A ceramic product surface flatness detection method based on impedance control

Abstract

The application discloses a kind of ceramic product surface flatness detection methods based on impedance control, as follows: construct force / pose hybrid control system;System includes: impedance controller, pose compliance controller, servo driver and six-dimensional force sensor;The robot Z-axis force f z , f z It is obtained by force filtering and subtracted from the expected force f d , and the Z-axis force error is obtained;Z-axis reference position is obtained by impedance controller, and joint angle θ of each movement of robot is obtained by inverse kinematics;The moment M xy It is measured by six-dimensional force sensor, and the input of pose compliance controller is obtained by moment filtering;The pose compliance controller is used to control the rotation direction of the X and Y axes of tool coordinate system;θ and θ c Addition as the input of servo driver, the interactive force of robot and environment and actual position in environment are obtained.The beneficial effect is: the surface flatness detection of ceramic product is more suitable and more accurate.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of defect detection, in particular to a ceramic product surface flatness detection method based on impedance control. BACKGROUND

[0002] The field of ceramic surface quality detection is still a blank in the domestic ceramic machinery industry. Ceramic surface quality detection is one of the most important links in the ceramic production industry, and at present, it is still largely in the manual detection stage in China, so the quality of ceramic detection is difficult to guarantee.

[0003] In the detection of ceramic quality factors, flatness detection is very important, and the flatness of ceramics is directly related to the decoration effect and use effect. Traditional ceramic surface detection is mostly for flat surfaces, while most bathroom ceramic products have complex curved surfaces, making it difficult to accurately establish a model, so there is no unified detection method. With the rapid development of electronic technology and computer technology, robot technology has developed rapidly in the past few decades and has been increasingly widely used in many fields. Robot-based automated detection methods have become an inevitable trend for high-quality production of ceramic products.

[0004] Non-contact detection methods based on optical principles convert feature point information into digital signals and obtain the flatness of the ceramic surface according to specific flatness algorithms. However, this method is strict in terms of environmental light intensity and illumination angle, and due to the low texture and smoothness of ceramic products, the placement of the ceramic product also has requirements. In summary, the non-contact detection method based on optical principles has limited applicability for ceramic product surface flatness detection. The non-contact and non-destructive detection method for ceramic tile surface flatness has the advantages of simple system structure, strong practicability, high detection accuracy, and simultaneous inspection of multiple samples, which can well solve the problems of inaccuracy and low efficiency caused by manual detection of ceramic tile surface quality, and this method can become a new detection method for ceramic tile production.

[0005] Contact detection is commonly used for surface defect detection in industries such as steel and glass, and detects whether the plane is flat by observing the change in force information of the sensor. This method is generally used for flatness detection, and is not suitable for detection of complex-shaped ceramic workpieces. For ceramic workpieces with complex surface shapes, existing robot detection processes generally first generate a robot detection program through offline programming software. However, due to factors such as positioning error and processing error of ceramic workpieces, the offline program cannot be used directly and needs to be adjusted by workers according to the actual operation effect, and the adjustment process accounts for a large part of the entire detection process.

[0006] Constant contact force control is also commonly used in industrial grinding and polishing processes, which require strict adherence to a set reference trajectory. However, during ceramic surface inspection, due to the accuracy of 3D reconstruction, there is always an error between the preset reference trajectory and the actual trajectory of the ceramic workpiece surface, and contact with the workpiece cannot always be guaranteed.

[0007] For flat ceramic inspection, the direction of the normal vector at each point on the workpiece surface is consistent. Under the condition that the tangential movement speed of the six-dimensional force sensor probe at the end of the robotic arm is constant, it is only necessary to control the contact force between the sensor and the workpiece to be constant. For curved ceramic inspection, the normal direction of each point on the ceramic surface will change with the change of curvature. The direction of the relative velocity should be maintained on the tangent plane of each contact point on the surface of the ceramic workpiece. Therefore, during the curved surface inspection process, the control system should apply the desired contact force in the normal direction at the contact point of the workpiece. This requires the controller to be able to calculate the normal direction of the surface of the ceramic workpiece being inspected based on the trajectory detected by the robot or the force information of the sensor, and adjust the direction of the force sensor probe to be consistent with the normal direction of the surface of the ceramic product. Summary of the Invention

[0008] In order to solve the problem of irregular curvature changes on complex curved surfaces, which makes it impossible to ensure that the robot is in normal contact with the workpiece, and thus causes flatness problems, the present application provides a method for detecting the surface flatness of ceramic products based on impedance control, which specifically includes the following steps:

[0009] S1. Construct a force / attitude hybrid control system; the hybrid control system includes: an impedance controller, an attitude compliance controller, a servo driver, and a six-dimensional force sensor;

[0010] S2, the robot's Z-axis force f measured by the six-dimensional force sensor z , f z After force filtering, we get and the expected force f d Subtract and get the Z-axis force error e f =f d -f; where e f As the input of the impedance controller, the impedance controller is used to control the Z direction of the robot tool coordinate system;

[0011] S3, obtain the Z-axis reference position through the impedance controller, and obtain the joint angle θ of each movement of the robot through inverse kinematics;

[0012] S4. Measure the torque M of the robot's X-axis or Y-axis through the six-dimensional force sensor xy , and is obtained by moment filtering

[0013] S5, As the input of the posture compliance controller, the posture compliance controller adjusts the joint angle of each motion of the robot c ; the posture compliance controller is used for controlling the rotation direction of the X and Y axes of the tool coordinate system;

[0014] S6, theta and theta c are added as the input of the servo driver, and finally the interaction force f of the robot and the environment s and the actual position theta in the environment.

[0015] The present application has the advantages that it can adapt to curved surfaces and adjust the posture of the mechanical arm to ensure normal contact with the workpiece, and has wider applicability and higher precision for surface flatness detection of ceramic products. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 is the architecture diagram of the force / posture hybrid control system of the present application;

[0017] Figure 2 is a schematic diagram of the pre-programmed path;

[0018] Figure 3 is a force diagram of the end effector polishing head of the mechanical arm in different postures. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical scheme and advantages of the present application clearer, the embodiments of the present application will be further described below with reference to the drawings.

[0020] The present application provides a ceramic product surface flatness detection method based on impedance control, which specifically comprises the following steps:

[0021] S1, a force / posture hybrid control system is constructed; the hybrid control system comprises an impedance controller, a posture compliance controller, a servo driver and a six-axis force sensor;

[0022] S2, the force f of the Z-axis of the robot measured by the six-axis force sensor z , f z After filtering by force, the force f of the Z-axis of the robot measured by the six-axis force sensor is obtained d , the force error e of the Z-axis is obtained by subtracting the desired force f f from the force f d ; wherein e f is the input of the impedance controller, and the impedance controller is used for controlling the Z direction of the tool coordinate system of the robot;

[0023] S3, the Z-axis reference position is obtained by the impedance controller, and the joint angle theta of each motion of the robot is obtained by inverse kinematics;

[0024] S4, measure the moment M of the robot X axis or Y axis by the six-dimensional force sensor xy , and get

[0025] S5, As the input of the posture compliance controller, adjust the robot individual motion joint angle θ c by the posture compliance controller; the posture compliance controller is used for controlling the rotation direction of the X and Y axes of the tool coordinate system;

[0026] S6, θ and θ c are added as the input of the servo driver, and finally get the interaction force f of the robot and the environment s and the actual position Θ in the environment.

[0027] In step S1, the impedance controller adopts an impedance control model with a contact force steady-state error of zero, as follows:

[0028]

[0029] Wherein, x, and are the actual position, velocity and acceleration of the robot arm end respectively; x d , and are the desired position, velocity and acceleration of the robot arm end respectively; f d is the desired contact force; f is the actual contact force; M is the mass of the robot arm end effector, and B is the damping coefficient.

[0030] In the impedance controller, the PD control method is adopted to increase the damping term to adjust the damping coefficient B, and then balance the system oscillation caused by the mass M of the robot arm end effector.

[0031] The control rate of the PD control method is as follows:

[0032]

[0033] Wherein, b kp is the contact force error gain, b kd is the contact force error differential gain, and the impedance controller adjusts the damping term

[0034] The posture compliance controller controls the rotation direction of the X and Y axes of the tool coordinate system, wherein the posture adjustment angle θ y is as follows:

[0035]

[0036] where S is the s-parameter of impedance model, K is the stiffness coefficient of robot, M y is the moment of friction force along Y axis when the end effector of the robot moves downward.

[0037] The pose compliant controller controls the rotation direction of the X axis of the tool coordinate system, wherein the pose adjustment angle θ x is as follows:

[0038]

[0039] M x is the moment of friction force along X axis when the end effector of the robot moves downward.

[0040] The following takes a seven-degree-of-freedom robot detecting a ceramic workpiece as an example to illustrate the detailed steps of the method.

[0041] First is the pre-programmed path. The pre-programmed path is a series of path points given in advance according to the three-dimensional reconstruction result, which is used as a reference path for subsequent control strategies. In the process of planning the pre-programmed path, the accurate three-dimensional model of the workpiece is not required for programming, but a simple two-dimensional plane path (such as a series of straight line segments), as shown in Figure 2 .

[0042] The normal constant force impedance control ensures the contact throughout the detection process, and the pose compliant control ensures the normal contact with the workpiece. Each path point in the path contains the position and pose of the tool coordinate system in the robot base coordinate system, which can usually be described using a homogeneous transformation matrix.

[0043] In the subsequent experimental process of this paper, the defect area to be detected is first obtained by the three-dimensional reconstruction method, and several key path points of 10mm*10mm square voxels are selected around the defect. Between each two adjacent key path points, the position and pose between the starting point and the ending point are linearly interpolated to obtain

[0044] The starting point X s and the ending point X e of a path are:

[0045]

[0046] The position of the intermediate path point is obtained by directly linearly interpolating the positions of X s and X e in the Euclidean space:

[0047]

[0048] wherein n is the number of interpolation points between the two points.

[0049] Since the path start pose R s and the end pose R e given in rotation matrix, linear interpolation cannot be directly performed, here first find the rotation matrix s R e from R

[0050]

[0051] Then convert ΔR into a rotation vector representation (axis-angle representation) and perform linear interpolation:

[0052] v = mtov(ΔR)(1-4)

[0053]

[0054] In the formula, mtov is the conversion method of rotation matrix to rotation vector, vtom is the conversion method of rotation vector to rotation matrix, v is the rotation vector equivalent to ΔR, and n is the number of interpolation points between two points.

[0055] Second, the design of the impedance controller in this application.

[0056] According to whether the end effector is in contact with the environment during the movement of the robot, the movement of the robot can be divided into free space movement and constrained space movement.

[0057] In free space, the robot is not in contact with the environment and no interaction force is generated, at this time the robot is mainly position control.

[0058] When contact occurs between the end effector and the workpiece, the movement is position constrained and interaction force is generated between the robot and the environment. Entering the constrained space, the robot needs to perform force control at this time.

[0059] Impedance control is a control method that can be applied to free space and constrained space, and is one of the most important methods to achieve contact control between the robot and the environment. It adjusts the dynamic and static response characteristics of the robot arm under external force by changing the equivalent inertia, damping or stiffness parameters of the robot system.

[0060] Impedance control is decoupled in each direction axis of the rectangular coordinate system.

[0061] Considering that impedance control is only performed in one dimension of space,

[0062] The expected impedance equation can be written as:

[0063]

[0064] where M is the mass, B is the damping, and K is the stiffness. x, and are the actual position, velocity and acceleration of the end of the robot arm, respectively, x d , and are the desired position, velocity and acceleration of the end of the robot arm, respectively. e = x - x d represents the position correction amount of impedance control, e f = f d -f represents the force error between the desired contact force and the actual contact force.

[0065] The contact force between the end of the robot arm and the ceramic is simplified as f = K e (x e -x), where K e represents the environmental stiffness. The actual position of the end of the robot arm is

[0066]

[0067] When the robot arm is in a stable state its contact force steady-state error can be expressed as:

[0068]

[0069] According to formula (1-8), the steady-state error of the contact force is proportional to the stiffness parameter of the impedance model, and the larger the stiffness parameter, the larger the contact force steady-state error.

[0070] Therefore, by designing the stiffness parameter K = 0 of the impedance model, the steady-state error of the contact force theoretically tends to 0. So the impedance control model with zero contact force steady-state error can be expressed as:

[0071]

[0072] In order to obtain e ss = 0, an adaptive variable impedance control is introduced to compensate for the time-varying error.

[0073] The mass coefficient of the impedance model is easy to cause system oscillation, so the damping coefficient is usually adjusted to ensure stability. According to the contact force error and its first-order differential, the damping coefficient of the impedance model is adjusted online dynamically, and the control rate of the damping and the contact force deviation is established by using the idea of PD controller.

[0074] The control rate of the PD controller can be expressed as:

[0075]

[0076] where b kp is the contact force error gain, b kdKt is the contact force error differential gain, the variable impedance controller adjusts the damping term according to the contact force error

[0077] In the impedance controller, the damping parameter is adjusted by two contact gain error coefficients to achieve compliant contact between the robot and the environment.

[0078] To verify the effectiveness of the impedance controller of the present application, it is proved by Lyapunov's second method.

[0079] The stability of the system is determined by the Lyapunov stability criterion, and the range of gain parameters is also determined, and the system is designed according to the asymptotic stability criterion (Lyapunov's second method).

[0080]

[0081] Where e x = x-x d ,

[0082] Take Lyapunov function

[0083]

[0084] Its derivative is

[0085]

[0086]

[0087] According to Lyapunov stability theory, if the following two conditions are met. (1) Lyapunov function (2) The time differential of Lyapunov function The system is asymptotically stable. The parameters of the controller should have the following constraints:

[0088]

[0089] Put the damping term of the gain increase parameter into the impedance control model, and formula (4-18) can be obtained by Laplace transform:

[0090] Ms 2 α(s)+Bsα(s)+b kp δ(s)+b kd sδ(s)=-δ(s)(1-16)

[0091] Where δ(s)=-e f ,

[0092] For a stable system, the steady-state error e ssIt is defined based on Laplace transform. For its convergence judgment, the steady-state error e ss You can get:

[0093]

[0094] When the input is a step function, it takes the form From formula (1-17), we can conclude that:

[0095]

[0096] so

[0097]

[0098] When t→∞, f→f d The contact force between the robot and the environment converges to the dynamic desired force when F(s) is not a constant, like the sine function in the experiment, the tracking error can be verified to be 0.

[0099] Finally, the design of the attitude compliance controller in this application is presented.

[0100] The main function of the attitude compliance controller is to control the attitude of the sensor probe in real time during the detection process so that the direction of the constant force control always coincides with the normal direction of the workpiece surface.

[0101] The force exerted by the workpiece on the sensor probe in different postures during the robot detection process is analyzed, such as Figure 3 As shown. Figure 3 In the posture shown on the left, the grinding head moves downward and generates an oblique upward friction force f, which generates a torque + M along the Y axis. y , in order to achieve Figure 3 The attitude sensor probe shown in the middle needs to be adjusted to an attitude angle of θ in the positive direction of the Y axis. y , using the robot impedance control method, the torque M y Get the attitude adjustment angle θ y :

[0102]

[0103] When the sensor probe is in the detection process Figure 3 In the state shown on the right, the sensor probe is subjected to the extrusion force n and friction force f of the ceramic workpiece, generating a moment -M along the Y axis. y , we can get the same relationship between the attitude adjustment angle and the torque.

[0104] Similarly, the posture control method of the sensor probe along the X-axis direction is as follows:

[0105]

[0106] Therefore, the constant force impedance controller is used to control the axial force of the sensor probe during the detection process, and the impedance compliance control is used to adjust the posture of the sensor probe in real time according to the torque information, and the appropriate impedance parameters are adjusted, so that the axial direction of the sensor probe is along the normal direction of the workpiece surface and the constant contact force is maintained. The posture compliance is a dynamic adjustment process, and the posture compliance controller adjusts the posture of the mechanical arm in real time and dynamically according to the sensor torque information during the detection process.

[0107] The beneficial effects of the present application are:

[0108] Firstly, compared with the existing non-contact detection method based on optical principle, the constant force detection controller using force / posture hybrid control can solve the problem that the ceramic product itself has low texture, smooth and shiny, and is affected by the light intensity and illumination angle of the environment. The detection system can adapt to the curved surface and adjust the posture of the mechanical arm to ensure the normal contact state with the workpiece. The surface flatness detection of the ceramic product has wider applicability and higher precision. Secondly, compared with the existing constant contact force control method, the preset reference trajectory needs to be strictly followed. Due to the influence of three-dimensional reconstruction accuracy, there is a certain error between the preset reference trajectory and the actual trajectory of the ceramic workpiece surface, which cannot always guarantee the contact with the workpiece. In the process of planning the pre-programmed path, the precise three-dimensional model of the workpiece is not needed for programming, but a simple two-dimensional plane path is needed. The normal constant force impedance control ensures the contact during the detection process, and the posture compliance control ensures the normal contact with the workpiece.

[0109] The above only describes the preferred embodiments of the present application and does not limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for detecting the flatness of a ceramic product surface based on impedance control, characterized by: The method comprises the following steps: S1, constructing a force / pose hybrid control system; the hybrid control system comprises an impedance controller, a pose compliance controller, a servo driver and a six-dimensional force sensor; S2, the robot Z-axis force f measured by the six-dimensional force sensor z , z After force filtering, the force f is obtained Subtracting the desired force f d , the Z-axis force error e f = f d -f; where e f is input to the impedance controller, which is used to control the Z direction of the robot tool coordinate system; S3, obtaining a Z-axis reference position through the impedance controller and obtaining joint angles θ of each movement of the robot through inverse kinematics; S4, measure the moment M of the X or Y axis of the robot by the six-dimensional force sensor xy and obtain by moment filtering S5、 as an input to a pose compliant controller to adjust the robot's joint angles θ c ; the pose compliant controller is configured to control the rotational orientation of the X and Y axes of the tool coordinate system; S6, θ, and θ c The sum is added as an input to the servo driver, resulting in the interaction force f of the robot with the environment s and the actual position Θ in the environment; In step S1, the impedance controller adopts an impedance control model with a contact force steady-state error of zero, as follows: where x, vx, and ax are the actual position, velocity, and acceleration of the end of the robot arm, respectively; and are the desired position, velocity, and acceleration of the end of the robot arm, respectively; d , and are the desired position, velocity, and acceleration of the end of the robot arm, respectively; d is the desired contact force; f is the actual contact force; M is the mass of the end effector of the robot arm, and B is the damping coefficient; The impedance controller adopts PD control method and increases damping term The damping coefficient B is adjusted to balance the system oscillation caused by the mass M of the end effector of the mechanical arm. The control rate of the PD control method is as follows: where b kp is the contact force error gain, b kd is the contact force error derivative gain, and the impedance controller adjusts the damping term based on the contact force error 2. The method for detecting the flatness of a ceramic product surface based on impedance control according to claim 1, characterized in that: The pose compliant controller controls the rotation direction of the X and Y axes of the tool coordinate system, wherein the pose adjustment angle θ y The following formula: where S is the s-parameter of impedance model, K is the stiffness coefficient of the robot, M y is the moment of the friction force along the Y axis when the end effector of the robot moves downward.

3. The method for detecting the flatness of the surface of a ceramic product based on impedance control according to claim 2, characterized in that: The pose compliant controller controls a rotation direction of an X axis of a tool coordinate system, wherein a pose adjustment angle θ x The following equation: M x The moment of the frictional force along the X axis generated when the end effector of the robot arm moves downward.

Images