Abstract: Many underwater operation systems rely on hydraulic drives. This paper designs a gripping force sensor and studies its performance. An electro-hydraulic position servo system for controlling a robotic gripper is established. Based on this, a robotic gripper gripping force control system based on the electro-hydraulic position servo system is constructed. A modulo controller with an automatically adjustable intelligent weight function is used to control the gripping force of the robotic gripper, and experimental studies are conducted. Experiments show that this control method has a fast system response, small overshoot, high control accuracy, and can meet the gripping force control requirements of the robotic gripper during grasping operations. Keywords: gripping force sensor; electro-hydraulic servo system; modulo controller; robotic gripper Introduction The robotic gripper is an important part of a robot's dexterous operation, and its dexterous grasping operation is an important indicator of the robot's intelligence level. Electro-hydraulic servo systems are easily affected by changes in system pressure, oil temperature, etc., and system parameters are prone to variation, making precise control difficult. For underwater robotic grippers using electro-hydraulic servo control, the problem of effective, wide-range, and precise gripping force control has not been well solved. Therefore, in-depth research on the gripping force control technology of hydraulic manipulators is of significant theoretical and practical engineering importance for improving the operational level of manipulators and realizing their intelligent operation. 1. Structure and Working Principle of the Manipulator Gripper The structure of the manipulator gripper is a typical linkage mechanism, as shown in Figure 1. The linear motion of the slider drives the opening and closing of the two parallel fingers of the gripper. The manipulator gripper can be simplified to the linkage mechanism shown in Figure 2. ABC is a single unit, where AB = 34 mm, BC = 34 mm, and AC = 60 mm; D is the slider, which moves linearly along the Y direction, driving ABC through the linkage BD to achieve the opening and closing of the gripper. The maximum stroke of D is 15 mm; C is a point on the base of the fingers. Since the fingers move parallel, point C can only move along the x direction. Therefore, the displacement of point C is the feed dimension when the fingers open and close. In Figure 2, point D represents the initial position, i.e., the position of the slider when the gripper is closed. Let θ be the angle of rotation of AC around A, with counterclockwise as positive. At the position shown in Figure 2, θ = 0°. When the slider is in the initial position, i.e., Y = 0, the angle θ = 0°, and the gripper is closed. When the slider is in the extreme position, i.e., Y = 15mm, θ = 42.5°. At this point, the gripper is open to its maximum. The relationship between the finger displacement x and the angle θ is: X = AC * sinθ = 60sinθ. Therefore, the maximum finger displacement is 40.5mm, meaning the maximum distance the gripper is open is 81mm. 2 Electro-hydraulic Position Servo System The electro-hydraulic position servo system consists of a hydraulic power source, an electro-hydraulic servo valve, a linear cylinder, an angular displacement sensor, and a controller, as shown in Figure 3. In the electro-hydraulic position servo system, the electro-hydraulic servo valve uses a CSDY15 jet tube servo valve. The hydraulic power source is set to a working pressure of 10MPa. The cylinder is an asymmetric linear hydraulic cylinder, i.e., a single-rod cylinder, with a piston diameter D=30mm and a piston rod diameter d=18mm. The piston linear stroke is 15mm. When the piston rod extends, the gripper opens; when the piston retracts, the gripper closes. The angular displacement sensor uses a precision potentiometer, and the controller is a lead-lag controller implemented using analog circuitry. 3. Grip Force Sensor The grip force sensor is a vertical chain diaphragm structure. Strain gauges are attached to the deformation zone of the diaphragm to detect the magnitude of the gripping force. Four strain gauges form a full-bridge to improve the linearity and sensitivity of the sensor, and mutually compensate for errors and drift caused by factors such as temperature. The grip force sensor has two functions: first, to detect the magnitude of the vertical force acting on the object when the robotic arm grasps it; and second, to generate an easily controllable force on the object by relying on the deformation of its deformation zone. Specifically, the gripping force on the object grasped by the grip force sensor (Figure 4) is generated by the deformation of its deformation zone. The grip force sensor is mounted on the finger surface and directly contacts the object being grasped. To increase the coefficient of friction between the sensor and the object, enhance finger flexibility, and reduce the impact force on the object during grasping, a layer of rubber is attached to the surface of the grip force sensor in contact with the object. The force loading test of the grip force sensor showed that the relationship between the sensor's output signal s and the applied force F is shown in Figure 4. The test results show that this sensor has good linearity, small backlash error, and high accuracy, which can meet the needs of the robotic arm for measuring the gripping force during grasping operations. The relationship between s and F is S = 0.075F + 0.08. The gripper was allowed to grasp a rigid object, and the same displacement was fed into the gripper each time from the start of contact. The relationship curve between the gripper's feed displacement d and the grip force sensor's output signal S is shown in Figure 5. Since the output signal s of the grip force sensor and the applied force are linearly related, it can be seen from Figure 5 that the relationship between the gripper displacement and the force is nonlinear and can be divided into three stages: (1) 0≤dx<0.6 (2) 0.6<~dx<1.7 (3) 1.7≤dx≤2.8 In stage (1), the slope of the curve is very small, indicating that the deformation of the grip force sensor deformation zone is very small each time it is fed. This is because the rubber on the sensor surface bears most of the deformation. In stage (2), the slope of the curve increases significantly. This is because the rubber on the sensor surface has basically stopped deforming. The deformation of the sensor caused by the gripper displacement is mainly borne by the deformation zone of the sensor. In stage (3), the slope of the curve increases again. At this time, the rubber no longer deforms. The deformation of the sensor caused by the gripper displacement is entirely borne by the deformation zone of the sensor. Piecewise fitting of the curve shown in Figure 5 yields: 4 Fuzzy control technology of gripper force Fuzzy control technology is a digital control technology with a closed-loop structure based on fuzzy mathematics, fuzzy language knowledge representation and fuzzy logic reasoning, and computer control technology. By using fuzzy logic reasoning, for n fuzzy control rules, rt input-output relation matrices R₁, R₂, ..., R_n can be obtained. Thus, by the fuzzy rule synthesis algorithm, the total fuzzy relation matrix of the system can be obtained. For any system error E and error change DE, the corresponding fuzzy controller output U is: By performing precise calculation on the fuzzy control quantity U obtained from equation (1), the system object can be directly controlled. However, in practical applications, since the fuzzy relation matrix R is a high-order matrix, if the instantaneous control output U is calculated by synthesizing the system error E and error change DE at any instant using equation (1), it will take a lot of time, making the system's real-time control performance worse. Therefore, conventional fuzzy controllers often use the lookup table method in practical applications. However, once the fuzzy control table is determined using the lookup table method, the control rules of this fuzzy controller are fixed. For different controlled objects, a simple fuzzy controller using unchanging control rules cannot obtain the expected control effect. Especially for time-varying, nonlinear, and complex systems, when using fuzzy control. To achieve good control performance, the fuzzy controller must have relatively complete control rules. These control rules are the operator's summary of fuzzy information about the controlled process and the summary of operational experience. Due to the influence of factors such as nonlinearity, high order, time-varying nature, and random disturbances of the controlled process, the fuzzy control rules may be coarse or imperfect, which will affect the control performance to varying degrees. In order to make up for its shortcomings and make the control rules automatically adjust and improve during the control process, so as to continuously improve the control performance of the system, the fuzzy controller with adjustable control rules has emerged. Equation (2) is a fuzzy control rule with an adjustment factor. When n is large, it indicates that the importance of DE is high, so the response is fast, the overshoot is large, the oscillation amplitude is large, and the settling time is long; when (1-n) is large, it indicates that the importance of DE is high, so the response is slow and the overshoot is small. Therefore, when using a fuzzy controller with a self-adjusting factor, a better control performance can be obtained by adjusting the adjustment factor after appropriately determining the error and the domain of error change. Using a fuzzy controller with adjustment factors not only simplifies the design of the control table but also avoids errors caused by excessive information loss in the minimax synthesis method. Furthermore, the adjustment factors have clear physical meanings and can simulate the human's trade-offs between error and error variation during actual control. Different adjustment factors can be used for different controlled objects. Experienced operators always adjust the control strategy appropriately based on the current error and its variation. For example, when the error is large, the main challenge is to eliminate the error, thus requiring a larger weight factor for the error. When the error is small, to reduce overshoot and oscillation and improve the system's speed and stability, the weight factor for error variation should be increased. However, while fuzzy controllers with multiple adjustment factors have better control performance, the number of adjustment factors increases with the increase in error, error variation, and the quantization level of the control quantity's domain. Moreover, the selection of multiple adjustment factors involves a degree of subjectivity and lacks effective guidance. To adapt to changes in the structure and parameters of the controlled object and simulate the learning process in manual control, a fuzzy control rule with intelligent weight functions, as shown in equation (3), can be used. This control rule automatically adjusts its weights according to the magnitude of the error and the error change, and the adjustment factor is only a function of the input variables. Because this automatic adjustment occurs throughout the entire domain, it better aligns with human thinking in the control decision-making process, possessing highly intelligent optimization characteristics and making it very easy to implement its control ideas in a timely manner. The structure of the fuzzy control system for the gripping force of the robotic arm is shown in Figure 6. The input of the fuzzy controller is the error DE between the current gripping force of the robotic arm and the given value. The output is the increment of the gripping force applied to eliminate the error. In the fuzzy controller, the domains of the fuzzy subsets of the error, error change, and control quantity are E = {-5, -4, -3, -2, -1, 0}, described by {negatively large, negatively large, negatively medium, negatively small, negatively very small, zero}. DE = {0, 1, 2, 3, 4, 5} is described by {zero, very small, small, medium, large, very large}. U = {0, 1, 2, 3, 4, 5} is described by {zero, very small, small, medium, large, very large;. By performing a precise calculation on the fuzzy control quantity U obtained from equation (3), the value of the command issued by the electro-hydraulic position servo system can be obtained, thereby controlling the magnitude of the clamping force. Figure 7 shows the curve of the output signal S of the gripping force sensor as a function of the number of sampling points n when a 20N clamping force is applied to a rigid body using the fuzzy control method. 5 Conclusion This paper conducts an in-depth theoretical study on the mechanism and motion law of the robotic gripper, establishes an electro-hydraulic position servo system, designs a gripping force sensor and conducts experimental research and calibration on its performance. Based on the above results, a robotic gripping force control system based on the electro-hydraulic position servo system is constructed; the gripping force is controlled by an adaptive fuzzy control rule with intelligent weight function. Experiments show that the system has a fast response, small overshoot, high control accuracy, and can meet the requirements of gripping force control during robotic gripper grasping operations. References [1] Li Fuyi, Hydraulic Technology and Hydraulic Servo System [M], Harbin Institute of Technology Press, 1992. [2] Shan Chengxiang, Theoretical and Design Basis of Sensors and Their Applications [M], Beijing: National Defense Press, 1999. [3] Li Shiyong, Fuzzy Control, Neural Control and Intelligent Control Theory [M], Harbin Institute of Technology Press, 1996. Click here to download the original text.