Resolution method for equivalent simulation of spacecraft kinematics characteristics by unmanned aerial vehicle

Abstract

The invention discloses a resolving method for equivalent simulation of spacecraft kinematics characteristics by an unmanned aerial vehicle, which comprises the following steps of: constructing an inertial coordinate system and a satellite orbit coordinate system required by an equivalent model, and establishing a relative motion equation in the orbit coordinate system; determining spacecraft orbit kinematics parameters and unmanned aerial vehicle equivalent kinematics parameters according to the equation; a dimension matrix is listed in combination with the basic dimensions of the parameters, and the number of basic parameters describing the physical process is determined according to a matrix rank; on the basis of the similarity between a model and a prototype, similar conditions are applied to dimensionless numbers, an equation is established to describe two systems, and then scale factors of kinematics parameters are deduced. According to the method, the controllable characteristics of the flight height, the flight speed and the vertical climbing / descending speed of the unmanned aerial vehicle are fully utilized, a reasonable space-time scaling criterion is formulated, and the kinematics characteristics of a spacecraft and the flight control technology of the unmanned aerial vehicle are fused, so that simulation of the unmanned aerial vehicle on the satellite motion process is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aerospace technology, in particular to a method for calculating the equivalent simulation of the kinematic characteristics of a spacecraft by a UAV. BACKGROUND

[0002] The present application relates to a scheme for simulating satellite motion by a UAV, which aims to simulate the kinematic characteristics of a satellite in space by a UAV, thereby providing an economical, efficient and safe means for simulating the kinematic characteristics of a satellite. The present application makes full use of the controllable characteristics of a UAV in terms of flight altitude, speed and vertical climbing / descending speed, and determines a reasonable time-space scaling criterion, combines the kinematic characteristics of a spacecraft and the flight control technology of a UAV, thereby achieving high-precision simulation of the motion process of a satellite by a UAV.

[0003] The actual physical space of a spacecraft in orbit is on the order of kilometers, while the relative motion distance of a spacecraft provided by a ground simulation system is only tens to hundreds of meters, which is far from meeting the requirements of the actual space.

[0004] In addition, the actual in-orbit motion speed and acceleration of a spacecraft are on the order of kilometers, and the simulation system built on the ground cannot meet the requirements. However, it is necessary to simulate the in-orbit motion of a spacecraft. SUMMARY

[0005] To solve the above problems, the present application establishes a scaling relationship model between the time and space of the actual space and the simulation system, thereby providing a time-space scaling equivalent design for the kinematic characteristics of a spacecraft based on the Buckingham Pi theorem, which embodies the physical quantity equivalence theory in the equivalent theory framework.

[0006] To solve the above problems, the technical solution adopted by the present application is as follows: A method for calculating the equivalent simulation of the kinematic characteristics of a spacecraft by a UAV, comprising the following steps: (1) determining the in-orbit model of a spacecraft and the relative motion equation in the orbit coordinate system.

[0007] (2) determining the necessary parameters of the equivalent model according to the relative motion equation; (3) determining the basic parameters describing the physical process according to the parameters of the relative motion equation model, and calculating a set of dimensionless numbers for describing the physical process of the prototype and the model.

[0008] (4) establishing an equation to describe the two systems of the prototype and the model according to the similarity between the model and the prototype through the set of dimensionless numbers.

[0009] (5) deriving the parameter scaling factor of the model and the prototype according to the two equations of the prototype and the model.

[0010] According to the scale factor of the prototype and the model, the unmanned aerial vehicle control force equivalent principle under the equivalent spacecraft condition is derived.

[0011] Further, the relative motion equation calculation method in the orbital coordinate system is as formula (1): Formula (1) Wherein, is the control force deceleration, is the perturbation force acceleration, which are the components of the control force and the perturbation force on the axes of the coordinate system, respectively, is the position vector of the pursuit spacecraft relative to the inertial coordinate system, is the true anomaly of the target spacecraft orbit, is the angular acceleration of the spacecraft, is the angular velocity of the spacecraft, is the average angular velocity of the target spacecraft orbit.

[0012] Further, according to the relative motion equation, the necessary parameters of the equivalent model are determined, and the motion parameters involved are the spacecraft mass m, the spacecraft position r in the inertial coordinate system, the spacecraft velocity v, the spacecraft acceleration a, the relative position of the spacecraft, the relative velocity of the spacecraft, the relative acceleration of the spacecraft,

[0013] Further, according to the relative motion equation model parameters, a set of dimensionless numbers used to describe the physical process of the prototype and the model are calculated. The dimensionless numbers are calculated as follows:

[0014] Further, the equation of the prototype and the model described by the dimensionless number is as formula (2): Formula (2) Wherein, is the dimensionless number of the prototype, is the dimensionless number of the model.

[0015] Further, based on the fact that the prototype and the model are the same physical phenomenon, the model and the prototype parameter scale factor is obtained:

[0016]

[0017]

[0018]

[0019]

[0020] Further, in the process of simulating the spacecraft by the unmanned aerial vehicle, in order to ensure the accuracy of the equivalent kinematic parameters, the force environment of the unmanned aerial vehicle and the force environment of the spacecraft need to be equivalent. Further, the dynamic equation of the spacecraft and the unmanned aerial vehicle is established as formula (3) as follows: Formula (3) Further, the force equivalent equation is arranged, and the calculation formula of the control force of the unmanned aerial vehicle is derived. Therefore, under the force equivalent model, the control force of the unmanned aerial vehicle is formula (4) as follows: Formula (4) If the above similarity criterion can be met at all concerned time points of the system, the spacecraft orbit kinematics problem meets the similarity relationship in the space and ground experimental environment. In addition, the parameters describing the problem are time-varying in the whole system time, so, as described above, the relationship of the scale factor is the relationship of the similarity phenomenon at the corresponding point and the corresponding time.

[0021] The beneficial effects of the present application are: By establishing the relative motion equation of the spacecraft, the parameters required to solve the kinematics problem of the spacecraft are obtained, the position and velocity vector of the spacecraft can be obtained by integrating the relative motion equation, and based on the principle of space-time scaling, a mathematical model describing the actual physical process, i.e. the on-orbit motion process of the spacecraft and the ground simulation system of the unmanned aerial vehicle, is established. By assuming that the two processes are the display of the same physical phenomenon, in this process, the known parameters are given, including the mass of the spacecraft and the unmanned aerial vehicle, the relative position, the task and the experimental time length, the relative velocity and acceleration scale factor of the spacecraft and the unmanned aerial vehicle are obtained by calculation, and the motion process of the spacecraft is simulated by observing the kinematic parameters of the unmanned aerial vehicle of the ground experimental system, solving the problem that the ground experimental system cannot meet the actual running process space shortage. The orbit motion of the spacecraft in the on-orbit operation is simulated through the mechanical flight control process of the rotor unmanned aerial vehicle. It is more safe, economical and efficient. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 It is a flowchart of a method for simulating the kinematic characteristics of a spacecraft by an unmanned aerial vehicle in the embodiment of the present application; Figure 2The model of coordinate system established when constructing the relative motion equation of the spacecraft for the example of the present application is shown in the figure, in which the Earth-centered inertial coordinate system (ECI), the satellite orbit coordinate system (Hill) are defined, and the position vector of the pursuing 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 DESCRIPTION

[0023] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of the present application.

[0024] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0025] It is assumed that the assumed spacecraft mass in the prototype field is 500 kg, the maximum relative distance of the task is 200 km, and the total duration of the task is 1 day. The mass of the unmanned aerial vehicle in the ground experiment system is 4 kg, the maximum range of the site is 20 m, and the total duration of the experiment is 20 min. The ground experiment system is used to simulate the prototype, and the proportion of the kinematic parameters under the corresponding conditions is calculated Reference is made to the accompanying Figure 1 A method for calculating the kinematic characteristics of an unmanned aerial vehicle equivalent to a simulated spacecraft, comprising the following steps: Step 1, determine the on-orbit model of the spacecraft, such as Figure 2 , including the Earth-centered inertial coordinate system (ECI), the satellite orbit coordinate system (Hill), the position vector of the pursuing 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.

[0026] According to Figure 2 , for the spatial relative motion, it is assumed that 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, the axis is outward along the direction of , the axis is perpendicular to and points to the local horizontal of the target spacecraft, so and both axes are in the orbital plane of the target spacecraft, the axis is perpendicular to the plane.

[0027] Determine To chase the position vector of the spacecraft relative to the inertial coordinate system,

[0028] Step two, determine the relative motion equation in the orbit coordinate system.

[0029] In this example, after establishing the coordinate system position according to step one, the relative motion equation in the orbit coordinate system can be obtained:

[0030] Wherein, is the control force acceleration, is the perturbation force acceleration, which are the components of the control force and the perturbation force on the axes of the coordinate system, is the target spacecraft orbit true anomaly, is the angular acceleration of the spacecraft, is the angular velocity of the spacecraft, is the average angular velocity of the target spacecraft orbit.

[0031] Step three, determine the necessary parameters of the equivalent model according to the relative motion equation. In this example, according to the relative motion equation obtained in step two, the motion parameters involved are the spacecraft mass m, the spacecraft position r in the inertial coordinate system, the spacecraft velocity v, the spacecraft acceleration a, the relative position of the spacecraft, the relative velocity of the spacecraft, and the task parameter task total time P. There are eight parameters in total.

[0032] Step four, according to the model parameters obtained in step three, combine the basic dimensions of each parameter to list the dimension matrix of the parameters. Among the eight parameters obtained in step three, the satellite parameter m and the task parameter T are given, and the remaining six parameters are orbit parameters. By integrating the relative motion equation, the position and velocity parameters of the spacecraft during the relative motion process can be obtained, and through the space-time scaling principle, the required position and velocity of the actual unmanned vehicle can be achieved.

[0033] In this example, the dimension matrix is as follows:

[0034] According to the dimension matrix obtained in step four, the rank of the dimension matrix is 3, so according to the Buckingham Pi theorem, there are five dimensionless quantities to describe the kinematics problem of the spacecraft.

[0035] Optionally, three parameters, such as are selected to derive five dimensionless parameters. The calculated dimensionless numbers are as follows.

[0036] 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.

[0037] 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:

[0038] 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.

[0039]

[0040] 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.

[0041] The corresponding parameters should have the following scaling factors.

[0042]

[0043] 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. 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.

[0044] 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.

[0045] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present application, and are used to illustrate the technical solutions of the present application, but not to limit the same. In the above examples, the scaling factor for the problem is finally obtained through a series of calculations. It should be understood by those skilled in the art that any person skilled in the art can still modify or easily think of changes to the technical solutions recorded in the foregoing embodiments, or make equivalent replacement to some of the technical features within the technical scope disclosed by the present application. The modifications, changes or replacements should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to 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) Formula (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 as described in claim 1, 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 1, characterized in that, In S4, the equations of the prototype and model described by the dimensionless number are as shown in formula (2): Formula (2).

6. The method for calculating the kinematic characteristics of an equivalent spacecraft using a UAV according to claim 1, 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 1, 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): Formula (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 1, 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: Formula (4).

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