost, the air compressor pump is commonly used to supply compressed air or gas to gripper pneumatic systems, allowing for the adjustment of the gripping force and speed [36,37]. However, this actuator has some disadvantages in terms of pressure control. Accurately controlling the pressure using a digital regulator can be challenging because it cannot provide fine-grained control over the desired pressure levels required for managing the grasping profile. The resulting operation is limited to on–off or step pressure controls. Additionally, the inability of this actuator to directly control the air volume makes it impossible to precisely regulate the grip force. Consequently, the grip force cannot be accurately controlled. When using an air compressor pump with the SPG, it cannot handle delicate objects such as tofu (Figure 1a). Although a screw air compressor pump can provide precise control of the pressure, volume, and grasping profile, it is too expensive for this case.

To overcome this issue, this study has used an air compressor pump with digital regulators and a pneumatic cylinder actuator [38,39] to control the grasping profile of the SPG. An air compressor pump with a digital regulator generate air pressure close to the desired point, while the pneumatic cylinder actuator fine-tunes and tracks the air pressure profile by controlling the pressure through linear motion. With this actuator set, advanced control techniques can be used to control the air pressure and volume of the gripper profile. The air compressor pump and pneumatic cylinder actuator precisely regulate the air pressure and volume, allowing for the effective manipulation of the grasping profile. The SPG can open and close the gripper fingers according to the desired profile using this actuator set, allowing it to handle delicate objects such as tofu (Figure 1b).

To control the grasping profile of the SPG, this study presents a system architecture and implementation of an air compressor pump with a digital regulator and pneumatic cylinder actuator. Furthermore, a control technique that involves an unknown nonlinear input observer is introduced to track the volume of the SPG, thereby controlling its grasping profile.

The following list outlines the contributions of this work:

• The design of an actuator set for controlling the SPG, comprising an air compressor pump with digital regulators and a pneumatic cylinder actuator along with its associated accessories.
• The development of a control technique that is capable of estimating unknown inputs of the system and effectively regulating the pressure and volume within the system.

The remaining sections of this article are organized as follows: Section 2 provides an overview of the system architecture, including the implementation details of the air compressor pump with a digital regulator and pneumatic cylinder actuator. This section also presents the mathematical model of the system, an unknown nonlinear input observer, and control techniques. The results and discussion of the proposed approach and its benefits are presented in Section 3. Finally, Section 4 presents the conclusions.

2. Materials and Methods

The soft gripper system comprises two main components, which are the system hardware and the control techniques. In Section 2.1, the system architecture of SPG is presented, while Section 2.2 focuses on the dynamic model and control technique for the system.

2.1. The System Architecture of Soft Pneumatic Gripper

Figure 2 illustrates the system components of the SPG, which primarily consist of the gripper and synergy pressure control system.

The SPG is a custom-made gripper that was developed in the Mechanical Engineering Laboratory at Chulalongkorn University using a casting technique. Autodesk Fusion 360, a three-dimensional computer-aided design, was used to design the gripper molds (Figure 3a). During the casting process, the SPG was fabricated using RA25RA silicone. To ensure the absence of air bubbles that can cause leakage in the SPG, the casting process was performed in a vacuum chamber. Subsequently, the molds were placed in an oven for 45 min to allow for the silicone to set. After the setting process, the gripper was carefully removed from the molds. The final fabricated SPG is shown in Figure 3b. Note that this study does not provide a detailed account of the fabrication process of SPGs. The focus of this study is not on the casting process, so the intricate details regarding the fabrication of the SPG are not discussed.

The synergy pressure control system (Figure 2) comprises an air compressor pump used to compress ambient air and store the compressed air in a Festo air reservoir, 750 mL, G1/4, CRVZS Series, 16-bar pressure tank. The pressure from the tank was regulated to the desired set point using a regulator (SMC E/P Regulator ITV2030-322S). However, the pressure tank and regulator valve alone cannot provide precise control over the required pressure and volume levels required for managing the grasping profile.

To achieve the desired pressure and volume control, a pneumatic cylinder, which is a magnetically coupled rodless cylinder, was used. This cylinder was connected and equipped with a linear stage, a ball screw linear stage with a 100 mm effective stroke, and a 16 mm linear shaft diameter. The ball screw position of the linear stage controls the position of the pneumatic cylinder piston. The ball screw position was driven using a DC motor (Leadshine Brushed DC Servo Motor DCM57207D-1000) and an encoder. The motor driver board, Smile Robotics PRIK-THAI, was used to control the DC motor.

To integrate the pressure from the pressure tank and pneumatic cylinder, two 3/2 solenoid valves were used (Figure 2b). A valve was used to switch the pressure channels to supply air to the SPG, while another valve was used to release pressure. The pressure tank and regulator provide a rough pressure level for the system, while the pneumatic cylinder allows for precise control of air pressure and volume, allowing for fine-grained adjustments to the desired pressure and volume levels.

Power was supplied to the system via AC77-02, which converts 220 VAC to 24 VDC. The overall system was controlled using a BBBWL-SC-562 BeagleBone Black controller board, which has programmable real-time units and supports the Simulink coder support package for BeagleBone Blue hardware via the MathWorks Embedded Coder team. This enables the program to be developed using real-time MATLAB Simulink [40]. With the synergy pressure control system, the grasping profile of the SPG can be effectively controlled.

2.2. Dynamic Model and Control Technique for the System

The dynamic model of the system used to control the pressure and volume of the SPG is defined in Section 2.2.1. Then, the unknown input observer used to estimate the gripper volume is presented in Section 2.2.2, and the control technique used to control the SPG is presented in Section 2.2.3.

2.2.1. Dynamic Model of the System

The system comprises a dynamic model of the DC motor with a ball screw linear stage, pneumatic cylinder, and SPG. By utilizing Newton’s second and Kirchhoff’s voltage laws, the dynamic equations for the DC motor with a ball screw linear stage can be derived. These equations are represented as Equations (1) and (2), with Equation (1) specifically describing the electric circuit of the motor.

$$L\frac{di}{dt}=-Ri-K_e\dot{\theta }+V$$

(1)

where $L$ is electric inductance, $i$ is electric current, $R$ is electric resistance, $K_e$ is electromotive force constant, $\theta$ is the angular position of the motor, $V$ is electric voltage, and $t$ is time.

The dynamic model of the rotor is shown in Equation (2).

$$J\ddot{\theta }=K_{t}i-b\dot{\theta }-\Delta F_D-\psi \left(\theta \right)$$

(2)

where $J$ is the moment of inertia of the rotor, $K_t$ is motor torque constant, $b$ is motor viscous friction constant, $\Delta =\frac{l}{2\pi {\eta }_{thread}{\eta }_{thrust}}$, with $l$ as the pitch of the ball screw and ${\eta }_{thread}$ and ${\eta }_{thrust}$ are the efficiencies of the thread and thrust bearing of the ball screw linear stage, respectively [41], $F_D$ is the reaction force from the pneumatic cylinder, and $\psi$ is the nonlinear friction of the system [42].

For the pneumatic cylinder, its free body diagram is shown in Figure 4a, and the pneumatic cylinder equations are shown in Equations (3) and (4).

$$m{\ddot{x}}_1=P{A}_1-F_D$$

(3)

$$x_1=\frac{l\theta }{2\pi }$$

(4)

where $m$ is the mass of the pneumatic cylinder piston, $x_1$ is the position of the piston, $P$ is air pressure, $A_1$ is the cross-section area of the piston, and $l$ is the pitch of the ball screw.

The gripper’s deformation or position may be modeled as a pneumatic cylinder attached to a spring. Additionally, the free body diagram of the gripper is shown in Figure 4b, and the gripper equation is shown in Equation (5).

$$M{\ddot{x}}_2=P{A}_2-k{x}_2-d{\dot{x}}_2$$

(5)

where $M$ is the mass of the gripper, $x_2$ is the deformation or position of the gripper, $A_2$ is the cross-section area of the equivalent piston, $k$ is the spring stiffness of the gripper, and $d$ is the damping coefficient of the gripper.

Based on Boyle’s law, the pressure in the system is defined by

$$P\left(v_1+A_1{x}_1+v_2+A_2{x}_2\right)=P^{\prime }\left(v_1+v_2\right),$$

(6)

$$P=\frac{P^{\prime }\left(v_1+v_2\right)}{\left(v_1+A_1{x}_1+v_2+A_2{x}_2\right)}$$

(7)

where $P^{\prime }$ is the initial pressure of the system, $v_1$ is the initial volume of the pneumatic cylinder, and $v_2$ is the initial volume of the SPG. $v_1+A_1{x}_1$ represents the volume of the pneumatic cylinder, and $v_2+A_2{x}_2$ represents the volume of the SPG.

If Equation (4) is put into Equation (3) and then the result is put into Equation (2), Equation (2) becomes

$$\left(J-\Delta m\frac{l}{2\pi }\right)\ddot{\theta }=K_{t}i-b\dot{\theta }-\Delta A_{1}P-\psi \left(\theta \right)$$

(8)

where $P$ is defined by Equation (7).

With Equations (1), (5), and (8), the state space model of the system is defined by

$$\left[\begin{array}{c}\frac{di}{dt}\\ \ddot{\theta }\\ \dot{\theta }\end{array}\right]=\left[\begin{array}{ccc}-R/L& -K_e/L& 0\\ K_t/J_e& -b/J_e& 0\\ 0& 1& 0\end{array}\right]\left[\begin{array}{c}i\\ \dot{\theta }\\ \theta \end{array}\right]+\left[\begin{array}{c}1/L\\ 0\\ 0\end{array}\right]V+\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right]{\mu }_1+\left[\begin{array}{c}0\\ \psi \left(\theta \right)/J_e\\ 0\end{array}\right],$$

(9)

$${\mu }_1=-\frac{\Delta A_1}{J_e}\frac{P^{\prime }\left(v_1+v_2\right)}{\left(v_1+v_2+A_1\frac{l\theta }{2\pi }+A_2{x}_2\right)}$$

(10)

$$\left[\begin{array}{c}{\ddot{x}}_2\\ {\dot{x}}_2\end{array}\right]=\left[\begin{array}{cc}-d/M& -k/M\\ 1& 0\end{array}\right]\left[\begin{array}{c}{\dot{x}}_2\\ x_2\end{array}\right]+\left[\begin{array}{c}1\\ 0\end{array}\right]{\mu }_2$$

(11)

$${\mu }_2=\frac{A_2}{M}\frac{P^{\prime }\left(v_1+v_2\right)}{\left(v_1+v_2+A_1\frac{l\theta }{2\pi }+A_2{x}_2\right)}$$

(12)

where $J_e=\left(J-\Delta m\frac{l}{2\pi }\right)$.

For this system, the angular position of the motor, $\theta$, can be measured. The measurement equation is defined by

$$y=\left[\begin{array}{ccc}0& 0& 1\end{array}\right]\left[\begin{array}{c}i\\ \dot{\theta }\\ \theta \end{array}\right].$$

(13)

In summary, the dynamic model of the system is presented in Equations (9)–(13). The inputs of the system are voltage $V$ and initial pressure $P^{\prime }$, and the measurement output is the angular position of the motor $\theta$.

2.2.2. Unknown Input Observer

The gripper volume must be controlled to control the grasping profile of the SPG. The proportional–integral–derivative (PID) control is used to control the system [42]. Figure 5 illustrates the control architecture of the system. However, because direct measurement of the gripper volume is not feasible, an unknown input observer is introduced and used to estimate the gripper volume and system state.

This section presents a methodology for designing observers for the class of unknown input nonlinear systems described by

$$\dot{x}=\overline{A}x+\eta \left(x,u\right)+\overline{B}\mu ,$$

(14)

$$y=Cx$$

(15)

where $x$ is the state variable of the system, $u\in R^P$ are the known control inputs, $\mu \in R^P$ are the unknown inputs, and $y\in R^q$ are the output measurements. $\overline{A}\in R^{n\times n}$, $\overline{B}\in R^{n\times p}$, and $C\in R^{q\times n}$ are appropriate matrixes. The function $\eta \left(x,u\right):R^n\times R^p\to R^n$ is nonlinear. In addition, $\eta \left(x,u\right)$ is a differentiable nonlinear function with globally (or locally) bounded Jacobian.

According to unknown input estimation in Ref. [43], the relative degree of the system is defined, and Theorem 1 for single unknown input nonlinear estimation and multi unknown input nonlinear estimation is developed [43]. The estimated unknown input of the SPG system is then used to estimate the unknown gripper volume as follows:

$$\widehat{\mu }={\left(C{\overline{A}}^{r_{\mu }-1}\overline{B}\right)}^{-1}\left[y_f^{\left(r_{\mu }\right)}-C{\overline{A}}^{r_{\mu }}x-C{\overline{A}}^{r_{\mu }-1}\eta \left(x,u\right)\right],$$

(16)

where $\widehat{\mu }$ is the estimated unknown input, $r_{\mu }$ is the relative degree from $\mu$ to $y$, and $y_f$ is the output derivative. Also, the output derivatives, $y_f$, can be filtered using a low-pass filter to minimize noise.

Once the unknown input, $\mu$, is estimated, it can be substituted with the estimated unknown input, $\widehat{\mu }$, in Equation (14). Consequently, the problem statement comprising Equations (14) and (15) can be rearranged into the standard nonlinear form, defined as

$$\dot{x}=Ax+\mathsf{\Phi }\left(x,u\right)+g\left(y_f\right),$$

(17)

$$y=Cx$$

(18)

where $A\in R^{n\times n}$ are appropriate matrixes. The function $\mathsf{\Phi }\left(x,u\right):R^n\times R^p\to R^n$ is nonlinear. In addition, $\mathsf{\Phi }\left(x,u\right)$ are differentiable nonlinear functions with globally (or locally) bounded Jacobian.

Then, the system is defined via Equations (17) and (18) and the standard nonlinear form. Refs. [43,44] can be used for the problem. The standard observer is assumed to be of the form

$$\dot{\widehat{x}}=A\widehat{x}+\mathsf{\Phi }\left(\widehat{x},u\right)+g\left(y_f\right)+L\left(y-\widehat{y}\right),$$

(19)

$$\widehat{y}=C\widehat{x}{.}_{ }$$

(20)

where $\widehat{x}$ is the state estimation, $\widehat{y}$ is the measurement estimation, and $L$ is observer gain, which can be computed as a standard nonlinear observer [43,44].

To design the observer, first, the unknown input ${\mu }_1$ in Equation (10) must be estimated. Equations (9) and (13) are arranged in the form of Equations (14) and (15).

$$\overline{A}=\left[\begin{array}{ccc}-R/L& -K_e/L& 0\\ K_t/J_e& -b/J_e& 0\\ 0& 1& 0\end{array}\right],\eta \left(x,u\right)=\left[\begin{array}{c}1/L\\ 0\\ 0\end{array}\right]V+\left[\begin{array}{c}0\\ \psi \left(\theta \right)/J_e\\ 0\end{array}\right],\overline{B}=\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right]$$

(21)

$$C={\left[\begin{array}{ccc}0& 0& 1\end{array}\right]}_{ }$$

(22)

Then, ${\mu }_1$ can be estimated using Equation (16), and the estimation of ${\mu }_1$ is shown in Equation (23).

$${\widehat{\mu }}_1={\ddot{y}}_f-\frac{K_t}{J_e}\widehat{i}+\frac{b}{J_e}\widehat{\dot{\theta }}-\frac{\psi \left(\widehat{\theta }\right)}{J_e}$$

(23)

where ${\ddot{y}}_f$ is $\ddot{\theta }$ and it can be filtered via a low-pass filter to minimize noise.

Once ${\mu }_1$ is known, the deformation or position of the gripper $x_2$ can be estimated using the algebraic relation of Equation (10). Additionally, the volume of the SPG can be computed using $v_2+A_2{x}_2$. Then, the system can be defined in the form of Equations (17) and (18), and the standard nonlinear observer [43,44] can be used to solve the problem.

Most of the system parameters can be found in the component datasheets. However, because the SPG is a custom-made gripper, some experimentation is required to define its parameters. The initial volume of the SPG, $v_2$, is critical and difficult to determine.

Because of the variation in initial volumes in the SPG at different pressures, it is necessary to establish a relationship between pressure and SPG volume to accurately determine the initial volume. The initial volume at atmospheric pressure can be determined by measuring the volume of water injected into the SPG. Then, for the initial volume above atmosphere pressure, the approach involves introducing a specific volume of air into the SPG using a syringe and measuring the resulting pressure at various points. The setup of this experiment is shown in Figure 6a. Additionally, capturing images of the soft gripper’s movement serves as a reference for evaluating the experimental outcomes precisely. The relationship between pressure and SPG volume is shown in Figure 6b. A summary of the important parameters of the SPG system is shown in

Table 1. The important parameters of the SPG system.

Components	Parameters	Value	Unit
Pneumatic Cylinder	Volume, $v_1$	25.5	$\mathrm{mL}$
	Cross-Section Area of the Piston, $A_1$	16.67	${\mathrm{mm}}^2$
	Mass of the Piston, $m$	0.736	$\mathrm{kg}$
	Stroke Length	153	$\mathrm{mm}$
SPG	Volume, $v_2$ @1atm	23.6	$\mathrm{mL}$
	Mass of the Gripper	0.1	kg
DC Motor	Moment of Inertia of the Rotor, $J$	$4.73\times {10}^{-5}$	$\mathrm{kg}·{\mathrm{m}}^2$
	Electric Resistance, $R$	0.9	$\mathrm{ohm}$
	Electric Inductance, $L$	$3.6\times {10}^{-3}$	$\mathrm{H}$
	Electromotive Force Constant, $K_e$	$80\times {10}^{-3}$	$\mathrm{N}·\mathrm{m}/\mathrm{A}$
	Motor Torque Constant, $K_t$	$80\times {10}^{-3}$	$\mathrm{N}·\mathrm{m}/\mathrm{A}$
Linear Stage	Pitch of the Ball Screw, $l$		$\mathrm{mm}$
	Efficiencies of the Thread of Ball Screw, ${\eta }_{thread}$	0.9
	Efficiencies of the Thrust Bearing of Ball Screw, ${\eta }_{thrust}$	0.9
Encoder	Pulse per Revolution	4000	$\mathrm{ppr}$
	1 Pulse of Encoder	0.006375	$\mathrm{mm}$
The System	Dead Volume	17.15	$\mathrm{mL}$
	Atmospheric Pressure	1	$\mathrm{Bar}$

.

To verify the relationship among SPG volume, pressure, and gripper distance, a syringe with a scale is used to calibrate the gripper response because its behavior is not known a priori. In this experiment, the pressure was kept constant, and the syringe was used to introduce air into the gripper. The air capacity of the syringe was significantly lower than that of the air tank to ensure that pressure remained monitored and constant throughout the experiment. Consequently, the air volume was incrementally pumped into the gripper using a scaled syringe at various pressures, including 0, 0.5, 1, and 1.5 bars.

As air is introduced, the gripper bends, and its position is measured using image processing. The resulting data were then used to generate a correlation between the fed air volume and the distance between the gripper’s tips. The results of the experiment are shown in

Table 2. The relationship between SPG volume, pressure, and gripper distance.

Gripper Volume Setting via a Syringe (mL)	Gripper Distance, D (mm)
	Gripper Distance with Syringe Pressure Control	$\mathbf{Initial} \mathit{p} = 0 \mathbf{bar}$	$\mathbf{Initial} \mathit{p} = 0.5 \mathbf{bar}$	$\mathbf{Initial} \mathit{p} = 1 \mathbf{bar}$	$\mathbf{Initial} \mathit{p} = 1.5 \mathbf{bar}$
24	48.5	42.0	-	-	-
25	30.0	33.1	-	-	-
27	23.4	22.3	22.2	-	-
29	16.9	14.4	15.8	17.3	-
31	9.7	6.2	9.3	9.7	10.5
33	3.7	0	3.2	2.6	3.7
36	0	0	0	0	0

. The same air volume introduced into the gripper leads to slightly different gripper positions at various air pressures, particularly at higher pressures.

To verify the unknown input observer, the simulation was implemented in MATLAB R2023a, and the simulation setup is shown in Figure 7. The results of the simulation are shown in Section 3.

2.2.3. Control Technique

PID control was selected for the system to control the volume of the SPG. The measurement of the SPG volume can be estimated using an unknown input observer. The control architecture of the system is shown in Figure 5.

In this case, the standard PID controller was used to control the SPG volume. The signal from the motor encoder sensor was used as an input to the unknown input observer. The volume of the SPG can be estimated using the unknown input observer. To achieve high-speed control, the PID control for motor position control was designed in real-time using MATLAB Simulink [40] (Figure 8). The Simulink also included the stage flow to control the sequence and logic control of the system. Then, using the Simulink package and MathWorks Embedded Coder team BeagleBone Blue hardware, a sample rate of 1000 Hz was achieved with the system. The PID control was designed to control the motor position, and the feedback control was calculated using the estimated SPG volume. In this case, the Ziegler–Nichols method [43] was employed as a guideline for fine-tuning the PID gains of the system.

3. Experimental Results and Discussion

3.1. The Simulation Results of Unknown Input Observer

Figure 9 shows the estimated SPG volume based on the design of the unknown input observer and its implementation in MATLAB, as described in Section 2.2.2. The results demonstrate that the estimated SPG volume quickly converges on the corrected actual value from the initial guess value. The SPG volume ranges from 20 to 28 mL, and the estimated volume closely matches the actual value. Consequently, the unknown input observer can be successfully used to estimate the volume of the SPG.

3.2. Experimental Results of the System

To control the volume of the SPG, the PID control and the unknown input observer were implemented, as described in Section 2.2.3. The PID parameters must be tuned to optimize the SPG volume response. The experiment was set up as follows: first, the initial SPG volume was set to 24 mL, and then the SPG volume was commanded to 30 mL, as shown in the reference value curve in Figure 10. Figure 10 also presents the SPG volume response with various sets of PID parameters.

Based on the results in the figure, the PID parameters with $K_p=5$ and $K_d=0.01$ provide the best SPG volume response in terms of the setting time, overshoot, and steady-state error. The setting time is less than 1 s, the overshoot is zero, and the steady-state error is close to zero. Therefore, these PID parameters are deemed suitable for the system.

To verify the tracking response of the system, the experiment was set up as follows: the SPG volume was made to track a step-up and down function by first commanding the system to a volume of 28 mL (gripper close), and then changing it to a volume of 20 mL (gripper open) and repeating this cycle. The results of the tracking response are shown in Figure 11, indicating that the SPG volume (red line) successfully tracks the desired volume (black line) with a low steady-state error, no overshoot, and a setting time of less than 1 s.

The SPG volume tracking behavior was evaluated in the following experiment when the initial pressure was set at different levels using a regulator valve. The experimental setup was as follows: The initial pressure was adjusted to various values, namely 0, 0.06, 0.08, 0.13, and 0.18 bars above the atmospheric pressure. Subsequently, the desired SPG volume was set to 33 mL for all initial pressure conditions. For each initial pressure, the gripper’s steady-state pressure and gripper position in the steady-state were compared. The experimental results are shown in Figure 12.

Figure 12 shows that the system can adjust the SPG volume to 33 mL for most initial pressure values, except for the 0.18 bar. In this scenario, the initial gripper volume is already close to 33 mL, so the system makes no further adjustments.

Furthermore, when the steady-state pressure for each case was considered, the system performed effectively when the initial pressure was compressed within the range of 0.05–0.13 bar. The steady-state pressure and gripper elongation posture values obtained were consistent with the results of the experiments that determined the relationship between the gripper volume and pressure.

For initial pressures of 0 and 0.18 bar, the obtained values for the gripper’s steady-state pressure and elongation posture deviated from the expected results based on the experimental relationship equation between the initial SPG volume and pressure. This deviation could be due to the nonlinear behavior of the SPG. Therefore, this behavior could be corrected by fine-tuning the control law. Based on the experimental results in Figure 12, the system can be operated within the pressure range of 0.05–0.13 bar, which would ensure a more accurate and reliable measurement of the gripper volume.

3.3. Discussion

The system consisting of an air compressor pump with a digital regulator and pneumatic cylinder actuators is designed in a systematic manner. The system, along with its components such as the syringe, tube, and connectors, adheres to pneumatic standards. Although the system may experience minimal leakage during operation, it functions as a closed-loop control system. This enables the regulation of the pressure within the system, ensuring efficient performance and functionality.

Force is an important parameter that needs to be controlled. If the force is too high, it can cause damage to the object. However, controlling the force alone is not sufficient to handle delicate objects, which are soft, have low stiffness, and are elastic. Delicate objects are susceptible to damage due to momentum. Momentum is related by the mass and velocity of the SPG during grasping, and therefore, the velocity must be controlled. Using on–off pressure control to manipulate the SPG does not effectively control the grasping velocity. In this developed technique, the SPG force can be controlled using pressure control, while the SPG velocity can be managed through the developed system and controller for the grasping profile control. Consequently, using this developed technique, the SPG becomes capable of handling delicate objects.

For the control system, the air compressor pump with a digital regulator and pneumatic cylinder actuators are used to control the grasping profile of the SPG. The air compressor pump with a digital regulator generates air pressure close to the desired point. Then, the pneumatic cylinder actuator is used to fine-tune and track the air pressure profile created by the developed system through linear motion. Also, the developed controller technique can be used to control the air pressure and volume of the gripper profile. Air compressor pumps and pneumatic cylinder actuators provide precise regulation of the air pressure and volume, allowing for the effective manipulation of the grasping profile. The SPG can open and close the gripper fingers according to the desired profile using this actuator set, allowing it to handle delicate objects. However, due to the incorporation of the new developed technique, the control system may appear complex in nature.

In order to establish a suitable grasping profile for delicate objects, a series of experiments need to be conducted to determine a suitable grasping profile. Once the desired grasping profile is identified or designed, the actuator set and developed control technique are used to regulate and track the grasping profile of the SPG, ensuring that it aligns with the designed profile.

In summary, both the simulation and experimental results demonstrate that the developed control technique and unknown input observer are effective in controlling the volume and pressure of the SPG. Consequently, the grasping profile of the SPG can be controlled, allowing for precise and delicate gripping actions. The SPG can accurately open and close its gripper fingers according to the desired profile using the synergy pressure control system and the developed control technique, as depicted in Figure 1b. This capability enables the handling of delicate objects, such as tofu, with enhanced control and precision.

4. Conclusions

To achieve delicate gripping with a soft pneumatic robotic gripper, a synergy pressure control system was implemented to overcome the limitations of simple on–off pressure control using a regulator valve. This system incorporated a pressure tank and a regulator to establish a rough pressure level for the entire system. Additionally, the precise control of the air pressure and volume was enabled through the integration of a pneumatic cylinder, facilitating fine adjustments to the desired pressure and volume levels. Furthermore, a PID control technique, complemented by an unknown input observer, was developed to track the volume of the gripper. This approach ensures the accurate tracking of the desired volume level by estimating the gripper’s volume using the unknown input observer and employing PID control to fine-tune the pneumatic cylinder. The simulation and experimental results validate the efficacy of the developed control technique and unknown input observer in effectively managing the gripper volume and pressure. Consequently, this advancement enables precise and delicate gripping actions, allowing for the proficient handling of delicate objects like tofu.

With the successful development of the actuator set and controller, the control of the gripper fingers in the SPG becomes significantly easier. Consequently, in future research, the emphasis will be placed on studying the grasping of objects with different shapes and materials. The focus will be on exploring methods for generating or selecting appropriate grasping profiles for each specific object. This study will involve analyzing the characteristics and requirements of various objects to develop effective grasping strategies. The goal is to enhance the SPG’s versatility and adaptability in handling a wide range of objects.