A trajectory planning method and system for high-efficiency active observation of a non-cooperative target with strong security

Abstract

The application is directed to the non-cooperative target observation task with large navigation information error and low update frequency, thereby a strong security efficient non-cooperative target active observation trajectory planning method is provided, and the application relates to the field of spacecraft orbit optimization technology. The state gain reachable set is calculated from the navigation initial error by the matrix differential equation, and the spacecraft structure size compensation is carried out, the boundary of the safety strategy is taken as the path inequality constraint, the optimization model with the path fuel consumption and the path length as the composite performance index, the optimization variable is the observation path state and the corresponding control, and the trajectory planning model is established comprehensively, and then the model prediction control is used to solve the optimization problem, so as to obtain the corresponding path state. The application is suitable for the trajectory planning of the non-cooperative target active observation in the space orbit optimization.

Description

Technical Field

[0001] This invention relates to the field of spacecraft orbit optimization technology, specifically to a trajectory planning method for active observation of non-cooperative targets using state gain reachability sets and fast model predictive control. Background Technology

[0002] In recent years, the rapid development of on-orbit service (OOS) technology has not only made the maintenance and repair of failed or malfunctioning spacecraft possible, but has also significantly increased the sensitivity to non-cooperative targets and their potential threats. These technological achievements fully demonstrate the potential of on-orbit servicing. Therefore, accurately identifying the main functions of non-cooperative spacecraft and the degree of their threat is particularly important.

[0003] Traditional on-orbit identification methods rely on orbital trajectories generated by periodic solutions of the HCW equations. The servicing spacecraft orbits and observes the target's payload and structure, using the target's navigation error ellipsoid as a safety boundary, to calculate its attitude pointing and relative orbital state. However, this method has two major limitations:

[0004] First, the navigation error ellipsoid increases over time due to velocity measurement errors. In non-cooperative observation scenarios with large positioning and velocity measurement errors and low navigation information update frequency, the navigation error ellipsoid often significantly underestimates the range of possible target states, thereby increasing the risk of spacecraft center-of-mass collisions. Furthermore, the navigation error ellipsoid fails to reflect the size and structural characteristics of two spacecraft, further increasing the probability of structural collisions.

[0005] Secondly, because the orbital observation relies on closed trajectories generated by the periodic solutions of the HCW equations, the observation mission cycle is typically at least one target orbital period, much longer than the ground orbit determination period. This approach has poor information concealment, easily revealing the mission target and intent, putting us in a passive position. An effective way to shorten the mission cycle is to actively advance the orbital observation target, which requires solving the corresponding mathematical programming model to obtain the observation trajectory sequence and its corresponding control sequence. Classical methods for solving trajectory planning problems include pseudo-Puer's method, sequential convex optimization, and heuristic algorithms, but these methods all have poor timeliness. Summary of the Invention

[0006] This invention addresses the challenges of non-cooperative target observation tasks with large navigation information errors and low update frequencies, proposing a novel spacecraft observation method: a highly efficient and secure trajectory planning method for active observation of non-cooperative targets.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] This invention proposes a highly efficient and secure trajectory planning method for active observation of non-cooperative targets, the method comprising the following steps:

[0009] Step S1: Based on the navigation information output by the non-cooperative target spacecraft, determine the target navigation estimation state and the target navigation error covariance matrix;

[0010] Step S2: Determine the attainable set of state gains for the non-cooperative target spacecraft based on the target navigation estimated state and the target navigation error covariance matrix;

[0011] Step S3: Use the state gain reachable set of the non-cooperative target spacecraft to perform size compensation on the structure of the non-cooperative target spacecraft and the service spacecraft, and determine the safe observation ellipsoid of the non-cooperative target spacecraft and the service spacecraft;

[0012] Step S4: During the active observation of non-cooperative targets, the servicing spacecraft must avoid entering the safe observation ellipsoid;

[0013] Step S5: Select the body diagonal plane of the non-cooperative target spacecraft as the planning plane for the observation trajectory, and take the four intersection points of the two diagonals in the planning plane and the safe observation ellipsoid as observation nodes. Connect these four observation nodes in sequence to form a reference closed trajectory that satisfies the observation mission.

[0014] Step S6: Select the discretized observation trajectory sequence and its corresponding control sequence as optimization variables from the reference closed trajectory, select the distance-energy hybrid quadratic index as the optimization index, use the discretized inequality as the path constraint, and calculate the corresponding optimized trajectory sequence and corresponding control sequence by using a trajectory planning solver.

[0015] Furthermore, the navigation information output above is represented in the form of a navigation error ellipsoid;

[0016] The navigation error ellipsoid is X0=ε(x0,p -1 X0), where p is the confidence level, the center of the navigation error ellipsoid x0 represents the target navigation estimation state, and the shape of the navigation error ellipsoid X0 represents the target navigation error covariance matrix.

[0017] Furthermore, substituting the target navigation estimated state x0 and the target navigation error covariance matrix X0 into the following differential equation:

[0018]

[0019] By performing the calculation, the reachable set of state gains can be obtained;

[0020] Where A represents the coefficient matrix in the HCW dynamic equation, A ú This represents the transpose of matrix A.

[0021] Furthermore, the attainable set of the aforementioned state gain can be represented as:

[0022]

[0023] Among them, [t0,t f [This refers to the time range of the exercise.]

[0024] Furthermore, the aforementioned safe observation ellipsoid is represented as:

[0025]

[0026] Among them, e At This represents the state transition matrix for a time interval t. represents the transpose of the state transition matrix, and I represents the 6×6 identity matrix.

[0027] Furthermore, the expression for why service spacecraft must avoid entering the safe observation ellipsoid is:

[0028]

[0029] Furthermore, the trajectory planning method is applicable in the following scenarios: the non-cooperative target and the servant spacecraft are located in the same near-circular orbit, and the navigation and guidance system measures that the non-cooperative target is located within the error ellipsoid ε(x0,X0) with a confidence level p = 98%.

[0030] The trajectory planning method for active observation of non-cooperative targets with strong security described in this invention can be entirely implemented using computer software. Therefore, correspondingly, this invention also provides a trajectory planning system for active observation of non-cooperative targets with strong security. The system includes a storage device, which is used to execute the trajectory planning method and steps for active observation of non-cooperative targets with strong security described above.

[0031] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the trajectory planning method for active observation of non-cooperative targets with strong security as described in any one of the above claims.

[0032] The present invention also provides a computer device, which includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes the trajectory planning method for active observation of non-cooperative targets with strong security as described in any one of the above-mentioned methods.

[0033] The beneficial effects of this invention are as follows:

[0034] 1. This invention proposes a highly efficient and secure trajectory planning method for active observation of non-cooperative targets, which enhances the safety of observation missions while significantly shortening the mission cycle. The principle is as follows: The reachable set of state gain is calculated from the initial navigation error using matrix differential equations, and spacecraft structural dimensions are compensated for. The boundary of this safety strategy is used as a path inequality constraint. An optimization model is established with path fuel consumption and path length as composite performance indicators. The optimization variables are the observation path state and its corresponding control. This is comprehensively established as a trajectory planning model. Model predictive control is then used to solve this optimization problem to obtain the corresponding path state.

[0035] Furthermore, based on the state gain reachable set theory, this invention proposes an analytical safety ellipsoid model, which effectively improves the safety of collision avoidance strategies while ensuring real-time performance, and solves the problems of poor timeliness and inability to describe structural dimensions in traditional navigation error ellipsoids.

[0036] Furthermore, compared with traditional passive observation methods, the active observation trajectory designed in this invention achieves comprehensive acquisition of target information by completing a single orbit, solving the problems of low information acquisition efficiency and unclear task intent caused by the long cycle of current passive observation tasks.

[0037] Furthermore, the applicable scenario of this invention is: the non-cooperative target and the service spacecraft are located near the same near-circular orbit, the navigation and guidance system measures that the non-cooperative target is within the error ellipsoid ε(x0,X0) with a confidence level p = 98%, and active observation of the non-cooperative target is achieved in a shorter mission cycle while ensuring safety.

[0038] This invention is applicable to trajectory planning for active observation of non-cooperative targets in aerospace orbit optimization. Attached Figure Description

[0039] Figure 1 This is a flowchart of a highly efficient and secure trajectory planning method for active observation of non-cooperative targets, as described in this invention.

[0040] Figure 2 This is a schematic diagram of the safe collision avoidance strategy based on the navigation error ellipsoid and its reachability set as described in this invention;

[0041] Figure 3 This is a schematic diagram of the active observation trajectory of the non-cooperative target spacecraft described in this invention;

[0042] Figure 4 These are the parameters of the non-cooperative observation simulation scenario described in this invention;

[0043] Figure 5 The present invention describes the safety collision avoidance ellipsoid and path point distribution, wherein Figure (a) shows the path point distribution with initial drift value and Figure (b) shows the path point distribution with initial period value.

[0044] Figure 6 This is a comparison of the computational efficiency of the security strategies described in this invention;

[0045] Figure 7 This is the drift initial value non-cooperative target active observation trajectory described in this invention;

[0046] Figure 8 Actively observe the relative trajectory of non-cooperative targets to determine initial drift conditions;

[0047] Figure 9 The initial value of the period is the active observation trajectory of the non-cooperative target;

[0048] Figure 10 The initial value of the period is used for active observation of the relative trajectory of non-cooperative targets;

[0049] Figure 11 This is a non-cooperative target observation control sequence. Detailed Implementation

[0050] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0051] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention.

[0052] Implementation Method 1, see [link] Figure 1 This implementation method addresses the challenges of non-cooperative target observation missions with significant navigation information errors and low update frequencies. It proposes a novel spacecraft observation method: a highly efficient and secure trajectory planning method for active non-cooperative target observation. This method enhances mission safety while significantly shortening the mission cycle. The principle is as follows: The reachable set of state gain is calculated from the initial navigation error using matrix differential equations, and spacecraft structural dimensions are compensated for. The boundary of this safety strategy is used as a path inequality constraint. An optimization model is constructed with path fuel consumption and path length as composite performance indicators. The optimization variables are the observation path state and its corresponding control. This comprehensive approach forms a trajectory planning model. Model predictive control is then used to solve this optimization problem to obtain the corresponding path state.

[0053] like Figure 1 As shown, the path planning method includes the following steps:

[0054] Step S1: Based on the navigation information output by the non-cooperative target spacecraft, determine the target navigation estimation state and the target navigation error covariance matrix;

[0055] Step S2: Determine the attainable set of state gains for the non-cooperative target spacecraft based on the target navigation estimated state and the target navigation error covariance matrix;

[0056] Step S3: Use the state gain reachable set of the non-cooperative target spacecraft to perform size compensation on the structure of the non-cooperative target spacecraft and the service spacecraft, and determine the safe observation ellipsoid of the non-cooperative target spacecraft and the service spacecraft;

[0057] Step S4: During the active observation of non-cooperative targets, the servicing spacecraft must avoid entering the safe observation ellipsoid;

[0058] Step S5: Select the body diagonal plane of the non-cooperative target spacecraft as the planning plane for the observation trajectory, and take the four intersection points of the two diagonals in the planning plane and the safe observation ellipsoid as observation nodes. Connect these four observation nodes in sequence to form a reference closed trajectory that satisfies the observation mission.

[0059] S6: Select the discretized observation trajectory sequence from the reference closed trajectory [x] (k) ;x (k+1) ;...;x (k+N) ] and its corresponding control sequence [u (k) ;u (k+1) ;...;u (k+N) As the optimization variable, the distance-energy hybrid quadratic index is selected as the optimization index, and the discretized inequality is used as the path constraint condition. The corresponding optimized trajectory sequence and the corresponding control sequence are obtained by using a trajectory planning solver.

[0060] Implementation Method 2: This implementation method provides a detailed explanation of the trajectory planning method for active observation of non-cooperative targets with strong security proposed in Implementation Method 1 above.

[0061] First, the relative orbital dynamics model is described:

[0062] Both the service spacecraft and the non-cooperative target spacecraft operate in circular orbits, and their relative distance is much smaller than the orbital radius due to the limited effective range of the observation payload. To describe their relative motion, this implementation chooses to establish an LVLH coordinate system with a virtual point near both objects as the origin. In this coordinate system, their relative motion can be approximated by linearized HCW equations:

[0063]

[0064] Among them, u x (t),u y (t),u z (t) represents the acceleration components caused by all external forces other than gravity; r represents the average angular velocity of the orbit containing the origin of the reference frame. c Let be the average orbital radius of the orbit containing the origin of the coordinate system, and μ be the Earth's gravitational constant.

[0065] The above linear time-invariant system (1) can be rewritten in the following state-space form:

[0066]

[0067] Where x(t) is the state vector, u(t) is the control vector, u(t) = [u x (t),u y (t),u z (t)] u′ ∈R 3 A represents the coefficient matrix of the dynamic equation, and B represents the control matrix of the dynamic equation.

[0068] In the linear time-invariant system (2), given the initial state x(t0) and the control input u(t), the corresponding analytical solution is:

[0069]

[0070] Wherein, the state transition matrix It is the homogeneous solution matrix of the above dynamic equation (2).

[0071] Let the sampling period be Δt, and adopt the zero-order hold hypothesis: u (k) =u(t),kΔt≤t<(k+1)Δt, the above formula (3) can be discretized as:

[0072] x (k+1) =A d x (k) +B d u (k) , k=1,...,N (4)

[0073] Among them, A d With B d These correspond to the discrete state matrix and control matrix of a continuously thrust spacecraft, respectively:

[0074] A d =e AΔt ,

[0075] This implementation method establishes a relative orbital dynamics model, which can describe the motion laws of all spacecraft and serves as the basis for the operation of this implementation method. At the same time, the state gain reachable set designed subsequently is the result of the motion of the navigation error ellipsoid in the relative orbital dynamics model.

[0076] Then, a safe collision avoidance strategy based on the navigation error ellipsoid and its reachability set is constructed.

[0077] The minimum safe zone for non-cooperative target observation is typically determined by the navigation error sphere generated by the Kalman filter. This static estimation method of the target state range suffers from significantly reduced conservatism as the navigation information update frequency decreases. To overcome the limitations of traditional methods, this implementation investigates the expansion characteristics of the navigation error sphere shape under the influence of celestial dynamics based on matrix differential equations, accurately revealing the time-varying law of the navigation error sphere (the reachable set of state gain). Based on the safety strategy of the reachable set of state gain, even after expanding the spacecraft size, it possesses the advantages of maintaining conservatism over time and effectively avoiding spacecraft structural collisions, thereby significantly improving the overall safety of the observation mission.

[0078] Specifically:

[0079] Navigation and guidance systems rely on navigation information output by the Extended Kalman Filter (EKF), which is presented in the form of a navigation error ellipsoid. The navigation error ellipsoid consists of the following elements: the center x0 representing the estimated state of the Gaussian distribution of the error; the shape described by a symmetric positive definite covariance matrix X0, used to quantify the uncertainty of the estimated state; and the corresponding confidence level p. In other words, the navigation information indicates that the target state x(t0) lies within the navigation error ellipsoid X0 = E(x0, p) with confidence probability p. - 1 X0):

[0080] X0={x(t0)∈R 6 |(x(t0)-x0) ú X0 -1 (x(t0)-x0)≤p} (5)

[0081] Under the influence of the dynamic system, the initial value estimation ellipsoid of the target is X0=E(x0,p -1The position of X0 will shift and expand rapidly over time. When the navigation information is updated at a low frequency, the original navigation error ellipsoid X0 will deviate significantly from the position of the set of possible target states and severely underestimate the size of the set, significantly increasing the risk of collision.

[0082] Therefore, the collision avoidance strategy based on the state gain reachability set in this implementation can effectively ensure that the trajectory of the service spacecraft avoids the center of mass of the target spacecraft, thereby significantly reducing the risk of center-of-mass collision. However, to eliminate the risk of structural collision as much as possible, structural size compensation is also required for the state gain reachability set. Traditional reachability set calculation relies on numerical traversal to solve the boundary, which is computationally inefficient and difficult to adapt to the application requirements of space platforms with limited computing resources. This implementation uses a Kalman filter to represent navigation error information as a shape matrix and a central function. It focuses on studying and analytically solving the time-varying characteristics of the covariance matrix X0 through matrix differential equations, and integrates it with the central function into the state gain reachability set. This method achieves real-time solution of the reachability set, meets the practical application requirements of low-computing-power platforms, and significantly improves its practicality.

[0083] Define the reachable set of state gain as: given the motion time range [t0, t] f The system equations satisfy The final state x(t) of all elements in the initial state set X0 that are in free motion f The set consisting of () is called the state gain reachable set, defined as:

[0084]

[0085] For a non-cooperative target spacecraft, the navigation system estimates its initial state set as X0 = E(x0, p -1 X0), whose shape function X0 is a symmetric positive definite matrix. Since a symmetric positive definite matrix remains a symmetric positive definite matrix after a linear transformation, the shape function X0(t) after the integral summation transformation is also a symmetric positive definite matrix.

[0086] The above properties guarantee that the state gain is reachable set R(t) f The set X0 is still an ellipsoid, and its shape function X0(t) and center function x0(t) satisfy the following differential equations under the influence of gravity:

[0087]

[0088] When the initial conditions are X0(t0) = X0 and x0(t0) = x0, the above differential equation (7) can be solved analytically directly by integration:

[0089]

[0090] Therefore, the specific form of the reachable set of state gains is as follows:

[0091]

[0092] When the sampling period is Δt, and the distance from the step size is k∈Z + At that time, the discrete state gain set is:

[0093]

[0094] in, Therefore, the reachable set of state gains can be simply written as:

[0095]

[0096] The state gain reachability set proposed in this embodiment solves the problem of increasingly distorted target centroid state estimation over time using the navigation error ellipsoid, accurately providing the upper bound of the target state range at any time. However, due to the large physical dimensions of spacecraft, relying solely on the reachability set for collision detection may lead to structural collision risks. Therefore, structural size correction is needed for the reachability set boundary. The size correction coefficient is defined as ρ. P +ρ I +ρ, where ρ P and ρ I Let represent the structural envelopes of the service spacecraft and the target spacecraft, respectively, and ρ be the tolerance distance. By correcting the structural dimensions of the reachability set boundary, potential risk areas are effectively covered, thereby significantly improving the conservatism and accuracy of the collision avoidance strategy. Specifically, as follows... Figure 2 As shown.

[0097] The result of extrapolating an ellipsoid from its boundary is still an ellipsoid. Although this process is conceptually relatively simple, there is currently a lack of mathematical tools capable of analytically representing it. To solve for the extrapolated ellipsoid in real time, this implementation method, while maintaining conservatism, appropriately sacrifices some accuracy to approximate a slightly more conservative analytical solution. Therefore, this implementation introduces an auxiliary function δ. * This function is used to describe any direction vector l∈R 6 The distance from the intersection point with the ellipsoidal shell E(q,Q) to the center of the ellipsoid:

[0098] δ * (l,E(q,Q))=(l,q)+(l,Ql) 1 / 2 (12)

[0099] Where (·,·) denotes the vector dot product. The auxiliary function δ * (l, E(q, Q)) describes the geometric properties of the ellipsoid in the direction l. For example... Figure 2As shown, the distance difference Δδ between the extended ellipsoid and the state gain can be achieved from the outer shell in any direction is... * All are ρ P +ρ I +ρ:

[0100]

[0101] in, These are the center and shape matrices of the outwardly expanding ellipsoid, respectively. The outward expansion of the ellipsoid does not change the position of its center, that is: Therefore, the distance difference Δδ * The difference in shell dimensions between the old and new ellipsoids caused by the shape matrix:

[0102]

[0103] Where, I∈R 6×6 It is an identity matrix. Because... It is necessary to satisfy formula (14) in any direction l. Directly solving this matrix is ​​very complex and inefficient. Since the square root function f(x) = x 1 / 2 Since it is a strictly concave function, we can use the Chinsen inequality. Scaling the above inequality:

[0104]

[0105] Therefore, the shape function of the safe collision avoidance ellipsoid can be approximated by an analytical form that is more conservative and can be calculated in real time.

[0106]

[0107] Analytical approximation solution The tolerance distance ρ is set as the optimization variable, and the accuracy is improved by reducing the approximation error Δd:

[0108]

[0109] After solving for the optimal fault tolerance distance ρ * Subsequently, taking into account the timeliness of navigation information, the size of the spacecraft structure, and the real-time nature of calculations, this implementation method designs the following safe collision avoidance strategy:

[0110]

[0111] Based on the aforementioned safety collision avoidance strategy, during the active observation of non-cooperative targets, the servicing spacecraft must avoid entering the safe observation ellipsoid; represented as:

[0112]

[0113] Finally, spacecraft active observation safe trajectory planning based on fast model predictive control (FMPC);

[0114] Although the above-mentioned safety collision avoidance strategy (17) effectively characterizes all possible states and structural dimensions of non-cooperative targets, clearly defines the trajectory no-go zones in the observation mission, and directly applies them as path constraints to the trajectory planning model, effectively reducing potential collision risks. However, in the observation mission of non-cooperative spacecraft, in addition to considering safety factors such as collisions, it is also necessary to improve mission concealment to avoid the leakage of our own intentions as much as possible. Currently, space situational awareness relies on ground orbit determination information. Once the non-cooperative party calculates the orbital root number of our service spacecraft, it can infer our mission intentions and the observed object, causing us to be in a very passive position. Therefore, the traditional free-flight observation method, which requires at least one orbital cycle, obviously cannot meet the concealment requirements and is not suitable for non-cooperative target observation missions with high concealment requirements. To solve this problem, this implementation method designs an observation trajectory that can obtain all key information of the target in a single orbit and tracks the trajectory by active thrust, significantly shortening the mission cycle. Finally, based on the Fast Model Predictive Control (FMPC) strategy (computational complexity is approximately O(N)), 3 (where N is the total distance step length), which enables rapid calculation of high-complexity trajectory planning, providing an efficient and reliable solution for covert observation of non-cooperative targets.

[0115] Specifically:

[0116] Active observation trajectories for non-cooperative target spacecraft need to satisfy multiple complex constraints, including nonlinear inequality path constraints for dynamic collision avoidance ellipsoids, equality path constraints for reaching specific observation positions, and model constraints that satisfy dynamic model and control amplitude conditions in real time. To achieve accurate identification of non-cooperative targets, the service spacecraft's sensor field of view must completely cover the target, and its focal length must meet the identification accuracy requirements. This means the observation trajectory must stably remain near the target trajectory. Typically, the semi-major axis of the navigation error ellipsoid for ground-based measurements of high-value orbital satellites such as GEO satellites is greater than or equal to 50m, while the structural dimensions of traditional satellite bodies and critical payloads do not exceed 6m in diameter. A simple estimation shows that if the service spacecraft's sensor field of view angle is ≥3.5°, it can completely cover the target satellite body and its critical payloads.

[0117] For traditional CubeSats, a large field-of-view sensor aligned with its body diagonal can cover all three body planes of the target in a single pass. Based on this, this implementation selects the body diagonal plane of a non-cooperative target as the planning plane for the observation trajectory, and designs the four intersection points of the two diagonals within this plane with the collision avoidance ellipsoid as observation nodes. These four observation nodes are sequentially connected to form a reference closed trajectory that satisfies the observation mission. Following the mission trajectory iteratively planned from this initial observation trajectory, the servicing spacecraft can fully acquire the target's critical payloads and platform sensor information during a single orbit. A specific observation diagram is shown below. Figure 3 As shown.

[0118] Let the attitude angle of the non-cooperative target spacecraft relative to the LVLH coordinate system be... (If the rotation order is zyx), then the direction vector of the diagonal of the spacecraft body is:

[0119]

[0120] in, Let be the direction vector of the diagonal of the cube body, and and Located on two opposite diagonals:

[0121]

[0122] The above complete derivation and construction of four key observation nodes are provided. The servicing spacecraft needs to align the sensor optical axis with the diagonal direction of the target body at these four nodes to comprehensively acquire all information about the non-cooperative target body and key payloads. This is achieved by simultaneously solving the safety ellipsoid equation (17) and the two diagonal direction vectors p in the diagonal plane of the target body. i The specific coordinates of these four key observation nodes can be obtained by using quadratic programming at their intersection points.

[0123] according to Figure 4 The scene parameters listed in the image are used to draw the image. Figure 5 The safe collision avoidance ellipsoid and path point distribution, Figure 5 Figures (a) and (b) show the safe collision avoidance ellipsoids calculated with different initial navigation error matrices X0(t0). Differences in the initial values ​​cause changes in the shape and size of the safe ellipsoid, which directly affects the positional distribution of the four key observation nodes, and consequently, the desired path x in the secondary index. p (kΔt) has an impact. Furthermore, the safety collision avoidance ellipsoid, as a trajectory no-go zone, directly affects the coefficient matrix in the inequality path constraints. The value of .

[0124] Therefore, the initial trajectory is designed as a closed curve sequentially connecting the four observation nodes. To track the desired state while minimizing energy consumption, the following optimization objective function is chosen:

[0125]

[0126] Among them, l:R 9 →R is a convex quadratic index function, specifically in the form:

[0127]

[0128] In the index function (21), Q∈R 6×6 , R∈R 3×3 All are symmetric positive definite matrices, x p Let u(t) be the desired trajectory, and u(t) ∈ R. 3 This is the control vector.

[0129] Furthermore, avoiding structural collisions between spacecraft during observation is a constraint that must be considered in path planning. The above fully considers constraints such as information update cycle and spacecraft structural dimensions, constructing a sufficiently conservative safety collision avoidance ellipsoid (17). Therefore, the observation path planning should satisfy the inequality constraints of the safety avoidance ellipsoid at every discrete time k:

[0130]

[0131] Where, x (k) To serve the current state of the spacecraft, and These are the center state and shape matrix of the safe collision avoidance ellipsoid, respectively:

[0132]

[0133] Nonlinear and nonconvex inequality constraints (22) are difficult to handle in trajectory planning. This implementation linearizes them using a first-order Taylor expansion, ensuring the linearity of the simplified constraints while also making the problem convex, thus significantly reducing computational complexity. Let the constraint function (22) be: By its effect on the current iteration result Performing a first-order Taylor expansion at the point, the original constraints can be convexened into the following linear constraints:

[0134]

[0135] Direct linearization of non-convex constraints ignores higher-order small quantities, inevitably leading to some states that meet constraint (24) entering the collision avoidance ellipsoid. To reduce the impact of linearization error on safety, a corresponding safety margin ρ has been designed above for error compensation. Combining formulas (22) and (23), the linearly simplified safety constraint can be expressed as:

[0136]

[0137] Constraint (25) can be simplified to matrix form:

[0138]

[0139] in:

[0140]

[0141] Furthermore, due to the amplitude limitation of the thrust of the servicing spacecraft, the control inputs need to satisfy the following inequality constraints:

[0142] u min ≤u (k) ≤u max , k=0,1,...,N (27)

[0143] For ease of calculation, the above constraints can be transformed into matrix form:

[0144] F u u (k) ≤f u (28)

[0145] in:

[0146]

[0147] Based on the above task analysis and constraint transformation process, the trajectory planning problem for actively observing non-cooperative targets can be summarized as the following optimization problem:

[0148]

[0149] The optimization variable for solving the above optimization problem is the trajectory sequence x. (1) ,K,x (N) and control sequence u (0) ,K,u (N -1) , where N is the prediction time domain. This quadratic programming problem is defined by the following parameters:

[0150] x p (k) A d B d ,Q,R,F x ,Fu ,f x ,f u (30)

[0151] Finally, the corresponding optimized trajectory sequence and the corresponding control sequence are calculated using a fast model predictive control-based trajectory planning solver (FMPC).

[0152] Implementation Method 3: This implementation method provides a detailed explanation of the optimized trajectory sequence and corresponding control sequence calculated by the trajectory planning solver (FMPC) based on fast model predictive control described in Implementation Method 2 above.

[0153] The convex quadratic programming problem (29) proposed in the above-mentioned implementation method 2 is a classic optimization problem. The fast model predictive control (FMPC) method used in this implementation method is an efficient explicit MPC, and its problem solver is an interior point method - the original barrier method.

[0154] First, define the optimization variable sequence z and the expected sequence z. p for:

[0155]

[0156] Using the above definition, the original problem can be rewritten in compact matrix form:

[0157]

[0158] Where H is the quadratic term matrix of the index function; P and h (C and b) correspond to the parameter matrices of the inequality constraints (equality constraints), respectively. The specific matrix structures are as follows:

[0159]

[0160]

[0161] The original barrier method introduces a barrier function to embed the inequality constraints in the optimization problem (32) into the objective function, thereby transforming the original problem into an optimization problem containing only equality constraints without changing the KKT optimality conditions. The new optimization problem can be solved efficiently by constructing a residual sequence and using Newton's iteration method. Therefore, optimization problem (32) can be equivalently transformed into:

[0162]

[0163] The barrier function φ has the following expression:

[0164]

[0165] in, Let be the i-th row vector of the inequality constraint coefficient matrix P.

[0166] During the iterative solution of the new optimization problem (33), the weighting coefficient γ of the barrier function will be reduced proportionally to 1 / 10 of its original value in each iteration, gradually weakening the violation of the inequality constraints. Finally, when γ→0, the solution of the new optimization problem (33) will gradually converge to the optimal solution of the original optimization problem (32).

[0167] The active observation trajectory planning problem for non-cooperative targets (32) is a complex constrained optimization problem, characterized by numerous constraints and high dimensionality, making it almost impossible to directly construct the initial trajectory and control sequence within the feasible region. Although the standard Newton-Raphson iteration method is highly efficient, it requires the initial values ​​to strictly satisfy all constraints, which places stringent requirements on the construction of the initial values. In contrast, the initial point infeasibility Newton method alleviates the difficulty of guessing the initial values ​​by relaxing the stringent condition that the initial values ​​must satisfy the equality constraints, while retaining the high computational efficiency of the Newton-Raphson iteration method.

[0168] To quickly solve optimization problems using this solver (33), the Lagrangian function L(z,ν) corresponding to the problem must first be defined:

[0169] L(z,ν)=(zz p )H(zz p )+γφ(z)+ν(Cz-b) (35)

[0170] Where, ν∈R 6N It is the Lagrange multiplier corresponding to the equality constraint Cz-b=0. According to the minima principle, the zeros of the two partial differential equations of the Lagrange equation (35) with respect to (z,ν) are a necessary condition for the optimal solution:

[0171]

[0172] Among them, γP ú d is the gradient of γφ(z), an implicit expression of the inequality constraint Pz < h; vector d ∈ R 9N+6 The specific expression is: P i Represents the i-th row of the inequality coefficient matrix P; (z * ,ν * ) are the optimal independent variable sequence and the optimal dual variable sequence, respectively.

[0173] Let the system of equations (36) be F(z) * ,ν * Given that ) = 0, the general solution to this nonlinear system of equations is Newton's iteration method. This involves selecting initial values ​​within the solution neighborhood and successively decreasing the residual of the function F(z,ν) to approximate the solution (z). k,ν k The solution gradually converges to the true solution (z). * ,ν * ).

[0174] To solve the system of equations (36) using Newton's iterative method, we first need to consider the current iteration point (z). k ,ν k At point ), perform a first-order Taylor expansion of the function F(z,ν):

[0175]

[0176] Among them, ▽F(z) k ,ν k ) represents the function F(z,ν) in (z k ,ν k The gradient matrix at point (z). To make the equation gradually approximate the zero residual condition, we take F(z) as... k+1 ,ν k+1 If ) = 0, then the residual and update direction satisfy:

[0177]

[0178] Where Δz and Δν are the update directions of the state and its dual, respectively; F(z) k ,ν k ) represents the residual, and its component dual residuals Compared with the original residual The specific expression is as follows:

[0179]

[0180] Calculate the coefficient matrix ▽F(z) k ,ν k Substituting this into equation (38), we obtain the update equation for the k-th round of Newton iteration:

[0181]

[0182] Among them, γP ú diag(d) 2 P is the Hessian matrix of the implicit inequality constraint γφ(z); Δz and Δν are the state update direction and dual update direction, respectively.

[0183] Therefore, the updated iteration state (z) k+1 ,ν k+1 )satisfy:

[0184] z k+1 =z k +sΔz,ν k+1 =ν k +sΔν (41)

[0185] Unlike the traditional Newton's method, the initial point infeasible Newton's method introduces weight coefficients s∈(0,1] during the state update process to ensure that the updated result satisfies the inequality constraint Pz. k+1 <h.

[0186] As can be seen from the process of constructing an infeasible initial point using Newton's method, the initial value z of the state variable... 0 The inequality constraint Pz must be strictly satisfied. 0 <h; while the equality constraint Cz k =b is corrected by dual residuals The iterations are completed step by step until the constraints are fully satisfied, therefore the initial value z 0 No equality constraints need to be satisfied. Similarly, the initial value ν of the dual variable... 0 Either option can be chosen arbitrarily. Ultimately, as the residual continuously decreases, the iterative solution (z)... k ,ν k This will gradually approach the optimal solution (z) within the error threshold. * ,ν * ).

[0187] Solving the iterative update direction (40) is the most computationally complex part of the initial point infeasible Newton's method. Typically, solving the linear equation system (40) requires calculating the coefficient matrix ▽F(z). k ,ν k L ú DL decomposition is used to solve for its inverse matrix. And the L... ú The computational complexity of deep learning decomposition is high, which significantly affects the computational efficiency of Newton's method for infeasible initial points.

[0188] Compared to traditional explicit MPC, the efficiency of FMPC is mainly reflected in its ability to quickly solve high-dimensional linear equation systems (40). The coefficient matrix of the equation system (40) is a symmetric positive definite block diagonal matrix, which can be equivalently reduced to a low-dimensional matrix through Schul decomposition, thereby significantly reducing the dimension and computational complexity of the equations. The new equation system after the reduction still maintains a symmetric positive definite coefficient matrix. Furthermore, the equation system solution method combining the Klaussky decomposition method and the matrix block elimination method is adopted. This computational efficiency is much higher than that of the traditional L... ú A method for solving a system of equations by matrix inversion after DL decomposition. Through the simplification process described above, the dimensionality and solution complexity of the system of equations are significantly reduced, resulting in a substantial improvement in overall solution efficiency.

[0189] First, this implementation method performs equivalent dimensionality reduction on the coefficient matrix of equation system (40) through Schur decomposition, so that the dimension of the new equation system is the same as that of the submatrix Φ=2H+γP. ú diag(d) 2P is the same. The submatrix Φ is a block symmetric positive definite matrix, and its inverse matrix is:

[0190]

[0191] The original system of equations (40) can be equivalently reduced in dimension and decoupled by Schur decomposition into equations that concern only the dual update direction Δν:

[0192] CΦ -1 C ú Δν=r p -CΦ -1 r d (43)

[0193] The coefficient matrix of the linear system of equations (43) is Y = CΦ -1 C ú The constant vector is β = -r p +CΦ -1 r d Therefore, it is easy to find the root of the system of equations: Δν = -Y -1 β. Solving traditional linear equation systems relies on performing LDL on the coefficient matrix Y. ú Decompose and then solve for the inverse matrix Y. -1 To obtain the solution to the equation; in contrast, the Klaussky LL method is used. ú After decomposing the coefficient matrix Y, the system of equations is solved by elimination twice, with the latter having a greater advantage in computational complexity.

[0194] After Klausski decomposition, the coefficient matrix Y can be decomposed into a lower triangular matrix L, satisfying the equation Y = L / L. ú The specific form of matrix L is as follows:

[0195]

[0196] The submatrices of matrix L can be calculated through recursive decomposition, and the specific steps are as follows:

[0197] 1. Factorize the first element Y of the main diagonal. 11 Solve for L 11 :

[0198] 2. Solve for the off-diagonal element L 21 :

[0199] 3. Decompose the main diagonal elements To solve L 22 Y 22 -L 21 L 21 =L 22 L 22 ;

[0200] 4. Following the above process, recursively continue until the entire matrix is ​​decomposed.

[0201] The above iterative calculation process can be summarized by the following formula:

[0202]

[0203] By performing a Clauski decomposition on the coefficient matrix Y, the original equation YΔν=-β is equivalently transformed into an equation with two triangular coefficient matrices: L ú Δν = y and Ly = -β. The system of equations with trigonometric coefficient matrices obtained after decomposition can be solved efficiently using the matrix block elimination method. Then, substituting Δν back into the original equation (40), we obtain the expression for Δz: Δz = Φ -1 (-r d -C ú Δν).

[0204] Implementation Method Four, see below Figures 6 to 11 This embodiment describes the simulation results of a highly efficient and secure trajectory planning method for active observation of non-cooperative targets, as described in the above embodiments.

[0205] The non-cooperative target to be observed is orbiting in a GEO orbit with an average angular velocity of n = 7.277 × 10⁻⁶. -5 rad / s. The navigation information for a target determined by a ground-based orbit determination and navigation system includes the estimated state x0(t0) (mm / s) and its corresponding 98% confidence level error covariance X0(t0) (m / s). 2 m 2 / s 2 The initial state x(t0)(mm / s) and other scenario information of the spacecraft being serviced by our side are summarized as follows: Figure 4 As shown.

[0206] The relative orbital state of a spacecraft in orbit can be categorized into two typical relative trajectories according to the solutions of the HCW equations: periodic solutions and drift solutions. This implementation method designs two representative simulation scenarios based on this classification. Specifically, the periodic solution corresponds to a spacecraft whose relative orbit exhibits periodic changes, and the trajectory is a closed curve of ellipse or circle. Its initial values ​​must satisfy… The drift solution corresponds to the spacecraft's orbit gradually deviating from its initial state, with the trajectory exhibiting a spiral curve shape.

[0207] The range of values ​​for target navigation covariance is typically determined by the accuracy of the navigation system. For example, using GPS navigation as a reference, its ground positioning accuracy is approximately 10 meters, and its velocity measurement accuracy is approximately 0.2 m / s. GPS navigation accuracy is affected by the target distance; the greater the distance, the lower the navigation accuracy. Generally, in orbit determination missions targeting non-cooperative targets in space, the navigation positioning error is between 10 and 100 meters, while the velocity measurement error is between 0.1 and 1 m / s. For this paper, the simulation scenario is designed on a GEO orbit, and the scenario scale is on the order of kilometers; therefore, a positioning error of approximately 50 meters and a velocity measurement error of approximately 0.25 m / s are chosen.

[0208] Furthermore, the envelope size of the satellite and its associated structures generally does not exceed 10 meters. This implementation assumes that the target and service spacecraft sizes are the upper limit ρ. P =ρ I =10m. The tolerance distance ρ has no special range and is selected as 10m. Figure 6 The optimized value is given. It is also assumed that the attitude angle of the non-cooperative target relative to the LVLH coordinate system is... The rotation order is zyx.

[0209] The model predictive control used requires solving a discrete optimization problem (30), and the prediction time domain is set to N = 50, with a discrete time step Δt = 20s. Discrete dynamic parameters A d B d Calculated according to equation (4) above. In explicit model predictive control (32): the index matrix H∈R N(6+3)×N(6+3) State and control weight submatrix Q = I 6×6 R = I 3×3 ; Expected trajectory z p Calculated according to equation (31), where the expected observed trajectory x p The curves are used to sequentially link the observation nodes and fit the safe collision avoidance ellipsoid; the state and control constraint submatrices F in the inequality constraint coefficient matrix P,h x ,f x Calculated according to equation (26), this is the result of the current iteration. The function; F u ,f u The control constraint u is calculated using equation (28). max =-u min =1m / s 2 The initial weighting coefficient of the barrier function is γ = 1, the maximum number of iterations is 1000, and the termination error threshold is 1e-8. The preset time for the safe collision avoidance ellipsoid is selected as the time interval N / 5·Δt = 200s between the four observation nodes. Specific simulation results are as follows... Figures 7 to 11 As shown; where, Figure 7 and Figure 9 The absolute observation trajectories for two typical scenarios were plotted, and Figure 8 and Figure 10 This then displays the corresponding relative observation trajectory. Figure 11 This demonstrates a non-cooperative target observation control sequence. The absolute observation trajectory is presented as a curve encircling a tubular safety zone drawn by safety avoidance ellipsoids at different times; the corresponding relative observation trajectory is a closed curve surrounding the safety avoidance ellipsoid. Different safety avoidance ellipsoids affect the shape of the absolute observation trajectory by influencing the "radius" of the tubular safety zone; they also directly affect the minimum orbital radius of the relative observation trajectory. This implementation, based on the trajectory planning strategy proposed by FMPC, can calculate an observation trajectory that does not traverse the safety avoidance ellipsoid, enabling servicing spacecraft to conduct covert, efficient, and safe orbital observations of non-cooperative targets.

[0210] In summary, the trajectory planning method for active observation of non-cooperative targets proposed in this invention, which features strong security, reduces the task time for observing non-cooperative targets from 1 day to 1000 seconds, and avoids entering the safety ellipsoid, thus significantly shortening the task cycle while maintaining good security.

[0211] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A highly efficient trajectory planning method for active observation of non-cooperative targets with strong security, characterized in that, The method is as follows: S1: Based on the navigation information output by the non-cooperative target spacecraft, determine the target navigation estimation state and the target navigation error covariance matrix; The output navigation information is represented in the form of a navigation error ellipsoid; The navigation error ellipsoid is ,in The center of the navigation error ellipsoid is the confidence level. The shape of the navigation error ellipsoid represents the target navigation estimation state. Represents the target navigation error covariance matrix; S2: Determine the state gain attainable set of the non-cooperative target spacecraft based on the target navigation estimated state and the target navigation error covariance matrix; Specifically: Target navigation estimation state Covariance matrix of target navigation error Substitute into the following differential equation: And perform the solution to obtain the reachable set of state gains; in, This represents the coefficient matrix in the HCW dynamic equations. represent The transpose of a matrix; The reachable set of state gain is represented as: in, The time range of the movement; S3: The state gain reachable set of the non-cooperative target spacecraft is used to perform size compensation on the structure of the non-cooperative target spacecraft and the service spacecraft, and the safe observation ellipsoid of the non-cooperative target spacecraft and the service spacecraft is determined. The safe observation ellipsoid is represented as: in, The time interval is represented as The state transition matrix, I represents the transpose of the state transition matrix. The identity matrix; S4: During active observation of non-cooperative targets, the servicing spacecraft must avoid entering the safe observation ellipsoid; S5: Select the body diagonal plane of the non-cooperative target spacecraft as the planning plane for the observation trajectory, and take the four intersection points of the two diagonals in the planning plane and the safe observation ellipsoid as observation nodes. Connect these four observation nodes in sequence to form a reference closed trajectory that satisfies the observation mission. S6: Select the discretized observation trajectory sequence and its corresponding control sequence as optimization variables in the reference closed trajectory, select the distance-energy hybrid quadratic index as the optimization index, use the discretized inequality as the path constraint, and calculate the corresponding optimized trajectory sequence and corresponding control sequence by using the trajectory planning solver.

2. The trajectory planning method for active observation of non-cooperative targets with strong security according to claim 1, characterized in that, The expression for why service spacecraft must avoid entering the safe observation ellipsoid is: 。 3. The trajectory planning method for active observation of non-cooperative targets with strong security according to claim 1, characterized in that, The trajectory planning method is applicable in scenarios where a non-cooperative target and a servant spacecraft are located in the same near-circular orbit, and the navigation and guidance system measures the non-cooperative target's position within a certain confidence level. Error ellipsoid Inside.

4. A highly efficient trajectory planning system for active observation of non-cooperative targets with strong security, characterized in that, The system includes a storage device for performing the method and steps of claim 1.

5. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the trajectory planning method for active observation of non-cooperative targets with strong security, as described in any one of claims 1-3.

6. A computer device, characterized in that, The device includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes the trajectory planning method for active observation of non-cooperative targets with strong security, as described in any one of claims 1-3.

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