Spacecraft game maneuvering control method for evading multi-source threats
By constructing a cost function using differential game theory and solving the Riccati equation using the Hamilton-Jacobi method, the spacecraft was able to safely avoid multiple threats, thus solving the collision risk when multiple non-cooperative targets approached. This method is applicable to spacecraft orbit control in engineering practice.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIHANG UNIV
- Filing Date
- 2023-07-05
- Publication Date
- 2026-08-04
AI Technical Summary
In existing technologies, spacecraft lack effective avoidance and control strategies when facing multiple non-cooperative targets approaching, especially in multi-source threat scenarios. It is difficult to reduce the risk of collisions in multiple directions through active orbital maneuvering control. Existing research mainly focuses on rapidly approaching non-cooperative targets rather than avoiding them.
By employing differential game theory and constructing a cost function, the Hamilton-Jacobi method is used to solve the Riccati equation, establishing a full-state linear feedback control solution for the mission spacecraft. Through orbital control engines, multiple non-cooperative targets are kept collinear with the mission spacecraft, reducing fuel consumption and increasing the approach time cost of non-cooperative targets, thus avoiding multi-source threats.
It enables spacecraft to safely avoid multiple threats, reduces collision risks, and improves spacecraft space safety. It is applicable to practical engineering scenarios involving multiple non-cooperative targets.
Smart Images
Figure CN116880175B_ABST
Abstract
Description
[Technical Field]
[0001] This invention relates to a spacecraft maneuver control method for avoiding multi-source threats, and more particularly to an orbital maneuver control method designed for a mission spacecraft that is simultaneously approached by multiple non-cooperative targets (spacecraft or space debris, the same below). The method utilizes the fact that multiple non-cooperative targets are collinear with the mission spacecraft during the approach process to avoid multi-source threats approaching from multiple directions and angles. This invention belongs to the field of spacecraft orbital control. [Background Technology]
[0002] With the development of space technology, the number of satellites in orbit has increased dramatically. This has also brought with it a large amount of space debris. Spacecraft providing on-orbit servicing face various potential threats, including collisions between space debris and mission spacecraft, and approaching mission spacecraft by non-cooperative spacecraft, either actively or uncontrollably. To address these potential space threats, especially when multiple non-cooperative targets approach mission spacecraft, mission spacecraft need to adopt certain control strategies. This includes active orbital maneuvering to reduce the threat of collisions from multiple directions and sources of non-cooperative targets—in other words, avoiding multi-source threats.
[0003] Research on the spacecraft pursuit-escape game problem mainly focuses on techniques for autonomous approach to non-cooperative targets. The approaches can be broadly categorized into one-sided optimal control methods based on robust control theory and two-sided optimal control methods based on differential game theory. While one-sided optimal control methods based on robust control theory are applicable to approach control of space debris and faulty spacecraft, they struggle to reflect the adversarial relationship between the non-cooperative target and the mission spacecraft when establishing the control system; they only address the approach control problem of the non-cooperative target on the mission spacecraft. Two-sided optimal control based on differential game theory can simultaneously obtain saddle point solutions for both the non-cooperative target and the mission spacecraft under a specific game condition. The control strategy obtained from this saddle point solution is more reasonable and feasible as a safety-oriented evasion control strategy for the mission spacecraft.
[0004] Differential game theory is a mathematical model and theoretical method for dynamic real-world scenarios involving elements of cooperation and competition. It uses differential equations to describe the dynamic processes of two- or multi-party dynamic games. Anderson studied the in-plane pursuit problem of two spacecraft with maximum thrust. He solved the standard solution of the two-point boundary value problem and then inversely integrated the Riccati equation, using the difference between the current state and the ideal state to obtain the updated value of the conjugate state. Stupik J, in his study of the spacecraft pursuit problem, established a linearized relative motion orbital dynamic model based on the CW equation. He used particle swarm optimization and nonlinear programming to obtain an open-loop numerical solution. He then used spatial local interpolation to fit the obtained open-loop solution to obtain an approximate closed-loop feedback control solution. Finally, simulations verified that this method can quickly obtain the control output for small perturbation problems in the pursuit problem. However, the existing applications of differential game theory in the aerospace field are mostly used to solve problems on how to quickly approach non-cooperative targets. There are few problems on spacecraft active avoidance control based on differential game theory, and research is just beginning. There are also few publicly published results in China, especially research on avoidance control under multi-source threat scenarios. [Summary of the Invention]
[0005] The purpose of this invention is to address the challenges of multiple non-cooperative targets approaching a spacecraft in space applications. Existing technologies mostly focus on how the spacecraft can quickly approach these targets, with little research on evasion techniques or unilateral optimal maneuvering control. These approaches fail to consider the impact of non-cooperative targets on control strategies, making their application in practical engineering difficult. This invention proposes a game-theoretic maneuvering control method for evading multi-source threats, specifically targeting a scenario where multiple non-cooperative targets approach a single spacecraft in a circular orbit. A schematic diagram of this scenario is attached. Figure 1 By using orbital control engines, multiple non-cooperative targets and the mission spacecraft are kept as straight as possible during the approach process, so that safety threats such as collisions from non-cooperative targets come from only a single direction, avoiding space safety risks under multiple threats. Based on the optimal control method of differential game theory, the mission spacecraft can avoid multiple threats.
[0006] To address the aforementioned problems, the technical solution of this invention is as follows: Assuming both the non-cooperative target and the mission spacecraft operate in circular orbits, and the mission spacecraft employs finite continuous thrust for orbital maneuver control, the influence of orbital perturbation can be neglected. First, considering only the relative orbital motion of the non-cooperative target and the mission spacecraft, a dynamic model incorporating their relative motion states is established, namely the CW equations. Then, using the concept of differential games, cost functions for both sides of the game are constructed. Finally, the Hamilton-Jacobi method is employed to solve the Riccati equations, yielding the full-state linear feedback control solution for the mission spacecraft.
[0007] Taking a scenario where two non-cooperative targets approach a mission spacecraft as an example, the specific operational steps are as follows:
[0008] Step 1: Applying this invention is based on the following assumptions
[0009] To obtain an accurate dynamic model for this scenario and solve for the expression of the maneuver control law, the following assumptions 1 to 4 must be made:
[0010] Assumption 1: Since the time for the non-cooperative target to approach and the mission spacecraft to maneuver and avoid it is very short compared to the orbital period, the influence of orbital perturbation is ignored, and the orbital motion of the spacecraft and the non-cooperative target is simplified to a two-body problem;
[0011] Assumption 2: The reference orbits for the relative motion of the spacecraft and the non-cooperative target are both circular orbits. When establishing the equations of relative orbital motion, i.e. the CW equations, second-order minor quantities are ignored.
[0012] Assumption 3: The radius of the reference orbit is much larger than the range of the spacecraft's orbital maneuvers;
[0013] Assumption 4: The spacecraft uses finite continuous thrust for orbital maneuvers;
[0014] Step 2: Establish a dynamic model that includes the relative motion states of the two non-cooperative targets and the mission spacecraft; specifically, this includes the following steps:
[0015] Step 2.1: Define the coordinate system
[0016] This invention is aimed at spacecraft in a geocentric orbital coordinate system;
[0017] a. Geocentric equatorial inertial coordinate system f i (O i x i y i z i )
[0018] The origin of the geocentric equatorial inertial coordinate system is fixed at the Earth's center O. i Above, O i x iThe axis lies in the equatorial plane and points towards the vernal equinox, O i y i The axis lies in the equatorial plane and intersects with O. i x i The axis points vertically east, O i z i Shaft and O i x i O i y i The axes form a right-handed orthogonal coordinate system;
[0019] b. Reference spacecraft orbital coordinate system f o (O o x o y o z o )
[0020] The reference spacecraft O is defined so that its initial center of mass coincides with the center of mass of the mission spacecraft E. The origin of the reference spacecraft's orbital coordinate system is fixed at the spacecraft's center of mass O. o Above, O o x o The axis points along the Earth's center towards the spacecraft's center of mass O; O o y o The axis is in the orbital plane and intersects with O o x o The axis points perpendicularly to the velocity direction of the reference spacecraft; O o z o Shaft and O o x o O o y o The axes form a right-handed orthogonal coordinate system;
[0021] Step 2.2: Establish the relative positions of non-cooperative targets and mission spacecraft
[0022] When mission spacecraft E faces pursuit from multiple non-cooperative targets, a reasonable maneuvering strategy can be used to maximize the fuel consumption required for the non-cooperative targets to approach the mission spacecraft, thereby increasing their time cost. Furthermore, the maneuvering strategy can be used to reduce the directional sources of threats during the approach. Therefore, an avoidance method is proposed: E, P1, and P2 should maintain a straight line as much as possible during the pursuit. The desired relative positional relationship between mission spacecraft E and P1 and P2 is shown in the appendix. Figure 2 This positional relationship reduces the direction of approaching threats for spacecraft E. Furthermore, for a non-cooperative target P1 to approach spacecraft E, it must bypass P2, thus increasing the maneuvering time and fuel consumption required for a collision with the non-cooperative target. The geometric relationship is as follows:
[0023]
[0024] Where, r E This is represented as the position vector of mission spacecraft E in the geocentric equatorial inertial coordinate system; κ represents the position vectors of non-cooperative targets P1 and P2 in the geocentric equatorial inertial coordinate system; κ represents the coefficient that determines the relative distance between mission spacecraft E and non-cooperative targets P1 and P2.
[0025] The above equation can be simplified to:
[0026]
[0027] Define relative motion position By differentiation, we can obtain
[0028] Step 2.3: Establish a dynamic model that includes the relative motion states of the two non-cooperative targets and the mission spacecraft.
[0029] Based on assumptions 1-4, the CW equations for mission spacecraft E and non-cooperative targets P1 and P2 are established (the CW equations are the fundamental equations of the spacecraft's relative orbital motion, and will not be elaborated further):
[0030]
[0031]
[0032]
[0033] Where n represents the orbital angular rate of the circular orbit in which the spacecraft is located; Represented as the velocity and acceleration of mission spacecraft E; Represented as the velocity and acceleration of the non-cooperative target P1; Represented as the velocity and acceleration of the non-cooperative target P2; u E , This represents the orbital control parameters for mission spacecraft E, and non-cooperative targets P1 and P2 (if the non-cooperative target is space debris, there are no active orbital control parameters). (Consider it as the zero vector).
[0034] Combining the definition of relative position and equations (3) to (5), we can obtain:
[0035]
[0036] Let the state space vector be A dynamic model including the relative motion states of the two non-cooperative targets and the mission spacecraft:
[0037]
[0038] Wherein, the state transition matrix Control coefficient matrix of mission spacecraft Control coefficient matrix of non-cooperative target P1 Control coefficient matrix of non-cooperative target P2
[0039] Step 3: Design of the evasion control law for the mission spacecraft
[0040] Step 3.1: Construct the cost function for non-cooperative target and mission spacecraft
[0041] The mission requirement of the spacecraft is to distance itself from multiple non-cooperative targets, minimizing the positional error while keeping these targets collinear with the spacecraft, and conserving its own fuel while increasing the energy cost of approaching the non-cooperative targets. Using the concept of differential games, a cost function is constructed as follows:
[0042]
[0043] Where t0 represents the initial moment when the mission spacecraft begins its evasive maneuver; the cost corresponding to the spacecraft's state at a certain moment is represented as... Q in the formula E R E , For adjustable control parameters; for mission spacecraft, the expected cost function It reaches a minimum value;
[0044] Step 3.2: Construct the Hamiltonian function
[0045] Constructing the Hamiltonian function for a linear control system:
[0046]
[0047] Where the costate variable is denoted by λ; the function Represented as
[0048] According to the system's extreme value condition, we can obtain:
[0049]
[0050] The solution for the control system taking extreme values can be obtained from equation (9):
[0051]
[0052] The cost function J can eventually be reduced to a function of x. E2 The form of the quadratic form:
[0053]
[0054] Where P(t) is constant during the game time, and the costate variable takes the value of
[0055] Step 3.3: Avoidance Control Laws for Mission Spacecraft
[0056] Ultimately, solving the Hamilton-Jacobi equation can be transformed into solving a Riccati differential equation of the following form:
[0057]
[0058] Substituting the solved P into λ, we can finally obtain the linear full-state feedback control solution for the mission spacecraft E:
[0059]
[0060] The present invention provides a spacecraft game-theoretic maneuver control method for avoiding multi-source threats. Its advantages and effects are as follows: 1) In the scenario of multi-source threats, the present invention establishes a dynamic equation describing the state space of the system by giving constraints on the relative positional relationship between multiple non-cooperative targets and the mission spacecraft. Using differential game theory, the cost functions of the two sides of the game are constructed. The Hamilton-Jacobi method is used to solve the Riccati equation and obtain the control law for avoiding multi-source threats of the mission spacecraft, so that the mission spacecraft has the ability to get rid of collision threats from non-cooperative targets from multiple directions.
[0061] 2) When designing the evasion maneuver control law for mission spacecraft, this invention considers the use of a cooperative approach control law for non-cooperative targets (i.e., when establishing the dynamic equations and payoff functions, multiple non-cooperative targets are regarded as a cooperative whole, and the ultimate goal of this whole in the pursuit and escape game is to minimize the overall energy consumption while completing their respective mission objectives). In this case, the mission spacecraft can also evade multiple threats. In the actual operation of the spacecraft, if the non-cooperative target has orbital maneuver control capability, it is very likely to adopt a cooperative control approach strategy. If it does not have maneuver control capability, this evasion maneuver method can still effectively deal with it. Therefore, this invention is more in line with engineering practice.
[0062] 3) This invention addresses the space application scenario where multiple non-cooperative targets approach a single mission spacecraft. It has broad application prospects in space safety applications, and can avoid potential threats such as collisions between mission spacecraft and on-orbit space debris, active approach of non-cooperative spacecraft, and collisions with malfunctioning spacecraft, thus ensuring the safety of on-orbit mission spacecraft. It can meet the requirements of actual engineering and is in line with actual engineering applications. [Attached Image Description]
[0063] Figure 1 A schematic diagram of a spacecraft on a non-cooperative target pursuit mission.
[0064] Figure 2This is a schematic diagram of a maneuvering target for a mission spacecraft.
[0065] Figure 3 This is a schematic diagram showing the relative positions of the spacecraft.
Detailed Implementation Methods
[0066] The following is in conjunction with the appendix Figure 1-3 When a mission spacecraft detects a threat from two non-cooperative targets that have already approached the mission spacecraft at a certain distance, the implementation process of this invention will be specifically explained using the scenario of the spacecraft's evasive maneuver as an example.
[0067] First, the initial conditions and relevant simulation parameters for non-cooperative target and mission spacecraft are as follows:
[0068]
[0069] Assuming the non-cooperative objective employs a cooperative approach control law, as shown in the appendix. Figure 3 As shown, let Where θ1 is a vector The angle between the two points. The ultimate goal of a non-cooperative objective is to achieve the following within a finite time: and The convergence is achieved by minimizing the fuel consumption of both stars.
[0070] The following steps involve setting the spacecraft maneuver control parameters for the mission spacecraft to avoid multi-source threats.
[0071] 1. The application of this invention is based on the following assumptions.
[0072] Make the assumptions as described in step 1 above.
[0073] 2. Establish a dynamic model that includes the relative motion states of the two non-cooperative targets and the mission spacecraft.
[0074] 2.1 Define the coordinate system: Define the relevant coordinate system according to step 2.1 above.
[0075] 2.2 Establishing the relative positions of non-cooperative targets and mission spacecraft
[0076] Following step 2.2 above, establish the relative positional relationship between the non-cooperative target and the mission spacecraft, and set the coefficient κ = 1.001.
[0077] 2.3 Establish a dynamic model that includes the relative motion states of the two non-cooperative targets and the mission spacecraft.
[0078] A dynamic model containing the relative motion states of the two non-cooperative targets and the mission spacecraft is established according to step 2.3 above.
[0079] 3. Design of evasion control laws for mission spacecraft
[0080] 3.1 Constructing the cost function for non-cooperative target and mission spacecraft
[0081] Construct the cost function for the non-cooperative target and mission spacecraft as described in step 3.1 above:
[0082]
[0083] Where t0 represents the initial moment when the mission spacecraft begins its evasive maneuver; the cost corresponding to the spacecraft's state at a certain moment is represented as...
[0084] To ensure the existence of solutions to the Riccati equation, the weight coefficient matrix is constructed as follows: Q E It is a 6×6 diagonal matrix, where the first three parameters on the diagonal represent r. E2 In the cost function J E The weights in the equation, the last three parameters on the diagonal represent The weights in the cost function can therefore be set as follows: Where I3 is a 3×3 identity matrix; R E , Both are 3×3 diagonal matrices, representing the weights of the accelerations of the indexed mission spacecraft in the cost function. Therefore, let R... E =q E3 ·I3、
[0085] The case value is:
[0086]
[0087] 3.2 Constructing the Hamiltonian Function
[0088] Construct the Hamiltonian function as described in step 3.2 above.
[0089] 3.3 Avoidance Control Laws for Mission Spacecraft
[0090] The avoidance control law of the mission spacecraft is calculated according to step 3.3 above.
[0091] In summary, the present invention adopts an orbital maneuver control scheme based on differential games. In the case study, a cooperative approach control law is adopted for the non-cooperative target, and an analytical form of the avoidance control law formula (14) is adopted for the mission spacecraft, which enables the mission spacecraft to avoid the approach of the non-cooperative target.
[0092] This invention introduces a spacecraft game-theoretic maneuvering control method for avoiding multi-source threats. Its key feature is that, in space application scenarios where multiple non-cooperative targets approach a mission spacecraft, the mission spacecraft needs to evade them. This control method utilizes reasonable maneuvers to maximize the fuel consumption of the non-cooperative targets, increase their pursuit time, and reduce the directional sources that can directly threaten the mission spacecraft during the approach. This method proposes an evasion strategy for the mission spacecraft, ensuring that during the pursuit, multiple non-cooperative targets and the mission spacecraft remain as close to a straight line as possible. This ensures that safety threats such as collisions from non-cooperative targets originate from only a single direction, avoiding space safety risks under multi-source threats. Taking a scenario with two non-cooperative targets as an example, firstly, a dynamic model is established including the relative motion states of the two non-cooperative targets and the mission spacecraft; then, the cost functions of both sides in the game are constructed using the idea of differential game theory; finally, the Hamilton-Jacobi method is used to solve the Riccati equation, obtaining the full-state linear feedback control solution for the mission spacecraft. This method has not yet been studied in the field of spacecraft pursuit and escape game theory, but it has high practicality in real space missions. It can minimize the approach of other non-cooperative targets to spacecraft in orbit, avoid potential threats such as collisions from multiple directions and sources, and provide strong protection for the safety of spacecraft.
Claims
1. A spacecraft game-theoretic maneuver control method for threat avoidance, characterized in that: Includes the following steps: Step 1: Propose the following hypothesis: Assumption 1: Since the time for the non-cooperative target to approach and the mission spacecraft to maneuver and avoid it is very short compared to the orbital period, the influence of orbital perturbation is ignored, and the orbital motion of the spacecraft and the non-cooperative target is simplified to a two-body problem; Assumption 2: The reference orbits for the relative motion of the spacecraft and the non-cooperative target are both circular orbits. When establishing the equations of relative orbital motion, i.e. the CW equations, second-order minor quantities are ignored. Assumption 3: The radius of the reference orbit is much larger than the range of the spacecraft's orbital maneuvers; Assumption 4: The spacecraft uses finite continuous thrust for orbital maneuvers; Step 2: Establish a dynamic model that includes the relative motion states of the two non-cooperative targets and the mission spacecraft, including: defining a coordinate system; establishing the relative positional relationship between the non-cooperative targets and the mission spacecraft; and establishing the dynamic model. Step 3: Design of evasion control law for the mission spacecraft, including: constructing the cost function between the non-cooperative target and the mission spacecraft; constructing the Hamiltonian function; and designing the evasion control law. In step 3, given that the mission requirement of the spacecraft is to stay away from multiple non-cooperative targets, minimize the position error when the non-cooperative targets remain collinear with the spacecraft, and conserve its own fuel as much as possible while increasing the energy cost of approaching the non-cooperative targets, the cost function is constructed as follows: (8) in, It is a state-space vector. , , Represented as orbital control quantities for mission spacecraft E, and non-cooperative targets P1 and P2; This represents the initial moment when the mission spacecraft begins its evasive maneuver; the cost corresponding to the spacecraft's state at a certain moment is represented as... In the formula , , , For adjustable control parameters; for mission spacecraft, the expected cost function It reaches a minimum value; In step 3, the Hamiltonian function of the linear control system is constructed: (9) Wherein, the costate variable is represented as ;function Represented as ； in, Here is the state transition matrix. This is the control coefficient matrix for the mission spacecraft. The control coefficient matrix for non-cooperative target P1. The control coefficient matrix for non-cooperative target P2; Based on the system's extreme value conditions, we obtain: (10) The solution for the control system taking extreme values is obtained from equation (9): (11) Cost function J Ultimately, it turned into something about The form of the quadratic form: (12) in, The time interval is constant, and the costate variable takes the value of... ; In step 3, solving the Hamilton-Jacobi equation is transformed into solving a Riccati differential equation of the following form: (13) Solved P Substitution Finally, the linear full-state feedback control solution for mission spacecraft E is obtained: (14)。 2. The spacecraft game-theoretic maneuver control method for threat avoidance according to claim 1, characterized in that: In step 2, the target is a spacecraft in a geocentric orbital coordinate system; a. Geocentric equatorial inertial coordinate system f i ( O i x i y i z i ) The origin of the geocentric equatorial inertial coordinate system is fixed at the center of the Earth. O i superior, O i x i The axis lies in the equatorial plane and points towards the vernal equinox. O i y i The axis lies in the equatorial plane and O i x i The axis points vertically eastward. O i z i shaft and O i x i , O i y i The axes form a right-handed orthogonal coordinate system; b. Reference spacecraft orbital coordinate system f o ( O o x o y o z o ) The reference spacecraft O is defined so that its initial center of mass coincides with the center of mass of the mission spacecraft E, and the origin of the reference spacecraft's orbital coordinate system is fixed at the spacecraft's center of mass. O o superior, O o x o The axis points from the Earth's center of gravity toward the spacecraft's center of mass O. O o y o The axis is in the orbital plane and O o x o The axis points perpendicularly to the velocity direction of the reference spacecraft. O o z o shaft and O o x o , O o y o The axes form a right-handed orthogonal coordinate system.
3. A spacecraft game-theoretic maneuver control method for threat avoidance according to claim 1 or 2, characterized in that: In step 2, when mission spacecraft E faces pursuit from multiple non-cooperative targets, a reasonable maneuvering strategy is used to maximize the fuel consumption required for the non-cooperative targets to approach the mission spacecraft, thereby increasing their time cost for approaching. Alternatively, the maneuvering strategy can be used to reduce the directional sources of threats during the approach. Therefore, the avoidance method is for E to maintain a straight line with P1 and P2 as much as possible during the pursuit. This positional relationship reduces the direction of incoming threats for spacecraft E. Furthermore, at this time, non-cooperative target P1 must bypass P2 to approach spacecraft E, thus increasing the maneuvering time and fuel consumption for collision with non-cooperative targets. The geometric relationship is as follows: (1) in, This is represented as the position vector of mission spacecraft E in the geocentric equatorial inertial coordinate system; , Represented as the position vectors of non-cooperative targets P1 and P2 in the geocentric equatorial inertial coordinate system; It represents the coefficient used to determine the relative distance between mission spacecraft E, non-cooperative targets P1 and P2.
4. The spacecraft game-theoretic maneuver control method for threat avoidance according to claim 3, characterized in that: Formula (1) simplifies to: (2) Define relative motion position By taking the derivative, we get , .
5. A spacecraft game-theoretic maneuver control method for threat avoidance according to claim 4, characterized in that: In step 2, based on assumptions 1-4, the CW equations for mission spacecraft E, non-cooperative targets P1 and P2 are established: (3) (4) (5) in, n Expressed as the orbital angular rate of the circular orbit in which the spacecraft resides; , Represented as the velocity and acceleration of mission spacecraft E; , Represented as the velocity and acceleration of the non-cooperative target P1; , Represented as the velocity and acceleration of the non-cooperative target P2; , , Represented as orbital control quantities for mission spacecraft E, and non-cooperative targets P1 and P2; Combining the definition of relative position and equations (3) to (5), we get: (6) Let the state space vector be A dynamic model including the relative motion states of the two non-cooperative targets and the mission spacecraft: (7) Wherein, the state transition matrix Control coefficient matrix of mission spacecraft The control coefficient matrix of non-cooperative target P1 The control coefficient matrix of non-cooperative target P2 .