1 Introduction

The continuous breakthroughs and innovations in high-tech have made robots increasingly widely used in society. The robotic arm is an important actuator of robots, which also requires higher flexibility and adaptability. Traditional robots are mainly made of materials such as metal, steel, and semiconductors. Due to the lack of good deformation ability of the material, the sensor has problems such as large volume and poor biocompatibility. Therefore, the design of remote control systems for robotic arms is greatly limited [1]. Therefore, many scholars have conducted relevant research on flexible biosensors. But so far, there is no flexible sensor that is stretchable, structurally complete, and inexpensive to meet the requirements and has been widely used [2]. The research topic is to develop a novel human–computer interaction system based on flexible biosensors made of polymer hydrogel materials for the control of mechanical fingers and the recognition of complex gestures. Therefore, designing a robotic arm flexible biosensor remote control system with strong flexibility, high cost-effectiveness, high recognition efficiency, and the ability to achieve human–computer interaction has certain research significance. Based on this, this research will select polymer hydrogel as the electrode material of the flexible sensor and polydimethylsiloxane (PDMS) as the base material of the research sensor to design a resistive flexible biosensor. The reason for selecting polymer hydrogels as electrode materials is that this material has high sensitivity and can produce significant resistance changes under the action of small forces. The flexibility of hydrogels is ideal for applications where skin or other irregular surfaces need to be fitted, such as wearables and human–machine interfaces. Polymer hydrogels generally have good biocompatibility, which makes them less likely to cause skin irritation or allergic reactions when attached to the skin for a long time. The reason for choosing PDMS as the substrate is that the material has excellent flexibility and ductility of silicon-based polymer materials, which is very suitable for the substrate of flexible electronic devices. PDMS has shown good chemical stability and durability under different environmental conditions, which is necessary for long-term reliable sensor applications. PDMS has good air permeability and moisture permeability, which are very important for applications near the skin and can reduce discomfort caused by prolonged wear. The feasibility of this flexible sensor was verified in the experiment by establishing a finger joint recognition model and combining it with pattern-matching algorithms. This study will design a wearable robotic finger remote control system based on flexible biosensor and proposal integration difference (PID) robotic finger control models to achieve effective recognition of robotic hand human–computer interaction. The main contribution of the research is to propose and validate a new gesture recognition method and implement a new mechanical finger remote control system. This research provides an innovative direction to adapt to the constantly developing robotics.

Based on the existing problems, the method constructed in this paper has innovative points for sensor improvement. Polymer hydrogel and PDMS are used as electrode materials and substrates of sensors. A resistive flexible biosensor is successfully designed, which improves the poor flexibility and large volume of traditional sensors and their sensitivity and stability. It can meet the needs of general-purpose sensors and has a stronger stretching ability. In this paper, a robot finger remote control system is designed by using a radial basis function neural network (RBFNN) tuned PID controller to improve control adaptability and stability. Finally, a real-time monitoring system and redundancy mechanism are introduced into the model to improve the stability and reliability of the system, including innovative thinking on how complex systems can keep operating efficiently and safely. The research method solves the poor flexibility and large volume of traditional robot sensors. By using polymer hydrogel and PMDS as electrode materials and substrates of sensors, the designed resistive flexible biosensor has good sensitivity and stability, small size, and good flexibility. The research enhances the precision of gesture recognition and simultaneously optimizes the stability and adaptability of the robotic finger remote control system.

The research structure consists of four parts. The second part is a summary of domestic and foreign scholars' research on biosensors and robotic arm control. The third part is to design the flexible biosensor and the manipulator control system and build the human–computer interaction gesture recognition system based on the flexible biosensor. The fourth part is the simulation experiment to verify the performance and practicability of the model. The fifth part summarizes and analyzes the research results and points out the shortcomings of the current research and the future research direction.

When intelligent robots develop, scholars have studied the production and application of flexible biosensors. Jiang’s team proposed the possibility of using highly active two-dimensional nanocomposites as flexible sensor materials, combining the unique advantages of individual components and the synergistic effects of composite materials. In this study, a combination of density functional theory simulation and volume-sensitive measurement was used to show the high electrocatalytic sensitivity of polyaniline nanocomposites. This provided a platform for the use of highly active two-dimensional nanocomposites for flexible gas sensors [3]. Cui and Shao et al. studied how to integrate the mechanical properties, self-viscosity, and strain sensitivity into hydrogel sensors. They enhanced the mechanical properties of the hydrogel by using the riboxylic acid aqueous solution and tannic acid-coated cellulose nanocrystals as nanofillers. They made the hydrogel suitable for wearable epidermal sensors through the antibacterial properties of chitosan and verified the performance of the sensor through simulation experiments [4]. Lim’s team considered the latest developments in soft materials and system integration technology to design various types of wearable flexible hybrid electronic devices. They combined integrated sensors in healthcare, energy, and the environment to study the limitations of current materials. Then, they summarized the requirements for material properties, sensor performance, electronic performance, and skin integration [5]. Feng and Liu et al. used the directional freezing method to prepare anisotropic conductive hydrogels to solve the problem of how to apply the traditional homogeneous conductive hydrogels and the flexible sensor anisotropy to a wider temperature range. The hydrogel has a wide temperature tolerance range of 36 to 25 °C. The application prospect of the anisotropic conductive hydrogel as a flexible sensor has been verified through experiments [6]. Kulkarni’s team proposed a hybrid nanocomposite based on polyaniline and tungsten oxide sensors that could be operated at room temperature. They used ethylene glycol polyphenylene dicarboxylate as the substrate to analyze the properties of the mixed nanocomposites through X-ray diffraction, field emission scanning electron microscope, transmission electron microscopy, and X-ray photoelectron spectroscopy. The results confirmed that the method had excellent stability and response reproducibility [7].

Scholars have studied the implementation of human–computer interaction through PID control. Mahm's team proposed an adaptive PID controller that relied on additional errors in the steering control signal to address the difficulty of adjusting parameters in customized PID controllers. This controller was more suitable for following motion due to the nonlinearity, parameter changes, and load stroke issues that occurred in the brushless direct current motor drive framework. The existing PID control methods have modeling errors and parameter uncertainties, and the experimental response is always different from the theoretical response [8]. Verma and Padhy proposed a new single variable adjustment method for online robustness and performance tuning. They verified the effectiveness of the proposed method through the optimal PID controller design of the existing optimal adjust rule, particle swarm optimization PID, and the experimental verification of a typical water tank system [9]. Phu and Hung et al. proposed a fuzzy PID control system that combined a PID controller with a fuzzy controller. They studied the qualitative properties of the system in the fuzzy number space through the differentiability of fuzzy valued functions and the concept of fuzzy integrals and verified the feasibility of the model through simulation experiments [10]. Ekinci and Hekimoğlu proposed a new adjustment method for PID controllers, which combined the objective function with the improved iterative knowledge-based algorithm (IKA) algorithm. This method optimized the transient response of the automatic voltage regulator (AVR) system by minimizing the maximum overshoot, stability time, rise time, and peak time values of the terminal voltage, and eliminated steady-state errors. The robustness analysis of this method verified that the IKA adjusting PID controller proposed in the study had better control performance [11]. At present, there is a lack of theory to explain how linear PID can effectively handle the problems of nonlinear uncertain dynamic systems. In response, Zhang's team proposed an improved PID controller. They extended these one-dimensional results to higher-dimensional nonlinear uncertain systems for error control and verified the stability and feasibility of this method through simulation experiments [12]. Chetia et al. studied the free vibration characteristics of a flexible torsion cantilever beam and drew the following conclusions from the results: the torsion angle had a significant effect on the vibration characteristics of a torsion cantilever beam. With the increase of tip mass, the vibration of the beam decreased as the natural frequency decreased significantly, but it had a different trend compared with the straight beam [13]. De et al. proposed a hybrid wrench and visual response control method for handling large (non-) rigid materials. The proposed method incorporated force–torque data and skeleton tracking to control the mobile manipulator intuitively by utilizing as much operator intelligence as possible. With this approach, tools such as path planning or object modeling were not essential to getting results. The hybrid controller was tested for stability, and the controller response was monitored when the mobile manipulator took steps and sine functions as inputs. Finally, the holistic approach was illustrated by a proof-of-concept task in which the flexible sheet was handled jointly by a mobile manipulator and a human operator [14].

To sum up, traditional robots have problems such as poor flexibility and large size. At present, the research on flexible biosensors is mainly applied to integrated sensors such as medical and energy sensors, but less applied in human–computer interaction gesture recognition. At the same time, the traditional PID controller has problems such as low control accuracy and slow response speed. In the application research of flexible biosensors, there are still many limitations, such as poor scalability and ductility, and the stability of the sensor has a large room for improvement. Therefore, this study will select polymer hydrogel as the electrode material of the sensor to design a gesture recognition flexible sensor. RBFNN is used to improve the PID controller, and a mechanical finger remote control system is designed to improve the flexibility and feasibility of the control system. The research attempts to address the limitations of existing technologies in terms of flexibility, accuracy, stability, and biocompatibility by developing novel flexible biosensors, optimizing gesture recognition algorithms, and improving control systems for remote robotic fingers.

2 Design of Flexible Biosensor-Based Human–Computer Interaction Gesture Recognition System Based on Polymer Hydrogel Sensor

Traditional robots are mainly made of materials such as metal, steel, and semiconductors. Due to the lack of good deformation ability of materials, sensors have problems such as large volume and poor biocompatibility, which greatly limit the design of remote control systems for robotic arms [15, 16]. This research will make a kind of flexible biosensor based on polymer hydrogel material, and design a flexible biosensor-based human–computer interaction gesture recognition system based on RBFNN–PID robot finger control model to solve problems related to the remote control of manipulator.

2.1 Flexible Biosensor-Specific Design Based on Polymer Hydrogel

In this study, the polymer hydrogel material is used to make the electrode material of the flexible biosensor, and the insulating flexible silica gel is used to encapsulate the sensor, that is, the flexible biosensor is made through the structure of substrate + electrode material + substrate. The studied polymer hydrogels are mainly composed of sodium chloride particles and polyacrylamide. Figure 1 shows a specific polymer hydrogel sensor.

Fig. 1
figure 1

Process flow diagram of the polymer hydrogel sensor

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Figure 1 shows the production process of a single biosensor. Firstly, the electrode material and the substrate material were selected. The electrode material used polymer hydrogel, the main component of which was polyacrylamide (PAAm), and other additives were selected sodium chloride particles (NaCl). The specific preparation method of hydrogel is to add 4 g acrylamide, 4.5 g sodium chloride nanoparticles, and 0.05 g persulfate imide into 30 ml deionized water. Then, drop 0.06 g of tetramethylenediamine (accelerator) into a beaker and stir constantly with an eyedropper until the reagent is completely dissolved. Pour this water into a glass bottle for 20 min and the gel is naturally formed. Next, the prepared gel is cut to the size required for the study, and leads are drawn at both ends to connect the external circuit, and the initial production of the ionic gel biosensor is completed. The substrate material selection of polydimethylsiloxane (PDMS), the purpose of which is to prevent the production of ionic adhesive adhesion and easy dehydration problems, the ionic adhesive and the substrate packaging together. Secondly, the prepared sample is coated with a layer of pre-treated non-curing PDMS as an adhesive on the surface of the PDMS film except for the rectangular gel intercepted in the study. After the PDMS is completely solidified, the sample is encapsulated with PDMS film to remove the bubbles in it, and it is placed in a vacuum environment for 30 min to be naturally solidified. Then, thin copper wire is used to connect the ionic adhesive electrode with the external circuit, and benzophenone is used to treat the connection part between the copper wire and gel to prevent falling off. Finally, a layer of PDMS colloidal solution is scraped on the de hydrogel array part of the base layer. Then, the base layer on the other side is paved on the ionic glue and the base film, and placed at room temperature for half a day until the two base layers adhere together. The packaging is completed. The study will verify the static characteristics of the biosensors through sensitivity, stability, mechanical properties, and limit values. Equation (1) stands for the relationship between the sensitivity of flexible biosensors and the rate of change in resistance.

$$\Delta R/R = G\sigma + \alpha \theta .$$
(1)

In Eq. (1), \(R\) stands for the sensor resistance, \(\Delta R\) stands for the change in resistance, \(G\) stands for the sensitivity of the sensor, \(\sigma\) stands for the sensor strain, \(\alpha\) stands for the temperature constant of the sensor, and \(\theta\) stands for the temperature change of the sensor. When the temperature is below 30 °C, its impact on the sensor is relatively small, and the temperature effect can be ignored. Equation (2) stands for the relationship between sensor sensitivity and resistance change rate at this time.

$$\Delta R/R = G\sigma .$$
(2)

This study mainly completed the design of the flexible biosensor-based human–computer interaction gesture recognition system. The entire hand of a person is mainly composed of four parts: wrist, palm, back of hand, and fingers. The phalanges of the fingers have a total of 14 joints, including the metacarpophalangeal joints of the five fingers. According to the mechanical characteristics of the finger joints, the research will achieve gesture recognition by arranging polymer hydrogel sensors on each joint. Equation (3) is the relationship between fingertip joint curvature and metacarpophalangeal joint curvature measured remotely.

$$\theta_{{\text{d}}} = (2/3) \times \theta_{{\text{m}}} .$$
(3)

In Eq. (3), \(\theta_{{\text{d}}}\) stands for the distal fingertip joint curvature. \(\theta_{{\text{m}}}\) stands for the metacarpophalangeal joint curvature. To simplify the design, the research will carry out remote gesture recognition requirements through five metacarpophalangeal joints. That is, the polymer gel sensor prepared by the research method will be cut appropriately and placed on the metacarpophalangeal joints for gesture recognition.

Since the ion gel sensor designed in the research only measures the resistance directly by the lead wire, there may be noise and other effects in the actual data acquisition, which may lead to the problem of unstable identification. Therefore, the research will add a filtering circuit and other processing to the resistance signal processing circuit of a single sensor. Figure 2 shows the signal processing of the sensor. The resistance signal processing circuit of the sensor mainly consists of a printed circuit board (PCB) board, which includes a microcontroller unit (MCU), HC05 Bluetooth module, multi-channel selection switch multiplexer (MUX), filtering circuit, and lithium battery part [17]. When the battery starts to supply power, the signal processing circuit starts to operate, and the sensor signal is transmitted to the MUX channel. The analog signal is filtered through the filtering circuit, and then the processed signal is input into the microcontroller MCU for data complexity reduction processing. Finally, the processed signal is transmitted to the personal computer (PC) through the HC05 Bluetooth module. When designing filtering circuits, research is conducted to reduce the impact of noise on data by introducing operational amplifiers to amplify the circuit. A low-pass filter is added to eliminate data signals that exceed the critical value in the circuit. Among them, the cutoff frequency of the low-pass filter needs to be higher than 9.5 kHz. Figure 3 shows the specific filtering circuit design.

Fig. 2
figure 2

Flowchart of sensor data acquisition signal

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Fig. 3
figure 3

Schematic diagram of the filtering circuit

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In Fig. 3, the right part of the circuit is a power frequency notch filter, which includes three low-pass filters to filter out 50 Hz interference noise. The left part of the circuit mainly includes a high-pass filter \(f_{{\text{h}}}\) and a low-pass filter fl, \(f_{{\text{h}}}\), and \(f_{{\text{l}}}\) in series to form a band-pass filter, used to reduce the impact of noise on the gesture recognition system. Equation (4) stands for the mathematical calculation of \(f_{{\text{h}}}\) and \(f_{{\text{l}}}\) filters.

$$\left\{ \begin{gathered} f_{{\text{h}}} = \frac{1}{(2 \times 3.14 \times R16 \times C6)} = 44.2\;{\text{Hz}} \hfill \\ f_{{\text{l}}} = \frac{1}{(2 \times 3.14 \times R8 \times C2)} = 0.8\;{\text{Hz}} \hfill \\ \end{gathered} \right..$$
(4)

In Eq. (4), \(f_{{\text{h}}}\) is the filtering frequency of the high-pass filter. \(f_{{\text{l}}}\) is the filtering frequency of the low-pass filter. \(R16\), \(C6\), \(R8\), and \(C2,\) respectively, represent the resistance 2 MΩ, capacitance 1 uF, resistance 3.6 kΩ, and capacitance 1 uF. The bandwidth of a band-pass filter in a circuit is related to the resistance and capacitance values of the filter. Equation (5) is the expression for the bandwidth of a band-pass filter.

$${\text{BW}} = f_{{\text{h}}} - f_{{\text{l}}}$$
(5)

In Eq. (5), \({\text{BW}}\) stands for the bandwidth of the band-pass filter, which is the difference between \(f_{{\text{h}}}\) and \(f_{{\text{l}}}\). Equation (6) stands for the magnification of the amplifier in the circuit.

$$A_{{\text{u}}} = \frac{R15}{{R14}} = \frac{36\;\Omega }{{3.6\;\Omega }} = 10.$$
(6)

In Eq. (6), \(A_{{\text{u}}}\) stands for the magnification of the amplifier in the circuit, which can be calculated to be 10.

2.2 Design of PID Mechanical Finger Control Model Based on RBFNN

After identifying and collecting joint data, it is necessary to classify and extract gesture features from the data to further control the mechanical finger. Gesture recognition models such as neural network classification and support vector machines need many samples to train the model, and the efficiency of feature extraction is low. Therefore, this study will use a template-matching algorithm for gesture feature recognition and extraction. This model recognizes gesture features through similarity testing. Using finger movement as the main feature, different types of finger states can be determined by calculating the angle of finger movement. By retrieving and comparing the phalange states with those in the gesture template library, the phalange states can be identified. Research is conducted to determine the state of the knuckles by calculating Euclidean distance, and Eq. (7) shows the calculation of Euclidean distance.

$$d(x,y) = \sqrt {(x_{1} - y_{1} )^{2} + (x_{2} - y_{2} )^{2} } = \sqrt {\sum\limits_{i - 1}^{n} {(x_{i} - y_{i} )^{2} } } .$$
(7)

In Eq. (7), \(d(x,y)\) stands for the Euclidean distance of the sensor. \(x_{1} ,...x_{n}\) represent the output data of the sensors, \(y_{1} ,...y_{n}\) represent the template data of the sensor databases, and \(x_{i}\) and \(y_{i}\) represent the ith output data and template data of the sensor. After extracting the gesture features, the research will design a remote control system to control the robotic finger. Figure 4 shows the overall flexible biosensor human–computer interaction-based remote gesture recognition system of the robotic arm.

Fig. 4
figure 4

Architecture of the human–machine interaction remote control system

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In Fig. 4, the control system studied is mainly divided into three parts: signal acquisition, signal analysis, and mechanical finger drive. Firstly, Sect. 2.1 is about signal acquisition, which mainly includes amplification circuits, filtering circuits, and analog-to-digital conversion circuits. Secondly, the main function of the signal analysis part is to recognize gestures, which includes two aspects: data preprocessing and gesture feature extraction. Finally, the driving module of the mechanical finger is mainly controlled by combining RBFNN–improved PID controller. This study adopts the neural network PID control method for mechanical finger control, and the optimized neural network selected is RBFNN. RBFNN is a dynamic neural network, and its stability control is very important. In this paper, the hidden layer size and basis function selection are designed to enhance the stability of the network. Proper selection of the number of hidden layer neurons can help avoid overfitting and underfitting, thus enhancing the stability of the model. Choosing the appropriate basis function and its parameters is crucial to ensure the smoothness and stability of the model. Equation (8) is the radial basis function of the RBFNN hidden layer node.

$$h_{j} = \exp \left( {\frac{{ - \left\| {X - C_{j} } \right\|^{2} }}{{2b_{j}^{2} }}} \right),(j = 1,2,...m).$$
(8)

In Eq. (8), \(h_{j}\) stands for the \(j\)th hidden layer node’s radial basis function. The radial basis vector is \(H = [h_{1} ,h_{2} ,...h_{j} ,...,h_{m} ]^{T}\). \(T\) stands for the sampling period, and \(X\) for the input layer vector of the neural network, \(X = [x_{1} ,x_{2} ,...,x_{n} ]^{T}\). \(C_{j}\) stands for the center vector of the \(j\)th node, \(j\) for the hidden layer nodes, \(m\) for the number of hidden nodes, and \(b_{j}\) for the base width vector of the \(j\)th node. Equation (9) is the output function of RBFNN [18].

$$y_{m} (k) = w_{1} h_{1} + w_{2} h_{2} + ... + w_{m} h_{m} .$$
(9)

In Eq. (9), \(y_{m} (k)\) stands for the output function value of RBFNN for the \(k\)th sampling. \(k\) stands for the number of PID sampling, and \(W = [w_{1} ,w_{2} ,...,w_{j} ,...w_{m} ]^{T}\) for the network’s weight vector. Equation (10) is the performance index expression of the RBFNN identifier.

$$J_{1} = \frac{1}{2}(y(k) - y_{m} (k))^{2} .$$
(10)

In Eq. (10), \(J_{1}\) stands for the performance indicator function of the identifier and \(y(k)\) for the input function of the neural network. The steps of RBFNN to adjust PID are divided into five steps. The first step is data acquisition, which needs to collect the historical operation data of the control system, including the input signal, PID controller parameters, and the output response of the system. PID parameters include proportional (P) parameters, integral (I) parameters, and derivative (D) parameters, which determine the direct strength of the relationship between the controller output and the error signal, eliminate the long-term accumulation of steady-state errors, and adjust the controller output. The second step is to train the RBFNN using the collected data. The goal is to enable the neural network to predict the optimal PID parameters based on the input signal and the current system state. For each sample in the training data set, the input to the neural network typically contains the error signal of the system and its derivatives, and the output is designed as the parameters of the PID controller. The third step is the network structure selection. The structure of the RBFNN needs to be designed according to the application characteristics and data dimensions, including determining the appropriate number of centers and the appropriate width of the basis function. The fourth step is online adjustment. After the network training is completed, the RBFNN and PID controller can be integrated into the control loop. During the control loop operation, RBFNN will receive the system error signal and its derivative information in real time and calculate the corresponding PID parameters and timely adjust the PID controller parameters to cope with system dynamic changes or disturbances. The fifth step is parameter update. The optimal PID parameters calculated by RBFNN will replace or modify the original PID parameters to ensure that the performance of the control system is always maintained in the best state. The update process can be continuous or triggered at a specific time. The adjustment process of RBFNN-optimized PID control is to select a set of random numbers as the connection weights between the hidden layer nodes and the output nodes. The input learning sample values are subtracted from the pre-determined target values by the neural network, and the resulting error values are modified according to the set rules. After repeated operations, the error can be reduced, control compensation can be achieved, and training can be completed to achieve the goal of improving the performance of the PID control system. Figure 5 shows the specific structure of the RBFNN–PID controller.

Fig. 5
figure 5

Structure diagram of the PID controller improved by the RBF neural network

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In Fig. 5, in the PID controller regulated by RBFNN, the input layer structure selection usually directly corresponds to the number of input variables in the problem, so the input layer node is 3, and the corresponding inputs are \(du\), \(y(k)\), \(y(k - 1)\). The dimension of the output layer depends on the number of variables that the problem needs to predict or control, and one node in the output layer is \(u\). The number of nodes in the hidden layer has a great influence on the control accuracy of the controlled object. To ensure the control accuracy and calculation speed of the system, based on the previous experience of RBF network PID controller design, the system has been tested many times. When the number of nodes in the hidden layer is 6, and the control requirements for the system can be met. When the number of nodes in the hidden layer is 6, Eqs. 11–12 are the initial settings for RBFNN parameters.

$$\left\{ \begin{gathered} W = [\begin{array}{*{20}c} {w_{1} } & {w_{2} } & {w_{2} } & {\begin{array}{*{20}c} {w_{4} } & {w_{5} } & {w_{6} } \\ \end{array} } \\ \end{array} ]^{T} \hfill \\ B = [\begin{array}{*{20}c} {b_{1} } & {b_{2} } & {b_{2} } & {\begin{array}{*{20}c} {b_{4} } & {b_{5} } & {b_{6} } \\ \end{array} } \\ \end{array} ]^{T} \hfill \\ \end{gathered} \right..$$
(11)

In Eq. (11), \(W\) stands for the weight vector, and \(B\) stands for the base width vector.

$$C = \left[ \begin{gathered} \begin{array}{*{20}c} {c_{11} } & {c_{12} } & {c_{13} } & {\begin{array}{*{20}c} {c_{14} } & {c_{15} } & {c_{16} } \\ \end{array} } \\ \end{array} \hfill \\ \begin{array}{*{20}c} {c_{21} } & {c_{22} } & {c_{23} } & {\begin{array}{*{20}c} {c_{24} } & {c_{25} } & {c_{26} } \\ \end{array} } \\ \end{array} \hfill \\ \begin{array}{*{20}c} {c_{31} } & {c_{32} } & {c_{33} } & {\begin{array}{*{20}c} {c_{34} } & {c_{35} } & {c_{36} } \\ \end{array} } \\ \end{array} \hfill \\ \end{gathered} \right].$$
(12)

In Eq. (12), \(C\) stands for the network’s center vector. Equations 13–15 represent the adjustment relationship between the RBFNN and PID control algorithm. Among them, Eq. (13) is the input of the PID controller.

$$\left\{ \begin{gathered} xc(1) = e(k) - e(k - 1) \hfill \\ xc(2) = e(k) \hfill \\ xc(3) = e(k) - 2e(k - 1) + e(k - 2) \hfill \\ \end{gathered} \right..$$
(13)

In Eq. (13), \(xc(1)\), \(xc(2)\), and \(xc(3)\) are the three input functions of PID. \(e(k)\) stands for the deviation value obtained from the \(k\)-th sampling. \(e(k - 1)\) stands for the deviation value of the \(k - 1\)th sampling. \(e(k - 2)\) stands for the deviation value of the \(k - 2\)th sampling. Equation (14) stands for the PID control algorithm after RBFNN adjustment.

$$u(k) = u(k - 1)\Delta u(k).$$
(14)

In Eq. 14, \(u(k)\) stands for the PID control rate of the \(k\)th sampling, \(u(k - 1)\) for the control rate of the \(k - 1\)th sampling, and \(\Delta u(k)\) for the incremental PID control rate. Equation (15) is the mathematical expression for \(\Delta u(k)\).

$$\Delta u(k) = k_{p} (e(k) - e(k - 1) + k_{i} e(k) + k_{d} e(k) - 2e(k - 1) + e(k - 2)).$$
(15)

In Eq. (15), \(k_{p}\) stands for the proportional coefficient of the PID control system, \(k_{i}\) for the integration coefficient, and \(k_{d}\) for the differential coefficient. Compared with simple PID control algorithms, the control algorithm of RBF adjustment is more complex. When simulating and modeling neural network control systems, the existing modules in Simulink cannot directly establish control models, and the program design of RBFNN–PID controllers needs to be completed through S-function modules. Figure 6 shows a specific RBFNN–improved PID control joint system simulation model.

Fig. 6
figure 6

Simulation model of the RBF neural network–PID control joint system

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In Fig. 6, the model has an input layer, RBF–PID, an output layer, and feedback mechanism. The input layer receives signals from the outside, which are usually state parameters of the object that the system needs to control. For example, in a mechanical finger control system, the input may include finger position, speed, or other relevant dynamic parameters. RBFNN is the core part of the simulation model. The PID controller receives the output of the RBF neural network and converts it into a specific control signal. The output layer generates the final control signal, which is used to regulate the behavior of the controlled system. In the case of mechanical fingers, this may involve adjusting the power and direction of the driving motor to achieve precise finger movement. The simulation model also includes a feedback link that feeds the actual response of the system back to the input layer. This allows the model to compare expected and actual outputs, allowing for real-time adjustments. The input variables of the controller are 10, including 4 discrete state vectors, namely radial basis vector \(H\), radial basis wide vector \(B\), center vector \(C\), and weight vector \(A\). Then, the Model Description Language (MDL) update program is written using a three-layer RBFNN, which includes six hidden layer nodes, resulting in a total of 99 discrete state elements in the program. Finally, the PID control parameter adjustment process is achieved by iteratively updating the radial basis vector, radial basis width vector, center vector, and weight vector in the RBF algorithm. In the above research methods, when the model is offline, it is difficult for the model to meet the demand for real-time feedback. Therefore, the study can introduce a real-time detection system into the model, using real-time detection to continuously detect the output of the sensor, while comparing it with the expected output and retrograde, to achieve real-time feedback [19]. Meanwhile, when the model is in an unstable state, the following transient consequences may occur: sensor failure, misidentification, and corresponding delay. To reduce these transient consequences, redundant mechanisms can be considered to ensure that the system can continue to operate safely or shut down in the event of transient problems [20]. Generally, to improve the reliability of human–machine gesture recognition systems based on biosensors, more critical data or states are required. The acquisition of these key data or difficult-to-measure state information involves collecting a rich data set through sensor technology and integrating data from different sources using computer vision algorithms.

3 Analysis of Experimental Results of Mechanical Finger Control Based on Flexible Biosensor

This study will verify the performance of the materials studied by testing the sensitivity, stability, limit values, and mechanical properties of the flexible ion adhesive sensor. Simulation experiments will be conducted to test the control effect of PID controller optimized using RBFNN [21,22,23]. Finally, the feasibility of the experimental method will be verified through actual computer experiments.

3.1 Flexible Biosensor Human–Computer Interaction Gesture Recognition Results and Analysis

In the experiment, RBFNN architecture is set to three layers, including input layer, hidden layer, and output layer. The RBFNN training process involves two main steps, the first is to determine the hidden layer center and width, and the second is to adjust the output layer weight. The K-means algorithm can be used to cluster the input data and determine the RBF center. The width parameter of the RBF is calculated by the maximum distance of the data points within the cluster or other statistical properties. The weight of output layer is calculated by linear least square method. The parameter adjustment method of RBFNN tuning the performance of the control system can adjust the RBFNN weight and PID parameters by feedbacks in real time during the operation of the control system. By comparing the error between the system output and the expected output, the controller parameters are dynamically adjusted to reduce the error. The experiment tested the static properties and mechanical properties of the polymer hydrogel flexible sensor. At the same time, the experiment also analyzed the performance of the researched and designed mechanical finger control system. Therefore, research had high requirements for the experimental environment. To deal with common problems in gesture recognition, the research aims to overcome common challenges including lighting changes, ambient noise and photographic equipment changes through the collaborative application of multiple technologies. Specific strategies include adaptive threshold algorithm and light correction algorithm to cope with light changes in different environments, anti-interference circuit design and noise filtering algorithm to reduce the impact of environmental noise, and standardization processing and multi-camera fusion technology to ensure consistency between devices. In addition, the system integrates deep learning technology, uses CNN and LSTM models to process gesture diversity and dynamic gesture recognition, and combines multi-modal data to improve the robustness of the system, ensuring accurate discrimination even in the case of gesture occlusion. Table 1 shows the specific experimental hardware and software environment.

Table 1 Experimental hardware and software environment
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The gesture feature extraction method selected in this study is the template-matching method. This method first preprocessed the flexible sensor data and then conducted gesture recognition between the data and the data in the gesture database template. A standard gesture library was set up for 30°, 60°, 90°, and 120° based on the bending characteristics of finger joints, and template-based gesture-matching experiments were conducted. Table 2 shows the corresponding relationship between the relative resistance of flexible biosensors and finger curvature in the gesture library.

Table 2 Standard gesture library correspondence
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To verify the performance of the polymer hydrogel biosensor, the research tested the electrical and mechanical properties of the sensor through the experimental tension, that is, the sensitivity, limit value, stability, and mechanical properties of the sensor. Firstly, a study was conducted using the probe of a multi-meter to pull the ionic adhesive through a cyclic stretching motion, reflecting the electrical performance of flexible biosensors through the degree of stretching and the rate of resistance change. Figure 7 shows the sensitivity and stability results of the tested sensors.

Fig. 7
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Sensor sensitivity and stability results chart

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In Fig. 7a, the slope GF of the stretching curve stands for sensor sensitivity. Through curve fitting, the sensitivity of the studied individual flexible sensor was 0.7269, and the stretching curve coincided with the recovery curve, indicating that the sensor had high sensitivity and good stretching performance. Figure 7b shows the resistance change rate and stretching amount curve of the ion adhesive sensor stretched 60 times. The sensitivity only had a small error when the stretching amount was 18% and 65%. The overall error of 60 stretching amounts was within a certain range, indicating that the sensor still had good stability during multiple repeated stretching and recovery processes. To verify the mechanical properties of a single sensor, experiments were conducted at different environmental temperatures to test the relationship between the sensor's tensile strength and tensile value. The ion adhesive material was stretched to complete damage in the experiment, and the limit value of the sensor was tested in Fig. 8.

Fig. 8
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Mechanical performance test results of sensors

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In Fig. 8a, the stretching amount was positively correlated with the sensor pulling force value, meaning that as the stretching amount increased, the pulling force value also increased. The pulling force value was negatively correlated with the ambient temperature. When the ambient temperature was 0 °C, the required pulling force value for the sensor was relatively maximum. In Fig. 8b, before the tensile value reached 200%, the curve was relatively smooth, indicating a relatively stable curve. When the tension value was between 200 and 300%, there was a slight fluctuation in the curve, indicating slight damage to the sensor. After the tensile value exceeded 300%, the curve fluctuated significantly, and the resistance change rate remained unchanged or decreased, indicating sensor damage. It can be concluded that the tensile limit of the sensor in this study was 300%. The study introduced sensors of different materials and conducted comparative experiments on sensor limits, analyzing the superiority of materials through sensor thickness, sensitivity, and tensile strength. The substrate materials introduced in the study include BASF Ecoflex and silica gel materials, and the electrode materials introduced include liquid metal, conductive ink, and carbon black filler in Fig. 9.

Fig. 9
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Comparison diagram of flexible sensors made of different materials

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In Fig. 9a, the thickness of the research material was 0.16 mm, which reduced the thickness of the biosensors by 58–91% compared to other biosensors, greatly reducing thickness of the biosensor. In Fig. 9b, the sensitivity of the studied sensor was 0.73, which had higher performance compared to other materials, that is, achieving the same sensor resistance only required a lower stretching amount. In Fig. 9c, the research sensor achieved 100% pull-up, meeting the requirements of a universal sensor. The flexible biosensors studied significantly improved in sensor thickness and sensitivity compared to existing relevant biosensors. To further compare the effect of flexible sensors of different materials, linear error, hysteresis error, and long-term stability indexes were used for evaluation, and the results are shown in Table 3.

Table 3 Performance effects of flexible sensors with different materials
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In the results of Table 3, the polymer hydrogel–PDMS sensor has excellent performance on these three indexes, with linear error less than 5%, hysteresis error less than 3%, and long-term stability change rate less than 2%, showing its superiority in complex human–computer interaction applications. In contrast, other sensors perform slightly worse on these indicators, especially Ecoflex–carbon black filler sensors with large linear errors and low long-term stability. The results show that the proposed sensor has obvious advantages and is suitable for various complex wearable devices and human–computer interaction application scenarios. To comprehensively evaluate the performance of the polymer hydrogel–PDMS flexible biosensor, a test was carried out under different temperature, humidity, and pressure conditions. The evaluation index adopted the resistance change rate and sensitivity transformation, and the results are shown in Table 4.

Table 4 Sensor performance evaluation in different environments
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The results in Table 4 show that under different temperature, humidity, and pressure conditions, the change of resistance rate and sensitivity of the polymer hydrogel–PDMS flexible biosensor are kept in a small range. This shows that the sensor shows good stability and reliability under a variety of environmental conditions, and is suitable for a variety of complex application scenarios, including extreme temperature and high humidity environments. The life cycle of the proposed sensor is evaluated by using resistance change rate, sensitivity change, tensile strength change, and tensile limit change. The finger bending angle was set to 90° and 120°, and the finger bending was performed 20,000 times in total, as shown in Table 5.

Table 5 Sensor life cycle assessment
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The results in Table 5 show that the polymer hydrogel–PDMS flexible biosensor has been tested for 20,000 cycles in bending and stretching cycles, and the resistance change rate, sensitivity change, tensile strength change, and tensile limit change of the sensor are all kept within the acceptable range, less than 3%, 3%, 2.5% and 2.5%, respectively. This shows that the sensor has stable performance in long-term use, has good durability and reliability, and is suitable for application scenarios that require frequent bending and stretching, such as wearable devices and complex human–computer interaction systems. The calculation cost comparison results of different sensors are shown in Table 6.

Table 6 Comparison of calculation costs of different sensors
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The results in Table 6 show that the polymer hydrogel–PDMS sensor has a higher cost than other sensors. However, in terms of accuracy and stability, the sensors used in the study have better performance and have a wider range of applications.

3.2 Analysis of Mechanical Finger Control Results Based on Improved PID Algorithm

The study introduced traditional data gloves for comparison. Through the template-matching method and flexible biosensor electronic skin device designed in this research, gesture recognition experiments were carried out. Recognizing accuracy and recall were introduced to analyze the gesture recognition effect.

In Fig. 10a, the flexible biosensor recognition accuracy studied was 92.8%, which improved the recognition accuracy by 8.1% compared to traditional data glove sensors, and the sensor curve studied was smoother. After 50 iterations, it reached a convergence state and the recognition process of the sensor was more stable. In Fig. 10b, the recall rate of the research sensor’s gesture recognition was 57.81%, which was 8.07% higher than the traditional data glove sensor’s. For the remote control system of robot fingers, an improved PID controller based on RBFNN was designed to realize human–computer interaction gesture recognition, and the control effect of the controller before and after the improvement was verified through simulation experiments. Figure 11 shows the comparison results of the step response curve and sine response curve of the system before and after improvement.

Fig. 10
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The experimental results based on template-matching method

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Fig. 11
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Comparison diagram of system sine and step response curves

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Figure 11a shows the comparison of step response curves of the system before and after improvement. The response speed of the RBF–PID control system was faster, reaching the expected value at 0.28 s, while the PID control system reached stability at 0.52 s. There was no oscillation phenomenon in the response curve before and after improvement, indicating good system stability. Figure 11b shows a comparison of the sine response curves of the system before and after improvement. The initial response stage had a significant error, and after 1/4 cycle, the response tended to stabilize. Among them, the error of the unimproved PID control system was between 0.04 rad, and the error of the RBF–PID control system was controlled within 10 to 3 rad, indicating that RBFNN adjusting PID controller had better adaptability. To further verify the output performance of the control system, a square wave response curve was introduced to analyze the stability of the controller. Figure 12 shows the square wave response and error curves of the controller before and after improvement.

Fig. 12
figure 12

Comparison diagram of square wave response and error curve

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In Fig. 12a, there were differences in the square wave response curves of the PID controller before and after improvement compared to the system input square wave curve, and there were cases of jumping values at the time of signal change. However, the RBF–PID control system achieved convergence relatively quickly. In Fig. 12b, the error curve of the RBF–PID control system only underwent instantaneous changes when the expected value changed, and the response error at other times was 0. However, the error curve of the unmodified PID control system reached the rate of convergence more slowly, and there was still fluctuation in the case of the same jump. Overall, the finger joint control system studied had certain nonlinear characteristics, and the RBF–PID controller had higher performance and controlled the system output faster and more stably. The study established actual experimental scenarios to verify the feasibility of the research method. Figure 13 shows the actual scenario validation results.

Fig. 13
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Actual scenario experimental verification results

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In Fig. 13, the study selected two finger bending angles of 90° and 120° for human–computer interaction scene experiments and collected finger bending angle signals through flexible biosensor electronic skin. When the finger was bent at 90°, the mechanical finger also bent and successfully held the experimental car. When the finger was bent at 120°, the angle of the mechanical finger also changed. Through scenario experiments, the flexible biosensor-based human–computer interaction gesture recognition system in this study achieved the expected results and had certain feasibility. To further verify the performance of the controller, the indexes of rise time, settling time, and overshoot rate were used for evaluation, and the results are shown in Fig. 14.

Fig. 14
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Controller performance verification results

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In Fig. 14, the rise time of the PID controller was about 1.0 s, and it started to stabilize after 1.5 s, and the overshoot rate of the PID controller reached about 10%. The rise time of the RBF–PID controller was about 0.6 s and started to stabilize after 1.0 s, and the overshoot rate of the RBF–PID controller was about 5%. Compared with the performance of the two controllers, the RBF–PID controller had a shorter rise time, indicating that the system output was boosted to the target value faster, showing a faster response speed. The RBF–PID controller had a longer stability time, which meant that the fluctuation of the RBF–PID controller after reaching a steady state was reduced faster so that a stable state was reached faster. The RBF–PID controller had a lower overshoot rate, indicating that the RBF–PID controller had less overshoot when it reached the final steady-state value, indicating that the control of the system was more accurate and stable. The results in Figs. 13 and 14 further verify the wide applicability and high reliability of the polymer hydrogel–PDMS flexible sensor in practical applications. The high recognition rate of complex gestures and long-term stability in different environmental conditions ensure the superior performance of the sensor in a variety of applications such as medical rehabilitation, virtual reality, smart home, outdoor health monitoring, industrial automation, and smart clothing. These results enhance the application feasibility and user experience of the sensor in different practical scenarios and lay a solid foundation for its promotion and application in a wide range of fields.

After the above experiments, the results show that RBFNN can adapt PID parameters to achieve optimal control performance by learning the dynamic characteristics of the system, especially when the system model is unknown or changing. RBFNN can process many input data and system responses, find the key parameters that affect the system performance through an iterative process, and optimize them. In real-time applications, RBFNN can dynamically adjust the control parameters based on current and historical data to adapt to changes in the environment and real-time changes in sensor readings. In addition, the RBF–PID controller has a shorter rise time, which means that the controller can respond more quickly to input changes and quickly push the system output toward the target value, which is a very important feature in applications that require fast dynamic responses. The RBF–PID controller shows an earlier stabilization time, which indicates that the controller can reduce the output fluctuations of the system more quickly and reach a steady state. This in applications means shorter wait times as well as less energy consumption, especially when the system needs to respond frequently. The RBF–PID controller has a lower overshoot rate, which indicates that it can adjust the steady-state value of the target more accurately and stably. In the field of precision control, such as medical equipment, high-precision robotic systems, etc., the low overshoot rate reduces the possible risk of shock or damage to the system when it reaches the target position. In summary, the RBF–PID controller demonstrates its strong adaptability and robustness in the face of time-varying characteristics or complex dynamics of the system.

4 Conclusion

The research successfully designed and tested a new resistive flexible biosensor, which is mainly made of PDMS and polymer hydrogel materials, breaking through the limitations of traditional sensors in flexibility and volume. The design of remote control systems for robotic arms is greatly limited. This study will solve related problems by designing a flexible biosensor-based human–computer interaction gesture recognition system based on resistive flexible biosensors. Polymer hydrogel was selected as the electrode material of the flexible sensor, and PDMS was used as the base material of the sensor. The feasibility of the flexible sensor was verified by the mode-matching algorithm. A remote control system for mechanical fingers was designed using a PID controller adjusted by RBFNN, and the feasibility of the research system was verified through simulation and scenario experiments. The experimental results showed that the sensor showed a sensitivity of 0.7269 and a tensile limit of 300%, which meant that the sensor not only had high performance, but also showed excellent reliability and adaptability in the face of complex mechanical movement and deformation. Especially in practical applications, such as highly flexible robotic arm remote control systems or complex human–computer interaction application scenarios, this performance greatly improved the operational flexibility and efficiency of the system. Compared with the traditional data glove, the flexible sensor in the study increased the accuracy rate of gesture recognition by 8.1–92.8%, which opened a new way for the development of gesture recognition technology in the future, especially in the fields of virtual reality and remote operation. The optimized PID controller with RBFNN showed remarkable performance advantages in both stability and response accuracy. The improved PID control system quickly reached the expected value in the step response and showed excellent adaptability in the sinusoidal response curve. This showed that this control approach had strong potential and wide applicability in the face of complex systems. In summary, the main message of the research is to provide a new methodology, based on flexible biosensors, through advanced control theory, to achieve more flexible and accurate robotic arm control. The experimental results verify the feasibility and superior performance of this new sensor in human–computer interaction and open new application prospects for future robotics and wearable devices. The research contribution is the successful design of a resistive flexible biosensor. This new sensor is significantly more flexible, compact, and biocompatible than traditional sensors, and is adapted to the needs of modern robotics. The problem of poor flexibility and large volume of traditional sensors is improved, and the sensor's ability to sense small changes is improved. The research mainly fills the gaps in the design, sensitivity, stability, and application of flexible biosensors in complex human–computer interaction systems. In particular, it solves the problem of improving the sensor sensitivity and reducing the volume, while proposing a new PID control model based on RBFNN to improve the accuracy and response speed of the remote control system. Despite the good performance results of the current study, stability in long-term use remains a challenge, and the sensor gradually degrades under repeated stretching, bending, and other mechanical stresses, which can affect its performance and life. In addition, environmental factors also have a certain impact on sensor performance, although some environmental tests have been conducted, they may lead to more deviations in practical applications. Through the analysis of polymer hydrogel–PDMS flexible biosensor and RBFNN–PID control system, the research shows its wide application potential in many fields such as medical health, wearable devices, human–computer interaction and entertainment games. Future research directions will focus on optimizing sensor materials and design, improving the recognition ability of complex gestures and dynamic gestures, expanding the control of multi-degree-of-freedom robot systems, and combining deep learning and multi-modal data fusion to further improve the accuracy, stability, and adaptability of the system, thus promoting the continuous development and application expansion of flexible electronics and intelligent control technologies.