A rigid body center of mass measurement method based on inertial sensors

Abstract

The application provides a rigid body centroid measurement method based on an inertial sensor, which comprises the following steps: installing an inertial sensor at any known position of a measured rigid body, wherein the inertial sensor comprises a three-axis acceleration sensor and a three-axis angular velocity sensor; collecting three-axis acceleration data of a sensor mounting point and three-axis angular velocity data of the rigid body; determining an initial attitude angle of the rigid body according to the three-axis acceleration data in a stationary state, making the rigid body produce free rotation, and calculating a real-time attitude angle of the rigid body in combination with the three-axis angular velocity data; establishing a coupling relationship model among three-axis acceleration of the sensor mounting point, angular motion parameters of the rigid body, gravitational acceleration and coordinates of the sensor mounting point in a centroid system, constructing an equation group and solving the equation group to obtain the coordinates of the sensor mounting point in the centroid system, and further determining the position of the centroid of the rigid body. The application only needs to arrange the inertial sensor at a single point of the rigid body, does not need to measure multiple points or complex support structures, and can quickly and accurately measure the position of the centroid of the rigid body in a dynamic environment.

Description

Technical Field

[0001] This invention relates to the field of rigid body inertial parameter testing and measurement technology, specifically to a method for measuring the center of mass of a rigid body based on an inertial sensor. Background Technology

[0002] Pulse wind tunnels (such as detonation-driven shock tunnels and free-piston-driven shock tunnels) possess significant application value in hypersonic aerodynamics and power technology research due to their high Mach numbers and high enthalpy values. However, these wind tunnels typically have only millisecond-level effective test times, and their operation is accompanied by intense structural vibrations and transient impact loads, posing a severe challenge to traditional force measurement techniques. Existing widely used strain gauge force measurement methods rely on structural supports and force transmission paths, resulting in limited dynamic response capabilities and vibration resistance. Under short-term, high-frequency disturbances, they are prone to measurement lag and signal distortion, leading to distorted or unstable force measurement data. Existing research indicates that the frequency response capability of traditional wind tunnel balance systems is insufficient to meet the high-frequency measurement requirements of unsteady aerodynamic forces.

[0003] To overcome the aforementioned problems, research on free-flight force measurement technology has been gradually carried out both domestically and internationally in recent years. This method effectively avoids the direct interference of wind tunnel structural vibrations on the measurement system by placing the model in an unconstrained or weakly constrained state during the experiment. For example, the Japan Aerospace Exploration Agency (JAXA) conducted free-flight measurement research in a high-enthalpy shock tunnel, enabling the experimental model to achieve completely free flight within a millisecond timescale, thereby acquiring multi-component aerodynamic data. This type of method can significantly reduce mechanical coupling errors and improve the reliability of force measurement results, but it also places higher demands on the measurement accuracy of the model's motion parameters.

[0004] In free-flight force measurement systems, aerodynamic forces are typically obtained through inversion calculations of the model's motion parameters, such as acceleration, attitude, and displacement. Currently, methods for measuring motion parameters mainly include optical measurement methods (such as high-speed photography and 3D reconstruction) and sensor measurement methods based on inertial sensors (such as triaxial accelerometers and triaxial angular velocity sensors). While optical measurement methods offer the advantage of non-contact measurement, they are susceptible to factors such as field of view limitations, marker obstruction, and wind tunnel vibrations. In contrast, inertial sensor-based measurement methods offer advantages such as high sampling frequency, good time synchronization, and strong environmental adaptability, and have gained increasing attention in recent years. They can directly acquire model motion information during free flight, exhibiting significant advantages in data continuity and stability.

[0005] In pulse wind tunnel free-flight force measurement applications, accurately obtaining the center of mass position of the test model is a crucial fundamental parameter for achieving high-precision aerodynamic force inversion. Existing center of mass measurement methods are mainly based on the principle of static equilibrium, including the suspension method, the multi-point weighing balancing method, and the tilt measurement method. Among them, the suspension method determines the intersection of the lines of action of gravity by repeatedly changing the hoisting position, and is suitable for irregular small components; the multi-point weighing balancing method solves for the center of mass position by measuring the load at each support point and combining it with the moment balance equation, and is currently the most widely used method in engineering practice; for the test object that requires obtaining the height of the center of mass, the tilt measurement method is usually used, which calculates it by changing the tilt angle of the support platform and analyzing the load changes.

[0006] However, the above-mentioned centroid measurement methods generally suffer from problems such as complex operation process, low measurement efficiency, high requirements for test environment, and difficulty in being applied to dynamic or transient conditions, making it difficult to meet the demand for rapid and high-precision measurement of centroid parameters in pulse wind tunnel free-flight force measurement.

[0007] Therefore, it is necessary to propose a measurement method that is simple in structure, suitable for dynamic measurement environments, and capable of quickly obtaining the position of the center of mass of any rigid body, so as to provide accurate center of mass parameters for pulse wind tunnel free-flight force measurement technology and improve the accuracy and reliability of aerodynamic measurement results. Summary of the Invention

[0008] To address the problems of existing rigid body center of mass measurement methods that mainly rely on the principle of static equilibrium, which have issues such as complex measurement process, low measurement efficiency, and difficulty in applying to dynamic environments and high vibration, short-term test conditions, this invention proposes a rigid body center of mass measurement method based on inertial sensors to achieve rapid and accurate measurement of the position of the rigid body center of mass under dynamic conditions.

[0009] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0010] A method for measuring the center of mass of a rigid body based on an inertial sensor includes the following steps:

[0011] (1) Install an inertial sensor at any known sensor mounting point A of the rigid body being measured. The inertial sensor includes a triaxial accelerometer and a triaxial angular velocity sensor.

[0012] (2) The acceleration information of sensor mounting point A is collected using the triaxial accelerometer, and the angular velocity information of the rigid body under test is collected using the triaxial angular velocity sensor;

[0013] (3) Determine the initial attitude information of the rigid body under test based on the relationship between the measurement information collected by the triaxial accelerometer and the gravitational acceleration in the static state of the rigid body;

[0014] (4) Calculate the real-time attitude information of the rigid body during its motion based on the initial attitude information and the angular velocity information during the motion of the rigid body under test;

[0015] (5) Based on the rigid body kinematics theory, establish the acceleration information, rigid body angular motion parameters, gravitational acceleration, and coordinate vector of sensor mounting point A in the center-of-mass coordinate system for sensor mounting point A. A coupling relationship model is established between them, and based on the coupling relationship model, three unknown spatial coordinate components of the sensor mounting point A in the centroid coordinate system are constructed. , and The system of equations;

[0016] (6) Solve the system of equations to obtain the coordinates of the sensor mounting point A in the centroid coordinate system. The position of the center of mass of the rigid body under test is determined based on the coordinates of the sensor mounting point A.

[0017] As a preferred embodiment of the present invention, the specific process of step (3) is as follows: In the initial state, the rigid body under test is kept at rest. The initial attitude angle of the rigid body under test is determined according to the projection relationship of the gravitational acceleration vector measured by the triaxial accelerometer in the rigid body coordinate system. Since the triaxial accelerometer cannot obtain attitude information about the direction of gravity in the static state, the initial attitude angle component about the direction of gravity is set to a preset value.

[0018] As a preferred embodiment of the present invention, the specific process of step (4) is as follows: based on the initial attitude information and the triaxial angular velocity information collected within a preset time period, the real-time attitude information of the rigid body under test during motion is obtained through the attitude calculation method.

[0019] As a preferred embodiment of the present invention, the coupling relationship model in step (5) is expressed as follows:

[0020] (3);

[0021] In the above formula, Let A be the acceleration vector at sensor mounting point A; It is the vector of gravitational acceleration; The rigid body angular velocity vector; It is the rigid body angular acceleration vector; Let A be the coordinate vector of the sensor mounting point A in the centroid coordinate system. ; For the rigid body being measured Real-time attitude information relative to the ground inertial coordinate system.

[0022] As a preferred embodiment of the present invention, the three unknown spatial coordinate components of the sensor mounting point A in the centroid coordinate system constructed in step (5) are... , and The system of equations is as follows:

[0023] (4);

[0024] In the above formula, This is the equation residual vector corresponding to the p-th sampling time.

[0025] The spatial coordinates of sensor mounting point A in the centroid coordinate system can be solved by the above equation set (4).

[0026] As a preferred embodiment of the present invention: the coupling relationship model is valid at any moment during the rigid body motion process. By collecting inertial measurement data at multiple moments, a set of equations for the three unknown coordinate components of the sensor mounting point A at the corresponding moment are established respectively.

[0027] The system of equations established at multiple time points is combined to form an overdetermined system of equations containing information from multiple measurement time points:

[0028] (5);

[0029] The three coordinate components of the sensor mounting point A in the centroid coordinate system are used as unknowns to be solved, and the least squares optimization method is used to solve them together; or the coordinates of the sensor mounting point A at each time point are solved separately, and the multiple solution results are fused to improve the accuracy of the centroid position measurement.

[0030] As a preferred embodiment of the present invention: when solving the system of equations for the three unknown coordinate components of the sensor installation point A at the corresponding time, multiple coordinate estimation results of the sensor installation point A are obtained, and the data fusion method is used to optimize the solution results at multiple times to reduce random measurement errors, improve the accuracy of the coordinate estimation of the sensor installation point A, and further improve the accuracy of the centroid position determination.

[0031] The data fusion method includes, but is not limited to, at least one of the following: arithmetic mean, weighted average, median value, and least squares-based error optimization method;

[0032] When the data fusion method employs the least squares optimization method, it constructs an objective function that minimizes the sum of squared residuals between the solution results at multiple time points and the coordinates of the sensor installation point A to be estimated.

[0033] (6);

[0034] By solving the above objective function The minimum value is used to obtain the coordinate vector of sensor mounting point A in the centroid coordinate system. The optimal coordinate estimation results.

[0035] As a preferred embodiment of the present invention: the inertial sensor is only set at one measurement position of the rigid body being measured, and the position of the center of mass of the rigid body being measured is determined by single-point inertial measurement data.

[0036] As a preferred embodiment of the present invention, both the initial attitude information and the real-time attitude information adopt Euler angles, quaternions, rotation matrices, axis angles, rotation vectors, or other mathematical representations that can characterize the attitude of a rigid body.

[0037] As a preferred embodiment of the present invention: the inertial sensor includes a triaxial acceleration sensor for measuring triaxial acceleration information at sensor mounting point A and a triaxial angular velocity sensor for measuring triaxial angular velocity information of the rigid body under test; the triaxial acceleration sensor and the triaxial angular velocity sensor can be integrated into an integrated inertial measurement unit, or they can be composed of independent sensors.

[0038] By adopting the above technical solution, the present invention has the following beneficial effects:

[0039] This invention only requires the placement of an inertial sensor at a single point on the rigid body, without the need for multi-point measurement or complex support structures, and can quickly and accurately measure the position of the center of mass of the rigid body in dynamic environments.

[0040] Compared with the prior art, the present invention has the following features and advantages:

[0041] (1) Realize centroid measurement under dynamic environment

[0042] Based on rigid body kinematics theory, this invention establishes a coupling relationship model between the acceleration information of the sensor mounting point, the angular motion parameters of the rigid body, the gravitational acceleration, and the position of the center of mass. The position of the center of mass of the rigid body can be solved using the inertial measurement data during the rigid body's motion. This invention breaks away from the limitation of traditional center of mass measurement methods that mainly rely on static equilibrium, and realizes the rapid determination of the position of the center of mass of the rigid body under dynamic motion.

[0043] (2) High measurement efficiency

[0044] This invention only requires installing one set of inertial sensors at any known position of the rigid body under test. It eliminates the need for multiple measurement devices or repeated changes in support state. Inertial measurement data at multiple moments can be obtained in a single test, enabling the determination of the position of the rigid body's center of mass. This effectively improves measurement efficiency and shortens the test cycle.

[0045] (3) Simple structure and convenient engineering implementation

[0046] This invention eliminates the need for multi-point weighing devices, complex support mechanisms, or large optical measurement systems. It can complete the measurement of the center of mass using only a triaxial accelerometer and a triaxial angular velocity sensor. The system has a simple composition, low requirements for experimental equipment and environment, and is easy to implement in engineering and promote its application.

[0047] (4) High measurement accuracy and good stability

[0048] Since the established coupling relationship model holds true at any moment during the rigid body motion, multiple sets of equations can be established using inertial measurement data from multiple moments. These equations can be solved by constructing an overdetermined set of equations and performing joint least squares solutions. Alternatively, the estimated coordinates of sensor mounting point A at each moment can be solved separately and then the data can be fused. This effectively reduces random measurement errors and improves the stability and measurement accuracy of the centroid position calculation results.

[0049] (5) Wide range of applications

[0050] This invention has no special requirements on the structure, dimensions, and mass distribution of the rigid body being measured. It only requires that the installation position of the inertial sensor be known to complete the measurement of the center of mass. Therefore, it is applicable to the measurement of the center of mass position of rigid bodies of different sizes, structures, and types, and has good versatility.

[0051] (6) Applicable to pulse wind tunnel free flight tests

[0052] This invention is particularly suitable for short-time, high-vibration test environments such as pulse wind tunnels. It can quickly obtain the center of mass position of the test model, providing accurate basic parameters for aerodynamic inversion in free-flight force measurement technology, which is beneficial to improving the accuracy and reliability of aerodynamic measurement results.

[0053] This invention utilizes inertial measurement data during rigid body motion to establish a model for solving the center of mass position, realizing the direct solution of the center of mass position of a rigid body under dynamic motion conditions. It provides a new technical solution for measuring the inertial parameters of rigid bodies in dynamic environments, which is beneficial to expanding the application of inertial sensors in the field of rigid body inertial parameter identification and measurement. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. Obviously, the following drawings are only some embodiments of the present invention, and those skilled in the art can obtain other related drawings based on these drawings without creative effort.

[0055] Figure 1 This is a schematic diagram of the spatial relationship between the inertial sensor and the rigid body under test in the rigid body center of mass measurement method based on inertial sensor of the present invention. It shows the positional relationship between the inertial sensor installation point A, the coordinate system of the rigid body center of mass and the ground inertial coordinate system.

[0056] Figure 2 This is a flowchart illustrating the overall implementation of the rigid body center of mass measurement method based on inertial sensors according to the present invention.

[0057] Figure 3 This is a schematic diagram of the rigid body under test in an initial static state using a flexible suspension method in an embodiment of the present invention.

[0058] The annotations in the attached figures are explained as follows:

[0059] 1-The rigid body under test; 2-A three-axis angular velocity sensor; 3-A three-axis accelerometer; 4-Flexible suspension rope; 5-Suspension support structure. Detailed Implementation

[0060] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, other embodiments obtained by those skilled in the art without creative effort according to the technical solutions disclosed in the present invention are all within the protection scope of the present invention.

[0061] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0062] like Figures 1-3 As shown, this embodiment provides a method for measuring the center of mass of a rigid body based on an inertial sensor, including the following steps:

[0063] S1, Inertial sensor installation

[0064] An inertial sensor is installed at any known location A on the rigid body 1 being measured. The inertial sensor includes a triaxial accelerometer 3 and a triaxial angular velocity sensor 2.

[0065] An inertial sensor is placed at only one measurement location on the rigid body being measured, and the position of the center of mass of the rigid body is determined through single-point inertial measurement data.

[0066] In this context, sensor mounting point A is a known reference position on the rigid body 1 being measured, used to establish the positional relationship between the sensor measurement point and the center of mass of the rigid body. Sensor mounting point A is set at a known position on the rigid body being measured that is convenient for installation and positioning, and the position of the center of mass of the rigid body being measured is determined by the measured positional relationship of sensor mounting point A relative to its center of mass.

[0067] To achieve an initial static state for the rigid body, in this embodiment, the rigid body 1 under test is constrained by a flexible suspension method. The flexible suspension structure includes at least two flexible suspension ropes 4, one end of which is connected to the rigid body 1 under test, and the other end is connected to the top solid wall 5 or other supporting structure, so that the rigid body 1 under test is in a stable static state.

[0068] After the initial attitude measurement is completed, the flexible suspension constraint is released, allowing the measured rigid body 1 to enter a state of free motion.

[0069] To describe the rigid body motion relationships, a ground inertial coordinate system is established. and the center-of-mass coordinate system fixed to the rigid body being measured. Among them, the origin of the centroid coordinate system Located at the center of mass of the rigid body being measured, the coordinate axes are fixed to the rigid body and remain unchanged as the rigid body moves.

[0070] To describe the rigid body motion relationships, a ground inertial coordinate system is established. and the center-of-mass coordinate system fixed to the rigid body being measured. Among them, the origin of the centroid coordinate system Located at the center of mass of the rigid body being measured, the coordinate axes are fixed to the rigid body and remain unchanged with the motion of the rigid body. Initially, the coordinate system of the center of mass of the rigid body... Axial direction and ground inertial coordinate system The axes are aligned, both in the direction of gravity.

[0071] S2, Inertial Data Acquisition

[0072] The triaxial acceleration information at sensor mounting point A is collected using triaxial accelerometer 3, and the triaxial angular velocity information of the rigid body 1 under test during its motion is collected using triaxial angular velocity sensor 2.

[0073] Among them, the triaxial accelerometer 3 is used to acquire linear acceleration measurement information at installation point A, and the triaxial angular velocity sensor 2 is used to acquire angular velocity information of the measured rigid body 1 around the three coordinate axes of the center of mass coordinate system.

[0074] During the motion of the rigid body 1 under test, data output from the triaxial accelerometer 3 and the triaxial angular velocity sensor 2 are continuously collected to provide a data basis for subsequent attitude calculation and centroid position determination.

[0075] S3. Initial attitude determination

[0076] In the initial state, the rigid body 1 under test is kept stationary by a flexible suspension.

[0077] In the initial state, the coordinate system of the rigid body's center of mass of Axial direction and ground inertial coordinate system of The axes are aligned, both in the direction of gravity.

[0078] Since the rigid body 1 being measured is in a stationary state, the measurement value of the triaxial accelerometer 3 mainly reflects the projection of gravitational acceleration in the rigid body coordinate system.

[0079] Based on the projection relationship of the gravitational acceleration vector measured by the triaxial accelerometer 3 in the rigid body coordinate system under static conditions, the initial moment of the measured rigid body 1 can be determined. attitude angle In the initial state, in the established rigid body center-of-mass coordinate system... The axial direction relative to the ground inertial coordinate system The axes are aligned, all in the same direction as gravity. Since the triaxial accelerometer cannot acquire attitude information about the direction of gravity when stationary, the initial attitude angular component about the direction of gravity is set to a preset value, preferably 0; the initial attitude angle... It can be represented as:

[0080] (1);

[0081] in, Initial time The attitude angle information of the rigid body under test is preferably represented by Euler angle vectors. This is the gravitational acceleration vector.

[0082] Since the triaxial accelerometer can only acquire information about the direction of gravity when stationary, and cannot determine the rotation angle around the direction of gravity, the initial attitude angular component around the direction of gravity is set to a preset value, preferably 0.

[0083] S4, Real-time Attitude Measurement

[0084] After the rigid body 1 under test enters the motion state from the static state, the real-time attitude of the rigid body under test is calculated based on the initial attitude information obtained in step S3 and the angular velocity information collected by the triaxial angular velocity sensor 2 within a preset time period.

[0085] This embodiment uses an attitude calculation method based on angular velocity integral, but it can also be implemented using quaternion update method, rotation matrix update method, etc.

[0086] When using the angular velocity integral method, The real-time attitude information of the rigid body being measured is represented as follows:

[0087] (2);

[0088] in, For the rigid body being measured Real-time attitude information relative to the ground inertial coordinate system is preferably represented by Euler angle vectors. This is the rigid body angular velocity vector measured by a triaxial angular velocity sensor.

[0089] S5. Establish a model for solving the centroid position.

[0090] Based on rigid body kinematics theory, a coupling relationship model is established between the acceleration information of sensor mounting point A, rigid body angular motion parameters, gravitational acceleration, and the coordinate vector of sensor mounting point A in the center-of-mass coordinate system; this coupling relationship model is expressed as:

[0091] (3);

[0092] in, The acceleration vector at sensor mounting point A; It is the vector of gravitational acceleration; The rigid body angular velocity vector; It is the rigid body angular acceleration vector; Let A be the position coordinate vector of sensor mounting point A in the centroid coordinate system. ; For the rigid body being measured Real-time attitude information relative to the ground inertial coordinate system is preferably represented by Euler angle vectors.

[0093] Because the above relationship includes only the position vector of sensor mounting point A... Apart from the unknown parameters, all other parameters can be obtained from inertial sensor measurement data or attitude calculations, thus allowing the establishment of a [system / mechanism] framework. , and A system of equations with three unknown coordinate components.

[0094] In the At each sampling time, three independent equations of the following form can be established:

[0095] (4);

[0096] in, Let be the residual vector of the equation corresponding to the p-th sampling time. The spatial coordinates of the sensor mounting point A in the centroid coordinate system can be solved using the above system of equations.

[0097] S6. Multi-time joint solution and centroid determination

[0098] Since the above coupling model holds true at any moment during the rigid body motion, inertial measurement data can be continuously collected at multiple moments during a single motion test, and equations can be established for the three unknown coordinate components of the sensor mounting point A at the corresponding moments.

[0099] When collecting After obtaining data at each time point, the equations corresponding to multiple time points can be combined again to form a system of equations concerning the unknowns. The overdetermined system of equations:

[0100] (5);

[0101] Using the coordinate vector of sensor mounting point A To unify the unknowns, a joint solution is performed using the least squares optimization method; or the coordinates of the sensor installation point A at each time point are solved separately, and the multiple solution results are fused to improve the accuracy of the centroid position measurement.

[0102] When the equations for the three unknown coordinate components of the sensor installation point A at the corresponding time are solved, multiple coordinate estimation results for the sensor installation point A are obtained. The data fusion method is then used to optimize the solution results at multiple times to reduce random measurement errors, improve the accuracy of the coordinate estimation of the sensor installation point A, and further improve the accuracy of the centroid position determination.

[0103] Establish the objective function to minimize the sum of squared residuals:

[0104] (6);

[0105] By solving the objective function The minimum value is used to obtain the coordinate vector of sensor mounting point A in the centroid coordinate system. The optimal estimation result.

[0106] Furthermore, the equations established at different sampling times can be solved separately to obtain the coordinate vectors of multiple sensor installation points A. The estimated results are then processed through averaging methods such as arithmetic mean, weighted average, and median, or through error optimization methods based on least squares, to reduce random measurement errors and improve the stability of the measurement results.

[0107] Since the origin of the centroid coordinate system is defined as the position of the centroid of the rigid body being measured, the position of the centroid of the rigid body can be determined after obtaining the coordinates of the sensor mounting point A in the centroid coordinate system.

[0108] The initial attitude information and the real-time attitude information mentioned above are both expressed using Euler angles, quaternions, rotation matrices, axis angles, rotation vectors, or other mathematical representations that can characterize the attitude of a rigid body.

[0109] Implementation process

[0110] like Figure 3 As shown, the rigid body 1 is suspended from the top solid wall 5 or below the support structure using a flexible suspension rope 4.

[0111] There shall be no fewer than two flexible suspension ropes 4 to ensure that the rigid body 1 can remain stable and stationary.

[0112] The triaxial accelerometer 3 and the triaxial angular velocity sensor 2 are installed at a known position A on the rigid body 1 and connected to a data acquisition device to achieve inertial data acquisition.

[0113] When the rigid body 1 is stationary, the output data of the triaxial accelerometer 3 is read, and the initial attitude information of the rigid body is calculated according to equation (1), where the attitude angular component around the direction of gravity is set to 0.

[0114] The flexible suspension constraint is then released, and the rigid body 1 is brought into a state of free motion through external force excitation, mechanical drive, or other means.

[0115] During the motion, the acceleration data at point A output by the triaxial accelerometer 3 and the angular velocity data output by the triaxial angular velocity sensor 2 are recorded simultaneously.

[0116] Based on the angular velocity data and initial attitude information, the real-time attitude information of the rigid body during motion is calculated using equation (2).

[0117] Further combining the acceleration data of point A, real-time attitude information and rigid body angular motion parameters, a centroid position solution model is established according to equations (3) to (4), and equations (5) to (6) are used for joint solution to obtain the position coordinates of sensor mounting point A in the centroid coordinate system.

[0118] Since the position of the center of mass of a rigid body remains unchanged during motion, the final position of the center of mass can be obtained by optimizing the position estimation results obtained at multiple moments.

[0119] This invention utilizes single-point inertial measurement data to determine the position of the center of mass of a rigid body under dynamic conditions, avoiding the limitations of traditional methods such as multi-point weighing, multiple suspension measurements, and complex support structures. It is particularly suitable for short-term, high-vibration environments such as pulse wind tunnels, and can provide accurate center of mass position parameters for free-flight force measurement tests.

[0120] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications, substitutions, or equivalent transformations can be made to the technical solutions in the above embodiments without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications, substitutions, or equivalent transformations should be included within the scope of protection of the present invention.

Claims

1. A method for measuring the center of mass of a rigid body based on an inertial sensor, characterized in that, Includes the following steps: (1) Install an inertial sensor at any known sensor mounting point A of the rigid body being measured. The inertial sensor includes a triaxial accelerometer and a triaxial angular velocity sensor. (2) The acceleration information of sensor mounting point A is collected using the triaxial accelerometer, and the angular velocity information of the rigid body under test is collected using the triaxial angular velocity sensor; (3) Determine the initial attitude information of the rigid body under test based on the relationship between the measurement information collected by the triaxial accelerometer and the gravitational acceleration in the static state of the rigid body; (4) Calculate the real-time attitude information of the rigid body during its motion based on the initial attitude information and the angular velocity information during the motion of the rigid body under test; (5) Based on the rigid body kinematics theory, establish the acceleration information, rigid body angular motion parameters, gravitational acceleration, and coordinate vector of sensor mounting point A in the center-of-mass coordinate system for sensor mounting point A. A coupling relationship model is established between them, and based on the coupling relationship model, three unknown spatial coordinate components of the sensor mounting point A in the centroid coordinate system are constructed. , and The system of equations; (6) Solve the system of equations to obtain the coordinates of the sensor mounting point A in the centroid coordinate system. The position of the center of mass of the rigid body under test is determined based on the coordinates of the sensor mounting point A.

2. The method for measuring the center of mass of a rigid body based on an inertial sensor according to claim 1, characterized in that, The specific process of step (3) is as follows: In the initial state, the rigid body under test is kept at rest. The initial attitude angle of the rigid body under test is determined according to the projection relationship of the gravitational acceleration vector measured by the triaxial accelerometer in the rigid body coordinate system. Since the triaxial accelerometer cannot obtain attitude information about the direction of gravity in the static state, the initial attitude angle component about the direction of gravity is set to a preset value.

3. The method for measuring the center of mass of a rigid body based on an inertial sensor according to claim 1, characterized in that, The specific process of step (4) is as follows: based on the initial attitude information and the triaxial angular velocity information collected within a preset time period, the real-time attitude information of the rigid body under test during motion is obtained through the attitude calculation method.

4. The method for measuring the center of mass of a rigid body based on an inertial sensor according to claim 1, characterized in that, The coupling relationship model in step (5) is represented as follows: （3）； In the above formula, Let A be the acceleration vector at sensor mounting point A; It is the vector of gravitational acceleration; The rigid body angular velocity vector; It is the rigid body angular acceleration vector; Let A be the coordinate vector of the sensor mounting point A in the centroid coordinate system. ; For the rigid body being measured Real-time attitude information relative to the ground inertial coordinate system.

5. The method for measuring the center of mass of a rigid body based on an inertial sensor according to claim 1, characterized in that, The three unknown spatial coordinate components of the sensor mounting point A in the centroid coordinate system constructed in step (5) , and The system of equations is as follows: （4）； In the above formula, This is the equation residual vector corresponding to the p-th sampling time. The spatial coordinates of sensor mounting point A in the centroid coordinate system can be solved by the above set of equations (4).

6. The method for measuring the center of mass of a rigid body based on an inertial sensor according to claim 1, characterized in that: The coupling relationship model holds true at any moment during the rigid body motion process. By collecting inertial measurement data at multiple moments, equations are established for the three unknown coordinate components of the sensor mounting point A at the corresponding moment. The system of equations established at multiple time points is combined to form an overdetermined system of equations containing information from multiple measurement time points: （5）； The three coordinate components of the sensor mounting point A in the centroid coordinate system are used as unknowns to be solved, and the least squares optimization method is used to solve them together; or the coordinates of the sensor mounting point A at each time point are solved separately, and the multiple solution results are fused to improve the accuracy of the centroid position measurement.

7. The method for measuring the center of mass of a rigid body based on an inertial sensor according to claim 6, characterized in that: When the equations for the three unknown coordinate components of the sensor installation point A at the corresponding time are solved, multiple coordinate estimation results of the sensor installation point A are obtained. The data fusion method is used to optimize the solution results at multiple times to reduce random measurement errors, improve the accuracy of the coordinate estimation of the sensor installation point A, and further improve the accuracy of the centroid position determination. The data fusion method includes, but is not limited to, at least one of the following: arithmetic mean, weighted average, median value, and least squares-based error optimization method; When the data fusion method employs the least squares optimization approach, it constructs an objective function that minimizes the sum of squared residuals between the solution results at multiple time points and the coordinates of the sensor installation point A to be estimated. （6）； By solving the above objective function The minimum value is used to obtain the coordinate vector of sensor mounting point A in the centroid coordinate system. The optimal coordinate estimation results.

8. The method for measuring the center of mass of a rigid body based on an inertial sensor according to claim 1, characterized in that: The inertial sensor is set at only one measurement position of the rigid body being measured, and the position of the center of mass of the rigid body being measured is determined by the single-point inertial measurement data.

9. The method for measuring the center of mass of a rigid body based on an inertial sensor according to claim 1, characterized in that: Both the initial attitude information and the real-time attitude information adopt Euler angles, quaternions, rotation matrices, axis angles, rotation vectors, or other mathematical representations that can characterize the attitude of a rigid body.

10. The method for measuring the center of mass of a rigid body based on an inertial sensor according to claim 1, characterized in that: The inertial sensor includes a triaxial accelerometer for measuring triaxial acceleration information at sensor mounting point A and a triaxial angular velocity sensor for measuring triaxial angular velocity information of the rigid body under test; the triaxial accelerometer and the triaxial angular velocity sensor can be integrated into a single inertial measurement unit, or they can be composed of independent sensors.

Images