Design, Characteristic Analysis and Modeling of a Tailored Soft Robot for Phosphorite Grabbing

Abstract

The grabbing of phosphorite rocks is an important process in the mining industry. Traditional grabbing technology based on rigid robots faces challenges such as heavy weight, low flexibility, and insufficient safety. This study presents the structural design, characteristic analysis, and modeling of a novel tailored soft robot for phosphorite grabbing (TSRPG). The TSRPG is designed with soft, flexible materials, providing flexible movement and high safety in complex environments. The design inspiration of the robot comes from humans using their thumb and index finger to hold things, and the structural design mainly focuses on the flexibility and grabbing function of the robot. The grabbing function of the TSRPG is exhibited by several actual grabbing experiments. In addition, through characteristic analysis, we explore the robot’s motion properties under various input air pressure conditions. A mathematical model of the TSRPG is developed to depict its characteristics based on the nonlinear ARX model. The developed mathematical model provides a base for promoting the practical application of the TSRPG.

1. Introduction

In the production process of the phosphate rock industry, the grasping process of mineral raw materials plays a decisive role in product quality and production efficiency [1,2]. The operational efficiency of this link not only affects the operational effectiveness of the entire production line but also directly influences the cost control level of the enterprise. To this end, phosphate mining enterprises have continuously carried out technological innovation by introducing intelligent grasping equipment, reconfiguring production processes, implementing precise operation management, etc. [3,4]. This process optimization achieved through technological innovation not only effectively reduces the raw material loss rate and human error rate but also significantly enhances the enterprise’s cost control ability, thereby building a significant technological and economic advantage in industry competition.

In the field of phosphate rock raw material grasping, the rise of soft robot technology has provided a brand-new solution for the traditional operation mode. This type of robot is mainly constructed with flexible materials, and its driving mechanism also has excellent deformation characteristics [5]. With the breakthrough progress of intelligent material preparation technology and bionic drive technology, soft robots have become a cutting-edge research direction in the field of intelligent equipment [6,7]. At present, bionic soft grippers [8], soft bionic fish [9], soft-wing aircraft [10], etc., have been developed. Their inherent flexible characteristics not only ensure the safety of human–machine collaborative operations but also demonstrate unique adaptive advantages in the field of industrial grasping.

According to the driving mode of the soft robot, soft robots can be divided into soft pneumatics [11], soft hydraulic robots [12], soft electric robots [10], soft optical robots [13], soft thermal robots [14], soft magnetic robots [15] and so on. Due to the soft actuators of the above robots being made of soft smart materials, these soft robots are termed smart-material-based soft robots [16]. In the field of soft robots, soft smart materials usually include electroactive polymers [17], liquid crystal elastomers [18], shape memory polymers [19], and soft magnetic composite materials [20]. In the field of soft robot technology, the innovative application of intelligent materials shows significant potential for functional expansion. Although intelligent flexible materials represented by shape memory alloys and intermediate polymers can achieve the self-perception of deformation and multi-modal driving functions, their preparation costs are high, and there are engineering and technical problems with complex multi-field coupling response characteristics [21,22].

Compared with intelligent material-based robots, soft hydraulic robots not only have higher construction costs but also need to meet stringent sealing performance requirements for their core actuators [23], which poses a dual challenge for material processes and system design. Considering the manufacturing cost, process complexity and equipment reliability, pneumatically driven soft robots show stronger potential for engineering applications [24,25,26]. Currently, researchers have developed a variety of innovative pneumatic soft-bodied robots, such as bubble casting robots based on compressed air drive to realize controlled deformation [27], bionic robots using pneumatic muscle arrays to achieve agility of movement [28], and multi-environmental adaptability of the turtle-like soft pneumatic devices with multi-environmental adaptability [29]. In the field of industrial gripping, flexible gripping jaw systems based on bellow actuators [30] and adaptive pneumatic manipulators [31] are also gradually being developed. Overall, research on soft pneumatic grippers is just beginning. To the best of our knowledge, the exploration of soft pneumatic grippers when applied to mineral handling is scarce. The mechanical design, characteristic analysis, modeling, and control of the soft pneumatic grippers are facing great difficulties, providing researchers with a large number of research topics.

Inspired by the advantages of soft pneumatic robots, the tailored soft robot for phosphorite grabbing (TSRPG) has a huge research value and application potential, which can be used to conduct mineral beneficiation in a safe and efficient way. However, the design and manufacturing of the TSRPG confront difficulties. In addition, to enable the mineral beneficiation of the TSRPG to become flexible and controllable, an urgent problem to be solved is achieving its modeling and control. The most crucial problem is establishing a model of the TSRPG’s soft pneumatic actuator (SPA). However, the SPA has complicated hysteretic characteristics and creep characteristics, which pose great difficulties in its modeling [32]. For the construction of the SPA model, there are mainly two methods: theoretical modeling based on physical mechanisms and data-driven phenomenological modeling. Moseley et al. [32] constructed a three-dimensional structural mechanics model of SPA through the study of the constitutive relationship of superelastic materials. Shen et al. [33] established a comprehensive dynamic model covering load transfer and fluid dynamic characteristics from the perspective of multi-physics coupling. However, such local model construction methods often involve complex nonlinear coupling processes. To enhance the practicability of the model, some phenomenological modeling methods have been proposed. Dao et al. [34] effectively characterized the dynamic response characteristics of SPA by using the improved Bouc–Wen hysteresis model. Based on the Prandtl–Ishlinski modeling framework, Xie et al.’s [35] research group has achieved the description of the nonlinear hysteresis effect of the actuator. However, these phenomenological models are also complicated. In general, seeking a simple SPA modeling method is the key and prerequisite for implementing applications of the TSRPG.

In response to the above-mentioned problems, this study manufactures a TSRPG and presents its modeling method. The production of TSRPG is completed by integrating the soft pneumatic drive technology and the thermoplastic injection molding process. To verify the performance of TSRPG, two sets of experimental test systems (System A and System B) are constructed. Next, by using experimental testbench A, a series of grabbing experiments on the TSRPG are conducted to exhibit its grabbing function. Moreover, by using experimental testbench B and applying compressed air with four different pressure patterns to the SPA, the experimental study of the SPA is conducted to reveal its characteristics. After that, a dynamic model of the SPA is established based on the nonlinear ARX model and neural network. This research will significantly promote the application of TSRPGs in engineering practice, thereby improving the efficiency of auto production processes.

The rest of this paper is organized as follows. Section 2 introduces the design and manufacturing of the SPA and TSRPG. Section 3 builds two experimental test benches. Section 4 conducts some grabbing experiments on the TSRPG. Section 5 studies the characteristics of the SPA of the TSRPG. Section 4 establishes the SPA model. Finally, Section 6 provides the conclusion.

2. Structural Design and Manufacturing of TSRPG

This part describes the structural design of a new soft body pneumatic actuator SPA and completes the structural fabrication of the TSRPG by making two actual SPAs.

2.1. Design of SPA

Figure 1 shows the 3D engineering drawing of the SPA and its key dimensioning. The actuator body adopts a rectangular configuration with a length, width and height of 100 mm, 18 mm and 20 mm respectively, and six interconnected pneumatic chambers are integrated inside. The geometrical parameters and topological features of the cavity structure can be clearly observed through the magnified local section view.

Figure 2 presents the global profile structure of the SPA, which consists of a composite structure of the inlet port, deformation cavity, and silicone matrix with a constraining layer. The deformation mechanism of the actuator is shown as follows: after the compressed gas is injected into the cavity through the inlet port, the silicone matrix deforms elastically under the effect of air pressure, resulting in the expansion of the cavity volume with the pressure increase. Due to the deformation suppression properties of the constraining layer, the cavity side is significantly expanded while the constraining layer side is limited, resulting in a directional bending motion towards the constraining layer (see Figure 2). This asymmetric deformation mechanism provides the driving principle for the mechanical design of the subsequent gripping device.

2.2. Design of TSRPG

The 3D assembly model of the TSRPG is shown in Figure 3. The device consists of two sets of symmetrically distributed soft body pneumatic actuator units (SPA1 and SPA2) and a base plate. The SPAs are assembled with the base plate through assembly to form a grasping device with symmetric topological features.

The designed TSRPG has a certain novelty. Compared to existing soft pneumatic grippers reported in [8,31], the TSRPG has a smaller number of cavities. Specifically, the TSRPG has 6 cavities, and the grippers reported in [8,31] have 11 and 8 cavities. In addition, at the end of the TSRPG, there is not a cavity, but a solid structure with a sloping surface, which makes it easier for two fingers to close and grab. Compared to the gripper reported in [30], the TSRPG itself is both an actuator and a gripper, without the need to design additional gripping mechanisms. So the TSRPG has a simple structure.

The operating mechanism of TSRPG is based on the principle of pneumatic synergistic drive (see Figure 3 motion direction labeling). When the compressed air is synchronously injected into SPA1 and SPA2, the two actuators produce a phased bending motion under pneumatic excitation, and the gripping of phosphate rock is realized through the gradual closure of the end contact surfaces. During the process, the elastic deformation of the actuator units can be effectively converted into a soft gripping force, forming an adaptive wrapping effect. In the pneumatic unloading stage, the actuator unit restores its initial shape under the action of material intrinsic elasticity, realizing the lossless release of the ore. By controlling the air pressure injected into SPA1 and SPA2, the timing and strength of the gripping–releasing action can be controlled, which finally forms a complete cycle of the phosphorus ore sorting operation.

2.3. Manufacturing of SPA

In this subsection, two SPAs are manufactured by using the thermoplastic injection molding technology, and silicone (brand: SMOOTH-ON, product model: Dragon skin 20, shore hardness: 20A) is the main material. For the convenience of the split mold, we usually first manufacture an unsealed SPA by injection molding. Then, we conduct another injection molding to form a confining layer to cover the unsealed SPA. Through the above two injection moldings, a complete SPA can be manufactured.

According to Figure 4, the manufacturing processes of the unsealed SPA are listed below.

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Step 1: Design and manufacture molds

To manufacture the SPA, the design and manufacturing of molds should be conducted first. The mold includes the lower mold and the upper mold. According to the structures and dimensions of the SPA (see Figure 1 and Figure 2), the lower mold and upper mold are designed, whose 3D drawings are shown in Figure 4. Then, the lower mold and upper mold can be manufactured by 3D printing equipment or computer numerical control (CNC) engraving machines.

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Step 2: Prepare fluid silicone

This step involves preparing the fluid silicone that will be used for injection molding. Silicone is a flexible and soft material that is suitable for creating soft and compliant parts or components. To employ the integrated injection molding technology to manufacture the SPA, the silicone is prepared in a fluid state. In addition, the fluid silicone is usually mixed with a curing agent or catalyst to promote the curing process.

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Step 3: Inject mold

In this step, the prepared fluid silicone is injected into the cavity of the lower mold by using a syringe (Figure 4). The injection is carefully controlled to ensure that the entire cavity is filled with the fluid silicone without any air bubbles or voids.

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Step 4: Mount upper mold

Once the lower mold is filled with the fluid silicone, the upper mold is mounted onto it. The upper mold is designed to fit precisely onto the lower mold, forming a complete enclosure around the injected fluid silicone.

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Step 5: Cure

After the lower mold and upper mold are clamped, the curing process will be started. Curing is a chemical process. During the curing process, the fluid silicone undergoes polymerization and solidifies into the shape of the unsealed SPA. To accelerate the curing process, the molds are usually placed in oven equipment.

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Step 6: Split mold

After the curing process is complete, the upper and lower molds are split. Through the split mold process, the unsealed SPA can be obtained.

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Step 7: Inspect

In this last step, the manufactured unsealed SPA is carefully inspected. Any excess material or flash around the edges of the unsealed SPA may be trimmed or removed. Moreover, the dimensions and shapes of the manufactured unsealed SPA are carefully inspected to ensure its good quality.

According to the above manufacturing processes, an actual unsealed SPA is manufactured. After that, to obtain a completed SPA, we conduct another thermoplastic injection molding to form a confining layer to seal the unsealed SPA. Similar thermoplastic injection molding processes are employed to accomplish the sealing task. According to Figure 5, we first design and manufacture a base mold. Next, the fluid silicone is injected into the base mold. After that, the unsealed SPA is placed onto the base mold. Then, the whole mold is cured by placing it into oven equipment. When the mold is split, a complete SPA, shown in Figure 6, is obtained. After inspection, the dimensions and shape of the SPA are qualified.

2.4. Manufacturing of the TSRPG

In this subsection, we use two actual SPAs and a base plate to manufacture the TSRPG. The base plate is fabricated using 3D printing technology, and the material is the photosensitive curing resin with a hardness of 78 to 87 HA after curing. An actual TSRPG prototype shown in Figure 7 is manufactured. This actual TSRPG prototype is assembled by a based plate and two SPAs (i.e., SPA1 and SPA2).

3. Experimental Testbench

In this section, two experimental testbenches are built to conduct experiments for the TSRPG. The first one is employed to conduct grabbing experiments on the TSRPG. The second one is employed to study the characteristics of the manufactured SPA of the actual TSRPG prototype.

3.1. Experimental Testbench A

To evaluate the operational performance of the TSRPG, a dedicated experimental testbench A (Figure 8) is built. The platform consists of a power module, a computer, a pump, a regulator, a manipulator, and a fabricated TSRPG. During the testing process, the TSRPG is connected to the end of the manipulator through an interface, and the gripping operation is realized through the TSRPG after the manipulator completes the spatial positioning.

3.2. Experimental Testbench B

To investigate the characteristics of the manufactured SPA of the actual TSRPG prototype, the experimental testbench B is built. As shown in Figure 9, the experimental testbench B mainly includes a power supply module, a computer, a pump, a pressure regulation valve (Model: Festo VPPE-3-1-1/8-1-010-E1, resolution: 1.25% F.S., range: 0.01 MPa to 1 MPa), an I/O board (Model: NI PCIe-6323, resolution: 16 digits, range: −10 V to 10 V), a displacement sensor (Model: Keyence LK-H152, resolution: ±0.02%, range: ±40 mm) and the manufactured SPA. The local enlarged sectional view in Figure 9 clearly shows the SPA fixed in the experimental testbench B.

The power management module is dedicated to the proportional regulator drive, and the rest of the equipment is powered by an industrial-grade AC regulated power supply (220 V/50 Hz). The system takes the computer as the core control unit and realizes pneumatic pressure command generation, actuator deformation monitoring, and multi-physical quantity data acquisition through the integrated software platform. The air pump is used to provide air pressure to the SPA. The proportional regulator realizes the adjustment of the air pressure to the SPA according to the control instruction. The displacement sensor is used to detect the bending displacement of the SPA, and the I/O board builds the transmission path between the pneumatic command signal and the displacement feedback signal to form a complete electromechanical signal chain. In addition, the control and data acquisition software is MATLAB 2023a/Simulink with real-time analogue input and output functions. The sampling frequency for pressure and displacement signals is 100 Hz. The pressure is measured inside the pipeline before the SPA inlet using a pressure regulating valve.

4. Grabbing Experiments and Characteristic Analysis of TSRPG

In this section, the grabbing performance of the TSRPG is experimentally tested by using the experimental testbench A. Then, the motion characteristics of the TSRPG are studied by using the experimental testbench B.

4.1. Grabbing Experiments of TSRPG

In grabbing experiments, we employed the TSRPG to grab some parts with different shapes and dimensions to test its grabbing ability. As shown in Figure 10, the screws, T-nut, stainless steel washer and spiral spring could be successfully grabbed by the TSRPG. Therefore, the manufactured TSRPG has good grabbing ability, which indicates the TSRPG has the potential to grab phosphorite rocks.

4.2. Characteristic Analysis of TSRPG

The characteristics of the SPA have a huge impact on the performance of the TSRPG. Under the actuation of compressed air with different air pressure, the characteristics of the SPA are different. In this section, the actuation experiments of the SPA were conducted to research its characteristics, which will lay the base for the applications of the TSRPG.

To research the characteristics of the SPA, compressed air with four kinds of pressures (denoted as p) is applied. Specifically, Figure 11a shows a sine pneumatic pressure with different amplitudes and different frequencies (denoted as SP1), Figure 11b shows a sine pneumatic pressure with a fixed amplitude and frequency (denoted as SP2), Figure 12a shows a triangle pneumatic pressure with a different amplitudes and different frequencies (denoted as SP1), and Figure 12b shows a triangle pneumatic pressure with a fixed amplitude and frequency (denoted as SP2). Moreover, in Figure 11 and Figure 12, t is denoted as the time, and y is the displacement of the SPA.

According to Figure 11 and Figure 12, the characteristics of the SPA include hysteresis and creep characteristics. These complicated characteristics pose great difficulties in the applications of the TSRPG. To promote the actual application of the TSRPG, a model of its SPA should be established to describe the hysteresis and creep characteristics.

5. Modeling of SPA

In this section, a model of the SPA is built to describe its hysteresis and creep characteristics to promote the applications of the TSRPG. Then, the built-in Levenberg–Marquardt algorithm is used for model identification.

5.1. SPA Modeling Based on Nonlinear ARX Model

According to Figure 11 and Figure 12, the SPA of the TSRPG has complicated nonlinear hysteresis and creep characteristics. The hysteresis characteristic of the SPA is particularly complicated because its displacement not only depends on the current state, but also depends on the past states, which brings a huge challenge to the modeling of the SPA. To deal with this challenge, the nonlinear ARX model-based modeling method is a good optional selection to establish the model of the SPA.

Based on the nonlinear ARX model, the structure of the SPA model is shown in Figure 13. The traditional nonlinear ARX model consists of regressors and an output module. This structure makes it possible to use the nonlinear ARX model to model complex nonlinear characteristics by flexibly selecting its output module as wavelet network, tree partition, sigmoid network or other nonlinear functions. In Figure 13, the basic structure of the traditional nonlinear ARX model is retained. On this basis, a neural network is set to be the output module to establish the SPA model. This is because the neural network has the advantages of a simple structure and strong fitting capability.

According to Figure 13, the SPA model consists of regressors and a neural network. Pneumatic pressure p and displacement y of the SPA are employed as the inputs of the regressors. U expressed as (1) is the output of the regressors. y is the model output.

$$U={\left[\begin{array}{c}p\left(t-1\right),p\left(t-2\right),\cdots ,p\left(t-i\right)\cdots ,p\left(t-N_p\right),\hfill \\ y\left(t-1\right),y\left(t-2\right),\cdots ,y\left(t-j\right),\cdots ,y\left(t-N_Y\right)\hfill \end{array}\right]}^T$$

(1)

where $p\left(t-i\right)$ and $y\left(t-j\right)$ are the history terms of p and y, respectively. $N_p$ and $N_Y$ are the numbers of the history terms of p and y, respectively.

The structure of the neural network is shown in Figure 14. In addition, the motion of the neural network can be expressed as

$$Y_k=F_k\left(W_k{X}_k+b_k\right),k=1,2,\cdots ,N$$

(2)

where k represents the kth layer of the neural network, N is the total number of neural network layers. $W_k$, $b_k$ and $F_k$ are the weight coefficient matrix, bias vector, and activation function of the kth layer of the neural network. $X_k$ and $Y_k$ are the input and output of the kth layer of the neural network. In particular, the input $X_1$ of the first layer of the neural network is the input U of the whole neural network, i.e., $X_1=U$. In addition, the output $Y_N$ of the last layer (i.e., the Nth layer) of the neural network is the output y of the whole motion model of the SPA and $y=Y_N$.

5.2. Model Identification

In the section, the experimental data in the training set are obtained by applying compressed air with pressure SP1 (see Figure 11a,c,e) to the SPA. Based on the training set, the parameters of the established SPA model are identified by model training using the Levenberg–Marquardt algorithm.

To compare the model output and experimental data in model identification, they are plotted in Figure 15a,c. Figure 15a shows the comparison of displacement vs. time curves corresponding to model output and experimental data. Figure 15c shows the comparison of displacement vs. pressure curves corresponding to model output and experimental data. According to these comparison results, the SPA model can effectively reflect the characteristics of the SPA.

5.3. Model Validation

In this section, the experimental data in validation sets are obtained by applying compressed air with pressure SP2 (see Figure 11b,d,f), pressure TP1 (see Figure 12a,c,e) and pressure TP2 (see Figure 12b,d,f) to the SPA. The corresponding model validation results are shown in Figure 15b,d, Figure 16a,c, and Figure 16b,d, respectively. According to the above comparison results, the SPA model can effectively reflect the characteristics of the SPA under different pressure patterns.

6. Conclusions

In this study, a TSRPG is designed and manufactured based on soft pneumatic technology. First, the structural design and manufacturing of the SPA and TSRPG are conducted. Next, two experimental testbenches are built. Then, the grabbing function of the TSRPG is exhibited by conducting a series of grabbing experiments on experimental testbench A. In addition, by applying compressed air with pressure SP1, pressure SP2, pressure TP2 and pressure TP2 to the SPA on experimental testbench B, the experimental results show that the SPA has complicated hysteresis and creep characteristics. By using a neural network as the output module of the nonlinear ARX model, the dynamic model of the SPA is established to reflect the above characteristics. The effectiveness of the established model is examined via some different experimental data. The results of this study will promote the applications of the TSRPG in the field of phosphorite beneficiation.

For the designed SPAs, we mainly focused on their functional realization, and the study of their geometric shape is not deep enough. In our future research, we plan to design a new SPA with a smooth face by rounding its edges and corners to reduce the tension concentration, and to optimize the structure of the SPA via simulations using the finite element analysis (FEA) method for its force output, bending angle, or durability relevant to phosphorite handling. Meanwhile, we will research the material wear and energy consumption of the SPA to help enhance its lifetime and analyze the lifecycle of silicone manufacturing and disposal to verify whether the developed soft robot is environmentally sustainable. In addition, the control of the SPAs would be an interesting research field. In future research, we will also study the control of SPAs to enable them to perform more precise operations.