1. A multi-spacecraft distributed cooperative formation control method is characterized by comprising the following steps: defining a geocentric inertial coordinate system, and establishing a local vertical local horizontal coordinate system, namely an LVLH coordinate system, by using the geocentric inertial coordinate system as a reference; establishing a multi-spacecraft kinematic equation according to the LVLH coordinate system, wherein the multi-spacecraft kinematic equation comprises at least two spacecrafts; defining task targets according to an LVLH coordinate system and a multi-spacecraft motion dynamics equation, wherein the task targets comprise a first task target and a second task target; the first task target comprises a formation structure and a maintenance task target, and the second task target comprises a formation structure, a formation maintenance and a trajectory tracking target; designing a first potential function and a second potential function, wherein the first potential function comprises a potential function for avoiding collision among the spacecrafts and maintaining topological connectivity, and the second potential function comprises an obstacle avoidance potential function; designing a first guidance law according to the first task target, the first potential function and the second potential function, wherein the first guidance law comprises a multi-spacecraft formation construction and a guidance keeping law; designing a second guidance law according to the second task target, the first potential function and the second potential function, wherein the second guidance law comprises a multi-spacecraft trajectory tracking guidance law; and finishing the distributed collaborative formation control of the multiple spacecrafts according to the first guidance law and/or the second guidance law.

2. The multi-spacecraft distributed cooperative formation control method according to claim 1, characterized in that: the multi-spacecraft formation and maintenance guidance law comprises an anti-collision and topological connectivity maintenance item, an obstacle avoidance item, a formation and maintenance item and a formation traveling speed item.

3. The multi-spacecraft distributed cooperative formation control method according to claim 1, characterized in that: the multi-spacecraft trajectory tracking guidance law comprises a collision avoidance and topology connectivity maintaining item, an obstacle avoidance item, a formation and maintaining item and a trajectory tracking item.

4. The multi-spacecraft distributed cooperative formation control method according to claim 1 or 2, characterized by: formation and guidance maintaining law of multi-spacecraft formation

Wherein the content of the first and second substances,to keep the terms for collision avoidance and topological connectivity,in order to avoid the barrier item, the barrier layer is provided with a plurality of barriers,for formation of formation and holding entries, - (v)_i-v_d) In order to form the traveling speed item for the formation,for constructing and maintaining guidance law for multi-spacecraft formation, i is 1,2, …, n, j is 1,2, …, n, n is the total number of spacecraft in the multi-spacecraft formation, p_iFor the position of the ith spacecraft in the LVLH coordinate system,to avoid collision among the spacecrafts and keep topological connectionSexual potential function, | p_ijI | is the relative distance between the ith and jth space vehicles, k is 1,2, …, m, m is the number of obstacles,set of exclusion zones for the k-th obstacle in the ith spacecraft, δ_ikTo ensure the stability of the multi-spacecraft formation system,for the obstacle avoidance function between the ith spacecraft and the kth obstacle, o_k(k∈[1，2，…，m]) Is the position of the k-th obstacle, N_iSet of contiguous space vehicles, p, for the ith space vehicle_ijFor the current relative position vectors of the ith and jth spacecraft,for the expected position of the ith spacecraft in the LVLH coordinate system, v_iIs the current speed, v, of the ith spacecraft_jIs the current velocity, v, of the jth spacecraft_dThe desired multi-space vehicle formation travel speed is achieved.

5. The multi-spacecraft distributed cooperative formation control method according to claim 1 or 3, characterized by comprising: the multi-spacecraft trajectory tracking guidance law

Wherein the content of the first and second substances,to maintain items of collision avoidance and communication topology connectivity,in order to avoid the barrier item, the barrier layer is provided with a plurality of barriers,in order to construct and maintain the entries for the formation,for ballistic tracking term, v_tFor reference to the velocity of the trajectory,acceleration of the reference trajectory, p_itFor the current relative position vector of the ith spacecraft and the target,a relative position vector is expected for the ith spacecraft and the target.

6. The multi-spacecraft distributed cooperative formation control method according to claim 1, characterized in that: potential function for avoiding collision among spacecrafts and maintaining topological connectivity

Wherein the content of the first and second substances,for the minimum allowable relative distance between the ith spacecraft and the jth spacecraft,is the maximum communication distance between the ith spacecraft and the jth spacecraft,for the expected position of the ith spacecraft in the LVLH coordinate system,is the expected position of the jth spacecraft in the LVLH coordinate system.

7. The multi-spacecraft distributed cooperative formation control method according to claim 1, characterized in that: obstacle avoidance function

Wherein the content of the first and second substances,is the minimum allowable relative distance between the ith spacecraft and the kth obstacle,the maximum distance between the ith spacecraft and the kth obstacle at which a mutual repulsion force can be generated.

8. The multi-spacecraft distributed cooperative formation control method according to claim 1, characterized in that: formation of formation and maintenance of task objectives includes

9. The multi-spacecraft distributed cooperative formation control method according to claim 1, characterized in that: formation, formation maintenance and trajectory tracking target includingWherein p is_itFor the current relative position vector of the ith spacecraft and the target,for the ith spacecraft and the target desired relative position vector, v_tIs the target speed.

10. The multi-spacecraft distributed cooperative formation control method according to claim 4, wherein: adaptive matrix for ensuring stability of multi-spacecraft formation system

Wherein, γ_iIs a normal number which is a positive integer, is composed ofThe pseudo-inverse of (1).

Background

During actual flight, the connectivity maintenance of the communication topology is very critical, and the influence is more prominent particularly on the formation of small spacecraft with limited computing and communication capacity. Collision avoidance maneuvers increase the relative distance between the spacecraft and increase the probability of losing communication with adjacent spacecraft in the team. Although a multi-spacecraft formation control law is proposed in the prior document, formation configuration and obstacle avoidance can be realized, but a distributed architecture is not realized and the problem of connectivity maintenance is solved. The prior art has no multi-spacecraft formation tracking control scheme which can simultaneously realize collision avoidance, obstacle avoidance and connectivity maintenance, and the requirement of formation flight safety is difficult to meet.

Disclosure of Invention

The invention mainly aims to provide a multi-spacecraft distributed cooperative formation control method to at least solve the problems.

The invention provides a distributed cooperative formation control method for multiple spacecrafts, which comprises the following steps: defining a geocentric inertial coordinate system, and establishing a local vertical local horizontal coordinate system (LVLH) coordinate system by using the geocentric inertial coordinate system as a reference; establishing a multi-spacecraft kinematic equation according to the LVLH coordinate system, wherein the multi-spacecraft kinematic equation comprises at least two spacecrafts; defining a task target according to an LVLH coordinate system and a multi-spacecraft motion dynamics equation, wherein the task target comprises a first task target and a second task target, the first task target comprises a formation structure and a task maintaining target, and the second task target comprises a formation structure, a formation maintaining target and a trajectory tracking target; designing a first potential function and a second potential function, wherein the first potential function comprises a potential function for avoiding collision among the spacecrafts and maintaining topological connectivity, and the second potential function comprises an obstacle avoidance potential function; designing a first guidance law according to the first task target, the first potential function and the second potential function, wherein the first guidance law comprises a multi-spacecraft formation construction and a guidance keeping law; designing a second guidance law according to the second task target, the first potential function and the second potential function, wherein the second guidance law comprises a multi-spacecraft trajectory tracking guidance law; and finishing the distributed collaborative formation control of the multiple spacecrafts according to the first guidance law and/or the second guidance law.

Further, the multi-spacecraft formation and maintenance guidance law comprises an collision avoidance and topology connectivity maintenance item, an obstacle avoidance item, a formation and maintenance item and a formation traveling speed item.

Further, the multi-spacecraft trajectory tracking guidance law comprises a collision avoidance and topology connectivity maintaining item, an obstacle avoidance item, a formation and maintaining item and a trajectory tracking item.

Further, the formation and the maintenance guidance law of the multi-spacecraft formation

Wherein the content of the first and second substances,to keep the terms for collision avoidance and topological connectivity,in order to avoid the barrier item, the barrier layer is provided with a plurality of barriers,for formation of formation and holding entries, - (v)_i-v_d) In order to form the traveling speed item for the formation,for constructing and maintaining guidance law for multi-spacecraft formation, i is 1,2, …, n, j is 1,2, …, n, n is the total number of spacecraft in the multi-spacecraft formation, p_iFor the position of the ith spacecraft in the LVLH coordinate system,to avoid collision between spacecraft and maintain the potential function of topological connectivity, | | p_ijI | is the relative distance between the ith and jth space vehicles, k is 1,2, …, m, m is the number of obstacles,set of exclusion zones for the k-th obstacle in the ith spacecraft, δ_ikFor ensuring moreAn adaptive matrix of spacecraft formation system stability,for the obstacle avoidance function between the ith spacecraft and the kth obstacle, o_k(k∈[1,2,…,m]) Is the position of the k-th obstacle, N_iSet of contiguous space vehicles, p, for the ith space vehicle_ijFor the current relative position vectors of the ith and jth spacecraft,for the expected position of the ith spacecraft in the LVLH coordinate system, v_iIs the current speed, v, of the ith spacecraft_jIs the current velocity, v, of the jth spacecraft_dThe desired multi-space vehicle formation travel speed is achieved.

Further, the multi-spacecraft distributed collaborative formation control method is characterized in that the multi-spacecraft trajectory tracking guidance law

Wherein the content of the first and second substances,to maintain items of collision avoidance and communication topology connectivity,in order to avoid the barrier item, the barrier layer is provided with a plurality of barriers,in order to construct and maintain the entries for the formation,for ballistic tracking term, v_tFor reference to the velocity of the trajectory,acceleration of the reference trajectory, p_itCurrent relative position vector for ith spacecraft and target，A relative position vector is expected for the ith spacecraft and the target.

Further, potential functions for avoiding collision among spacecrafts and maintaining topological connectivity

Wherein the content of the first and second substances,is the minimum allowable relative distance between the ith spacecraft and the jth spacecraft,is the maximum communication distance between the ith spacecraft and the jth spacecraft,for the expected position of the ith spacecraft in the LVLH coordinate system,is the expected position of the jth spacecraft in the LVLH coordinate system.

Further, avoiding barrier potential function

Wherein the content of the first and second substances,is the minimum allowable relative distance between the ith spacecraft and the kth obstacle,the maximum distance between the ith spacecraft and the kth obstacle at which a mutual repulsion force can be generated.

Further, formation construction and protectionTask object support includes

Further, formation construction, formation maintenance and ballistic tracking targets includeWherein p is_itFor the current relative position vector of the ith spacecraft and the target,for the ith spacecraft and the target desired relative position vector, v_tIs the target speed.

Further, an adaptive matrix for ensuring stability of a multi-spacecraft formation system

Wherein, γ_iIs a normal number which is a positive integer,is composed ofThe pseudo-inverse of (1).

The invention has the advantages and beneficial effects that: by applying the technical scheme of the invention, a multi-spacecraft formation tracking control scheme with collision prevention, obstacle prevention and connectivity maintenance is designed and provided, and the formation flight safety is obviously improved. The invention firstly designs a series of new artificial potential functions to meet the requirement of keeping the connectivity of adjacent spacecrafts and simultaneously avoid the mutual collision among the spacecrafts and the formation flight safety requirements of avoiding obstacles and the like. By combining a consistency concept, a distributed control law for constructing and maintaining multi-spacecraft formation is designed, the connectivity of an interactive topology is maintained, and then the proposed formation control law is expanded into ballistic tracking and meets the requirement of safety.

Drawings

Fig. 1 is a flowchart of a multi-spacecraft distributed cooperative formation control method according to an embodiment of the present invention.

Fig. 2 is a schematic diagram of the geocentric inertial frame and the LVLH frame according to an embodiment of the present invention.

Fig. 3 is a schematic diagram of the collision zone, the repulsion zone, and the induction zone provided in accordance with an embodiment of the present invention.

Fig. 4 is a relationship between the magnitude of a potential function and the relative distance between the spacecraft, which is provided for avoiding collision between the spacecraft and maintaining topological connectivity according to an embodiment of the present invention.

Fig. 5 is a two-dimensional potential field around a spacecraft provided in accordance with an embodiment of the present invention for avoiding collision between the spacecraft and maintaining topological connectivity.

Fig. 6 is a diagram illustrating the relationship between the amplitude of the obstacle avoidance function and the relative distance between the spacecraft and the obstacle according to an embodiment of the present invention.

Fig. 7 is a two-dimensional potential field around a spacecraft for obstacle avoidance provided in accordance with an embodiment of the present invention.

Detailed Description

The following further describes a multi-spacecraft distributed cooperative formation control method provided by the present invention as follows:

step 1, defining a geocentric inertial coordinate system, and establishing an LVLH coordinate system by using the geocentric inertial coordinate system as a reference.

After the state space is constructed in the step 1, in order to describe the motion of the spacecraft, the step 2 is entered, and a multi-spacecraft motion dynamics equation is established according to the LVLH coordinate system, wherein the multi-spacecraft motion dynamics equation comprises at least two spacecrafts.

After the multi-spacecraft kinematics equation is established in the step 2, in order to realize formation of a formation, formation maintenance and trajectory tracking, the step 3 is entered, a task target is defined according to the LVLH coordinate system and the multi-spacecraft kinematics equation, the task target comprises a first task target and a second task target, the first task target comprises formation and maintenance of the task target, and the second task target comprises formation, formation maintenance and trajectory tracking targets.

After the task target is defined in the step 3, in order to avoid collision among the spacecrafts, keep topological connectivity and avoid obstacles, the method proceeds to a step 4, and a first potential function and a second potential function are designed, wherein the first potential function comprises a potential function for avoiding collision among the spacecrafts and keeping topological connectivity, and the second potential function comprises an obstacle avoiding potential function.

After the potential functions are designed in the step 4, in order to realize the construction and the maintenance of the multi-spacecraft formation, the step 5 is carried out, and a first guidance law is designed according to the first task target, the first potential functions and the second potential functions, wherein the first guidance law comprises the construction and the maintenance of the multi-spacecraft formation.

After the multi-spacecraft formation is designed and the guidance law is kept in the step 5, in order to realize multi-spacecraft trajectory tracking, the step 6 is carried out, and a second guidance law is designed according to a second task target, a first potential function and a second potential function, wherein the second guidance law comprises the multi-spacecraft trajectory tracking guidance law; and finishing the distributed collaborative formation control of the multiple spacecrafts according to the first guidance law and/or the second guidance law. And completing the distributed cooperative formation control of the multiple spacecrafts according to the formation and maintenance guide law of the formation of the multiple spacecrafts and/or the tracking guide law of the multiple spacecrafts trajectory.

For further understanding of the present invention, the method for controlling distributed cooperative formation of multiple spacecraft of the present invention is described in detail below with reference to fig. 1 to 7.

Step 1, defining a geocentric inertial coordinate system, and establishing an LVLH coordinate system by taking the geocentric inertial coordinate system as a reference, which specifically comprises the following steps:

defining a geocentric inertial frame S, as shown in FIGS. 1 and 2_I(O_Ix_Iy_Iz_I) In, the origin is taken as the geocentric O_IX of it_IThe axis points to the intersection of the meridian and equatorPoint, z_IAxis directed north, y_IThe axes are determined by the right hand rule. In LVLH (local-vertical/local-horizontal) coordinate system S_R(O_Rx_Ry_Rz_R) In, the origin is taken as a certain reference point O on the track_R，x_RThe axis pointing from the centre of the earth to a reference point, z_RParallel to the orbital angular momentum vector, i.e. pointing in the normal direction of the orbit, y_RThe axes are determined by the right hand rule. Edge x in LVLH coordinate system_R、y_RAnd z_RThe three components of the axis point in the radial (radial), tangential-tracking (azimuthal-tracking) and transverse-tracking (cross-tracking) directions, and the LVLH coordinate system tracks the local horizontal plane (local horizontal plane) as indicated by y_RAnd z_RAxis determination and local vertical plane (parallel to x)_RA shaft).

Establishing LVLH coordinate system based on the earth-centered inertial coordinate system, which is defined by the earth-centered inertial coordinate system { S }_IConverting to LVLH coordinate system S_RThe conversion matrix of is defined as L_RI,

Wherein u is_RIs the angle of lift-over (argument of perigee omega)_RAnd true paraxial angle θ_ROf (a) and (b), i.e. u_R＝ω_R+θ_R)，i_RFor track inclination, omega_RThe right ascension at the ascending intersection of the reference points.

Step 2, establishing a multi-spacecraft kinematic equation according to the LVLH coordinate system, wherein the multi-spacecraft kinematic equation comprises at least two spacecrafts, and specifically comprises the following steps:

as shown in fig. 2, multiple spacecraft are tracking target trajectories. In order to describe the relative dynamic relationship of the multi-spacecraft formation, an elliptical reference orbit which is not interfered by the outside world and a reference point are defined, and the motion of the reference point can be described asWherein r is_RDistance between reference point and center of earth, a_RIs a semi-major axis of the reference track, e_RIs the eccentricity of the elliptical orbit. True proximal angle θ_RRate of change ofWhereinIs theta_RThe first derivative of (a) is,is theta_RSecond derivative of, mu_e＝3.98574405096×10¹⁴m³/s²Is the gravitational constant of the earth, m is meter, s is second, B_RAs the point of intersection of the reference tracks, D_RIs the descending point of the reference track.

Defining the position of the ith spacecraft in the LVLH coordinate systemWhereinIs the position of the ith spacecraft in the x direction of the LVLH coordinate system,is the position of the ith spacecraft in the y-direction of the LVLH coordinate system,is the position of the ith spacecraft in the z-direction of the LVLH coordinate system.

In LVLH coordinate system of ith spacecraft { S_LThe kinetic equations in (c) can be expressed asWherein the content of the first and second substances,is p_iThe second derivative of (a) is, is p_iThe first derivative of (a) is,to an equivalent guidance law, f_iIs a nonlinear term in the kinetic model, the upper bound of which isu_iIs the commanded acceleration of the ith spacecraft relative to the earth's center inertial frame.

m_iIs the mass of the ith spacecraft,and the distance between the ith spacecraft and the earth center is represented by i, 1,2, …, and n is the total number of the spacecraft in the multi-spacecraft formation. J of ith spacecraft₂Power of taking a photographIn the centroid inertia system { S_IIn (f) can be expressed as,

wherein J₂＝0.0010826267，R_E6378.137km, whereinAt the x direction of the geocentric inertial coordinate system of the ith spacecraftIn the upward position of the container, the container is,is the position of the ith spacecraft in the y direction of the geocentric inertial frame,is the position of the ith spacecraft in the z direction of the geocentric inertial frame. Thus, J₂The expression of the perturbation force in the LVLH coordinate system is as follows

And 3, defining a task target according to the LVLH coordinate system and the multi-spacecraft motion dynamics equation, wherein the task target comprises a first task target and a second task target, the first task target comprises a formation structure and a task maintaining target, and the second task target comprises a formation structure, a formation maintaining target and a trajectory tracking target.

The spacecraft in the multi-spacecraft formation need to construct and maintain a preset formation form and maintain a desired formation traveling speed. Meanwhile, the spacecraft also needs to achieve penetration of enemy obstacles, avoid collision with space debris, and maintain connectivity of communication topology, that is, the relative distance between adjacent spacecrafts does not exceed the maximum communication distance. In addition, multiple spacecraft also require ballistic tracking of the maneuvering trajectory.

At an initial moment, the spacecraft in the multi-spacecraft formation are in different positions, and the speed (including magnitude and direction) of each spacecraft is different. When multiple spacecraft arrive at the desired formation, the relative positions of the spacecraft will meet the requirements and the relative velocities between the spacecraft will remain at zero. In addition, for the formation to remain mission, the entire multi-spacecraft formation needs to fly at a certain travel speed. Definition of p_ij＝p_i-p_jIs the current relative position vector, p, of the ith and jth spacecraft_iIs the position of the ith spacecraft in the LVLH coordinate system, p_jFor the position of the jth spacecraft in the LVLH coordinate system,for the expected position of the ith spacecraft in the LVLH coordinate system,can be obtained according to the formation. Current velocity v of the ith spacecraft_iThe expected multi-spacecraft formation traveling speed is v_d. Then, when the relative position error and the speed error are zero, the multi-spacecraft is defined to achieve the task goal of formation and maintenance, namely

In the ballistic tracking task, if the formation of the formation, the formation maintenance and the ballistic tracking can be realized by the multi-spacecraft formation, the following conditions need to be satisfied, namelyWherein p is_itFor the current relative position vector of the ith spacecraft and the target,for the ith spacecraft and the target desired relative position vector, v_tIs the target speed.

And 4, designing a first potential function and a second potential function, wherein the first potential function comprises a potential function for avoiding mutual collision among the spacecrafts and maintaining topological connectivity, and the second potential function comprises an obstacle avoidance potential function.

As shown in fig. 3, to achieve the objectives of collision avoidance, obstacle avoidance and communication topology connectivity between spacecrafts, we set a collision region, a repulsion region and an induction region around the spacecraft, with respective radii r^Col、r^RepAnd r^Sen. Defining when the relative distance of two objects (two spacecrafts or a spacecraft and an obstacle, etc.) is less than r^ColThen the two objects have collided. If the relative distance between a spacecraft and an obstacle is less than or equal to r^RepThe spacecraft will generate a repulsive force to circumvent the obstacleAnd (4) the prevention is realized and the interception is avoided. To ensure communication between two spacecrafts, the relative distance between the two spacecrafts needs to be kept less than or equal to r^Sen. In this context, to ensure that formation of multiple spacecraft is safer, we consider each spacecraft to be a sphere, so r^ColIs greater than the sum of the two spherical radii. In addition, supposeI.e. the radius of the impact zone is smaller than the minimum desired relative distance.

Considering that each spacecraft is a sphere with a certain radius, the potential functions of avoiding collision among the spacecrafts and maintaining topological connectivityIs designed as

Wherein p_ij||＝||p_i-p_j| | is the relative distance between the ith spacecraft and the jth spacecraft,for a desired relative distance between the two spacecraft,for the expected position of the ith spacecraft in the LVLH coordinate system,for the desired position of the jth spacecraft in the LVLH coordinate system,is the minimum allowable relative distance between the ith spacecraft and the jth spacecraft,the maximum communication distance between the ith spacecraft and the jth spacecraft.

As shown in fig. 4, if and only if the relative distance between the ith spacecraft and the jth spacecraft is the desired relative distanceTime, non-negative potential functionBecomes zero. When the relative distance is far awayWhen the temperature of the water is higher than the set temperature,will become sharply larger and even infinite.The two-dimensional potential field of (2) is shown in figure 5.

Assuming that m enemy obstacles exist in the space and are positioned in the exclusion zone of the ith spacecraft, the obstacle avoidance function between the ith spacecraft and the kth obstacleIs designed as

Wherein o is_k(k∈[1,2,…,m]) Is the position of the k-th obstacle, | | p_i-o_kThe relative distance between the ith spacecraft and the kth obstacle.Is the minimum allowable relative distance between the ith spacecraft and the kth obstacle,for the ith spacecraft and the ithThe maximum distance between k obstacles for generating mutual repulsive force, and the action distance of the k obstacle to the ith spacecraft is defined asI.e. when the relative distance between the kth obstacle and the ith spacecraft is smaller thanIn time, the spacecraft adopts some maneuvers to avoid being intercepted, and the defense is achieved; when the relative distance between the two is less than or equal toAnd judging that the spacecraft is intercepted by the barrier.

As shown in fig. 6, whenWhen, the magnitude of the potential function will become infinite,the two-dimensional potential field of (2) is shown in figure 7. In addition, if the k-th obstacle is in the exclusion zone of the i-th spacecraft, the definition is madeIs the set of repulsion zones for the kth obstacle in the ith spacecraft.

And 5, designing a formation of the multi-spacecraft formation and maintaining a guidance law according to the first task target, the first potential function and the second potential function.

Equivalent distributed guidance law for formation and maintenance of multi-spacecraft formation

Wherein the content of the first and second substances,to keep the terms for collision avoidance and topological connectivity,in order to avoid the barrier item, the barrier layer is provided with a plurality of barriers,for formation of formation and holding entries, - (v)_i-v_d) For formation of the travel speed term, δ_ikIs an adaptive matrix for ensuring the stability of a multi-spacecraft formation system, and the expression is

Wherein the current velocity of the jth spacecraft is v_j，γ_iIs a normal number which is a positive integer,is composed ofThe pseudo-inverse of (a) is,

the formation and maintenance guidance law of the multi-spacecraft formation can meet the requirements of relative position consistency, collision avoidance between the spacecrafts, obstacle avoidance and communication topology connectivity maintenance and formation traveling speed consistency under the premise of a first theorem.

The first theorem is defined as assuming that the initial relative distance and relative velocity errors are bounded, namely:

wherein delta_v1And delta_v2Is a bounded normal number. p is a radical of_i(0) Is the initial position of the ith spacecraft in the LVLH coordinate system, p_j(0) Initial position of jth spacecraft in LVLH coordinate system, o_k(0) Is the initial position of the k-th obstacleSetting the initial speed of the ith spacecraft to be v_i(0) The initial velocity of the jth spacecraft is v_j(0)，Is the initial value of the speed error of the ith spacecraft,

the multi-spacecraft formation control target can be realized by constructing and maintaining the distributed guidance law by using the multi-spacecraft formation, namely:

1) relative position consistency:

for theAnd

meaning that the desired relative positions of the spacecraft in the multi-spacecraft team are achieved, i.e. the construction of the desired formation is achieved.

2) Collision among the spacecrafts is avoided, obstacle avoidance and communication topology connectivity are kept:

for theAnd

meaning that during the formation process, the ith spacecraft will not collide with other spacecraft in the formation and can also prevent interception by enemy obstacles. At the same time, connectivity of the communication topology is maintained.

3) Formation travel speed consistency:

for the

Meaning that the relative velocity error of two spacecraft of the multi-spacecraft team will become zero, and the flight velocity of the multi-spacecraft team will converge to the desired travel velocity v_d。

And 6, designing a multi-spacecraft trajectory tracking guidance law according to the second task target, the first potential function and the second potential function.

Spacecraft trajectory tracking guidance lawWherein the content of the first and second substances,to maintain items of collision avoidance and communication topology connectivity,in order to avoid the barrier item, the barrier layer is provided with a plurality of barriers,in order to construct and maintain the entries for the formation,for ballistic tracking term, v_tAndrepresenting the velocity and acceleration of the reference trajectory. Variable delta_ikFor ensuring the stability of the formation of the multi-spacecraft system, the adaptive matrix is designed

Wherein gamma is_iIs a normal number, and is,is composed ofThe pseudo-inverse of (1).

The spacecraft trajectory tracking guidance law of the invention can meet the relative position consistency, avoid collision among the spacecrafts, avoid obstacles, maintain communication topology connectivity and relative speed consistency on the premise of the second theorem

Given a multi-spacecraft space flight dynamics model, and a designed equivalent formation control law, the second theorem is defined as bounded initial relative position and velocity errors, namely:

wherein delta_v1And delta_v2Is a bounded normal number.

Then, the control law is utilized to realize the control targets of the multi-spacecraft formation, wherein the control targets of the multi-spacecraft formation comprise relative position consistency, collision avoidance between the spacecrafts, obstacle avoidance, communication topology connectivity maintenance and relative speed consistency

Relative position consistency:

for theAnd

means that the spacecraft in the multi-spacecraft team reach the desired position, i.e. the formation completes the desired formation and the tracking of the reference trajectory is achieved.

Collision among the spacecrafts is avoided, obstacles are avoided, and communication topology connectivity is maintained:

for theAnd

meaning that during the formation process, the ith spacecraft will not collide with other spacecraft in the formation and can also prevent interception by enemy obstacles. At the same time, connectivity of the communication topology is maintained.

Relative velocity consistency:

for the

Meaning that the relative speed of the spacecraft in the multi-spacecraft team is zero, and the formation traveling speed is consistent with the reference ballistic speed.

In conclusion, the multi-spacecraft distributed collaborative formation control method provided by the invention provides a multi-spacecraft formation tracking control scheme with collision prevention, obstacle avoidance and connectivity maintenance, and the formation flight safety is obviously improved. The invention designs a series of new artificial potential functions to meet the requirement of maintaining the connectivity of adjacent spacecrafts and simultaneously avoid the mutual collision among the spacecrafts and the formation flight safety requirement of avoiding obstacles and the like. By combining a consistency concept, a distributed control law for constructing and maintaining multi-spacecraft formation is designed, the connectivity of an interactive topology is maintained, and then the proposed formation control law is expanded into ballistic tracking and meets the requirement of safety.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.