A method for solving the kinematic characteristics of an unmanned aerial vehicle equivalent simulation spacecraft

Abstract

The application discloses a kind of solving method of unmanned aerial vehicle equivalent simulation spacecraft kinematics characteristics, steps are as follows: the inertial coordinate system required for constructing equivalent model and satellite orbit coordinate system, relative motion equation in orbit coordinate system is established;According to the equation, the spacecraft orbit kinematics parameters and unmanned aerial vehicle equivalent kinematics parameters are determined;Combining each parameter basic dimension, dimension matrix is listed, and the basic parameter quantity describing physical process is determined according to the rank of matrix;Based on the similarity of model and prototype, the similarity condition is applied to dimensionless number, the equation describing two systems is established, and then the scale factor of each kinematics parameter is derived.The method makes full use of the controllable characteristics of unmanned aerial vehicle flight height, speed and vertical climbing / descending speed, and realizes the simulation of satellite motion process by unmanned aerial vehicle through formulating reasonable space-time scaling rules, combining spacecraft kinematics characteristics and unmanned aerial vehicle flight control technology.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and in particular to a method for calculating the kinematic characteristics of an equivalent spacecraft using an unmanned aerial vehicle (UAV). Background Technology

[0002] The UAV-based satellite motion simulation scheme design involved in this invention aims to provide an economical, efficient, and safe means of satellite kinematics simulation by simulating the orbital kinematics characteristics of satellites in space using UAVs. This invention fully utilizes the controllable characteristics of UAVs in terms of flight altitude, speed, and vertical climb / descent speed. By determining reasonable spatiotemporal scaling criteria and combining spacecraft kinematic characteristics with UAV flight control technology, it achieves high-precision simulation of satellite motion processes using UAVs.

[0003] In the actual physical space where spacecraft operate in orbit, the distance is on the order of kilometers, while the relative motion distance of spacecraft provided by ground simulation systems is mostly tens to hundreds of meters, which is far from meeting the actual space requirements.

[0004] Furthermore, the actual on-orbit speed and acceleration of spacecraft are on the order of kilometers per second, which ground-based simulation systems cannot meet. Therefore, simulations of spacecraft's on-orbit motion are essential. Summary of the Invention

[0005] This invention addresses the aforementioned problems by establishing a reasonable scaling model of time and space between the actual space and the simulation system, thereby providing a spacetime scaling equivalent design of spacecraft orbital kinematics based on Buckingham Pi's theorem. It embodies the physical quantity equivalence theory within the equivalence theory framework.

[0006] To solve the above problems, the technical solution adopted by the present invention is as follows:

[0007] A method for calculating the kinematic properties of an equivalent spacecraft using a UAV includes the following steps:

[0008] (1) Determine the on-orbit model of the spacecraft and determine the relative motion equations in the orbital coordinate system.

[0009] (2) Determine the necessary parameters of the equivalent model based on the equations of relative motion;

[0010] (3) Based on the parameters of the relative motion equation model, determine the basic parameters describing the physical process. Calculate a set of dimensionless numbers used to describe the physical processes of the prototype and the model.

[0011] (4) Based on the similarity between the model and the prototype, equations are established using this set of dimensionless numbers to describe the two systems, the prototype and the model.

[0012] (5) Based on the two equations of the prototype and the model, derive the scaling factor of the model and prototype parameters.

[0013] Based on the scaling factor between the prototype and the model, the equivalent principle of UAV control force under equivalent spacecraft conditions is derived.

[0014] Furthermore, the method for calculating the relative motion equations in the orbital coordinate system is as shown in formula (1):

[0015] Formula (1)

[0016] in, To control the deceleration force, For perturbation acceleration, its These are the components of the control force and the perturbation force on each axis of the coordinate system. To catch up with the spacecraft's position vector relative to the inertial coordinate system, The true perihelion angle of the target spacecraft's orbit. , where is the angular acceleration of the spacecraft. , where is the angular velocity of the spacecraft. , where is the average angular velocity of the target spacecraft's orbit.

[0017] Furthermore, based on the equations of relative motion, the necessary parameters for the equivalent model are determined. These parameters include the spacecraft mass *m*, the spacecraft position *r* in the inertial coordinate system, the spacecraft velocity *v*, the spacecraft acceleration *a*, and the spacecraft's relative position. The relative speed of the spacecraft The relative acceleration of spacecraft And the task parameters, including the total task duration P.

[0018] Furthermore, based on the parameters of the relative motion equation model, a set of dimensionless numbers is calculated to describe the physical processes of the prototype and the model. The dimensionless numbers are calculated as follows:

[0019]

[0020] Furthermore, the equations for the prototype and model, described using dimensionless numbers, are as shown in formula (2):

[0021] Formula (2)

[0022] in, Dimensionless numbers based on the prototype Let be the dimensionless number of the model.

[0023] Furthermore, based on the fact that the prototype and the model represent the same physical phenomenon, a scaling factor for the parameters of the model and the prototype is derived:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] Furthermore, in the process of simulating spacecraft by unmanned aerial vehicles (UAVs), in order to ensure the accuracy of kinematic parameter equivalence, it is also necessary to ensure that the force environment experienced by the UAV is equivalent to that experienced by the spacecraft.

[0030] Furthermore, the dynamic equations for the spacecraft and the drone are established as follows: (3)

[0031] Formula (3)

[0032] Furthermore, by rearranging the force equivalent equation, the calculation formula for the UAV control force is derived. Therefore, under the force equivalent model, the control force of the UAV is as follows (4):

[0033] Formula (4)

[0034] If the above similarity criteria are satisfied at all moments of interest in the system, then the spacecraft orbital kinematics problem satisfies a similarity relationship in both space and ground experimental environments. Furthermore, the parameters describing the problem are time-varying throughout the entire system time; therefore, as mentioned earlier, the relationship of the scaling factors represents the relationship between similar phenomena at corresponding points and corresponding moments.

[0035] The beneficial effects of this invention are as follows:

[0036] By establishing the relative motion equations of the spacecraft, the parameters needed to solve the spacecraft's kinematic problems are derived. Integrating the relative motion equations yields the spacecraft's position and velocity vectors. Based on the principle of spacetime scaling, mathematical models describing the actual physical process—the spacecraft's on-orbit motion—and the UAV ground simulation system are established. By assuming that these two processes represent the same physical phenomenon, given known parameters including the mass of the spacecraft and the UAV, their relative positions, mission duration, and experiment duration, the relative velocity and acceleration scaling factors of the spacecraft and the UAV are calculated. By observing the UAV's kinematic parameters in the ground experimental system, the spacecraft's motion process is simulated, solving the problem of insufficient space in ground experimental systems to meet the actual operational requirements. The mechanical flight control process of the rotorcraft UAV simulates the orbital motion of the spacecraft during on-orbit operation. This approach is safer, more economical, and more efficient. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of a method for calculating the kinematic characteristics of an equivalent spacecraft using a drone, according to an embodiment of the present invention.

[0038] Figure 2 The coordinate system model diagram established when constructing the relative motion equation of the spacecraft in the example of this invention is shown. The geocentric inertial coordinate system (ECI) and the satellite orbital coordinate system (Hill) are defined in the diagram. The position vector of the chasing spacecraft relative to the inertial coordinate system, the position vector of the target spacecraft relative to the inertial coordinate system, and the relative position vector of the spacecraft are defined according to the coordinate system. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below 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, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0041] Assume the prototype spacecraft has a mass of 500 kg, a maximum relative distance of 200 km, and a total mission duration of 1 day. The ground-based experimental system uses a 4 kg UAV with a maximum azimuth of 20 m and a total experimental duration of 20 minutes. Use this ground-based experimental system to simulate the prototype and determine the proportions of kinematic parameters under the corresponding conditions.

[0042] Reference Appendix Figure 1 A method for calculating the kinematic properties of an equivalent spacecraft using a UAV includes the following steps:

[0043] Step 1: Determine the spacecraft's on-orbit model, such as... Figure 2 This includes the geocentric inertial coordinate system (ECI) and the satellite orbital coordinate system (Hill). Based on the coordinate system, the position vector of the chasing spacecraft relative to the inertial coordinate system, the position vector of the target spacecraft relative to the inertial coordinate system, and the relative position vector of the spacecraft are defined.

[0044] according to Figure 2 For spatial relative motion, assume the position vector of the target spacecraft in the inertial coordinate system N is... The origin of the moving coordinate system (Hill coordinate system) is on the target spacecraft. shaft edge The direction is outward. Axis perpendicular to And it points to the local level of the target spacecraft, therefore and All axes are within the orbital plane of the target spacecraft. The axis is perpendicular to the plane.

[0045] Sure To catch up with the spacecraft's position vector relative to the inertial coordinate system,

[0046] Step 2: Determine the equations of relative motion in the orbital coordinate system.

[0047] In this example, after establishing the coordinate system position according to step one, the relative motion equations in the orbital coordinate system can be obtained:

[0048]

[0049] in, To control force acceleration, For perturbation acceleration, its These are the components of the control force and the perturbation force on each axis of the coordinate system. The true perihelion angle of the target spacecraft's orbit. , where is the angular acceleration of the spacecraft. , where is the angular velocity of the spacecraft. , where is the average angular velocity of the target spacecraft's orbit.

[0050] Step 3: Determine the necessary parameters of the equivalent model based on the relative motion equations. In this example, based on the relative motion equations derived in Step 2, the relevant motion parameters include the spacecraft mass m, the spacecraft position r in the inertial coordinate system, the spacecraft velocity v, the spacecraft acceleration a, and the spacecraft's relative position. The relative speed of the spacecraft The relative acceleration of spacecraft There are eight parameters in total, including the total task duration P.

[0051] Step 4: Based on the model parameters obtained in Step 3, and combining the basic dimensions of each parameter, list the dimension matrix of the parameters. Among the eight parameters obtained in Step 3, the satellite parameter m and the mission parameter T are known and given, and the other six parameters are orbital parameters. By integrating the equations of relative motion, the position and velocity parameters of the spacecraft during the relative motion process can be obtained. And through the principle of spatiotemporal scaling, the required position and velocity can be realized in the actual equivalent case of the UAV.

[0052] The dimension matrix listed in this example is as follows:

[0053]

[0054] Based on the dimensional matrix obtained in step four, the rank of the dimensional matrix is ​​3. Therefore, according to Buckingham Pi theorem, there are a total of 5 dimensionless quantities used to describe the spacecraft kinematics problem.

[0055] Optionally, three parameters can be selected, for example... Let's derive five dimensionless parameters. The calculated dimensionless numbers are as follows.

[0056]

[0057] Step 5: Based on the similarity between the model and the prototype, establish the following equations for the five dimensionless parameters to describe the two systems, the prototype and the model.

[0058] Furthermore, since the model and the physical prototype are identical representations of the same physical phenomenon, the equations for the prototype and the model, described using dimensionless numbers, are as follows:

[0059]

[0060] Step 6: Based on the equivalent equation, find the expression for each dimensionless number, and the scaling factor of each kinematic parameter in this example can be derived.

[0061]

[0062] in, This is the scaling factor between the spacecraft velocity and the drone velocity in the inertial coordinate system. This is the scaling factor for spacecraft acceleration and UAV acceleration in the inertial coordinate system. This is the scaling factor between the relative positions of the spacecraft and the drone. This is the ratio factor between the relative velocities of the spacecraft and the drone. This is the ratio factor between the relative acceleration of the spacecraft and the relative acceleration of the drone. This is the ratio factor between the total task duration and the total experiment duration.

[0063] The corresponding parameters should have the following scaling factors.

[0064]

[0065] Using this scaling parameter, the equivalent trajectory of the spacecraft after scaling down to the ground test system can be obtained. By using the UAV to track the trajectory, the kinematic equivalent flight of the UAV to the spacecraft can be realized.

[0066] If the above similarity criteria are satisfied at all moments of interest in the system, then the spacecraft orbital kinematics problem satisfies a similarity relationship in both space and ground experimental environments. Furthermore, since the parameters describing the problem are time-varying throughout the entire system time, as mentioned earlier, the relationship of the scaling factors represents the relationship between similar phenomena at corresponding points and corresponding moments.

[0067] Therefore, by using UAVs to track the equivalent spacecraft's position and velocity at dense points in a time sequence, the equivalent process of the UAV's kinematic characteristics and the spacecraft's kinematic parameters can be achieved.

[0068] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. In the above examples, a series of calculations were used to derive the scaling factor for the problem. Those skilled in the art should understand that any person skilled in the art, within the scope of the technology disclosed in the present invention, can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.

Claims

1. A method for calculating the kinematic characteristics of an equivalent spacecraft using a UAV, characterized in that, Includes the following steps: S1. Determine the on-orbit model of the spacecraft and determine the relative motion equations in the orbital coordinate system; S2. Determine the necessary parameters of the equivalent model based on the equations of relative motion; S3. Based on the parameters of the relative motion equation model, determine the basic parameters describing the physical process, and calculate a set of dimensionless numbers used to describe the physical processes of the prototype and the model. S4. Based on the similarity between the model and the prototype, use this set of dimensionless numbers to establish equations to describe the two systems, the prototype and the model. S5. Based on the two equations of the prototype and the model, derive the scaling factors of the model and prototype parameters; S6. Based on the scaling factor between the prototype and the model, derive the equivalent principle of UAV control force under equivalent spacecraft conditions.

2. The method for calculating the kinematic characteristics of an equivalent spacecraft using a UAV as described in claim 1, characterized in that, The method for calculating the relative motion equations in the orbital coordinate system is as follows: (1) Official (1) in, To control the deceleration force, For perturbation acceleration, its These are the components of the control force and the perturbation force on each axis of the coordinate system. To catch up with the spacecraft's position vector relative to the inertial coordinate system, The true perihelion angle of the target spacecraft's orbit. , where is the angular acceleration of the spacecraft. , where is the angular velocity of the spacecraft. , where is the average angular velocity of the target spacecraft's orbit.

3. The method for calculating the kinematic characteristics of an equivalent spacecraft using a UAV as described in claim 1, characterized in that, In S2, the necessary parameters of the equivalent model are determined according to the relative motion equation. These parameters include the spacecraft mass *m*, the spacecraft position *r* in the inertial coordinate system, the spacecraft velocity *v*, the spacecraft acceleration *a*, and the spacecraft's relative position. The relative speed of the spacecraft The relative acceleration of spacecraft And the task parameters, including the total task duration P.

4. The method for calculating the kinematic characteristics of an equivalent spacecraft using a UAV according to claim 3, characterized in that, In S3, the set of dimensionless numbers used to describe the physical processes of the prototype and model includes: 。 5. The method for calculating the kinematic characteristics of an equivalent spacecraft using a UAV according to claim 4, characterized in that, In S4, the equations of the prototype and model described by the dimensionless number are as shown in formula (2): Official (2).

6. The method for calculating the kinematic characteristics of an equivalent spacecraft using a UAV according to claim 5, characterized in that, In S5, the scaling factor for the model and prototype parameters includes: ， in, This is the scaling factor between the spacecraft velocity and the drone velocity in the inertial coordinate system. This is the scaling factor for spacecraft acceleration and UAV acceleration in the inertial coordinate system. This is the scaling factor between the relative positions of the spacecraft and the drone. This is the ratio factor between the relative velocities of the spacecraft and the drone. This is the ratio factor between the relative acceleration of the spacecraft and the relative acceleration of the drone. This is the ratio factor between the total task duration and the total experiment duration.

7. The method for calculating the kinematic characteristics of an equivalent spacecraft using a UAV according to claim 6, characterized in that, In S6, the equivalent principle of UAV control force, in the prototype spacecraft operating environment and in the ground UAV simulation system, the spacecraft dynamics system and the UAV dynamics model can be expressed as formula (3): Official (3) in, For control forces during spacecraft operation, For environmental perturbations during spacecraft operation, This is the acceleration generated solely by Earth's gravity and the choice of the coordinate system, excluding the control forces, in the equations of relative motion; it is called spatial inertial acceleration. For gravity, For air resistance, This refers to the total lift generated by the rotor.

8. The method for calculating the kinematic characteristics of an equivalent spacecraft using a UAV according to claim 7, characterized in that, In S6, the aforementioned UAV control force equivalence principle requires applying control forces to the UAV to simulate the force environment during spacecraft operation in a real-world environment. The calculation of the applied control force is as follows: Official (4).

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