Sliding mode control method for microsatellite cluster assembly based on satellite-borne GPS positioning

Abstract

The invention discloses a sliding-mode control method for microsatellite cluster assembly based on satellite-borne GPS positioning, and belongs to the technical field of spacecraft flight. According to the method, a dynamical model is established based on heterogeneous spacecraft formation tasks, a control program is provided, meanwhile, a controller is combined with the satellite-borne GPS technology, and the satellite-borne GPS positioning is combined with the satellite-borne GPS positioning technology; noise generated in an information receiving process is filtered by using a filter, so that the precision and the practicability of a program are further improved; the method can avoid the problem of low control accuracy caused by traditional PD control, has great practical value, and has wide application prospects in the fields of spacecraft docking separation, on-orbit assembly, formation flight and the like.

Description

Technical Field

[0001] The invention belongs to the technical field of spacecraft flight, and in particular relates to a sliding mode control method for assembling a micro-satellite cluster based on onboard GPS positioning. Background Art

[0002] Compared with on-orbit deployment technology, the great appeal of on-orbit assembly lies in: (1) breaking through the size limitation, it is possible to build space structures of hundreds of meters or even kilometers; (2) according to the mission requirements, the modules can be flexibly unlocked and reconnected to achieve on-orbit reconstruction of the structure; (3) in the event of component failure, it is easy to replace the module. Therefore, in order to avoid the safety risks brought by ground remote control and astronauts' participation in assembly, scholars have proposed a variety of autonomous assembly concepts and methods in recent years. For example, Rhodes et al. of NASA's Langley Research Center demonstrated an automatic assembly process of a large aperture antenna using 102 tetrahedral trusses and 12 hexagonal panels (Rhodes MD, Will RW, Quach CC. Verification tests of automated robotic assembly of space truss structures [J]. Journal of Spacecraft and Rockets, 1995, 32 (4): 686-696.). Lee et al. from the California Institute of Technology designed a 100m modular space telescope architecture based on in-orbit deployment, space robotics and formation flying technology (Lee NN, Burdick JW, Backes P, et al. Architecture for in-space robotic assembly of a modular space telescope[J]. Journal of Astronomical Telescopes, Instruments, and Systems, 2016, 2(4): 041207.).

[0003] In addition to conceptual design, traditional space powers have already planned or carried out on-orbit assembly space experiments. For example, in 1997, the Engineering Test Satellite 7 (ETS-VII) of the Japan Aerospace Exploration Agency successfully used a robotic arm to complete the on-orbit assembly of a 2m diameter antenna for the first time in the world (Suzuki Y, Tsuchiya S, Okuyama T, et al. Mechanism for assembling antenna in space [J]. IEEE Transactions on Aerospace and Electronic Systems, 2001, 37 (1): 254-265.). Funded by the US Defense Advanced Research Projects Agency, Space Systems Loral launched the "Dragonfly" project, attempting to use a space robotic arm system to assemble a large antenna reflector on-orbit (Lymer J, Doggett WR, Dorsey J, et al. Commercial application of in-space assembly [M]. AIAA SPACE 2016. 2016: 5236.). Although my country started late in the research on on-orbit assembly technology, it has also proposed a series of mission concepts and on-orbit assembly plans in the past decade. For example, the team of Cui Naigang and Guo Jifeng from Harbin Institute of Technology (Guo Jifeng, Wang Ping, Cui Naigang. Space In-orbit Assembly Mission Planning [M]. Beijing: National Defense Industry Press, 2014) used several algorithms such as two-level hierarchical intelligent planning to design the in-orbit assembly task sequence of large space truss structures. The Qian Xuesen Space Technology Laboratory and Harbin Institute of Technology jointly proposed the concept of using space robots to build a modular giant space solar power station (SSPS) (Cheng ZA, Hou X, Zhang X, et al. In-orbit assembly mission for the space solar power station [J]. Acta Astronautica, 2016, 129: 299-308.). The team of Academician Hu Haiyan from Nanjing University of Aeronautics and Astronautics conducted dynamic analysis and controller design on the assembly process of flexible spacecraft (Chen Ti. Flexible spacecraft state consistency and autonomous assembly control [D]. Nanjing University of Aeronautics and Astronautics, 2017). Professor Wu Zhigang's team from Dalian University of Technology used the assembled space power station as the research background to study the dynamic modeling, inertia identification and vibration control of large space structures (Wang Enmei, Wu Shunan, Wu Zhigang. Dynamic modeling of on-orbit assembled space structures for active control [J]. Chinese Journal of Mechanics, 2020, Vol. 52(3):805-816).

[0004] On-orbit assembly is a technology that splits a large space structure into one or several groups of easy-to-build modules, launches them independently from the ground, and then assembles them in space to build a complete structure. On-orbit assembly can be divided into two categories according to the working method: the first category is the use of space robots to grasp, transport and assemble components; the second category is the rapid rendezvous of modules with autonomous maneuverability, and interconnection through standardized interfaces to form a large space structure. Compared with the first category, the second type of assembly mode can realize on-orbit assembly more quickly and is conducive to the vibration suppression of super-large space structures after assembly. The construction process of the International Space Station successfully verified the second type of assembly technology, but the assembly process of the International Space Station took 15 years and cost $100 billion. This on-orbit assembly technology is difficult to meet the future needs of super-large structure construction. Therefore, high-efficiency and low-cost on-orbit autonomous assembly technology is one of the areas that my country's aerospace science and technology urgently needs to develop. In the assembly process of complex space structures, there are likely to be multiple types of assembly modules, so it is necessary to solve the dynamics and control problems involved in the on-orbit assembly of heterogeneous intelligent spacecraft.

[0005] At the same time, the assembly and control of space structures such as satellite formations cannot be achieved without accurate absolute and relative orbit information of satellites. The GPS positioning system has the characteristics of low cost and high precision, and is more suitable for combination with satellite formation technology. In recent years, a considerable number of scholars have conducted research in related fields: the earth resources satellite LANDSAT-4 launched in 1982 was equipped with a satellite-borne GPS receiver for the first time. This was the first low-orbit satellite mission to successfully apply orbit determination. A few years later, the Topex / Poseidon ocean altimetry satellite launched in 1992 used satellite-borne GPS technology, which increased the orbit accuracy from the expected 13cm to 3-4cm, making considerable progress in accuracy. In terms of accuracy, GPS receivers have been equipped on many satellites, such as Germany's CHAMP satellite, the US-Germany GRACE satellite, Russia's MetOp-A, and the European Space Agency (ESA)'s GOCE.

[0006] The development of on-orbit assembly technology can solve the problem that the expansion of spacecraft scale is constrained by launch conditions, provide on-orbit maintenance services such as on-orbit replacement and assembly of spacecraft components, and enable various new technologies to be applied to spacecraft. At the same time, micro-satellite clusters can improve the efficiency of completing tasks by adjusting their own configurations when completing specific observation tasks, which is of great significance. Therefore, it is necessary to study the assembly technology of on-orbit spacecraft so as to apply it to the micro-satellite cluster system. At the same time, in order to facilitate the development of experiments, it is necessary to study the differential GPS positioning program to measure the position coordinates and apply them.

[0007] my country is at the initial stage in the field of super-large space structure assembly. Existing public reports only contain a small amount of research on the basic mission concepts of space assembly and the details of the assembly process. Therefore, it is necessary to solve the dynamics and control problems involved in the on-orbit assembly process based on heterogeneous intelligent spacecraft; in terms of modeling, there is a lack of high-precision flexible spacecraft dynamics models for mission planning and controller design. The relative dynamics model of rigid spacecraft is relatively mature, but there is a lack of research on the relative dynamics modeling and control of flexible spacecraft-rigid spacecraft, that is, analyzing the impact of flexible vibration on the traditional relative dynamics model and control effect. Summary of the invention

[0008] The present invention provides a sliding mode control method for micro-satellite cluster assembly based on satellite-borne GPS positioning. The method establishes a dynamic model based on heterogeneous spacecraft formation missions and provides a control program. At the same time, the controller is combined with the satellite-borne GPS technology, and a filter is used to filter out the noise generated in the process of information reception, thereby further improving the accuracy and feasibility of the program.

[0009] To achieve the above objectives, the present invention adopts the following technical solutions:

[0010] A sliding mode control method for micro-satellite cluster assembly based on onboard GPS positioning comprises the following steps:

[0011] S1: Determine the positions of the tracking spacecraft and the target spacecraft;

[0012] S2: Pre-assembly phase: Control the tracking spacecraft to make it reach a relatively close relative distance with the target spacecraft and keep it relatively still;

[0013] S3: Assembly phase: Control the tracking spacecraft to slowly approach the target spacecraft, so that the two spacecraft are completely docked.

[0014] In the above steps, the modified Rodrigues parameters are used in S1 to represent the position and attitude motion equations of the tracking spacecraft approaching the target spacecraft in space:

[0015]

[0016] Among them, S is the antisymmetric matrix of the elements, r is the tracking spacecraft position vector, σ is the modified Rodriguez parameter describing the tracking spacecraft attitude; v and ω are the tracking spacecraft velocity and angular velocity, respectively; f c and τ c They are the control force and control torque acting on the tracking spacecraft, respectively. These quantities are in the tracking spacecraft body coordinate system F c In the figure, m and J are the mass and moment of inertia matrices of the tracking spacecraft, respectively, and μ is defined as μ = μ g / ||r|| 3 , μ g is the gravitational constant of the earth; I3 is the 3×3 unit matrix;

[0017] The target spacecraft's position and attitude motion equations are:

[0018]

[0019] Among them, r t , σ t , v t and ω t are the position, attitude, velocity and angular velocity of the target spacecraft respectively; m t and J t are the mass and moment of inertia matrices of the target spacecraft, respectively. These quantities are all in the target spacecraft body coordinate system F t In the expression, μ t Defined as μ t =μ g / ||r t || 3 ;

[0020] is the geocentric inertial coordinate system, and are the body coordinate systems fixed to the tracking spacecraft and the target spacecraft respectively; {r,r e} and {r t} are respectively in F c and F t Relative position vector expression in the coordinate system; the controller acts on the tracking spacecraft, so the center of mass C of the tracking spacecraft tracks the center of mass T of the target spacecraft, the coordinate system F c Tracking coordinate system F t ;

[0021] In actual situations, the tracking spacecraft may collide with the target spacecraft or other objects when approaching the expected position. Therefore, it is necessary to add collision avoidance force in the pre-assembly stage to prevent the occurrence of collision. In the pre-assembly stage, the sliding mode control plus collision avoidance force method is used to adjust the relative position and relative attitude between the tracking spacecraft and the target spacecraft. The collision avoidance force f generated by the collision avoidance potential field is designed. p ,

[0022]

[0023] Among them U rep represents the collision potential field, N is the number of other spacecraft that the current spacecraft needs to consider as obstacles, and r i The current spacecraft and i The relative distance of obstacles, and Represent the radius of the danger zone and the collision avoidance zone respectively. 0,1 The sum of the tracking and target spacecraft radii is taken as 0.5 m, δ 0,1 Take 5m, k i Defined as

[0024]

[0025] Therefore, based on the negative gradient of the collision avoidance potential field, f p Can be designed as:

[0026]

[0027] Design of active control forces acting on tracking spacecraft:

[0028] f=f c +f b +f p

[0029] Among them, f c is the control force acting on the tracking spacecraft, f b is the compensation force acting on the tracking spacecraft, f p is the collision avoidance force generated based on the collision avoidance potential field;

[0030] During the assembly phase, the traditional PD control law is used to adjust the relative position between the tracking spacecraft and the target spacecraft, and the active control force acting on the tracking spacecraft is designed:

[0031] f=-k p1 (r e12 -r d )-k d1 v e12

[0032] Among them, k p1 With k d1 is a manually adjusted parameter, r e12 With v e12 is the relative position and relative velocity of spacecraft 1 and 2, r d is the target distance of the relative positions of the two spacecraft;

[0033] Control torque design of the whole stage:

[0034] τ c =τ f +τ b

[0035]

[0036] τ b =-k3s2

[0037] Noise processing using satellite-borne GPS and Kalman filtering:

[0038] Pseudorange differential is a differential positioning technology that uses the known coordinates of the base station to calculate the distance from the measuring station to the satellite, and compares it with the measured distance containing errors. The difference is then filtered using a filter to calculate the deviation, which is then used to make corrections to obtain the coordinates.

[0039] The pseudorange between station i and satellite j at time t is

[0040]

[0041] Where t j is the time on the satellite clock; i is the time on the receiver clock; δt j It is the clock difference of the satellite clock face relative to the standard time; δt i The clock difference between the receiver clock and the standard time; Indicates satellite S j To Observation Station T i The geometric distance between them; c is the speed of light; is the equivalent distance error of the ionospheric refraction delay at time t; δT i j is the equivalent distance error of the tropospheric refraction delay at time t; It is the distance deviation caused by the GNSS satellite ephemeris error;

[0042] Then, the pseudo-range observation model is used as the observation equation to construct a Kalman filter to filter the spacecraft position information. The specific parameter settings are as follows:

[0043] Taking the rectangular simulation to be implemented as an example, there are one tracking spacecraft and one target spacecraft. The filter state vector can be set to

[0044] x=[Δy T ,ΔB T ,cΔδt,ΔC D ] T

[0045] in is the relative position velocity vector, ΔB is the single difference carrier phase ambiguity, cΔδt is the differential receiver clock error, ΔC D is the differential atmospheric drag parameter, which is no longer considered because it is basically eliminated in the differential process;

[0046] Assume that the state vector conversion relationship between the two moments before and after is: k+1 =f(x k ), then the state transfer matrix can be expressed as

[0047]

[0048] Then according to Figure 4 The method shown in the block diagram can be obtained by continuous iteration.

[0049] Beneficial effects: The present invention provides a sliding mode control method for the assembly of a cluster of micro-satellites based on satellite-borne GPS positioning, which solves the dynamics and control problems involved in the on-orbit assembly process of heterogeneous spacecraft and establishes a high-precision dynamic model for it, and designs a controller for it; at the same time, it uses satellite-borne GPS and Kalman filtering technology to reduce the error in the parameter transfer process and improve the executability in practical applications. The sliding mode control method of the present invention improves the accuracy of on-orbit assembly of spacecraft, can avoid the problem of low control accuracy caused by traditional PD control, has great practical value, and has broad application prospects in the fields of spacecraft docking and separation, on-orbit assembly, formation flying, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 A schematic diagram of a coordinate system and related vectors in an embodiment of the present invention;

[0051] Figure 2 This is a specific operation flow chart of Kalman filtering in an embodiment of the present invention;

[0052] Figure 3 : It is a rectangular simulation result diagram in an embodiment of the present invention, wherein (a) is a schematic diagram of the rectangular on-orbit assembly simulation result in an embodiment of the present invention, (b) is the relative position (x-axis) of all target spacecraft and tracking spacecraft in the whole process; (c) is the relative position (y-axis) of all target spacecraft and tracking spacecraft in the whole process; (d) is the relative posture of all target spacecraft and tracking spacecraft in the whole process; (e) is the control force acting on all tracking spacecraft in the whole process;

[0053] Figure 4 1 is a diagram of the simulation results of the “I” shape in an embodiment of the present invention, wherein (a) is a schematic diagram of the simulation results of the “I” shape on-orbit assembly in an embodiment of the present invention, (b) is the relative position of all target spacecraft and the tracking spacecraft in the whole process (x-axis); (c) is the relative position of all target spacecraft and the tracking spacecraft in the whole process (y-axis); (d) is the relative posture of all target spacecraft and the tracking spacecraft in the whole process; (e) is the control force acting on all tracking spacecraft in the whole process. DETAILED DESCRIPTION

[0054] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments:

[0055] The present invention is an on-orbit spacecraft assembly control technology, which uses motors as actuators and takes into account the output saturation limitations of spacecraft in specific environments. A controller is designed to effectively control and assemble the spacecraft position and attitude to achieve the desired effect.

[0056] The specific implementation steps are as follows:

[0057] Step 1: Use Kalman filtering to detect the position of the spacecraft. The specific operation method is as follows: Figure 2 As shown;

[0058] a. Establish state equation and observation equation

[0059] b. Perform first-order linearization on the equation

[0060] c. Using Kalman filter iteration

[0061] d. Update the state vector

[0062] Step 2: Establish a mathematical model of the spacecraft's motion;

[0063] is the geocentric inertial coordinate system, and are the body coordinate systems fixed to the tracking spacecraft and the target spacecraft, respectively, {r,r e} and {r t} are respectively in F c and F t Relative position vector expression in the coordinate system; the controller acts on the tracking spacecraft, so the center of mass C of the tracking spacecraft tracks the center of mass T of the target spacecraft, the coordinate system F c Tracking coordinate system F t ;

[0064] Step 2.1: Give the position and attitude dynamics model of the target spacecraft:

[0065]

[0066] Among them, S is the antisymmetric matrix of the elements, r t , σ t , v t and ω t are the position, attitude, velocity and angular velocity of the target spacecraft respectively; m t and J t are the mass and moment of inertia matrix of the target spacecraft respectively. These quantities are all in the target spacecraft body coordinate system F t In the expression, μ t Defined as μ t =μ g / ||r t || 3;

[0067] Step 2.2: Use the modified Rodrigues parameters to express the position and attitude motion equations of the tracking spacecraft approaching the target spacecraft in space:

[0068]

[0069] Where r is the position vector of the tracking spacecraft, σ is the modified Rodriguez parameter describing the attitude of the tracking spacecraft; v and ω are the velocity and angular velocity of the tracking spacecraft respectively; f c and τ c They are the control force and control torque acting on the tracking spacecraft, respectively. These quantities are in the tracking spacecraft body coordinate system F c In the figure, m and J are the mass and moment of inertia matrices of the tracking spacecraft, μ g is the gravitational constant of the Earth; I 3 is the 3×3 identity matrix. μ is defined as μ=μ g / ||r|| 3 ;

[0070] The characteristic quantity of a single spacecraft model used in this embodiment is:

[0071] Target spacecraft: Mass: 250kg

[0072] Moment of inertia: J = [26.0417, 0, 0; 0, 26.0417, 0; 0, 0, 41.6667]

[0073] Initial angular velocity: ω = [0; 0; 0]

[0074] Tracking spacecraft: Mass: 62.5kg

[0075] Moment of inertia: J = [2.6, 0, 0; 0, 2.6, 0; 0, 0, 2.6];

[0076] Initial angular velocity: ω = [0; 0; 0]

[0077] Step 3: Control the assembly phase

[0078] In actual situations, the tracking spacecraft may collide with the target spacecraft or other objects when approaching the desired position, so it is necessary to add collision avoidance force in the pre-assembly stage to prevent the occurrence of collision;

[0079] In the pre-assembly stage, the sliding mode control plus collision avoidance force method is used to adjust the relative position and relative attitude between the tracking spacecraft and the target spacecraft, and the collision avoidance force f generated by the collision avoidance potential field is designed. p ,

[0080]

[0081] Where N is the number of other spacecraft that need to be considered as obstacles for the current spacecraft, r i The current spacecraft and i The relative distance of obstacles, and Represent the radius of the danger zone and the collision avoidance zone respectively. 0,1 The sum of the tracking and target spacecraft radii is taken as 0.5 m, δ 0,1 Take 5m, k i Defined as

[0082]

[0083] Therefore, based on the negative gradient of the collision avoidance potential field, f p Can be designed as:

[0084]

[0085] Design of active control forces acting on tracking spacecraft:

[0086] f=f c +f b +f p

[0087] Among them, f c is the control force acting on the tracking spacecraft, f b is the compensation force acting on the tracking spacecraft, f p is the collision avoidance force generated based on the collision avoidance potential field;

[0088] During the assembly phase, the traditional PD control law is used to adjust the relative position between the tracking spacecraft and the target spacecraft, and the active control force acting on the tracking spacecraft is designed:

[0089] f=-k p1 (r e12 -r d )-k d1 v e12

[0090] Among them, k p1 With k d1 is a manually adjusted parameter, r e12 With v e12 is the relative position and relative velocity of spacecraft 1 and 2, r d is the target distance of the relative positions of the two spacecraft;

[0091] Control torque design of the whole stage:

[0092] τ c =τ f+τ b

[0093]

[0094] τ b =-k3s2

[0095] The above description is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be regarded as within the protection scope of the present invention.

Claims

1. A sliding mode control method for micro-satellite cluster assembly based on onboard GPS positioning, characterized in that: The following steps are involved: S1: Use Kalman filtering to detect the spacecraft position and determine the positions of the tracking spacecraft and the target spacecraft; S2: Establishing mathematical models of the motion of the tracking spacecraft and the target spacecraft; S3: Pre-assembly phase: Control the tracking spacecraft so that it reaches a relatively close relative distance with the target spacecraft and keeps it relatively stationary; S4: Assembly phase: Control the tracking spacecraft to slowly approach the target spacecraft, so that the two spacecraft are completely docked.

2. The sliding mode control method for micro-satellite cluster assembly based on onboard GPS positioning according to claim 1 is characterized in that: The position and attitude motion equations of the tracking spacecraft described in S2 are: Among them, S is the antisymmetric matrix of the elements, r is the tracking spacecraft position vector, σ is the modified Rodrigues parameter describing the tracking spacecraft attitude; v and ω are the tracking spacecraft velocity and angular velocity respectively; f c and τ c are the control force and control torque acting on the tracking spacecraft, m and J are the mass and moment of inertia matrices of the tracking spacecraft, μ g is the Earth's gravitational constant; I3 is the 3×3 identity matrix; μ is defined as μ=μ g / ||r|| 3 .

3. The sliding mode control method for micro-satellite cluster assembly based on onboard GPS positioning according to claim 1 or 2, characterized in that: The position and attitude dynamics model of the target spacecraft described in S2: Among them, r t , σ t , v t and ω t are the position, attitude, velocity and angular velocity of the target spacecraft respectively; m t and J t are the mass and moment of inertia matrices of the target spacecraft, respectively, where μ t Defined as μ t =μ g / ||r t || 3 .

4. The sliding mode control method for micro-satellite cluster assembly based on onboard GPS positioning according to claim 1, characterized in that: In the pre-assembly stage of S3, the sliding mode control plus collision avoidance force method is used to adjust the relative position and relative attitude between the tracking spacecraft and the target spacecraft.

5. The sliding mode control method for micro-satellite cluster assembly based on onboard GPS positioning according to claim 4 is characterized in that: Design the collision avoidance force f generated by the collision avoidance potential field p for: where r i The current spacecraft and the i The relative distance of the obstacles, and Represent the radius of the danger zone and the collision avoidance zone, k i Defined as 6. The sliding mode control method for micro-satellite cluster assembly based on onboard GPS positioning according to claim 4 or 5, characterized in that: Design of active control forces acting on tracking spacecraft: f=f c +f b +f p Among them, f c is the control force acting on the tracking spacecraft, f b is the compensation force acting on the tracking spacecraft, f p is the collision avoidance force generated based on the collision avoidance potential field.

7. The sliding mode control method for micro-satellite cluster assembly based on onboard GPS positioning according to claim 1, characterized in that: Design of active control forces acting on tracking spacecraft during the assembly phase of S4: f=-k p1 (r e12 -r d )-k d1 v e12 Among them, k p1 With k d1 is a manually adjusted parameter, r e12 With v e12 In order to track the relative position and relative velocity of the spacecraft and the target spacecraft, r d is the target distance of the relative positions of the two spacecraft.

8. The sliding mode control method for micro-satellite cluster assembly based on onboard GPS positioning according to claim 1, characterized in that: Control torque design for the entire stage: t c =t f +t b t b =-k3s2.

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