Displacement measurement method for six-degree-of-freedom capacitive sensor

Abstract

The invention discloses a six-degree-of-freedom capacitive sensor displacement measurement method, a sensor comprises a receiving end polar plate and a transmitting end polar plate which are mounted between measured equipment, and a capacitance measurement gap is formed between the receiving end polar plate and the transmitting end polar plate; the sensor comprises eight capacitive sensors, namely four variable-area capacitive displacement sensors and four variable-distance capacitive displacement sensors; the measuring method comprises the following steps: detecting translation displacements along an X axis and a Y axis and a rotation angle around a Z axis through four variable-area capacitance displacement sensors; the translation displacement along the Z axis and the rotation angles around the X axis and the Y axis are detected through the four variable-distance capacitive displacement sensors; and according to the capacitance variation of the eight capacitance sensors, the six-degree-of-freedom pose parameters of the measured object in the space are solved.

Description

Technical Field

[0001] This invention relates to the field of sensor technology, and is applicable to the field of precision displacement detection. In particular, it relates to a displacement measurement method using a six-degree-of-freedom capacitive sensor. Background Technology

[0002] In modern high-end manufacturing and scientific research, the six-degree-of-freedom pose of an object in three-dimensional space (i.e., translation along the X, Y, and Z axes) is crucial. , , and rotation about the X, Y, and Z axes , , High-precision, non-contact, real-time measurement has become a key technology for ensuring system performance. For example, extreme requirements are placed on six-degree-of-freedom displacement sensing in extreme ultraviolet (EUV) lithography machines, atomic force microscopes (AFM), or space gravitational wave detection missions. Capacitive sensors, a common sensing technology that detects physical quantities (such as displacement, pressure, and acceleration) based on changes in capacitance, work by utilizing how changes in the measured physical quantity alter the geometric parameters of the capacitor (such as plate area, spacing, or dielectric properties), thereby causing a change in capacitance. With advantages such as simple structure, non-contact measurement, low power consumption, and fast response speed, capacitive sensors are widely used in numerous fields including consumer electronics, industrial control, medical equipment, and aerospace.

[0003] However, traditional single-capacitor sensors have significant technical bottlenecks: First, the signal-to-noise ratio is low, and the output signal of a single capacitor is easily masked by parasitic capacitance (such as distributed capacitance of wires and edge capacitance of plates) and environmental noise (such as electromagnetic interference and temperature drift), resulting in limited measurement accuracy. Second, the linearity is poor. Within a large displacement range, the edge effect of plates causes the capacitance displacement relationship to deviate from the ideal linearity, and single capacitors lack differential compensation mechanisms, resulting in large nonlinear errors. Third, the anti-interference capability is weak. Changes in ambient temperature and humidity will alter the dielectric constant and plate spacing, and single capacitors cannot cancel these common-mode interferences, leading to a decrease in measurement stability. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a six-degree-of-freedom capacitive sensor displacement measurement method. By arranging multiple sets of capacitor pairs in the same plane and in the same direction, differential processing is used to cancel common-mode interference, improve signal amplitude and linearity, and finally achieve high-precision six-degree-of-freedom pose measurement.

[0005] The objective of this invention is achieved through the following technical solution: A method for measuring displacement using a six-degree-of-freedom capacitive sensor, wherein the sensor includes a receiving end plate and a transmitting end plate mounted between the devices under test, with a capacitance measurement gap formed between the receiving end plate and the transmitting end plate; the sensor comprises eight capacitive sensors, divided into four variable-area capacitive displacement sensors and four variable-distance capacitive displacement sensors; the measurement method includes: The translational displacement along the X and Y axes and the rotational angle around the Z axis are detected by four variable area capacitive displacement sensors. The translational displacement along the Z-axis and the rotational angles around the X and Y axes are detected by four variable-distance capacitive displacement sensors. Based on the capacitance changes of the eight capacitive sensors, the six-degree-of-freedom pose parameters of the measured object in space are calculated.

[0006] Furthermore, the translational displacement along the Z-axis The solution method is as follows: using four variable distance capacitive sensors , , , Simultaneously measured, changes in distance along the Z-axis cause simultaneous changes in the capacitance of the four variable-distance capacitive sensors, as shown in the formula: ; in, Let i = 1, 2, 3, 4, where i represents the capacitance change of each variable distance capacitive sensor. The capacitance-displacement proportionality coefficient in the Z-axis direction.

[0007] Furthermore, the variable area capacitance sensor includes N sets of differential capacitor pairs, each set consisting of a fixed plate and a moving plate, with the moving plate moving along the X-axis. x causes a change in the area directly opposite the point of contact, which in turn leads to a change in capacitance: ; The moving plate moves along the Y-axis y causes a change in the area directly opposite, which in turn leads to a change in capacitance: ; Translational displacement along the X-axis and translational displacement along the Y-axis The solution method is as follows: using a variable area capacitance sensor , Calculate the translation distance along the X-axis: ; Using a variable area capacitance sensor , Calculate the translation distance along the Y-axis: ; Where N is the number of differential capacitor pairs. , These are the capacitance-displacement scaling factors in the X and Y axes, respectively.

[0008] Furthermore, the rotation angle around the X-axis The solution method is as follows: Of the four variable distance capacitive displacement sensors, , Located on one side of the positive Y-axis, , Located on the negative Y-axis side, and Symmetrical distribution about the X-axis and Symmetrical distribution about the X-axis, and , and , The Y-axis spacing between them is L; the displacement difference between the variable-distance capacitive displacement sensors in the positive and negative Y-axis directions is calculated using the following formula: ; in, The capacitance-displacement proportionality coefficient in the Z-axis direction. The translational displacement along the Z-axis, Let i represent the capacitance change of each variable distance capacitive sensor, i = 1, 2, 3, 4.

[0009] Furthermore, the rotation angle around the Y-axis The solution method is as follows: Of the four variable distance capacitive displacement sensors, , Located on one side of the positive X-axis, , Located on one side of the negative X-axis, and Symmetrical distribution about the Y-axis and Symmetrical distribution about the Y-axis, and , and , The X-axis distance between them is M; the displacement difference of the variable-distance capacitive displacement sensor in the positive and negative X-axis directions is calculated using the following formula: ; in, The capacitance-displacement proportionality coefficient in the Z-axis direction. The translational displacement along the Z-axis, Let i represent the capacitance change of each variable distance capacitive sensor, i = 1, 2, 3, 4.

[0010] Furthermore, the rotation angle around the Z-axis The solution method is as follows: Using a variable area capacitance sensor , Measuring displacement changes in the X-axis direction, using , Measure displacement changes in the Y-axis direction; The solution is derived from the relationship between tangential displacement and rotation angle, using the following formula: ; Where R is the distance from the geometric center of each variable area capacitive sensor to the Z-axis rotation center, k is the capacitance-displacement proportionality coefficient with uniformity in the X and Y axes under an ideal symmetrical layout, and N is the number of differential capacitor pairs. and These represent the translation distance along the X-axis and the translation distance along the Y-axis, respectively.

[0011] Furthermore, the variable area capacitive displacement sensor adopts a differential capacitor array structure, including N sets of differential capacitor pairs arranged in a straight line on the same plane; the moving plates of the odd and even sets are arranged alternately, forming a physically symmetrical layout, and the output signal is... k is the proportionality constant. This represents the translation distance along the X-axis.

[0012] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the six-degree-of-freedom capacitive sensor displacement measurement method.

[0013] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the six-degree-of-freedom capacitive sensor displacement measurement method.

[0014] Compared with the prior art, the beneficial effects of the technical solution of the present invention are: 1. A differential capacitor array design (variable area sensor) and a multi-sensor differential algorithm (variable distance sensor) are adopted; through differential processing using alternating odd and even moving plates, common-mode interference (such as changes in dielectric constant) caused by changes in ambient temperature and humidity is effectively canceled; the differential structure doubles the output signal amplitude. This significantly improves the effective signal strength. Utilizing an array arrangement (N groups), spatial periodic sampling of the target signal is achieved, smoothing the edge effect of a single plate and greatly improving the linearity of the measurement. It solves the problems of traditional single-capacitor sensors being susceptible to interference from parasitic capacitance (plate edge capacitance) and easily affected by environmental noise (electromagnetic interference, temperature drift), resulting in a low signal-to-noise ratio; and the nonlinear error caused by edge effects under large displacements.

[0015] 2. A specific spatially symmetrical layout of eight sensors (4 variable area capacitive displacement sensors + 4 variable distance capacitive displacement sensors) and corresponding geometric calculation algorithms. Through a specific algorithm, the rotational component around the axis can be accurately separated using geometric relationships, unaffected by the overall Z-axis translation. Utilizing multi-sensor data fusion, independent and accurate calculation of the pose parameters of the six degrees of freedom at minute angles is achieved. This addresses the problem that when an object moves in three-dimensional space, the displacements of each degree of freedom are often coupled together, making it difficult to accurately separate simple rotational or translational amounts using a single-dimensional sensor.

[0016] 3. Eight sensors are integrated into the same mounting structure and employ a non-contact measurement principle. The symmetrical and rationally integrated layout minimizes the sensor footprint, making it easy to embed in space-constrained high-end equipment such as extreme ultraviolet lithography machines. Non-contact measurement avoids wear and additional force / torque interference, making it particularly suitable for pose monitoring of fragile components or ultra-precision motion platforms. Solving multi-degree-of-freedom measurements typically requires stacking multiple independent sensors, which occupies a large space; and contact measurements can damage precision equipment or generate frictional interference.

[0017] 4. The capacitive sensing principle, combined with a simple algebraic solution algorithm (involving only addition, subtraction, multiplication, and division, without complex iterations), results in a fast system response and low computational load, meeting the real-time requirements of high-speed dynamic measurements. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the structure of a six-degree-of-freedom capacitive sensor in a specific embodiment.

[0019] Figure 2 This is a schematic diagram of the planar arrangement of a six-degree-of-freedom capacitive sensor in a specific embodiment.

[0020] Figure 3a and Figure 3b These are schematic diagrams showing the sensor layout and displacement changes. Detailed Implementation

[0021] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0022] like Figure 1 As shown in the figure, this embodiment provides a six-degree-of-freedom capacitive sensor, which is installed between two devices under test to form a stable capacitance measurement gap. A capacitor pair is formed by the receiving end plate and the corresponding transmitting end plate. When the devices under test undergo relative displacement (including translation along the X, Y, and Z axes and rotation around the X, Y, and Z axes), the capacitance of the capacitor pair changes with the displacement. By measuring the capacitance changes of the eight capacitive sensors, the six-degree-of-freedom displacement parameters can be calculated.

[0023] In this embodiment, the tops of the two devices under test arranged opposite to each other are provided with mounting brackets. The sensor group 2 is set on a square Invar frame 1. The Invar frame 1 constitutes the sensor housing. The Invar frame 1 is provided with several positioning holes 4. The Invar frame 1 with the sensor group 2 is fixed on the mounting bracket of the device under test through the positioning holes and positioning pins 3.

[0024] Specifically, the Inductor frame 1 has 4 M6 and 16 M5 screw mounting holes symmetrically distributed, as well as 4 mounting positioning pins. 4 Z-axis height positioning posts are designed at the 4 corners to ensure parallelism during installation. The sensor transmission line uses a relatively flexible ribbon cable to minimize the impact of cable stress during movement.

[0025] The eight sensors are divided into two categories: four variable area capacitive displacement sensors, denoted as follows: , , , It is used to detect translational displacement along the X and Y axes and rotational displacement about the Z axis; four variable distance capacitive displacement sensors: denoted as... , , , It is used to detect translational displacement along the Z-axis and rotational displacement about the X and Y axes, such as... Figure 2 As shown.

[0026] Specifically, the working principle of the variable area capacitance sensor is as follows: The variable area capacitive sensor consists of a fixed plate and a moving plate, with an initial capacitance value of: ; denoted as the total dielectric constant, A is the area of ​​the two plates facing each other, and d is the distance between the plates. When the moving plate moves to the right This causes a change in the area directly opposite the capacitor, which in turn leads to a change in capacitance. ; Where k is a proportionality coefficient (depending on the plate size, dielectric constant, etc.), representing the change in capacitance caused by a unit displacement.

[0027] Arrange N groups of differential capacitance pairs in a straight line direction on the same plane to form a differential capacitance array. The moving plates of odd-numbered groups and even-numbered groups are arranged staggeredly, and the physical layout is symmetrical, realizing spatial periodic sampling of the target signal to obtain the final output signal: ; where k is a proportionality coefficient (depending on the plate size, dielectric constant, etc.). This differential processing method can effectively cancel the common-mode interference and double the signal amplitude, significantly improving the measurement signal-to-noise ratio and linearity.

[0028] The working principle of the variable-distance capacitance sensor is as follows: The initial capacitance value of the variable-distance capacitance sensor also satisfies: ; When the measured object moves in the direction perpendicular to the plate plane (Z-axis), the plate spacing d changes, resulting in a capacitance change. The formula for the capacitance change is: ; z is the translational displacement along the Z-axis.

[0029] For a small displacement (i.e., Δx << d), a linear approximation can be made: ; is the capacitance-displacement proportionality coefficient in the Z-axis direction (depending on the dielectric constant ε, the plate area A, and the initial spacing d).

[0030] Specifically, the range of small displacements includes: The translational measurement range along the Z direction ≥ 500 μm; The translational measurement range along the X and Y directions ≥ 500 μm; The rotational measurement range along the X, Y, and Z axes ≥ ±250 μrad; The translational measurement accuracy along the X, Y, and Z directions ≤ ±75 nm; The rotational measurement accuracy along the X, Y, and Z axes ≤ ±1.5 μrad; The translational measurement resolution along the X, Y, and Z directions ≤ 1 nm @ 20 Hz, ≤ 3 nm @ 100 Hz; The rotational measurement resolution along the X, Y, and Z axes ≤ 5 mrad @ 20 Hz, ≤ 15 mrad @ 100 Hz; The translational measurement noise along the X, Y, and Z directions ≤ 1 nm @ 100 Hz @ 10 s; This embodiment provides a displacement measurement method based on a six-degree-of-freedom capacitive sensor, specifically as follows: (1) Translational distance measurement along the X-axis: The moving plate moves along the X-axis x causes a change in the area directly opposite the point of contact, which in turn leads to a change in capacitance: ; ; is the capacitance-displacement proportionality coefficient in the X-axis direction, and N is the number of differential capacitor pairs.

[0031] For the translational distance along the X-axis, the sensor uses two capacitive sensors. , Simultaneously, after measurement and calculation, we can obtain: ; (2) Measurement of translational distance along the Y-axis: The moving plate moves along the Y-axis y causes a change in the area directly opposite, which in turn leads to a change in capacitance: ; ; is the capacitance-displacement proportionality coefficient in the Y-axis direction, and N is the number of moving plates.

[0032] For the translational distance along the Y-axis, the sensor uses two capacitive sensors. , Simultaneously, after measurement and calculation, we can obtain: ; (3) Measurement of translational distance along the Z-axis: When the object being measured translates along the Z-axis At time z, four variable distance capacitive sensors , , , The capacitance changes all satisfy the following: ; ; ; ; For the translational distance in the Z-axis direction, four capacitive sensors are used. , , , Measurements show that changes in distance along the Z-axis cause simultaneous changes in the capacitance of the four sensors. The resulting change in horizontal displacement can be calculated. ; (4) Measurement of rotation angle along the X-axis: Sensor layout: using , , , Four variable-distance capacitive sensors are evenly distributed on both sides of the YZ plane. The specific layout is as follows: , Located in the positive Y-axis direction, , Located in the negative Y-axis direction, forming a symmetrical distribution about the X-axis, such as... Figure 3a and Figure 3b As shown.

[0033] Rotation along the X-axis At angles, four capacitive sensors are used. , , , This will generate a displacement difference along the Z-axis. , The displacement change measured by the sensor is averaged to obtain the displacement change AA' at point A. , The displacement change measured by the sensor is averaged to obtain the displacement change BB' at point B. Since the distance AB is known, the displacements AA' and BB' within the measurement range can be approximated as displacements in the vertical direction. A relationship of less than 1 radian can be approximated as linear: ; ; Where L is the distance between the sensor groups in the positive and negative directions of the Y-axis (i.e., , and , (The Y-axis distance between them). Using the center point O of the plates as a reference point, the rotation angle along the X-axis can be calculated.

[0034] The average displacement of the sensor group in the positive Y-axis direction is calculated as follows: ; The average displacement of the sensor group in the positive Y-axis direction is calculated as follows: ; Calculate the displacement difference: ; Calculate the X-axis rotation angle: ; (5) Measurement of rotation angle along the Y-axis: Rotation along the X-axis At angles, four capacitive sensors are used. , , , Measurement. , The displacement change measured by the sensor is averaged to obtain the displacement change CC' at point C. , The displacement change measured by the sensor is averaged to obtain the displacement change DD' at point D. Since the distance CD is known, the displacements of CC' and DD' within the measurement range can be approximated as vertical displacements. Using the center point O of the plate as a reference point, the rotation angle along the Y-axis can be calculated.

[0035] A relationship of less than 1 radian can be approximated as linear: ; ; Where M is the distance between the sensor groups in the positive and negative directions of the Y-axis (i.e., , and , (The X-axis distance between them). Using the center point O of the plates as a reference point, the rotation angle along the X-axis can be calculated.

[0036] The average displacement of the sensor group in the positive X-axis direction is calculated as follows: ; The average displacement of the sensor group in the positive Y-axis direction is calculated as follows: ; Calculate the displacement difference: ; Calculate the X-axis rotation angle: ; (6) Measurement of rotation angle along the Z-axis: For measuring the rotation angle in the Z-axis direction, similar to the X and Y-axis rotation angles described above, four variable area capacitive sensors are used. , , , The measurement of displacement changes can improve accuracy and calculate rotation angles.

[0037] When the object rotates around the Z-axis by an angle At this time, each sensor will generate tangential displacement. Under a small rotation angle ( <<1 radian), the relationship between tangential displacement and rotation angle is: ; ; ; ; Where R is the distance from the sensor to the Z-axis rotation center.

[0038] Calculate the displacement change of the sensor in the X-axis direction: ; Calculate the displacement change of the sensor in the Y-axis direction: ; Calculate the Z-axis rotation angle: ; in, and Let K and Y be the capacitance-displacement proportionality coefficients in the X and Y axes, respectively. They are approximately equal under an ideal symmetrical layout and are denoted as k.

[0039] Specifically, the X / Y axis calibration is as follows: Using a high-precision displacement platform, apply a known displacement (e.g., 50nm, 100nm, 150nm) along the X-axis, record the corresponding capacitance changes, and calculate... =Capacitance change / (N × displacement); The Y-axis is calibrated using the same method. value.

[0040] Z-axis calibration: Apply small, known displacements (e.g., 10nm, 20nm, 30nm) along the Z-axis, record the capacitance changes of the four Z-sensors, and calculate... Change in capacitance / displacement.

[0041] This invention is not limited to the embodiments described above. The above description of specific embodiments is intended to illustrate and explain the technical solutions of this invention. The specific embodiments described above are merely illustrative and not restrictive. Without departing from the spirit and scope of the claims, those skilled in the art can make many specific modifications based on the teachings of this invention, and these modifications all fall within the scope of protection of this invention.

Claims

1. A displacement measurement method using a six-degree-of-freedom capacitive sensor, characterized in that, The sensor includes a receiving electrode plate and a transmitting electrode plate installed between the devices under test, with a capacitance measurement gap formed between the receiving electrode plate and the transmitting electrode plate; the sensor contains eight capacitance sensors, divided into four variable area capacitance displacement sensors and four variable distance capacitance displacement sensors; the measurement method includes: The translational displacement along the X and Y axes and the rotational angle around the Z axis are detected by four variable area capacitive displacement sensors. The translational displacement along the Z-axis and the rotational angles around the X and Y axes are detected by four variable-distance capacitive displacement sensors. Based on the capacitance changes of the eight capacitive sensors, the six-degree-of-freedom pose parameters of the measured object in space are calculated.

2. The displacement measurement method of a six-degree-of-freedom capacitive sensor according to claim 1, characterized in that, Translational displacement along the Z-axis The solution method is as follows: using four variable distance capacitive sensors , , , Simultaneously measured, changes in distance along the Z-axis cause simultaneous changes in the capacitance of the four variable-distance capacitive sensors, as shown in the formula: ； in, Let i = 1, 2, 3, 4, where i represents the capacitance change of each variable distance capacitive sensor. The capacitance-displacement proportionality coefficient in the Z-axis direction.

3. The displacement measurement method of a six-degree-of-freedom capacitive sensor according to claim 1, characterized in that, The variable area capacitance sensor includes N sets of differential capacitor pairs. Each differential capacitor pair consists of a fixed plate and a moving plate, with the moving plate moving along the X-axis. x causes a change in the area directly opposite the point of contact, which in turn leads to a change in capacitance: ； The moving electrode plate moves along the Y-axis y causes a change in the area directly opposite, which in turn leads to a change in capacitance: ； Translational displacement along the X-axis and translational displacement along the Y-axis The solution method is as follows: using a variable area capacitance sensor , Calculate the translation distance along the X-axis: ； Using a variable area capacitance sensor , Calculate the translation distance along the Y-axis: ； Where N is the number of differential capacitor pairs. , These are the capacitance-displacement scaling factors in the X and Y axes, respectively.

4. The displacement measurement method of a six-degree-of-freedom capacitive sensor according to claim 1, characterized in that, Rotation angle around the X-axis The solution method is as follows: Of the four variable distance capacitive displacement sensors, , Located on one side of the positive Y-axis, , Located on the negative Y-axis side, and Symmetrical distribution about the X-axis and Symmetrical distribution about the X-axis, and , and , The Y-axis spacing between them is L; the displacement difference between the variable-distance capacitive displacement sensors in the positive and negative Y-axis directions is calculated using the following formula: ； in, The capacitance-displacement proportionality coefficient in the Z-axis direction. The translational displacement along the Z-axis, Let i represent the capacitance change of each variable distance capacitive sensor, i = 1, 2, 3, 4.

5. The displacement measurement method of a six-degree-of-freedom capacitive sensor according to claim 1, characterized in that, Rotation angle around the Y-axis The solution method is as follows: Of the four variable distance capacitive displacement sensors, , Located on one side of the positive X-axis, , Located on one side of the negative X-axis, and Symmetrical distribution about the Y-axis and Symmetrical distribution about the Y-axis, and , and , The X-axis distance between them is M; the displacement difference of the variable-distance capacitive displacement sensor in the positive and negative X-axis directions is calculated using the following formula: ； in, The capacitance-displacement proportionality coefficient in the Z-axis direction. The translational displacement along the Z-axis, Let i represent the capacitance change of each variable distance capacitive sensor, i = 1, 2, 3, 4.

6. The displacement measurement method of a six-degree-of-freedom capacitive sensor according to claim 3, characterized in that, Rotation angle around the Z-axis The solution method is as follows: Using a variable area capacitance sensor , Measuring displacement changes in the X-axis direction, using , Measure displacement changes in the Y-axis direction; The solution is derived from the relationship between tangential displacement and rotation angle, using the following formula: ； Where R is the distance from the geometric center of each variable area capacitive sensor to the Z-axis rotation center, k is the capacitance-displacement proportionality coefficient with uniformity in the X and Y axes under an ideal symmetrical layout, and N is the number of differential capacitor pairs. and These represent the translation distance along the X-axis and the translation distance along the Y-axis, respectively.

7. The displacement measurement method of a six-degree-of-freedom capacitive sensor according to claim 1, characterized in that, The variable area capacitive displacement sensor adopts a differential capacitor array structure, including N sets of differential capacitor pairs arranged in a straight line on the same plane; the moving plates of the odd and even sets are arranged alternately, forming a symmetrical physical layout, and the output signal is... k is the proportionality constant. This represents the translation distance along the X-axis.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the six-degree-of-freedom capacitive sensor displacement measurement method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the six-degree-of-freedom capacitive sensor displacement measurement method according to any one of claims 1 to 7.

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