Integrated Control Method for Multi-Spacecraft Formation System Based on Predictive Behavior Control

Abstract

An integrated control method for a multi-spacecraft formation system based on predictive behavior control, comprising the following steps: Step S1: Define the global tasks to be executed by the multi-spacecraft formation: formation keeping, movement; local tasks: obstacle avoidance, and then establish a composite task through the way of behavior control projection in the null space; Step S2: Design a trajectory tracker based on decentralized model predictive control to track the reference trajectory; Step S3: Feed the predicted trajectory back to the planning layer for predicting the future task priorities, and extend the single-step planning in the traditional null space to multi-step prediction. Applying this technical solution can obtain a trajectory tracking control problem without task constraints, greatly reducing the online calculation cost. In addition, the predicted information on the future state of the spacecraft is considered in the process of determining the task priorities, making its switching effect more ideal compared with the traditional logic switching method.

Description

Technical Field

[0001] The present invention relates to the field of aerospace engineering technology, and particularly to an integrated control method for a multi-spacecraft formation system based on predictive behavior control. Background Art

[0002] Since multi-spacecraft formation has advantages such as low communication cost, strong robustness, and high efficiency compared with single-spacecraft systems, it has received extensive attention in military and civil fields. As a multi-agent system, multi-spacecraft formation usually needs to complete multiple tasks, including moving along a preset trajectory, avoiding static and dynamic obstacles, maintaining a rigid formation, etc. However, the limited relative distance between spacecraft, the strong nonlinearity of dynamics, and the requirement of formation consistency all pose significant technical challenges to the control of spacecraft.

[0003] In the past few decades, many formation control architectures have been widely studied, including leader-follower formation, virtual leader-follower formation, and behavior-based control methods. Each of the above methods has its own advantages and disadvantages. Specifically, leader-follower gives clear feedback on the formation, but has poor anti-interference ability; while the virtual structure method lacks robustness and is open-loop; the behavior control method is simple to implement in the task design process, but the mathematical analysis is complex. Another key issue in formation control is obstacle avoidance. Obstacle avoidance techniques mainly include artificial potential field (APF) method, behavior-based control method, and optimization-based method. The artificial potential field method designs an attractive potential function and a repulsive potential function to avoid obstacles, but it is well known that it is easy to fall into local minima. The behavior-based control method, especially the null space-based behavior control (NSBC), is another method to achieve obstacle avoidance by solving task conflicts through null space projection. In addition, the optimization-based method regards obstacle avoidance as a non-linear and non-convex constraint, and takes obstacle avoidance and collision avoidance as constraints of the model predictive control problem, and solves them in the process of solving the optimization problem. However, with the increase in the number of spacecraft and obstacles, the underlying optimization algorithm has higher computational complexity and is difficult to solve in real time.

[0004] To overcome the limitations of the control technologies of each spacecraft, some scholars have proposed a two-layer control architecture to decompose complex control objectives: trajectory planning in the upper layer and reference tracking in the lower layer. For example, in the upper layer, a method based on artificial potential field is used to plan an obstacle-free path, while in the lower layer, distributed continuous progressive tracking control is used to track the path. However, this cannot solve the problem that the artificial potential field method is prone to falling into local minimum points. Some scholars have used the NSBC method to solve the collision avoidance problem and combined it with a sliding controller to achieve the robust control of the formation. However, there are problems of multi-constraint changes, lack of optimality, and control law jitter in this work. Recently, some scholars have also used NSBC to generate speed references for spacecraft formation and obstacle avoidance, but the reference trajectory generated in the upper layer does not involve future prediction information, which may reduce the performance or even violate the obstacle avoidance constraints. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a control integration method for a multi-spacecraft formation system based on predictive behavior control, which feeds the prediction information of the lower-layer controller back to the upper-layer planning layer, enabling the planning layer to optimize the future trajectory according to the future prediction information, so that the system overcomes the problem of selecting the timing of switching the task priority of null-space behavior control, thereby significantly improving the safety of the spacecraft while achieving the expected control objectives.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions: A control integration method for a multi-spacecraft formation system based on predictive behavior control, comprising the following steps:

[0007] Step S1: Define the global tasks to be executed by the multi-spacecraft formation: formation maintenance, movement; local tasks: obstacle avoidance, and then establish a composite task through the projection of null-space behavior control;

[0008] Step S2: Design a trajectory tracker based on decentralized model predictive control to track the reference trajectory;

[0009] Step S3: Feed the predicted trajectory back to the planning layer for the prediction of future task priorities, and extend the single-step planning of the traditional null-space to multi-step prediction.

[0010] In a preferred embodiment, the step S1 includes:

[0011] Step S11: Basic task design; The basic task design includes obstacle avoidance task design, rigid formation task design, and center-of-gravity movement task design;

[0012] Step S12: Design of the composite task.

[0013] In a preferred embodiment, the obstacle avoidance task is designed as follows: In the obstacle avoidance task, the spacecraft must avoid obstacles detected by sensors on a preset trajectory. By defining a virtual sphere as the range for avoiding obstacles:

[0014]

[0015] where p i = [p i,x p i,y p i,z T is the position of the i-th spacecraft, p i,o is the position of the obstacle, and σ i,od = d i is the safe distance between the spacecraft and the obstacle. Then the task function corresponding to the obstacle avoidance task speed is defined as:

[0016] σ i,o = (max{||p i - p i,o ||, d i} - ||v i - v i,o ||), (2)

[0017] where v_{i,o} represents the relative velocity between the i-th spacecraft and the obstacle;

[0018] J i,o = (p i - p i,o ) / ||p i - p i,o || is the Jacobian matrix in the obstacle avoidance task, i.e., the unit vector pointing in the direction of the obstacle. Then the desired velocity of the obstacle avoidance task is:

[0019]

[0020] where λ i,o is a positive definite matrix of gain. Additionally When indicates that the obstacle avoidance task is active, indicates that the obstacle avoidance task is inactive.

[0021] In a preferred embodiment, the rigid formation task is designed as follows:

[0022] The rigid formation task requires the spacecraft to move to a predefined position while maintaining a rigid relative position with respect to the formation center of gravity. The rigid formation task function is defined as:

[0023] σ r = [(p1 - p​g ) T ,...,(p n -p g ) T T , (4)

[0024] wherein, is the center of gravity of the spacecraft formation; the error of the mission function is defined as where σ r,d is the expected position of the spacecraft relative to the center of gravity of the spacecraft; the Jacobian matrix of the rigid formation mission is written as:

[0025] wherein,

[0026]

[0027] In the case of a fixed expected formation, i.e., then the output of the formation mission function is

[0028] In a preferred embodiment, the center of gravity movement mission design is specifically:

[0029] By designing the center of gravity movement mission, the spacecraft formation follows the movement of the center of gravity; the definition of the center of gravity movement mission function is:

[0030]

[0031] The time derivative of the center of gravity movement mission function is:

[0032]

[0033] wherein, the Jacobian matrix of the center of gravity movement mission is The 3-dimensional identity matrix is represented by I3; the velocity of the center of gravity movement mission is expressed as

[0034] In the formula, σ g,d is the expected value of the center of gravity movement mission function, i.e., the expected trajectory of the centers of all spacecraft.

[0035] In a preferred embodiment, step S12 is specifically:

[0036] The composite mission is the fusion of multiple basic missions through null space projection, and is defined as is the output of the m-th mission, wherein d m is the dimension of the m-th mission space, h is the number of missions; a priority sorting function is defined: s(·): ​It maps the task function space to a priority space; the following task hierarchy rules are defined:

[0037] The lowest-priority task d m has a dimension greater than so that the dimension n of the system is greater than the combined total dimension of all tasks;

[0038] Define a task priority function

[0039] w = s(T) (7)

[0041] where T = [1,..., h] is the ascending index of all tasks, and w is the task index vector with priority sorting from highest to lowest; for example, w = s([1, 2, 3]) = [2, 3, 1] means that among the three tasks, the second task has the highest priority, the third task has the second priority, and the first task has the lowest priority;

[0042] Finally, fuse the speeds of all tasks and project the low-priority tasks onto the null space of the high-priority tasks to eliminate task conflicts:

[0043]

[0044] where w(j) is the j-th element of w, and v d,w(j) (j = 1, 2,..., h) is the speed of the task with priority j.

[0045] In a preferred embodiment, step S2 is specifically:

[0046] Design a model predictive control tracking controller at the underlying layer; define the state space of the relative motion between the i-th spacecraft and the leader spacecraft as: x := [v i,x v i,y v i,z T , and take the thrusts of the spacecraft in the radial, in-orbit, and cross-track directions as control inputs, denoted as: u := [u i,x u i,y u i,z T , and write the non-linear model of the relative motion of the spacecraft as:

[0047] where:

[0048]

[0049] In the formula, m i is the mass of the i-th follower spacecraft, ​​is the rate of the latitude angle of the leader spacecraft, θ represents the latitude angle of the leader spacecraft; e c is the orbital eccentricity of the orbit, is the scalar radius of the leader spacecraft from the center of the Earth, a c is the semi-major axis of the leader spacecraft; μ is the gravitational constant, represents the distance from the center of the Earth to the i-th follower spacecraft, F id = [F id,x , F id,y , F id,z T are the disturbing forces of the i-th spacecraft respectively;

[0050] Design a decentralized MPC, where each spacecraft only optimizes its own control problem online; let the prediction horizon of the controller be N discrete sampling instants, and the input and state of the system from time k to k + N can be expressed according to the model as:

[0051] u(N - 1|k) = [u(k),..., u(k + N - 1)] and x(N|k + 1) = [x(k + 1),..., x(k + N)]; the design of the system cost function is:

[0052]

[0053] where, the weighted norm ‖·‖ W can be defined as The three weight matrices W1, W2, W3 are positive definite matrices, is the system state error;

[0054] Establish the nonlinear programming NLP problem of the system as:

[0055]

[0056] where, F(x m (k), u(k)) represents the discrete dynamic equation, represents the system state of the spacecraft at the k-th sampling instant; the sets U and X represent the saturation constraints of the system control and state respectively; by solving the NLP, an optimal control sequence u * (N - 1|k) = [u * (k),..., u * (k + N - 1)] is obtained; take the first control quantity element u * (k) and feedback it to the spacecraft for control to complete a typical sampling control operation of the MPC;

[0057] Adopt the optimal control sequence u * ​(N-1|k) Generate the predicted position trajectory: p(N+1|k+1) = [p(k+1), p(k+2),..., p(k+N), p(k+N)]; then at the k+1 sampling moment, the predicted task priority sequence will be obtained through the predicted trajectory; taking the three tasks designed in the previous section, namely the obstacle avoidance task, rigid formation, and center of gravity movement task, as examples, the task priority is determined by the following rules. For j = 1,..., N+1:

[0058]

[0059] Equation (11) shows that when the distance between the spacecraft position and the obstacle is less than the safety distance, the priority of the obstacle avoidance task is the highest, followed by the rigid formation, and the priority of the center of gravity movement is the lowest; when the distance between the system position and the obstacle is greater than the safety distance, the priority of the rigid formation is the highest, the center of gravity movement task is the second, and the obstacle avoidance priority is the lowest; through the N-step predicted trajectory of the future, the predicted task priority sequence at the k+1 sampling instant is W = [w1, w2,..., w N , to feedback the time-varying reference trajectory for the upper-layer null space behavior control planning.

[0060] In a preferred embodiment, step S3 is specifically:

[0061] Different from traditional model predictive control, predictive behavior control uses the optimal control sequence u * (N-1|k) to generate the predicted position trajectory p(N+1|k+1) = [p(k+1), p(k+2),..., p(k+N), p(k+N)],

[0062] obtain the predicted task priority sequence at the k+1 moment through the predicted trajectory;

[0063] Define x k as the predicted state trajectory obtained by the model predictive controller at the kth sampling moment; an important step in the predictive behavior control planning layer is to design a task supervisor, and the priority is determined by the task supervisor according to the task requirements and the state of the controlled system; for example, if the position of the controlled system is too close to the obstacle, the obstacle avoidance task is assigned the highest task; predictive null space behavior control interacts with the underlying model predictive controller to obtain the system predicted state information x k at the future N sampling moments, and then determine the task priorities at the N sampling moments;

[0064] Define the N-step task priority sequence as: W = [w 1 , w 2 ,..., w N , where the task priority vector w kIt is calculated from formula (5), and the n-step composite velocity of h tasks is: where the desired velocity at the k-th sampling instant Obtained by calculating from (6), the integrated planning and control predictive behavior control method feeds back the N-step state trajectory predicted by the controller to the planning layer.

[0065] The present invention also provides an integrated control method for a multi-spacecraft formation system based on predictive behavior control, including a processor, a memory, and a computer program stored on the memory. When the processor runs the program instructions, it can implement the integrated control method for a multi-spacecraft formation system based on predictive behavior control as described above.

[0066] The present invention also provides a computer-readable storage medium, on which computer program instructions are stored. When the instructions are loaded and executed by a processor, it can implement the integrated control method for a multi-spacecraft formation system based on predictive behavior control as described above.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] (1) The predictive null space behavior control proposed by the present invention extends the traditional one-step null space behavior control planner to a multi-step planner with trajectory prediction ability. The model predictive controller and the predicted trajectory feedback calculated by it help the null space behavior control planner generate a predicted task priority sequence, and finally generate a time-varying velocity reference at the next sampling moment. Such a reference can better guide the model predictive controller to obtain better control performance. The predictive behavior control overcomes the problem of improper switching timing of task priorities in the existing behavior control, thus significantly improving the safety of the spacecraft.

[0069] (2) With the help of the multi-task conflict resolution mechanism of null space behavior control, the present invention takes obstacle avoidance, stiffness formation, and spacecraft movement as tasks in the planning layer. The task fusion and resolution in the planning layer enable the model predictive controller in the tracking layer not to consider constraints. Compared with the traditional method of taking each task as a non-linear constraint for solving the optimal problem in the model predictive controller, the online calculation cost is greatly reduced, making online real-time operation possible. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is the integrated architecture diagram of predictive null space behavior planning and control in the background technology of the present invention;

[0071] Figure 2 is the comparison diagram of the method flow of two-layer MPC+NSBC and PNSBC in the background technology of the present invention;

[0072] Figure 3 is the relative trajectory diagram of each spacecraft in the preferred embodiment of the present invention;

[0073] Figure 4 It is a relative distance diagram between the obstacle and each spacecraft in the preferred embodiment of the present invention;

[0074] Figure 5 It is a comparison diagram of the 5th spacecraft in the preferred embodiment of the present invention using the PNSBC and NSBC methods;

[0075] Figure 6 It is a comparison diagram of the calculation time of the 5th spacecraft in the preferred embodiment of the present invention using PNSBC and MPC. Detailed implementation manners

[0076] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0077] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further descriptions of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0078] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary implementation manners according to the present application; as used herein, unless otherwise clearly specified in the context, the singular form is also intended to include the plural form. In addition, it should also be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0079] As Figure 1 shown; this embodiment provides an integrated method for planning and controlling a multi-spacecraft formation system based on predictive behavior control, including the following steps:

[0080] Step 1: Define the global tasks to be performed by the multi-spacecraft formation: formation maintenance, movement, etc., and local tasks: obstacle avoidance, etc., and then establish a composite task through the method of behavior control projection in the null space.

[0081] Step S11: Basic task design:

[0082] A. Obstacle avoidance task design:

[0083] In the obstacle avoidance task, the spacecraft must avoid the obstacles detected by the sensor on the preset trajectory by defining a virtual sphere as the range for avoiding obstacles:

[0084]

[0085] Among them, p i =[p i,x p i,y pi,z T is the position of the i-th spacecraft, p i,o is the position of the obstacle, σ i,od = d i is the safety distance between the spacecraft and the obstacle. Then the task function corresponding to the obstacle avoidance mission velocity can be defined as:

[0086] σ i,o = (max{||p i - p i,o ||, d i}- ||v i - v i,o ||), (2)

[0087] where v_{i,o} represents the relative velocity between the i-th spacecraft and the obstacle.

[0088] J i,o = (p i - p i,o ) / ||p i - p i,o || is the Jacobian matrix in the obstacle avoidance mission, that is, the unit vector pointing in the direction of the obstacle. Then the desired velocity of the obstacle avoidance mission is:

[0089]

[0090] where λ i,o is a positive definite matrix of gain. Additionally When indicates that the obstacle avoidance mission is active, indicates that the obstacle avoidance mission is inactive.

[0091] B. Rigid formation mission design:

[0092] The rigid formation mission requires the spacecraft to move to a predefined position while maintaining a rigid relative position with respect to the formation center of gravity. The rigid formation mission function is defined as:

[0093] σ r = [(p1 - p g ) T ,...,(p n - p g ) T T , (4)

[0094] where is the center of gravity of the spacecraft formation. The error of the mission function can be defined as where σ r,d is the desired position of the spacecraft relative to the center of gravity of the spacecraft. The Jacobian matrix of the rigid formation mission​​ It can be written as:

[0095] Among them,

[0096]

[0097] In the case of a fixed desired formation (i.e., ), then the output of the formation mission function is

[0098] C. Center of Gravity Movement Mission Design:

[0099] Through the design of the center of gravity movement mission, the spacecraft formation follows the movement of the center of gravity. The definition of the center of gravity movement mission function is:

[0100]

[0101] The time derivative of the center of gravity movement mission function is:

[0102]

[0103] Among them, the Jacobian matrix of the center of gravity movement mission is The 3D identity matrix is denoted as I3. The velocity of the center of gravity movement mission is expressed as

[0104] In the formula, σ g,d is the expected value of the center of gravity movement mission function, that is, the expected trajectory of the center of all spacecraft.

[0105] Step S12: Design of the Composite Mission:

[0106] The composite mission is the fusion of multiple basic missions through null space projection. Define as the output of the m-th mission, where d m is the dimension of the m-th mission space, and h is the number of missions. Define a priority sorting function: s(·): It maps the mission function space to a priority space. Define the following mission hierarchy rules:

[0107] The dimension of the lowest priority mission d m needs to be greater than so that the dimension n of the system is greater than the total combined dimension of all missions;

[0108] Define a mission priority function

[0109] w = s(T) (7)

[0111] , where \(T = [1,\ldots,h]\) is the ascending index of all tasks, and \(w\) is the task index vector with the priority sorted from the highest to the lowest. For example, \(w = s([1,2,3])=[2,3,1]\) means that among the three tasks, the second task has the highest priority, the third task has the second highest priority, and the first task has the lowest priority.

[0112] Finally, fuse the speeds of all tasks and project the low-priority tasks onto the null space of the high-priority tasks to eliminate task conflicts:

[0113]

[0114] where \(w(j)\) is the \(j\)-th element of \(w\), and \(v\) d,w(j) \((j = 1,2,\ldots,h)\) is the speed of the task with priority \(j\).

[0115] Step 2: Design a trajectory tracker based on decentralized model predictive control to track the reference trajectory.

[0116] At the lower layer, a model predictive control tracking controller is designed. The state space of the relative motion between the \(i\)-th spacecraft and the leader spacecraft is defined as: \(x:=[v\) i,x \(v\) i,y \(v\) i,z \) T , and the thrusts of the spacecraft in the radial, in-orbit, and cross-orbit directions are used as control inputs, denoted as: \(u:=[u\) i,x \(u\) i,y \(u\) i,z \) T , and the nonlinear model of the relative motion of the spacecraft is written as: where:

[0117]

[0118] In the formula, \(m\) i is the mass of the \(i\)-th follower spacecraft, is the rate of the latitude angle of the leader spacecraft, \(\theta\) represents the latitude angle of the leader spacecraft. \(e\) c is the orbital eccentricity of the orbit, is the scalar radius of the leader spacecraft from the center of the Earth, \(a\) c is the semi-major axis of the leader spacecraft. \(\mu\) is the gravitational constant, represents the distance from the center of the Earth to the \(i\)-th follower spacecraft, \(F\) id \(=[F\) id,x , \(F\) id,y , \(F\) id,z \) T are the disturbing forces of the \(i\)-th spacecraft respectively.

[0119] To reduce the burden of online computation, a decentralized MPC is designed, where each spacecraft only optimizes its own control problem online. Let the prediction horizon of the controller be N discrete sampling instants. The system inputs and states from time k to k + N can be expressed according to the model as: u(N - 1|k) = [u(k),..., u(k + N - 1)] and x(N|k + 1) = [x(k + 1),..., x(k + N)]. The system cost function is designed as:

[0120]

[0121] where the weighted norm ‖·‖ W can be defined as The three weight matrices W1, W2, W3 are positive definite matrices, is the system state error.

[0122] The nonlinear programming (NLP) problem of the system is established as:

[0123]

[0124] where F(x m (k), u(k)) represents the discrete dynamic equation, represents the system state of the spacecraft at the k-th sampling instant. The sets U and X represent the saturation constraints of the system control and state respectively. By solving the NLP, an optimal control sequence u * (N - 1|k) = [u * (k),..., u * (k + N - 1)] with N elements is obtained. Taking the first control quantity element u * (k) and feeding it back to the spacecraft for control completes a typical sampling control operation of the MPC.

[0125] Different from the traditional MPC, the optimal control sequence u * (N - 1|k) is used to generate the predicted position trajectory: p(N + 1|k + 1) = [p(k + 1), p(k + 2),..., p(k + N), p(k + N)]. Then at the (k + 1)-th sampling instant, the predicted task priority sequence is obtained through the predicted trajectory. Taking the three task avoidance tasks, rigid formation, and center-of-gravity movement tasks designed in the previous section as examples, the task priority is determined by the following rules for j = 1,..., N + 1:

[0126]

[0127] Equation (11) shows that when the distance between the spacecraft position and the obstacle is less than the safety distance, the priority of the obstacle avoidance task is the highest, followed by the rigid formation, and the priority of the centroid motion is the lowest. When the distance between the system position and the obstacle is greater than the safety distance, the priority of the rigid formation is the highest, the centroid motion task is the second, and the obstacle avoidance priority is the lowest. By predicting the trajectory of the next N steps, the predicted task priority sequence at the (k + 1)-th sampling instant can be obtained as W = [w1, w2,..., w N , to feedback the time-varying reference trajectory for the upper-layer null space behavior control planning.

[0128] Step 3: Feed the predicted trajectory back to the planning layer for predicting the future task priorities, and extend the single-step planning of the traditional null space to multi-step prediction.

[0129] Different from the traditional model predictive control, the predictive behavior control uses the optimal control sequence u * (N - 1|k) to generate the predicted position trajectory p(N + 1|k + 1) = [p(k + 1), p(k + 2),..., p(k + N), p(k + N)],

[0130] and obtains the predicted task priority sequence at the (k + 1)-th moment through the predicted trajectory.

[0131] Define x k as the predicted state trajectory obtained by the model predictive controller at the k-th sampling moment. An important step in the predictive behavior control planning layer is to design a task supervisor, and the priority is determined by the task supervisor according to the task requirements and the state of the controlled system. For example, if the position of the controlled system is too close to the obstacle, the obstacle avoidance task is assigned the highest priority. The traditional null space behavior control is a step-by-step planner because it can only use the current system state information to determine the priority of the task at the current moment. Instead, the proposed predictive null space behavior control interacts with the underlying model predictive controller to obtain the system predicted state information x k at the next N sampling moments, and then determines the task priorities at the N sampling moments.

[0132] Define the task priority sequence of N steps as: W = [w 1 , w 2 ,..., w N , where the task priority vector w k at the k-th sampling moment is calculated from Equation (5), and the n-step composite velocity of h tasks is: where for the desired velocity at the k-th sampling instant can be obtained from (6). The integrated planning and control predictive behavior control method feeds the N-step state trajectory predicted by the controller back to the planning layer, as Figure 2 shown.

[0133] Step 4: Simulation Comparison and Analysis

[0134] In the given simulation case, the predictive behavior control method and the behavior control are compared. In the null space behavior control planner, three task priorities are designed from high to low as follows: collision avoidance task, rigid formation task, and center-of-gravity motion task. In the collision avoidance task, the obstacle avoidance distance is set to d = 15 m, and the obstacle avoidance speed gain is λ k,o = 1. The rigid formation gain matrix is set to Λ r = 0.8I, and the maximum control thrust of each spacecraft is set to u ≤ 5. The initial position of each follower spacecraft relative to the initial position of the virtual leader spacecraft is P init,k = [x init,k , y init,k , z init,k . T And P init = [P init,1 ,..., P init,5 . Suppose there are two obstacles around the spacecraft, namely p o,1 = [60, 50, 17] and p o,2 = [118, 77, 45]. The initial positions and velocities of the follower spacecraft relative to the virtual leader spacecraft and the target position σ g,d after formation reconstruction are shown in Table 1. The spacecraft formation trajectory of the proposed integrated planning and control method for multi-spacecraft formation system based on predictive behavior control is as Figure 3 shown, the distances between each spacecraft in the spacecraft formation and the obstacle are as Figure 4 shown, and the comparison between the proposed predictive behavior control method and the traditional behavior control method for the 5th spacecraft is as Figure 5 shown, Figure 5 (a) is the trajectory comparison of the two methods, Figure 5 (b) is the comparison of the control quantities output by the two methods. It can be seen that the control quantity of the traditional behavior control method has relatively severe chattering, and the control quantity reaches the saturation state of the actuator in many places, Figure 5 (c) is the distance diagram between the 5th spacecraft and the obstacle of the two methods. It can be seen that the traditional behavior control method exceeds the safety distance, forming a safety hazard, while the predictive behavior control does not exceed the safety distance due to the information of future prediction. Figure 5 (d) is the comparison diagram of the switching moments of the task priorities of the two methods. The comparison of the computational amounts between the proposed double-layer formation method and the method of taking obstacle avoidance as a model predictive control constraint is as Figure 6 shown. The comparison of five spacecraft in the simulation case using PNSBC and NSBC in three dimensions of total mileage (TM), fuel consumption (FC), and safety distance violation (SVT) is shown in Table 2.

[0135]

[0136] Table 1

[0137]

[0138] Table 2

[0139] Table 1 shows the relative positions of the initial positions, velocities and targets of the five spacecraft in the embodiments of the present invention;

[0140] Table 2 is a performance comparison table of the formation of five spacecraft in the embodiments of the present invention using PNSNC and NSBC+MPC.

[0141] The above are only the preferred embodiments of the present invention. The present invention is not limited to the above embodiments. Any partial modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. An integrated control method for a multi-spacecraft formation system based on predictive behavior control, characterized in that, It includes the following steps: Step S1: Define the global tasks to be executed by the multi-spacecraft formation: formation keeping, movement; local tasks: obstacle avoidance, and then establish a composite task through the way of behavior control projection in the null space; Step S2: Design a trajectory tracker based on decentralized model predictive control to track the reference trajectory; Step S3: Feed the predicted trajectory back to the planning layer for predicting the future task priorities, and extend the single-step planning in the traditional null space to multi-step prediction; Specifically, step S2 is as follows: Design a model predictive control tracking controller at the underlying level; define the state space of the relative motion between the $i$-th spacecraft and the leader spacecraft as: $x := [v i,x v i,y v i,z T , take the thrusts of the spacecraft in the radial, in-track, and cross-track directions as control inputs, denoted as: $u := [u i,x u i,y u i,z T , and write the nonlinear model of the relative motion of the spacecraft as: ​​ Wherein: In the formula, m i is the mass of the i-th follower spacecraft, is the rate of the latitude angle of the leader spacecraft, θ represents the latitude angle of the leader spacecraft; e c is the orbital eccentricity of the orbit, is the scalar radius of the leader spacecraft from the center of the Earth, a c is the semi-major axis of the leader spacecraft; μ is the gravitational constant, represents the distance from the center of the Earth to the i-th follower spacecraft, F id = [F id,x , F id,y , F id,z T are the disturbing forces of the i-th spacecraft respectively;​ Design a decentralized MPC, where each spacecraft only optimizes its own control problem online; let the prediction horizon of the controller be N discrete sampling instants, and the input and state of the system from time k to k + N can be respectively expressed according to the model as: u(N - 1|k) = [u(k),..., u(k + N - 1)] and x(N|k + 1) = [x(k + 1),..., x(k + N)]; the design of the system cost function is: where the weighted norm ‖·‖ W can be defined as The three weight matrices W1, W2, and W3 are positive definite matrices, is the system state error; Establish the nonlinear programming NLP problem of the system as: x(k + j + 1) = F(x(k + j), u(k + j)), j = 1,..., N - 1, Among them, F(x m (k), u(k)) represents the discrete dynamic equation, represents the system state of the spacecraft at the k-th sampling moment; the sets and represent the saturation constraints of the system control and state respectively; by solving the NLP, the optimal control sequence u with N elements is obtained * (N - 1|k) = [u * (k),..., u * (k + N - 1)]; take the first control quantity element u * (k) and feedback it to the spacecraft for control to complete a typical sampling control operation of the MPC; Adopt the optimal control sequence u * (N-1|k) generates the predicted position trajectory: p(N+1|k+1) = [p(k+1), p(k+2),..., p(k+N), p(k+N)]; then at the (k+1)-th sampling time, the predicted task priority sequence will be obtained through the predicted trajectory; taking the three tasks designed in the previous section, namely the obstacle avoidance task, the rigid formation, and the centroid movement task, as examples, the task priority is determined by the following rules. For j = 1,..., N+1: Formula (11) shows that when the distance between the spacecraft position and the obstacle is less than the safe distance, the priority of the obstacle avoidance task is the highest, followed by the rigid formation, and the priority of the center-of-gravity movement is the lowest; when the distance between the system position and the obstacle is greater than the safe distance, the priority of the rigid formation is the highest, the center-of-gravity movement task is the second, and the obstacle avoidance priority is the lowest; through the prediction trajectory of the next N steps, the predicted task priority sequence at the (k + 1)-th sampling instant is W = [w1, w2,..., w N , to feedback the time-varying reference trajectory for the upper-layer null space behavior control planning; Step S3 is specifically as follows: Different from traditional model predictive control, predictive behavior control uses the optimal control sequence u * (N - 1|k) to generate the predicted position trajectory p(N + 1|k + 1) = [p(k + 1), p(k + 2),..., p(k + N), p(k + N)], Obtain the predicted task priority sequence at the (k + 1)-th moment through the predicted trajectory; Define x k as the predicted state trajectory obtained by the model predictive controller at the k-th sampling instant; an important step in the predictive behavior control planning layer is to design a task supervisor, and the priority is determined by the task supervisor according to the task requirements and the state of the controlled system; if the position of the controlled system is too close to the obstacle, the obstacle avoidance task is assigned the highest task; the predictive null space behavior control interacts with the underlying model predictive controller to obtain the system predicted state information x k for the next N sampling instants, and then determine the task priorities for the N sampling instants; Define the task priority sequence of N steps as: W = [w 1 , w 2 ,..., w N , where the task priority vector w k at the k-th sampling moment is calculated from formula (5), and the n-step composite speed of h tasks is: where the expected speed at the k-th sampling instant is obtained from (6), and the integrated planning and control prediction behavior control method feeds back the N-step state trajectory predicted by the controller to the planning layer.

2. The integrated control method for multi-spacecraft formation system based on predictive behavior control according to claim 1, characterized in that The said step S1 includes: Step S11: Basic task design; the basic task design includes obstacle avoidance task design, rigid formation task design, and center-of-mass movement task design; Step S12: Design of the composite task.

3. The integrated control method for multi-spacecraft formation system based on predictive behavior control according to claim 2, characterized in that Specifically, the obstacle avoidance task design is: in the obstacle avoidance task, the spacecraft must avoid the obstacles detected by the sensor on the preset trajectory, and define a virtual sphere as the range for avoiding obstacles: where p i = [p i,x p i,y p i,z T is the position of the i-th spacecraft, and p i,o is the position of the obstacle, and σ i,od = d i is the safe distance between the spacecraft and the obstacle; then the task function corresponding to the obstacle avoidance mission speed is defined as:​ σ i,o = (max{||p i - p i,o ||, d i}- ||v i - v i,o ||), (2) where, v_{i,o} represents the relative velocity between the i-th spacecraft and the obstacle; J i,o =(p i -p i,o ) / ||p i -p i,o || is the Jacobian matrix in the obstacle avoidance task, that is, the unit vector pointing in the direction of the obstacle. Then the expected velocity of the obstacle avoidance task is: where λ i,o is a positive definite matrix of gain, and in addition when indicates that the obstacle avoidance task is active, indicates that the obstacle avoidance task is inactive.

4. The integrated control method for multi-spacecraft formation system based on predictive behavior control according to claim 2, characterized in that, Specifically, the rigid formation task design is: The rigid formation task requires the spacecraft to move to a predefined position while maintaining a rigid relative position with the center of mass of the formation; define the rigid formation task function as: σ r = [(p1 - p g ) T ,...,(p n - p g ) T T , (4)​ Among them, is the center of gravity of the spacecraft formation; the error of the mission function is defined as where σ r,d is the expected position of the spacecraft relative to the center of gravity of the spacecraft; the Jacobian matrix of the rigid formation mission is written as: Among them, In the case of a fixed desired formation, namely then the output of the formation mission function is 5. The integrated control method for multi-spacecraft formation system based on predictive behavior control according to claim 2, wherein Specifically, the center-of-mass movement task design is: Through the design of the center-of-mass movement task, the spacecraft formation follows the movement of the center of mass; define the center-of-mass movement task function as: The time derivative of the center-of-mass movement task function is: Among them, the Jacobian matrix of the center-of-gravity movement task is , where I3 represents the 3D identity matrix; the velocity of the center-of-gravity movement task is expressed as where σ g,d is the expected value of the centroid motion task function, i.e., the expected trajectory of the centers of all spacecrafts.

6. The integrated control method for a multi-spacecraft formation system based on predictive behavior control according to claim 2, wherein Specifically, step S12 is as follows: The composite task is defined as the fusion of multiple basic tasks through null space projection is the output of the m-th task, where d m is the dimension of the m-th task space, h is the number of tasks; define a priority sorting function: It maps the task function space to a priority space; define the following task hierarchy rules: Lowest priority task d m The dimension of needs to be greater than so that the dimension n of the system is greater than the combined total dimension of all tasks; Define a task priority function w = s(T) (7) where T = [1,..., h] is the ascending index of all tasks, and w is the task index vector with the priority sorted from the highest to the lowest; w = s([1, 2, 3]) = [2, 3, 1] means that among the three tasks, the second task has the highest priority, the third task has the second priority, and the first task has the lowest priority; Finally, fuse the velocities of all tasks, and project the low-priority tasks onto the null space of the high-priority tasks to eliminate task conflicts: where w(j) is the j-th element of w, and v d,w(j) (j = 1, 2,..., h) is the task speed with priority j.

7. An integrated control method for a multi-spacecraft formation system based on predictive behavior control, characterized in that, It includes a processor, a memory, and a computer program stored in the memory. When the processor runs the program instructions, it can implement the integrated control method for the multi-spacecraft formation system based on predictive behavior control as described in any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that, It stores computer program instructions, which, when loaded and executed by a processor, can implement the integrated control method of the multi-spacecraft formation system based on predictive behavior control as described in any one of claims 1 to 6.

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