Rapid analysis method for collision risk of space object
By establishing the intersection coordinate system and constructing vector relationship equations in spatial object collision analysis, the minimum close distance and close moment between the two bodies are quickly calculated, and the problems of low computing efficiency and insufficient precision in the prior art are solved, and efficient and accurate collision risk assessment is achieved.
Patent Information
- Application Number
- CN202510233412.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-28
- Publication Date
- 2025-06-27
AI Technical Summary
In the prior art, when performing space object collision analysis, the calculation efficiency is low and it is difficult to obtain an accurate solution. Especially when the object size is small and the speed is very high, the numerical calculation method takes time and can only obtain an approximate solution. The analytical calculation method is complex and the calculation amount is large.
A rapid analytical method for the collision risk of space objects is proposed. By establishing an intersection coordinate system and constructing vector relationship equations in linear motion, the minimum close distance and close moments between the two bodies are calculated, and the collision risk is quickly evaluated.
This method significantly improves the efficiency of collision analysis calculation, ensures high-precision calculation results, avoids step size problems and complexity of analytical calculations, and is suitable for a wide range of application scenarios.
Smart Images
Figure CN120216830A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of collision analysis and applications, and particularly relates to a method for rapidly analyzing the collision risk of spatial objects. Background Art
[0002] Collision is a common natural phenomenon and human activity. In nature, there is a possibility of collision between the smallest microscopic particles and macroscopic galaxies (bodies). Collision analysis is an activity that analyzes and calculates whether collisions will occur between two or more objects based on their initial states, and the analysis results are important bases for collision warning, risk disposal, and seeking advantages and avoiding disadvantages.
[0003] Perform collision analysis of moving objects, that is, calculate the collision situation when moving objects approach. This problem can be expressed as: judging whether there is a situation where the distance between two objects in space is less than a given dangerous distance Dis within a given time interval [t B , t E ; if so, calculate the time and distance when the two objects reach the closest point. For this problem, there are usually two calculation methods: numerical and analytical.
[0004] Method 1: Numerical calculation method
[0005] First, establish a unified coordinate system, and determine the position vectors and velocity vectors of the two objects at the initial moment t B ; then calculate the position vectors, velocity vectors, and the relative distance between them at each moment step by step according to a certain time step until the end of the t E moment; obtain the minimum relative distance within the given time interval [t B , t E (the subscripts B and E represent Begin and End respectively) by comparing and checking one by one, and compare it with the given dangerous distance Dis to judge whether there is a collision risk. When using this method to solve, the problems brought by the calculation step must be considered. This is because only when the product of the time step and the relative velocity of the two is relatively small (at least less than the given dangerous distance Dis), can false alarms be avoided and an approximate solution of the minimum approach distance be obtained. Therefore, these calculations are very time-consuming, especially when the object size is small and the speed is high. Even if the algorithm is optimized with variable time steps, first calculate according to a larger time step to find the time range where the two objects are relatively close; then calculate with a small time step within this time range. Although this speeds up the calculation process to a certain extent, there is still a large amount of calculation. The numerical calculation method is a common method for solving collision problems, but this kind of calculation is often very time-consuming, especially when the object size is small and the speed is high; moreover, generally only an approximate solution rather than an exact solution of the problem can be obtained by the numerical calculation method.
[0006] Method 2: Analytical calculation method
[0007] To avoid the step size and precision problems in numerical calculations and improve the calculation efficiency and quality, an analytical calculation method can be used. In analytical calculations, linearization assumptions are often made based on the motion characteristics of high-speed objects (such as spacecraft and space debris moving at high speed by inertia in the Earth's orbit) when approaching. That is: Since the entire approaching process occurs within a very short few seconds (quasi-inertial process), the motions of the two objects can be considered linear, and the speeds are both constant. Based on the linear motion assumption, spatial projection and analytical geometry give an analytical algorithm for calculating the minimum approach distance. However, this algorithm is relatively complex, and the solution is very troublesome, involving various geometric relationship conversions. Summary of the Invention
[0008] In view of the deficiencies in the prior art, the present invention proposes a fast analytical solution for the collision risk of space objects; to improve the efficiency of collision analysis calculations and at the same time ensure the high precision of the calculation results.
[0009] The present invention has broad application prospects in the fields of celestial body collision analysis, satellite collision warning, dangerous object screening, high-speed particle collision, etc., and well balances the relationship between calculation efficiency and precision, with good benefits and broad prospects.
[0010] The first aspect of the present invention proposes a fast analytical method for the collision risk of space objects, and the method includes:
[0011] Step S1: Establish a rendezvous coordinate system describing the relative motion relationship according to the motion state parameters of the two objects;
[0012] Step S2: Use the relative position and velocity vector relationship during the motion of the two objects to construct a vector relationship equation for the time variation in the case of linear motion;
[0013] Step S3: Calculate the collision risk of the two objects based on the minimum approach distance and the approach time between the two objects.
[0014] In the method, the objects are high-speed moving objects, the motion characteristics of the two objects when approaching are linearized motion, and the approaching process of the two objects is a quasi-static process.
[0015] In the method, the two objects are object D and object S, and a rendezvous coordinate system S e (x, y, z) is established during the approaching process of object D and object S; where:
[0016] The origin O is on object S, the y-axis of the coordinate system is along the relative velocity vector direction, and the relative velocity vector The subscripts d and s represent object D and object S respectively;
[0017] The plane perpendicular to the relative velocity vector where the object S is located is the rendezvous plane, and the x-axis of the coordinate system points to the projection position of the object D on the rendezvous plane;
[0018] At the collision moment, the object D is in the rendezvous plane. On the rendezvous plane, the x-axis points to the position of the object D at the time of collision, and the z-axis of the coordinate system is determined by the right-hand rule;
[0019] At a given moment, the rendezvous coordinate system is unique. The position of the object D in the rendezvous coordinate system at the collision moment is (x e ,0,0), and x e represents the minimum approach distance between the two objects.
[0020] In the said method, at time t B , the object D and the object S enter the proximity region. The position and velocity vector of the object D are respectively The position and velocity vector of the object S are respectively Then the relative position vector and the relative velocity vector are respectively:
[0021]
[0022] In the proximity region, the relative velocity vector remains unchanged. After a time Δt, the relative position vector and the relative velocity vector are respectively:
[0023]
[0024] When and are not collinear, and constitute the xy plane in the rendezvous coordinate system. The starting point of the vector is on the object S, and the end point moves along the y-axis on the object D. According to the vector geometric relationship, the sufficient and necessary condition for the distance r ds between the object D and the object S to reach the minimum is That is
[0025] Solving for the time Δt, we get:
[0026]
[0027] The solution result of Δt is applicable to the case where and are collinear; when , Δt has a real solution; otherwise, Δt = ∞, the velocities of the object D and the object S are exactly the same, their relative positions remain unchanged, and there is no minimum approach distance;
[0028] Solving for the rendezvous moment t e , we get:
[0029] t e = t B + Δt
[0030] The rendezvous time t e The relative position vector of is:
[0031]
[0032] wherein, The direction of is the opposite direction of the x-axis in the rendezvous coordinate system, and its magnitude r dse is the minimum approach distance x e .
[0033] In the method, the minimum approach distance x e is compared with the given dangerous distance Dis to determine whether there is a collision risk between object D and object S; wherein, if x e ≤ Dis, there is a collision risk; otherwise, there is no collision risk.
[0034] The second aspect of the present invention proposes a rapid analysis system for the collision risk of space objects. The system includes a processing unit, and the processing unit is configured to execute:
[0035] Establish a rendezvous coordinate system describing the relative motion relationship according to the motion state parameters of two objects;
[0036] Construct a vector relationship equation of time variation in the case of linear motion by using the relative position and velocity vector relationship when two objects move;
[0037] Calculate the collision risk of two objects based on the minimum approach distance and approach time between the two objects.
[0038] The object is a high-speed moving object, the motion characteristics when the two objects approach are linearized motion, and the approach process of the two objects is a quasi-static process.
[0039] The two objects are object D and object S, and the processing unit is specifically configured to: establish a rendezvous coordinate system S e (x, y, z) during the approach process of object D and object S; wherein:
[0040] The origin O is on object S, the y-axis of the coordinate system is along the relative velocity vector direction, and the relative velocity vector The subscripts d and s respectively represent object D and object S;
[0041] The plane where object S is located and perpendicular to the relative velocity vector is the rendezvous plane, and the x-axis of the coordinate system points to the projection position of object D on the rendezvous plane;
[0042] At the collision moment, object D is in the rendezvous plane. The x-axis on the rendezvous plane points to the position of object D at the collision moment, and the z-axis of the coordinate system is determined by the right-hand rule;
[0043] At a given moment, the rendezvous coordinate system is unique. The position of object D in the rendezvous coordinate system at the collision moment is (x e ,0,0), where x e represents the minimum approach distance between the two objects.
[0044] At time t B , object D and object S enter the proximity region. The position and velocity vectors of object D are respectively The position and velocity vectors of object S are respectively Then the relative position vector and relative velocity vector are respectively:
[0045]
[0046] Within the proximity region, the relative velocity vector remains unchanged. After a time interval of Δt, the relative position vector and relative velocity vector are respectively:
[0047]
[0048] When and are not collinear, and form the xy-plane in the rendezvous coordinate system. The vector has its starting point on object S and its ending point moving along the y-axis on object D. According to vector geometry, the necessary and sufficient condition for the distance r ds between object D and object S to reach the minimum is That is
[0049] Solving for the time interval Δt, we get:
[0050]
[0051] The solution result of Δt is applicable to the case where and are collinear; when , Δt has a real solution; otherwise, Δt = ∞, the velocities of object D and object S are exactly the same, their relative positions remain unchanged, and there is no minimum approach distance;
[0052] Solving for the rendezvous moment t e , we get:
[0053] t e = t B +Δt
[0054] The rendezvous time t e The relative position vector is as follows:
[0055]
[0056] Among them, The direction of is the reverse direction of the x-axis in the rendezvous coordinate system, and its magnitude r dse Is the minimum approach distance x e .
[0057] The processing unit is specifically configured to: compare the minimum approach distance x e With the given dangerous distance Dis to determine whether there is a collision risk between object D and object S; among them, if x e ≤Dis, there is a collision risk; otherwise, there is no collision risk.
[0058] The present invention utilizes the relative vector relationship in two-body space motion to construct a rendezvous coordinate system and a vector relationship equation, and quickly analyzes and calculates the minimum approach distance and approach time between two bodies, which not only avoids the contradiction between calculation efficiency and accuracy in numerical calculation, but also reduces the complexity and calculation amount of traditional analytical methods. Therefore, the present invention well balances the relationship between calculation efficiency and accuracy, and has good application benefits and broad prospects. Brief Description of the Drawings
[0059] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.
[0060] Figure 1 It is a schematic diagram of a rendezvous coordinate system according to an embodiment of the present invention.
[0061] Figure 2 It is a schematic diagram of the velocity relationship in the rendezvous coordinate system according to an embodiment of the present invention.
[0062] Figure 3 It is a flowchart of a fast analysis method for the collision risk of space objects according to an embodiment of the present invention. Detailed Embodiments
[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part rather than all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.
[0064] The present invention first establishes an encounter coordinate system that describes the relative motion relationship based on the motion state parameters of two objects; then, using the relative position and velocity vector relationship during the motion of the two objects, constructs a vector relationship equation for the time variation in the case of linear motion, and analytically calculates the minimum approach distance and approach time between the two bodies, thereby improving the efficiency and accuracy of collision analysis and calculation.
[0065] First Embodiment
[0066] 1. Explanation of linearized motion
[0067] According to the motion characteristics during the approach of high-speed objects, an explanation of linearized motion is made; that is: since the entire approach process occurs within a very short few seconds (quasi-static process), the motions of the two objects are considered linear, and the velocity vectors are both constant.
[0068] 2. Construction of the encounter coordinate system
[0069] During the approach of the objects (denoted as object D and object S), an encounter coordinate system (encounter coordinatesystem) is defined, denoted as S e (x, y, z): The origin O is on object S, and the y-axis is along the relative velocity vector (the subscripts d and s represent object D and object S respectively) direction. The plane where object S is located and perpendicular to the relative velocity vector is called the encounter plane. The x-axis points to the projection position of object D on the encounter plane, as Figure 1 shown. At the encounter (collision) moment, object D is also in the encounter plane. The x-axis on the encounter plane exactly points to the position of object D at this time, and the z-axis is obtained by the right-hand rule. In the case of linear motion, for one approach event, this encounter coordinate system is unique at a given moment. At the encounter moment (when the two objects are closest), the position of object D in the encounter coordinate system is (x e , 0, 0), where x e represents the minimum approach distance between the two objects.
[0070] After defining this coordinate system, on the one hand, when calculating collision problems, the three-dimensional problem of the spatial motion of two objects can be transformed into a two-dimensional problem without losing any information in the calculation. This can greatly simplify the calculation and thus significantly improve the calculation efficiency. On the other hand, since the direction of projection onto the rendezvous plane is the direction of the relative velocity (which remains constant during the approach process) and there are no time-varying factors in the calculation, the time term is eliminated. When calculating the collision situation, only the distance between the two objects at the rendezvous moment needs to be concerned about.
[0071] 3. Calculate the minimum approach distance and time
[0072] At time t B moment, object D and object S enter the proximity region (the relative distance is relatively small and linearization approximation can be made). Given that their position and velocity vectors in a certain inertial coordinate system are respectively and As Figure 2 shown, the relative position vector and relative velocity vector are respectively:
[0073]
[0074] In the proximity region, according to the assumption of linear motion, the relative velocity vector remains unchanged. The relative position vector and relative velocity vector after a time interval of Δt can be calculated:
[0075]
[0076] Obviously, when and are not collinear, and can form a plane, that is, the xy plane in the rendezvous coordinate system. The starting point of the vector is on object S and the end point moves along the y-axis on object D. According to vector geometric relations, it is easy to know that the necessary and sufficient condition for the minimum distance r ds between object D and object S is That is:
[0077]
[0078] Substitute equation (2) into equation (3) to obtain a linear equation of one variable about time t, and solve to get the unique time Δt, that is:
[0079]
[0080] This formula also applies to the case where and are collinear. When When this equation has real solutions; otherwise, Δt = ∞, indicating that the velocities of object D and object S are exactly the same, their relative positions will never change, and there is no minimum approach distance. The rendezvous time t is obtained from equation (4). e as follows:
[0081] t e = t B + Δt (5)
[0082] Substituting equation (4) into equation (2) again, the relative position vector at the rendezvous time t e is obtained as:
[0083]
[0084] where is exactly in the opposite direction of the x-axis in the rendezvous coordinate system, and its magnitude r dse is the minimum approach distance x e .
[0085] 4. Calculate the collision risk
[0086] Compare the minimum approach distance x e obtained using equation (6) with the given dangerous distance Dis to determine whether there is a collision risk between object D and object S. If x e ≤ Dis, there is a collision risk; otherwise, there is no collision risk between object D and object S.
[0087] Second Embodiment
[0088] As Figure 3 shown, this embodiment calculates the rendezvous time and the minimum approach distance during the approach of the objects.
[0089] At t B = 0, the position and velocity vectors of object D and object S in a certain inertial coordinate system are respectively and Then the relative position vector and the relative velocity vector are respectively:
[0090]
[0091] Within the approach region, the relative velocity vector remains unchanged, and there is a minimum approach distance between object D and object S. Solving using equation (4) gives the unique time Δt, then there is:
[0092]
[0093] The rendezvous time t e is obtained as follows:
[0094] te = t B + Δt = 4.4 s
[0095] Then, the relative position vector at the rendezvous time t e is obtained:
[0096]
[0097] Then the magnitude of 2 km is the minimum approach distance x e . Finally, comparing 2 km with the given dangerous distance Dis can obtain the collision danger situation.
[0098] As can be seen from the above process, when calculating using the present invention, only 2 - 3 simple vector calculations are required. The calculation process is very simple, and there is no error in the result. Comparing with the result of using the numerical calculation method, as shown in the following table. It can be seen that the calculation efficiency and accuracy of the numerical calculation method are easily affected by the given time interval and time step. Even when the given time interval is relatively accurate (within a very small range near the rendezvous time) and the time step is relatively reasonable, the calculation efficiency and accuracy of the present invention are significantly better than those of the numerical calculation method.
[0099] Table 1: Comparison of calculation results of each method
[0100]
[0101]
[0102] In summary, the technical effects brought by the present invention include: (1) The construction of the rendezvous coordinate system can significantly simplify the calculation of the three - dimensional spatial relationship of moving objects, reducing the three - dimensional problem to a two - dimensional problem; (2) Utilizing the invariance of the relative velocity during the approach process of two - body objects to recursively deduce the relative position vector relationship during the approach process, the method is simple; (3) Utilizing the vector geometric relationship at the closest approach of two - body objects to establish a linear equation of one variable about time t, directly solving for the rendezvous time and the minimum approach distance, with high calculation efficiency and no calculation error; (4) The method of the present invention is applicable to analyzing linear or quasi - linear object collision situations, with strong applicability.
[0103] Please note that the technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as within the scope described in this specification. The above-described embodiments only represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the appended claims.
Claims
1. A method for rapid analysis of collision risk of space objects, characterized in that: The method comprises: Step S1, establishing an intersection coordinate system describing the relative motion relationship according to the motion state parameters of the two objects; Step S2, using the relative position and velocity vector relationship of the two objects when they are moving, construct a vector relationship equation of time change in the case of linear motion; Step S3: Calculate the collision risk of the two objects based on the minimum approach distance and approach time between the two objects.
2. A method for rapid analysis of space object collision risk according to claim 1, characterized in that: In the method, the object is a high-speed moving object, the motion characteristics of the two objects when approaching each other are linear motion, and the approach process of the two objects is a quasi-static process.
3. A method for rapid analysis of space object collision risk according to claim 2, characterized in that: In the method, the two objects are object D and object S, and an intersection coordinate system S is established during the approach of object D and object S. e (x,y,z); where: The origin O is on the object S, the y-axis of the coordinate system is along the direction of the relative velocity vector, and the relative velocity vector The subscripts d and s represent object D and object S, respectively; The plane where the object S is located and is perpendicular to the relative velocity vector is the intersection plane, and the x-axis of the coordinate system points to the projection position of the object D on the intersection plane; At the moment of collision, object D is in the intersection plane, the x-axis on the intersection plane points to the position of object D at the moment of collision, and the z-axis of the coordinate system is determined by the right-hand rule; At a given moment, the intersection coordinate system is unique. The position of object D in the intersection coordinate system at the moment of collision is (x e ,0,0),x e Indicates the minimum approach distance between two objects.
4. The method for rapid analysis of collision risk of space objects according to claim 3, characterized in that: In the method, at t B At time , object D and object S enter the approach area, and the position and velocity vectors of object D are The position and velocity vectors of object S are Then the relative position vector and relative velocity vector are: In the approaching area, the relative velocity vector remains unchanged. After Δt time, the relative position vector and relative velocity vector are: when and When not collinear, and The plane formed is the xy plane in the intersection coordinate system, and the vector The starting point is on object S and the end point is on object D moving along the y-axis. According to the vector geometry relationship, the distance between object D and object S is r ds The necessary and sufficient condition to achieve the minimum is Right now Solving for time Δt, we obtain: The solution for Δt is applicable to and Collinear situation; when When , Δt has a real number solution; otherwise, Δt=∞, the speeds of object D and object S are exactly the same, their relative positions remain unchanged, and there is no minimum approach distance; The intersection time t e Solving it, we get: t e =t B +Δt Intersection time t e The relative position vector is: in, The direction is the opposite direction of the x-axis in the intersection coordinate system, and its magnitude is r dse is the minimum approach distance x e .
5. A method for rapid analysis of space object collision risk according to claim 4, characterized in that: In the method, the minimum proximity distance x e Compare with the given danger distance Dis to determine whether there is a collision risk between object D and object S; if x e ≤Dis, there is a collision risk; otherwise, there is no collision risk.
6. A rapid analysis system for space object collision risk, characterized in that: The system comprises a processing unit configured to perform: According to the motion state parameters of the two objects, an intersection coordinate system describing the relative motion relationship is established; Using the relative position and velocity vector relationship of two objects in motion, construct the vector relationship equation of time change in linear motion; Based on the minimum approach distance and approach time between the two objects, the collision risk of the two objects is calculated.
7. A rapid analysis system for space object collision risk according to claim 6, characterized in that: The objects are high-speed moving objects, the motion characteristics of the two objects when approaching each other are linear motion, and the approach process of the two objects is a quasi-static process.
8. A rapid analysis system for space object collision risk according to claim 7, characterized in that: The two objects are object D and object S, and the processing unit is specifically configured to: establish an intersection coordinate system S during the approach process of object D and object S e (x,y,z); where: The origin O is on the object S, the y-axis of the coordinate system is along the direction of the relative velocity vector, and the relative velocity vector The subscripts d and s represent object D and object S, respectively; The plane where the object S is located and is perpendicular to the relative velocity vector is the intersection plane, and the x-axis of the coordinate system points to the projection position of the object D on the intersection plane; At the moment of collision, object D is in the intersection plane, the x-axis on the intersection plane points to the position of object D at the moment of collision, and the z-axis of the coordinate system is determined by the right-hand rule; At a given moment, the intersection coordinate system is unique. The position of object D in the intersection coordinate system at the moment of collision is (x e ,0,0),x e Indicates the minimum approach distance between two objects.
9. A rapid analysis system for space object collision risk according to claim 8, characterized in that: In t B At time , object D and object S enter the approach area, and the position and velocity vectors of object D are The position and velocity vectors of object S are Then the relative position vector and relative velocity vector are: In the approaching area, the relative velocity vector remains unchanged. After Δt time, the relative position vector and relative velocity vector are: when and When not collinear, and The plane formed is the xy plane in the intersection coordinate system, and the vector The starting point is on object S and the end point is on object D moving along the y-axis. According to the vector geometry relationship, the distance between object D and object S is r ds The necessary and sufficient condition to achieve the minimum is Right now Solving for time Δt, we obtain: The solution for Δt is applicable to and Collinear situation; when When , Δt has a real number solution; otherwise, Δt=∞, the speeds of object D and object S are exactly the same, their relative positions remain unchanged, and there is no minimum approach distance; The intersection time t e Solving it, we get: t e =t B +Δt Intersection time t e The relative position vector is: in, The direction is the opposite direction of the x-axis in the intersection coordinate system, and its magnitude is r dse is the minimum approach distance x e .
10. A rapid analysis system for space object collision risk according to claim 9, characterized in that: The processing unit is specifically configured to: set the minimum approach distance x e Compare with the given danger distance Dis to determine whether there is a collision risk between object D and object S; if x e ≤Dis, there is a collision risk; otherwise, there is no collision risk.