A six-degree-of-freedom platform load center of gravity and moment of inertia measuring device and a measuring method thereof

Abstract

The application relates to the technical field of measurement, and provides a center of gravity and rotational inertia measurement method of a six-degree-of-freedom platform load, which comprises the following steps: acquiring the position and posture of the six-degree-of-freedom platform at any moment and the electric cylinder thrust; calculating the position of the center of gravity of the load in the X direction and the Y direction according to the electric cylinder thrust in the initial posture static state; calculating the position of the center of gravity of the load in the Z direction according to the electric cylinder thrust in the specified position static state; and given the pitching, rolling and yawing movements, calculating the rotational inertia of the load according to the position and posture and the electric cylinder thrust in the corresponding movement process. The application solves the problems of large manual calculation error and the incapability of synchronously acquiring the rotational inertia by relying on the self-measurement of the platform body, and improves the control precision and safety.

Description

Technical Field

[0001] This application relates to the field of measurement technology, specifically to a device and method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load. Background Technology

[0002] The six-degree-of-freedom platform relies on six retractable actuators to drive the upper platform, enabling six degrees of freedom of motion: translation along the X / Y / Z axes and rotation (pitch, roll, yaw) around the X / Y / Z axes. It can accurately reproduce any spatial attitude and motion trajectory and is widely used in simulation testing, aerospace, shipbuilding, and industrial inspection.

[0003] In the application and debugging of a six-degree-of-freedom platform, accurately obtaining the load's center of gravity and moment of inertia is a crucial prerequisite for achieving high-precision attitude control, rationally selecting drive components, and ensuring safe equipment operation. Current technologies typically rely on manual estimation or external hoisting and testing equipment to obtain load center of gravity parameters. This method is not only cumbersome and inefficient, but also makes it difficult to simultaneously measure the moment of inertia. More importantly, traditional methods cannot autonomously identify parameters using the six-degree-of-freedom platform's own electric cylinder thrust and motion state data, leading to significant errors in the calculation results. This inaccuracy in parameter acquisition can easily cause a series of technical problems, such as deviations in electric cylinder force prediction, inaccurate dynamic load matching, decreased attitude control accuracy, and extended debugging cycles. Furthermore, under high-speed motion conditions, insufficient prediction of inertial loads can even lead to overload of drive components or damage to the mechanical structure. Therefore, there is an urgent need for a method that can achieve high-precision self-measurement of the load's center of gravity and moment of inertia based on the platform itself. Summary of the Invention

[0004] Purpose of the invention: To address the problems of large errors in the manual calculation of the center of gravity and moment of inertia of a six-degree-of-freedom platform load in the existing technology, and the inability to rely on the platform itself for self-testing, this application provides a measuring device and method for the center of gravity and moment of inertia of a six-degree-of-freedom platform load, realizing step-by-step decoupled self-testing of load inertia parameters based on the platform's own sensor data.

[0005] Technical solution: A method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load, characterized by comprising: (1) Obtain the position and attitude of the six-degree-of-freedom platform and the thrust of the electric cylinder at any time, and calculate the coordinates of the upper hinge point and the coordinates of the center of gravity containing unknown parameters of the upper platform based on the position and attitude according to the position inverse solution calculation method, and calculate the coordinates of the lower hinge point. (2) Calculate the position of the center of gravity of the six-degree-of-freedom platform load in the X and Y directions based on the electric cylinder thrust in the initial static position; (3) Based on the electric cylinder thrust in the static state at the specified position, calculate the position of the center of gravity in the Z direction based on the position of the center of gravity of the six-degree-of-freedom platform load in the X and Y directions, and specify the position as pitch or roll. (4) Given pitch, roll and yaw motions, based on the position and attitude of the corresponding motion process and the electric cylinder thrust, and based on the position of the center of gravity of the six-degree-of-freedom platform load in the X, Y and Z directions, the rotational inertia of the six-degree-of-freedom platform load.

[0006] In the above scheme, step (1) is to obtain the electric cylinder thrust by converting the torque of the servo motor or by adding a force sensor. Then, based on the coordinates of the upper hinge point and the coordinates of the lower hinge point, the distance between the projection of each electric cylinder on the XY plane, XZ plane and YZ plane and the center of the upper hinge circle of the upper platform is calculated. The distance is used as the lever arm.

[0007] Furthermore, the process of obtaining the position and attitude of the six-degree-of-freedom platform and the thrust of the electric cylinder at any given time is as follows: The thrust of the electric cylinder can be obtained by converting the torque of the servo motor or by adding a force sensor. Based on the position inverse kinematics calculation method, the coordinates of the upper hinge point and the coordinates of the center of gravity containing unknown parameters of the upper platform are calculated based on the position and attitude, and the coordinates of the lower hinge point are also calculated. Based on the coordinates of the upper hinge point and the lower hinge point, the distances of the projections of each electric cylinder onto the center of the upper hinge circle of the upper platform in the XY plane, the XZ plane, and the YZ plane are calculated and used as the lever arm.

[0008] Furthermore, the designated static position is a pose-holding state with zero angular acceleration, and the corresponding motion process is a dynamic process with angular acceleration.

[0009] The moment of inertia is calculated based on the moment balance equation of the projected surface; The torque balance equation is constructed by decomposing the electric cylinder thrust into the XY plane, XZ plane, and YZ plane, and then calculating the lever arm of each electric cylinder relative to the center of the upper hinge circle of the upper platform on the corresponding projection plane. The torque balance equation is constructed based on the components of the electric cylinder thrust on the corresponding projection plane and the lever arm.

[0010] Furthermore, the positions of the center of gravity of the six-degree-of-freedom platform load in the X and Y directions are calculated as follows: In the initial static pose, the position of the center of gravity of the six-degree-of-freedom platform load in the X direction is calculated based on the moment balance equation in the XZ plane. The moment balance equation in the XZ plane is: ; The position of the center of gravity of the six-degree-of-freedom platform load in the Y direction is calculated based on the moment balance equation in the YZ plane. The moment balance equation in the YZ plane is as follows: ; in, Number the electric cylinder. , , The first The components of the thrust of an electric cylinder in the X, Y, and Z directions. For the first The lever arm of the electric cylinder, projected onto the XZ plane, corresponds to the center of the hinge circle. For the first The lever arm of the electric cylinder, projected onto the YZ plane, corresponds to the center of the hinge circle. For load quality, It is the acceleration due to gravity. The position of the center of gravity of the six-degree-of-freedom platform load in the X direction. The position of the center of gravity of the six-degree-of-freedom platform load in the Y direction.

[0011] Furthermore, the position of the center of gravity of the six-degree-of-freedom platform load in the Z direction is calculated as follows: When given a pitch angle When in the pitch state, the position of the center of gravity of the six-degree-of-freedom platform load in the Z direction is obtained by inverse solving the moment balance equation in the YZ plane. The moment balance equation in the YZ plane is: ; When given a roll angle When in a tilted state, the position of the center of gravity of the six-degree-of-freedom platform load in the Z direction can be determined by inverse solving the moment balance equation of the XZ plane. The moment balance equation of the XZ plane is: ; in, The pitch angle, The roll angle is... The position of the center of gravity of the six-degree-of-freedom platform load in the Z direction.

[0012] Furthermore, given pitch, roll, and yaw motions, the moment of inertia of the six-degree-of-freedom platform load is calculated based on the corresponding position and attitude during the motion process and the thrust of the electric cylinder. Specifically: During pitch motion, an angular acceleration about the X-axis is introduced. The dynamic equilibrium equations are constructed to solve for the moment of inertia of the six-degree-of-freedom platform load about the X-axis. The dynamic equilibrium equation is: ; During the tilting motion, an angular acceleration about the Y-axis is introduced. Construct dynamic equilibrium equations to solve for the moment of inertia of the six-degree-of-freedom platform load about the Y-axis. The dynamic equilibrium equation is: ; During yaw motion, an angular acceleration about the Z-axis is introduced. The dynamic equilibrium equations are constructed to solve for the moment of inertia of the six-degree-of-freedom platform load about the Z-axis. The dynamic equilibrium equation is: ; in, For the first The electric cylinder is projected onto the center of the hinged circle in the XY plane.

[0013] Secondly, this application provides a device for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load, including a processor and a memory; Memory, used to store computer programs; The processor is used to implement the steps of the method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load as described above when executing the computer program.

[0014] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load as described in any one of claims 1 to 7.

[0015] Fourthly, this application also provides a six-degree-of-freedom platform, including an upper platform, a lower platform, a plurality of electric cylinders connecting the upper platform and the lower platform, and a control system, wherein the control system includes a device for measuring the center of gravity and moment of inertia of the load of the six-degree-of-freedom platform.

[0016] Beneficial Effects: Compared with existing technologies, this application employs a step-by-step decoupling measurement strategy. First, in an initial static pose, the horizontal position of the center of gravity is calculated using the torque balance of the XZ and YZ projection planes. Then, in an inclined static pose, the height of the center of gravity is calculated using the known horizontal position. Finally, under single-axis dynamic motion, angular acceleration is introduced to construct a dynamic equation to calculate the moment of inertia. This step-by-step decoupling mechanism transforms the complex spatial multi-parameter coupling identification problem into multiple independent planar mechanics problems, effectively reducing computational complexity, avoiding error accumulation caused by multi-parameter joint identification, and significantly improving measurement accuracy. Simultaneously, this method relies entirely on the electric cylinder thrust feedback and motion state data of the six-degree-of-freedom platform for self-testing, eliminating the need for additional external hoisting equipment or specialized testing fixtures. This solves the problems of large errors and low efficiency in traditional manual calculations, providing a precise parameter basis for dynamic optimization of electric cylinder output, overload warning, load installation and debugging, and motion control feedforward compensation, thereby improving the overall operational performance and safety of the platform. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the hinge point distribution structure of a six-degree-of-freedom platform according to an embodiment of this application; Figure 2 This is a schematic diagram of the coordinate distribution of the upper and lower hinge points of the six-degree-of-freedom platform according to an embodiment of this application; Figure 3 This is a schematic diagram of the layout of the six-degree-of-freedom platform electric cylinder and hinge point according to an embodiment of this application; Figure 4 This is a schematic diagram of the XY plane projection and lever arm of the six-degree-of-freedom platform according to an embodiment of this application; Figure 5 This is a schematic diagram of the XZ plane projection and thrust components of a six-degree-of-freedom platform according to an embodiment of this application; Figure 6 This is a schematic diagram of the YZ plane projection and thrust components of a six-degree-of-freedom platform according to an embodiment of this application.

[0018] Among them, 1-upper hinge circle, 2-lower hinge circle, 3-center of upper hinge circle, 11-electric cylinder No. 1, 12-electric cylinder No. 2, 13-electric cylinder No. 3, 14-electric cylinder No. 4, 15-electric cylinder No. 5, 16-electric cylinder No. 6, 21-upper hinge point No. 1, 22-upper hinge point No. 2, 23-upper hinge point No. 3, 24-upper hinge point No. 4, 25-upper hinge point No. 5, 26-upper hinge point No. 6, 31-lower hinge point No. 1, 32-lower hinge point No. 2, 33-lower hinge point No. 3, 34-lower hinge point No. 4, 35-lower hinge point No. 5, 36-lower hinge point No. 6. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application.

[0020] like Figures 1 to 3 As shown, this embodiment provides a method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load. This method relies on the six-degree-of-freedom platform's own drive and sensing system to achieve autonomous identification of the load's inertial parameters. Before executing the measurement method, it is necessary to first clarify the physical configuration and coordinate reference of the six-degree-of-freedom platform. The six-degree-of-freedom platform mainly includes an upper platform, a lower platform, and six electric cylinders connecting the upper and lower platforms. For ease of mechanical modeling and calculation, the upper and lower platforms are simplified as upper hinge circle 1 and lower hinge circle 2, respectively, and the six electric cylinders are designated as electric cylinder 11, electric cylinder 22, electric cylinder 33, electric cylinder 44, electric cylinder 5, and electric cylinder 616. The two ends of electric cylinders 11 to 616 are connected to the upper and lower platforms respectively through Hooke's joints, with their upper hinge points designated as upper hinge point 21 to upper hinge point 26, and their lower hinge points designated as lower hinge point 31 to lower hinge point 36. A global coordinate system CoordOXYZ is defined, with its origin O located at the center 3 of the upper hinge circle. The Z-axis points vertically upward, the positive X-axis points from the center 3 of the upper hinge circle to the midpoint of the line connecting the first upper hinge point 21 and the second upper hinge point 22, and the positive Y-axis is determined according to the right-hand rule. Based on the above hardware architecture and coordinate definition, the measurement method in this embodiment obtains the center of gravity and moment of inertia of the load sequentially through a step-by-step decoupling strategy, specifically including the following steps.

[0021] Step S1: Obtain the position and attitude of the six-degree-of-freedom platform and the thrust of the electric cylinder at any time.

[0022] Position and attitude data reflect the spatial pose of the upper platform relative to the lower platform, typically including linear displacement along the X, Y, and Z axes and angular displacement about these axes (i.e., pitch, roll, and yaw angles). The electric cylinder thrust is the direct power source for the platform to maintain its current pose or generate acceleration. In this embodiment, the position and attitude can be obtained in real time through the inverse kinematics algorithm within the platform control system, while the electric cylinder thrust can be calculated either through current or torque feedback from the servo motor combined with transmission efficiency, or it can be directly collected by a force sensor mounted on the electric cylinder body.

[0023] In this embodiment, the platform position and attitude at any given time include lateral displacement ΔX, longitudinal displacement ΔY, heave ΔZ, pitch angle Δα, roll angle Δβ, and yaw angle Δγ; the electric cylinder thrusts of the six electric cylinders are denoted as F1, F2, F3, F4, F5, and F6. The electric cylinder thrusts F1-F6 are calculated based on the servo motor torque. T is the torque, i is the reduction ratio, η is the transmission efficiency, and L is the lead screw, or can be obtained by adding a force sensor.

[0024] After obtaining the position and attitude, it is necessary to calculate the coordinates of the upper hinge point and the coordinates of the center of gravity (containing unknown parameters) of the upper platform based on the position and attitude using the inverse kinematics method, and then calculate the coordinates of the lower hinge point. Since the position and attitude of the upper platform continuously change during movement, the coordinates of the upper hinge point fixed on the upper platform in the global coordinate system also change accordingly. Using a homogeneous transformation matrix or Euler angle rotation and translation formula, the coordinates of the upper hinge point under the initial attitude can be transformed to the real-time coordinates under the current attitude. Simultaneously, the load center of gravity, as an unknown quantity to be solved, also includes the unknown parameter of the initial center of gravity coordinates in its coordinate expression under the current attitude; this expression will serve as the basis for establishing the torque balance equations. The lower hinge point is fixed to the lower platform, and its coordinates remain unchanged in the global coordinate system; preset structural parameters can be directly called. Based on this, using the coordinates of the upper and lower hinge points, the distances of the projections of each electric cylinder onto the center of the upper hinge circle of the upper platform in the XY, XZ, and YZ planes are calculated, serving as the lever arms.

[0025] The calculation of the lever arm involves determining the perpendicular distance from a point in a two-dimensional plane (the center 3 of the upper hinge circle) to a straight line (the projection line of the electric cylinder axis onto this plane). Taking the XY plane as an example... Figure 4 As shown, the equation of the projected line is determined by the projected coordinates of the first upper hinge point 21 and the first lower hinge point 31 in the XY plane. Then, the length of the perpendicular segment from the origin O to this line is calculated, which is the lever arm of the electric cylinder in the XY plane. Similarly, as Figure 5 and Figure 6 As shown, the lever arms in the XZ plane can be calculated separately. lever arm of the YZ plane This application uses dynamic lever arm calculation based on real-time coordinates to ensure the geometric accuracy of the mechanical model under any platform pose.

[0026] Step S2: Calculate the position of the center of gravity of the six-degree-of-freedom platform load in the X and Y directions based on the electric cylinder thrust in the initial static position.

[0027] The initial static pose refers to the condition where the six-degree-of-freedom platform is at a horizontal zero position and remains absolutely stationary. At this point, both the angular and linear accelerations of the platform are zero, and it is in static equilibrium under the influence of only gravity and the supporting force of the electric cylinders. In this state, the offset of the load's center of gravity in the horizontal plane (i.e., the coordinates in the X and Y directions) directly leads to a redistribution of the thrust of each electric cylinder. By reading the thrust of the six electric cylinders at this time and combining it with the known platform geometric parameters, the horizontal coordinates of the center of gravity can be independently calculated using the principle of static equilibrium. This application utilizes the characteristic that the inertial force is zero under static conditions to reduce the three-dimensional center of gravity problem to a two-dimensional planar problem, thereby avoiding the interference of the unknown Z-coordinate on the horizontal coordinate calculation.

[0028] The coordinates of the 6 upper hinge points are as follows: ; The centroid coordinates containing unknowns are represented as follows: ; In the formula, 1≤i≤6, X p(i) This represents the initial X-coordinate value of the hinge point on a six-degree-of-freedom motion platform; Y... p(i) This represents the initial Y-coordinate value of the hinge point on a six-degree-of-freedom motion platform; Z... p(i) This represents the initial Z-coordinate value of the hinge point on a six-degree-of-freedom motion platform; X m The X coordinate of the load's center of gravity; the Y coordinate. m Y-coordinate of the load's center of gravity; Z-coordinate m The Z-coordinate of the load's center of gravity.

[0029] Step S3: Calculate the position of the center of gravity of the six-degree-of-freedom platform load in the Z direction based on the electric cylinder thrust in the stationary state at the specified position. The specified position is either in a pitch state or a roll state.

[0030] Since changes in the center of gravity height do not generate an additional gravitational torque around the horizontal axis in a purely horizontal static state, the Z-axis coordinate cannot be directly observed from the horizontal pose. This step controls the platform to a non-horizontal designated position (e.g., pitching at a certain angle around the X-axis or tilting at a certain angle around the Y-axis) and keeps it stationary, so that the center of gravity height Z and the known horizontal center of gravity coordinates together generate a measurable gravitational torque effect. At this designated stationary position, the angular acceleration remains zero, and the system is still in static equilibrium, but the torque balance equations introduce trigonometric functions of the attitude angles. By substituting the precisely obtained X-axis or Y-axis center of gravity coordinates from step S2 as known quantities into the equations, the unique unknown Z-axis center of gravity coordinates can be solved. By utilizing the torque sensitivity difference caused by attitude changes, decoupled measurement of the center of gravity height and horizontal position is achieved, ensuring the convergence and accuracy of the Z-axis calculation.

[0031] Specifically, the expressions for calculating the distances (lever arms) between the projections of the six electric cylinders onto the centers of the hinged circles in the XY, XZ, and YZ planes are as follows: XY plane: ; XZ plane: ; YZ plane: ; In the formula, This represents the initial X-coordinate value of the hinge point under a six-degree-of-freedom motion platform; This represents the initial Y-coordinate value of the hinge point under the six-degree-of-freedom motion platform; This represents the initial Z-coordinate value of the bottom contact point of the six-degree-of-freedom motion platform.

[0032] Furthermore, the electric cylinder thrust is calculated. The components in the X, Y, and Z directions are calculated as follows: ; ; ; Then, the initial pose and the set of moment equilibrium equations for the stationary state are constructed, and the position of the center of gravity in the X and Y directions is calculated. At this time, .

[0033] ; ; ; ; In the formula, For load quality; This is the acceleration due to gravity.

[0034] Step S4: Given pitch, roll, and yaw motions, calculate the moment of inertia of the six-degree-of-freedom platform load based on the position and attitude during the corresponding motions and the thrust of the electric cylinder.

[0035] Moment of inertia is a physical quantity characterizing a rigid body's ability to resist angular acceleration. It only manifests as an inertial torque during dynamic processes involving angular acceleration. Therefore, this step differs from the aforementioned static measurement. The active control platform executes pitch motion around the X-axis, roll motion around the Y-axis, and yaw motion around the Z-axis. During these dynamic movements, the electric cylinders not only need to overcome the gravitational component but also provide the inertial force required to generate angular acceleration. By real-time acquisition of pose data (especially angular acceleration) and the corresponding electric cylinder thrust during the motion, a dynamic equilibrium equation including inertial terms is constructed. Since the three-dimensional coordinates (Xm, Ym, Zm) of the center of gravity have been completely determined through steps S2 and S3, the gravitational torque becomes a known quantity, leaving only the moment of inertia as an unknown in the equations. This allows for independent solutions to the moment of inertia around each axis. This step, through split-axis excitation and step-by-step solution, effectively avoids the difficulty of parameter identification caused by multi-degree-of-freedom coupled motion and significantly improves the measurement accuracy of the moment of inertia.

[0036] Based on the electric cylinder thrust at a specified position (pitch or tilt), the Z-axis position of the center of gravity is calculated as follows: When given a pitch angle hour: ; ; When given a pitch angle hour: ; ; Given pitch motion, based on the platform motion state at any one attitude angle during the motion ( Angular acceleration acc1), electric cylinder thrust Calculate the moment of inertia of the load. ： ; Given a tilting motion, based on the platform motion state (Δβ, angular acceleration acc2) at any one attitude angle during the motion, and the electric cylinder thrust F... i Calculate the moment of inertia of the load. : ; Given yaw motion, calculate the load moment of inertia based on the platform motion state (Δγ, angular acceleration acc3) and electric cylinder thrust at any attitude angle during the motion. : .

[0037] This application analyzes the temporal progression and data dependence, first decoupling the horizontal center of gravity using a static condition, then decoupling the vertical center of gravity using a tilted static condition combined with the horizontal center of gravity, and finally decoupling the rotational inertia using a dynamic condition combined with the complete center of gravity coordinates. By constructing a step-by-step decoupling architecture, the originally highly coupled six-degree-of-freedom spatial parameter identification problem is transformed into a series of low-dimensional, well-defined sub-problems. This not only reduces the algorithm's sensitivity to initial values ​​and computational complexity but also fundamentally eliminates the error accumulation and divergence risks commonly found in multi-parameter joint identification, providing reliable methodological support for the high-precision self-calibration of the six-degree-of-freedom platform.

[0038] To better understand the technical solution and specific calculation process of this application, some of the calculations will be further explained below.

[0039] (a) Calculate the position of the center of gravity of the six-degree-of-freedom platform load in the X and Y directions, including: in the initial static pose, based on the moment balance equation in the XZ plane, using the components of the electric cylinder thrust in the X and Z directions and the resultant moment about the stress arm, divided by the load weight, to calculate the position of the center of gravity of the six-degree-of-freedom platform load in the X direction. Specifically: first, obtain the real-time thrust values ​​of the six electric cylinders in the initial static pose, and combine the projection components of each electric cylinder in the XZ plane and its lever arm about the center 3 of the upper hinge circle. The magnitude of the thrust component of each electric cylinder in the XZ plane is correlated with the corresponding lever arm. Multiplying these gives the torque of a single electric cylinder about the center of the circle. Summing the torques of all six electric cylinders algebraically yields the total resultant torque in the XZ plane. Since this total resultant torque is necessarily balanced by the torque of the load's weight about the same point in a static state, and the torque generated by the load's weight in the XZ plane is equal to the load mass... Multiplied by gravitational acceleration Multiply by the centroid X coordinate Therefore, the total resultant moment in the XZ plane is divided by the load gravity ( The position of the center of gravity in the X direction can be directly calculated. This process can be represented by the following formula: ; In the formula, This represents the magnitude of the projected component of the thrust of the i-th electric cylinder in the XZ plane. This represents the lever arm of the i-th electric cylinder relative to the center of the hinge circle in the XZ plane. For load quality, This represents gravitational acceleration. It should be understood that the magnitude of the projected component here is obtained based on the thrust decomposition method, and its physical meaning is the effective component of the electric cylinder thrust in a plane perpendicular to the Y-axis.

[0040] Similarly, based on the torque balance equation in the YZ plane, the position of the center of gravity of the six-degree-of-freedom platform load in the Y direction is calculated by dividing the resultant torque of the electric cylinder thrust components in the Y and Z directions and about the stress arm by the load weight. Specifically, the position of the center of gravity in the Y direction is calculated using the projection components of each electric cylinder in the YZ plane and its lever arm. Calculate the total resultant moment in the YZ plane, then divide by the load weight to determine the position of the center of gravity in the Y direction. The calculation formula is as follows: ; In the formula, This represents the magnitude of the projected component of the thrust of the i-th electric cylinder in the YZ plane. Let represent the lever arm of the i-th electric cylinder relative to the center of the hinge circle in the YZ plane. Through the above method, this embodiment successfully decouples the originally coupled three-dimensional centroid solution problem into two independent two-dimensional plane problems under the initial static condition. This not only simplifies the calculation but also avoids interference from unknown Z-axis parameters on the horizontal coordinate solution, ensuring... and The measurement accuracy.

[0041] In other embodiments, the position of the center of gravity of the six-degree-of-freedom platform load in the Z-direction is calculated based on the thrust of the electric cylinder in a stationary state at a specified location. This corresponds to step S3 mentioned above. Since the gravity vector is always along the Z-axis in a purely horizontal stationary state, regardless of the change in the height of the center of gravity, its gravitational torque around the horizontal axis (X-axis or Y-axis) depends only on the horizontal offset and is not sensitive to the Z-axis coordinate. Therefore, it cannot be directly observed from the horizontal pose. To address this issue, this application controls the platform to a non-horizontal, designated position and keeps it stationary, so that the center of gravity height Z, together with the known horizontal center of gravity coordinates, generates a measurable gravitational torque effect.

[0042] (b) Calculating the position of the center of gravity of the six-degree-of-freedom platform load in the Z direction, including: when the platform is in a pitch state at a given pitch angle, based on the moment balance equation in the YZ plane, and combined with the already determined position of the center of gravity of the six-degree-of-freedom platform load in the Y direction, the position of the center of gravity of the six-degree-of-freedom platform load in the Z direction is solved inversely. Specifically, when the platform pitches around the X-axis by an angle Δα and remains stationary, although the direction of the load gravity vector in the global coordinate system remains unchanged, its lever arm relative to the center 3 of the upper hinge circle that tilts with the platform changes. In the YZ plane, the torque generated by gravity consists of two parts: one part is the torque generated by the center of gravity in the Y coordinate plane. The resulting torque component is another part caused by the Z-coordinate of the center of gravity. The resulting torque component. Due to The pitch angle Δα has been accurately measured in step S2 and is known, therefore The resulting torque component becomes a known quantity. At this point, by reading the electric cylinder thrust in the pitch-stationary state and calculating the total resultant torque in the YZ plane, this total resultant torque is equal to the total torque generated by gravity in the YZ plane. The known torque is then subtracted from the total gravitational torque. The component contribution, the remaining part is The component contribution can then be uniquely inversely solved. The solution logic after textual reconstruction is as follows: Equals (total moment in the YZ plane divided by the load weight, then subtracts) (The product of the pitch angle cosine and the pitch angle cosine) divided by the negative value of the pitch angle sine (or the corresponding trigonometric function relationship determined according to the coordinate system definition).

[0043] As an optional implementation, when the platform is in a tilted state at a given roll angle, the position of the center of gravity of the six-degree-of-freedom platform load in the Z direction is solved by inversely based on the moment balance equation in the XZ plane and the already determined position of the center of gravity in the X direction. Specifically, this process is completely symmetrical to the solution logic in the pitch state. When the platform tilts about the Y-axis by an angle Δβ and remains stationary, the gravitational moment in the XZ plane is also determined by… Components and The components together determine this. Utilizing the measured... Given the roll angle Δβ, calculate The generated torque component is then removed from the total resultant torque in the XZ plane to obtain the inverse solution. In practical engineering applications, Z-axis measurements can be flexibly performed in either pitch or tilt mode, depending on the platform's installation space limitations or load characteristics. Alternatively, measurements can be taken in both modes and the average value can be calculated to further improve the accuracy and robustness of the Z-axis center of gravity measurement.

[0044] In some embodiments, given pitch, roll, and yaw motions, the moment of inertia of the six-degree-of-freedom platform load is calculated based on the position and attitude during the corresponding motion and the thrust of the electric cylinder. In static measurements, the system is in a state of torque balance, and the inertial torque is zero; however, in the dynamic measurements of this step, the platform is actively excited to generate rotational motion, which is inevitably accompanied by non-zero angular acceleration. At this time, the driving torque output by the electric cylinder needs not only to overcome the gravitational torque caused by the shift of the center of gravity, but also to provide the inertial torque that causes the load to generate angular acceleration. Due to the three-dimensional center of gravity coordinates of the load ( , , Having been precisely measured through the aforementioned steps, the gravitational torque becomes a calculable known quantity. Therefore, by collecting the electric cylinder thrust and angular acceleration during the motion process in real time, a dynamic equilibrium equation including inertial terms can be constructed, allowing the independent calculation of the load's rotational inertia around each axis. This strategy of split-axis excitation and step-by-step solution effectively avoids the difficulty of parameter identification caused by multi-degree-of-freedom coupled motion, significantly improving the measurement accuracy and robustness of rotational inertia.

[0045] (c) During the pitch motion, an angular acceleration about the X-axis is introduced to construct a dynamic equilibrium equation including the resultant torque of the electric cylinder thrust, the gravitational torque, and the inertial torque. The moment of inertia of the six-degree-of-freedom platform load about the X-axis is solved. The six-degree-of-freedom platform is controlled to perform pitch motion about the X-axis, and the pitch angular acceleration acc1 and the thrust value of each electric cylinder are recorded in real time at any moment during this motion. Based on the torque balance construction method of the projection plane, the resultant torque of the components of all electric cylinder thrust in the YZ plane about the center 3 of the upper hinge circle is calculated and denoted as the total driving torque in the YZ plane. At the same time, the known load mass, gravitational acceleration, and Y-coordinate of the center of gravity are used. and Z coordinate Based on the current pitch angle, the gravitational torque generated by gravity in the YZ plane is calculated. According to the differential equation of rigid body rotation about a fixed axis, the total driving torque in the YZ plane is equal to the sum of the gravitational torque and the inertial torque. The inertial torque is equal to the moment of inertia Jx about the X-axis multiplied by the pitch acceleration acc1. Therefore, by subtracting the gravitational torque from the total driving torque in the YZ plane and then dividing by the pitch acceleration acc1, the moment of inertia Jx of the load about the X-axis can be obtained. The calculation formula can be expressed as: ; In the formula, This represents the magnitude of the projected component of the thrust of the i-th electric cylinder in the YZ plane. This represents the lever arm of the i-th electric cylinder relative to the center of the hinge circle in the YZ plane. For load quality, It is the acceleration due to gravity. The current pitch angle, and These are the measured Y and Z coordinates of the load's center of gravity. Let be the pitch acceleration about the X-axis. It should be understood that this formula is based on the direct application of Newton's second law to rotational motion. Its core lies in using known center of gravity parameters to separate the gravitational effect from the total torque, thereby purely extracting the inertial parameters.

[0046] In the roll motion, an angular acceleration about the Y-axis is introduced, and a dynamic equilibrium equation is constructed that includes the resultant torque of the electric cylinder thrust, the gravitational torque, and the inertial torque. The moment of inertia of the six-degree-of-freedom platform load about the Y-axis is then solved. This process is completely symmetrical with the solution logic for the pitch motion. The control system controls the platform to execute the roll motion about the Y-axis, and collects the roll angular acceleration acc2 and the thrust of each electric cylinder in real time. The resultant torque of the components of all electric cylinder thrust in the XZ plane about the center 3 of the upper hinge circle is calculated as the total driving torque in the XZ plane. The known X-coordinate of the center of gravity is used... and Z coordinate Based on the current roll angle, calculate the gravitational torque generated by gravity in the XZ plane. Then, subtract the gravitational torque from the total driving torque in the XZ plane, and divide by the roll acceleration acc2 to obtain the moment of inertia of the load about the Y-axis. Its calculation formula can be expressed as: ; In the formula, This represents the magnitude of the projected component of the thrust of the i-th electric cylinder in the XZ plane. This represents the lever arm of the i-th electric cylinder relative to the center of the hinge circle in the XZ plane. This is the current roll angle. and These are the measured X and Z coordinates of the load's center of gravity. This represents the roll acceleration around the Y-axis. By conducting independent pitch and roll motion tests, Jx and Jy can be obtained separately, avoiding interference from the cross-inertia product caused by dual-axis coupled motion and ensuring the accuracy of single-axis rotational inertia measurement.

[0047] In yaw motion, the angular acceleration of rotation about the Z-axis is introduced, and a dynamic equilibrium equation including the resultant torque of the electric cylinder thrust and the moment of inertia is constructed to solve for the rotational inertia of the six-degree-of-freedom platform load about the Z-axis. Yaw motion is a rotation about the vertical Z-axis. Since the gravity vector is parallel to the Z-axis and usually passes through or is close to the center of rotation, gravity does not produce a torque or produces a negligible torque in the XY plane. Therefore, the dynamic equation in the yaw direction is significantly simplified, and there is no need to deduct the gravity torque term as in pitch and roll. The control system controls the platform to execute yaw motion about the Z-axis, and collects the yaw angular acceleration acc3 and the thrust of each electric cylinder in real time. The resultant torque of the components of all electric cylinder thrust in the XY plane about the center 3 of the upper hinge circle is calculated as the total driving torque in the XY plane. This total driving torque is directly equal to the rotational inertia Jz about the Z-axis multiplied by the yaw angular acceleration acc3. Therefore, dividing the total driving torque in the XY plane by the yaw acceleration acc3 yields the moment of inertia Jz of the load about the Z-axis. The formula for this calculation is as follows: ; In the formula, This represents the magnitude of the projected component of the thrust of the i-th electric cylinder in the XY plane. This represents the lever arm of the i-th electric cylinder relative to the center of the hinge circle in the XY plane. Let be the yaw acceleration about the Z-axis. This simplified equation not only reduces the computational load but also eliminates the propagation effect of Z-axis measurement errors on the yaw inertia calculation, further improving... Measurement reliability.

[0048] It should be noted that the moment of inertia obtained from solving the above dynamic equations , , These are all moments of inertia relative to the origin of the global coordinate system (i.e., the center 3 of the upper hinge circle). In practical engineering applications, if the user needs to obtain the moment of inertia of the load about its own center of mass, they can obtain the three-dimensional center of mass coordinates (…). , , Based on the moment of inertia about the origin, a reverse correction is performed using the parallel axis shifting theorem. For example, the moment of inertia of the load about its own center of mass X-axis is equal to... Subtract the load mass multiplied by ( The square of and (The sum of the squares). This post-processing method enables the method of this application to not only meet the platform control algorithm's direct requirement for the origin inertia, but also flexibly adapt to the load characteristic analysis's requirement for the center of mass inertia, demonstrating the versatility and scalability of the technical solution in different application scenarios.

[0049] Test Example: To further verify the method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load provided in this application, this embodiment performs a complete calculation and reproduction based on a specific application case. In this case, the load of the six-degree-of-freedom platform is set as a regular cuboid with a mass m of 2000 kg and length, width, and height dimensions of 2000 mm, 2000 mm, and 1000 mm, respectively. According to geometric relationships, the theoretical center of gravity coordinates of this load are... =300mm =250mm =500mm (relative to the center of the upper hinge circle 3).

[0050] The horizontal position of the load's center of gravity was calculated under the initial static posture. The thrust values ​​of the six electric cylinders at the horizontal zero position were read as follows: Cylinder 11 thrust 5023.92N, Cylinder 22 thrust 5056.74N, Cylinder 33 thrust 4542.27N, Cylinder 44 thrust 4502.17N, Cylinder 55 thrust 2181.47N, and Cylinder 66 thrust 2188.75N. Based on the coordinate inverse kinematics and lever arm calculation method described in Example 2, the projection components and stress arms of each electric cylinder in the XZ and YZ planes were obtained. The thrust components of all electric cylinders in the XZ plane were multiplied by the stress arms d_xz and summed to obtain the total resultant torque in the XZ plane as -5883960.00N·mm; similarly, the total resultant torque in the YZ plane was obtained as -4903300.00N·mm. Divide the total resultant moment in the XZ plane by the load weight (2000kg × 9.806m / s²). 2 ), calculate the position of the center of gravity in the X direction. The value is 300.00 mm; the position of the center of gravity in the Y direction is calculated by dividing the total resultant moment in the YZ plane by the load weight. The result is 250.00 mm. This calculation result is completely consistent with the theoretical true value, verifying the accuracy of independently decoupling the horizontal centroid coordinates using the moment balance equation of the projected surface under pure static equilibrium conditions.

[0051] Calculate the height of the load's center of gravity while the load is stationary at a specified position. The control system tilts the platform 5° around the X-axis and maintains absolute stillness, at which point the angular acceleration is zero. The thrust of each electric cylinder in this attitude is read as follows: 4750.95N, 4783.69N, 4680.14N, 4632.28N, 2310.19N, and 2312.68N. Based on the current pose, recalculate the projection components and lever arms of each electric cylinder in the YZ plane, obtaining a total resultant torque of -4030530.19 N·mm in the YZ plane. Since the center of gravity's Y-coordinate is... =250.00mm has been taken as a known quantity. According to the reconstructed Z-axis inverse solution logic, that is... The result is equal to (the total moment in the YZ plane divided by the load weight minus the product of Ym and the cosine of the pitch angle) divided by the negative value of the sine of the pitch angle (considering the coordinate system direction), and then substituted into the numerical calculation. The result is 499.65 mm. The relative error between this result and the theoretical true value of 500 mm is only 0.07%, which fully demonstrates that the decoupling strategy of using the known horizontal center of gravity to solve for the vertical center of gravity under the tilted static condition has extremely high engineering accuracy and effectively avoids the calculation divergence problem introduced by attitude transformation in traditional methods.

[0052] Finally, the moment of inertia of the load about the X-axis is calculated during the dynamic motion process. The control system receives a sinusoidal pitch command with an amplitude of 8° and a period of 1s. At any moment during the motion (e.g., t=0.125s), it acquires real-time data showing a pitch angle of 5.657° and an angular acceleration acc1 around the X-axis of 3.902 rad / s². 2 (Note: The original angular acceleration has been converted to radians to conform to physical calculation standards.) Simultaneously, the instantaneous thrust of each electric cylinder was read as follows: 2953.91N, 3423.77N, 2399.84N, 7140.99N, 4609.13N, and 661.89N. Based on the pose at this moment, the total driving torque in the YZ plane was calculated to be 1771415.90 N·mm. Using the previously accurately measured three-dimensional centroid coordinates (… =300mm, =250mm, =499.65mm), and combined with the current pitch angle, the gravitational torque component generated by gravity in the YZ plane is calculated. According to the dynamic equilibrium equation, the gravitational torque is subtracted from the total driving torque in the YZ plane, and then divided by the angular acceleration acc1 to obtain the moment of inertia of the load about the X-axis. 1.4585×10 9 kg·mm 2 .

[0053] To verify the reliability of the dynamic measurement results, the theoretical moment of inertia of the load about the center 3 of the hinge circle was calculated using the parallel axis shift theorem. The theoretical calculation formula is the moment of inertia of the center of mass plus the mass multiplied by the square of the distance from the center of mass to the axis of rotation, i.e. Where w is the load width (2000mm) and h is the load height (1000mm). Substituting the parameters, the theoretical value is calculated to be 1.4583 × 10⁻⁶. 9 kg·mm 2 The comparison shows that the method used in this application measures [the correct measurement]. The relative error with the theoretical value is only 0.014%. This extremely high degree of agreement not only verifies the correctness of the constructed dynamic equations, but also intuitively demonstrates that this application, through a step-by-step decoupling strategy, can achieve high-precision self-testing of load inertia parameters solely based on the platform's own sensor data, without requiring any external hoisting equipment or specialized testing instruments. This self-testing capability provides a precise and reliable parameter basis for subsequent dynamic optimization of electric cylinder output, overload warning threshold setting, and motion control feedforward compensation, significantly improving the overall operational performance and safety of the six-degree-of-freedom platform.

[0054] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load, characterized in that, include: (1) Obtain the position and attitude of the six-degree-of-freedom platform and the thrust of the electric cylinder at any time, and calculate the coordinates of the upper hinge point and the coordinates of the center of gravity containing unknown parameters of the upper platform based on the position and attitude according to the position inverse solution calculation method, and calculate the coordinates of the lower hinge point. (2) Calculate the position of the center of gravity of the six-degree-of-freedom platform load in the X and Y directions based on the electric cylinder thrust in the initial static position; (3) Based on the electric cylinder thrust in the static state at the specified position, calculate the position of the center of gravity in the Z direction based on the position of the center of gravity of the six-degree-of-freedom platform load in the X and Y directions, and specify the position as pitch or roll. (4) Given pitch, roll and yaw motions, based on the position and attitude of the corresponding motion process and the electric cylinder thrust, and based on the position of the center of gravity of the six-degree-of-freedom platform load in the X, Y and Z directions, the rotational inertia of the six-degree-of-freedom platform load.

2. The method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load according to claim 1, characterized in that, Step (1) is to obtain the thrust of the electric cylinder by converting the torque of the servo motor or by adding a force sensor. Then, based on the coordinates of the upper hinge point and the coordinates of the lower hinge point, the distance between the projection of each electric cylinder on the XY plane, XZ plane and YZ plane and the center of the upper hinge circle of the upper platform is calculated. The distance is used as the lever arm.

3. The method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load according to claim 1, characterized in that, The designated static position is a pose-holding state with zero angular acceleration, and the corresponding motion process is a dynamic process with angular acceleration.

4. The method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load according to claim 1, characterized in that, The moment of inertia is calculated based on the moment balance equation of the projected surface; The torque balance equation is constructed by decomposing the electric cylinder thrust into the XY plane, XZ plane, and YZ plane, and then calculating the lever arm of each electric cylinder relative to the center of the upper hinge circle of the upper platform on the corresponding projection plane. The torque balance equation is constructed based on the components of the electric cylinder thrust on the corresponding projection plane and the lever arm.

5. The method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load according to claim 4, characterized in that, The specific calculations for the center of gravity of the six-degree-of-freedom platform load in the X and Y directions are as follows: In the initial static pose, the position of the center of gravity of the six-degree-of-freedom platform load in the X direction is calculated based on the moment balance equation in the XZ plane. The moment balance equation in the XZ plane is: ； The position of the center of gravity of the six-degree-of-freedom platform load in the Y direction is calculated based on the moment balance equation in the YZ plane. The moment balance equation in the YZ plane is as follows: ； in, Number the electric cylinder. , , The first The components of the thrust of an electric cylinder in the X, Y, and Z directions. For the first The lever arm of the electric cylinder, projected onto the XZ plane, corresponds to the center of the hinge circle. For the first The lever arm of the electric cylinder, projected onto the YZ plane, corresponds to the center of the hinge circle. For load quality, It is the acceleration due to gravity. The position of the center of gravity of the six-degree-of-freedom platform load in the X direction. The position of the center of gravity of the six-degree-of-freedom platform load in the Y direction.

6. The method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load according to claim 5, characterized in that, The position of the center of gravity of the six-degree-of-freedom platform load in the Z direction is calculated as follows: When given a pitch angle When in the pitch state, the position of the center of gravity of the six-degree-of-freedom platform load in the Z direction is obtained by inverse solving the moment balance equation in the YZ plane. The moment balance equation in the YZ plane is: ； When given a roll angle When in a tilted state, the position of the center of gravity of the six-degree-of-freedom platform load in the Z direction can be obtained by inverse solving the moment balance equation in the XZ plane. The moment balance equation in the XZ plane is: ； in, The pitch angle, The roll angle is... The position of the center of gravity of the six-degree-of-freedom platform load in the Z direction.

7. The method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load according to claim 6, characterized in that, Given pitch, roll, and yaw motions, calculate the moment of inertia of the six-degree-of-freedom platform load based on the corresponding position and attitude during the motion process and the thrust of the electric cylinder. Specifically: During pitch motion, an angular acceleration about the X-axis is introduced. The dynamic equilibrium equations are constructed to solve for the moment of inertia of the six-degree-of-freedom platform load about the X-axis. The dynamic equilibrium equation is: 1； During the tilting motion, an angular acceleration about the Y-axis is introduced.

2. Construct dynamic equilibrium equations to solve for the moment of inertia of the six-degree-of-freedom platform load about the Y-axis. The dynamic equilibrium equation is: ； During yaw motion, an angular acceleration about the Z-axis is introduced. The dynamic equilibrium equations are constructed to solve for the moment of inertia of the six-degree-of-freedom platform load about the Z-axis. The dynamic equilibrium equation is: 3； in, For the first The electric cylinder is projected onto the center of the hinged circle in the XY plane.

8. A device for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load, characterized in that, Including processor and memory; Memory, used to store computer programs; The processor is configured to implement the steps of the method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load as described in any one of claims 1 to 7 when executing the computer program.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for measuring the center of gravity and moment of inertia of a six-degree-of-freedom platform load as described in any one of claims 1 to 7.

10. A six-degree-of-freedom platform, comprising an upper platform, a lower platform, a plurality of electric cylinders connecting the upper platform and the lower platform, and a control system, characterized in that, The control system includes the center of gravity and moment of inertia measurement device for the six-degree-of-freedom platform load as described in claim 8.

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