Spatial Hostile Target Avoidance Interval Relaxation Planning Method for Motion Conflict

Abstract

The present invention belongs to the field of satellite mission planning technology, and specifically relates to an interval relaxation planning method for space hostile target avoidance facing action conflicts, comprising the following steps: S1: defining a task planning problem for satellite avoidance threats, S2: planning the structure of an algorithm, S3: planning to process numerical variables and expand nodes by searching, S4: using a heuristic function to estimate the cost of a node, measured by the number of actions required to reach a target problem from a boundary state, S5: using Z3 to verify the consistency of the planning, and assigning the most appropriate value to the numerical variable in its interval value, S6: outputting the final planning result, and completing the task planning for satellite avoidance threats. The present invention reduces the consumption of resources and time as much as possible under the premise of ensuring the safety of spacecraft, so that the overall performance of the system is optimized, and has great significance for ensuring the safety of national space assets, improving the continuous and stable operation capability of satellite services, and efficiently building a space power.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite mission planning, and in particular relates to a space hostile target avoidance interval relaxation planning method oriented to action conflicts. Background Art

[0002] With the continuous advancement of aerospace technology and the complexity of spacecraft missions, the traditional mission planning method based on manual instructions can no longer meet the autonomy requirements of spacecraft. Therefore, spacecraft autonomous mission planning technology came into being. From the earliest method based on rules and expert systems to the later method based on planning language and artificial intelligence technology, spacecraft autonomous mission planning technology has undergone great development, providing spacecraft systems with more advanced planning and decision-making capabilities;

[0003] Currently, there is a large amount of space debris around the Earth's orbit, which puts operating satellites, probes and other facilities at risk of collision. In addition, due to the continuous advancement and deployment of low-orbit giant constellation plans such as "Starlink" and "OneWeb", the density of orbital space has shown an exponential growth trend, the risk of collision has increased sharply, and space safety incidents have occurred frequently;

[0004] In the face of various orbital threats such as space debris, failed satellite collisions, and hostile satellite harassment, the current "space-ground large loop" threat handling method is usually adopted. First, the threat level of the threat target is determined by using the orbital information of the threat target measured on the ground and the downlink data measured by the spacecraft remote sensing equipment. Then, after analysis and decision-making by ground personnel, the attitude and orbit control instructions are injected into the spacecraft, and finally the threat is avoided through the attitude and orbit maneuvers of the spacecraft.

[0005] However, this method is heavily dependent on the ground, affecting the safety of spacecraft in orbit and business continuity, and will consume unnecessary resources on the satellite, making it difficult to adapt to the current space situation;

[0006] Satellite threat avoidance requires that satellites complete actions such as perception, decision-making, attitude and orbit change to avoid threatening targets in the shortest possible time, and achieve timely and appropriate autonomous response to orbital threats under the conditions of complex space environment and severe resource constraints;

[0007] Therefore, it is necessary to plan efficient and reliable action plans when satellites respond to orbital threats. Summary of the invention

[0008] The purpose of the present invention is to provide a space hostile target avoidance interval relaxation planning method for action conflicts, which can reduce the consumption of resources and time as much as possible while ensuring the safety of the spacecraft, so as to optimize the overall performance of the system.

[0009] The technical solution adopted by the present invention is as follows:

[0010] The method for space hostile target avoidance interval relaxation planning for action conflict includes the following steps:

[0011] S1: Define the mission planning problem of satellite threat avoidance;

[0012] S2: The structure of the planning algorithm. In the planning search, the concurrency problem and the numerical variable problem are handled by introducing numerical causality and interval-based numerical variable representation, action duration and control parameters. The planning algorithm uses the Z3 theorem prover to assign numerical variables and verify the consistency of the plan.

[0013] S3: Planning to process numerical variables and expand nodes through search;

[0014] S4: Using heuristic functions , estimated node The cost of The boundary state reaches the target problem Measured by the number of moves required;

[0015] S5: Use Z 3 to verify the consistency of the plan and assign the most appropriate value to the numerical variable in its interval value;

[0016] S6: Output the final planning results and complete the satellite's mission planning to avoid threats.

[0017] The technical effects achieved by the present invention are:

[0018] The present invention reduces the consumption of resources and time as much as possible while ensuring the safety of the spacecraft, so as to optimize the overall performance of the system. It is of great significance for ensuring the safety of national space assets, improving the continuous and stable operation capability of satellite services, and efficiently building a space power. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a planning result diagram of the satellite of the present invention for coping with orbital threats;

[0020] Figure 2 It is a resource consumption diagram of the satellite in the present invention for coping with orbital threats. DETAILED DESCRIPTION

[0021] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

[0022] like Figure 1-2As shown in the figure, the space hostile target avoidance interval relaxation planning method for action conflicts describes the threat scenario of satellites facing space hostile targets. The satellite is in orbit to perform routine tasks, such as earth observation, data relay, navigation, and communication. During this period, it will inevitably be subject to threat interference from hostile targets, such as space debris, patrol reconnaissance, and attack harassment. Among them, space debris has no maneuverability and poses a collision risk to satellites; patrol reconnaissance threats are hostile spacecraft with maneuverability, which can drift patrol or establish observation status for our satellites. Attack harassment is the malicious harassment of our spacecraft by hostile spacecraft using payloads. These space hostile target threats are occasional emergency tasks that may cause irreparable damage to the spacecraft or even cause the spacecraft to fail. After detecting a space hostile threat, the spacecraft needs to respond to the threat quickly. When planning the task, it is necessary to consider the time resource constraints of the system, coordinate the action sequence of each subsystem of the spacecraft, and achieve threat avoidance. The specific designed subsystem action names and functions are shown in Table 1 below:

[0023] Table 1 shows the subsystem action names and functions;

[0024] It specifically includes the following steps:

[0025] S1: Define the mission planning problem of satellite threat avoidance;

[0026] The satellite threat avoidance mission planning problem is a tuple , expressed as: in, is a set of satellite facts, a propositional Boolean variable, is a collection of satellite real-valued numerical resource variables, is the initial state of the threat under the orbital threat, and is the variable Partial assignment of is the target condition for the satellite to avoid the satellite, a set of propositional conditions and / or conditions on numerical variables; is a collection of continuous actions in the form of: in, Is a value between the upper and lower limits, indicating the action Duration of action The duration defines a time interval , which corresponds to the start of the action execution and end Time point, The value is the interval Length; It is necessary to A set of conditions that hold true, is a set of The end condition, yes A set of invariant conditions must be Maintained during execution, that is, throughout the interval Keep; yes A set of effects produced, and yes A set of effects produced; Describe the specified action The control parameters in is a numeric variable and is equated to a numeric variable ,therefore, The variables involved in the numerical expression and The variables defined in are used to model and the conditions or effects of

[0027] gather Contains satellite resource numerical state variables whose values ​​change as the problem is solved. The introduction of numerical variables provides a way to measure parameters that represent satellite resource consumption or any other type of quantity or range;

[0028] action Duration Combined with the time constraint and constrained to a certain interval, the duration constraint is expressed as: in, , is a Contains arithmetic operators For expressions involving numeric constants and variables, The value represents the interval The time that has passed in

[0029] action The condition set , is a set of propositional or numerical conditions. Propositional conditions are of the form The text of , or the form Negative text of ;

[0030] The numerical conditions are expressed as: The numerical constraints are expressed as ,and Same, one action The effect set, , It is propositional or numerical;

[0031] The form of the proposition effect is or ,in .action The proposition effect can be transformed into: Indicates at a point in time The proposition is deleted in the state. Indicates at a point in time The proposition is added in the state.

[0032] action A set of numerical effects, called , which is in the form of ,in, yes A variable in , This includes arithmetic operations with variable durations; that is, Operate on numeric constants and variables in . Use a numeric expression to perform operations on numeric constants and variables in . Update the value of ;

[0033] Satellite threat avoidance mission planning problem The solution to is a time-stamped sequence of actions, with associated durations, that transforms the initial state to a state that satisfies the goal, subject to all imposed conditions. The solution is defined as: in, and , the action specification can be satisfied by a variety of duration values, so the duration of the action is clear. Similarly, the problem The solution is necessary to include the specific values ​​of the control parameters of the action in the timestamp sequence;

[0034] Action specifications are satisfied by different duration values, so the duration of the action is clear and the problem The solution is necessary to include the specific values ​​of the control parameters of the action in the timestamp sequence.

[0035] S2: Structure of the planning algorithm;

[0036] In the planning search, concurrency and numerical variable problems are handled by introducing numerical causality and interval-based representation of numerical variables, action durations, and control parameters. The planning algorithm uses the Z3 theorem prover to assign values ​​to numerical variables and verify the consistency of the plan.

[0037] In time-value planning, the start and end times of actions become key entities for planning, since conditions or effects are required at these time points. Dealing with time and value features in planning means defining appropriate time and value relationships between action time points.

[0038] One action It consists of two time points, the start time point and end time point , in addition, the invariant condition It needs to be held within the open interval defined by the start and end of the movement;

[0039] When performing runtime numerical planning, the following two key operations are required:

[0040] S21: Introduce an action into the plan to satisfy the prerequisite of another action;

[0041] set up and are two actions in a plan, and causality is two actions at a point in time. and The relationship between , expressed as , which means the condition Depend on Effect support in action is called a producer action, It is called consumer action;

[0042] To pass The effects in support an invariant global condition , two causal relationships are necessary, one is the start of the action, which is: One is the end of the action: Ensure that the condition is in action Valid for the entire duration of

[0043] Time and The causal relationship between them implicitly establishes an order between the two actions, because the producer time point Must be in the consumer Sort by before. Supported conditions It can be a proposition, a negated proposition, or a numerical variable in a condition. In the latter case, the causal relationship indicates that The variable values ​​used to verify the numerical conditions come from Application of effects.

[0044] In said S22, the defect is determined by raising or lowering the defect time point. To solve this, lifting means introducing a sorting constraint of the form , reducing means introducing order constraints .

[0045] S22: Resolve conflicts between actions in the plan.

[0046] Dealing with defects in planning: There is a conflict between a certain time point in the plan and the causal relationship, which is called a defect. In causal relationship If the defect is caused Relative to and is unordered, and For the positive proposition and ,Right now:

[0047] Proposition At the point in time is deleted, or To negate the proposition and ;

[0048] That is, the proposition At the point in time is added, or is a numeric variable and is Update its value;

[0049] This defect definition protects numerical causal relationships from being affected by simultaneous changes to the values ​​of dependent variables. Defects can be prevented by raising or lowering the defect time point. Specifically, lifting means introducing an ordering constraint of the form , reducing means introducing order constraints Unlike causal relationships, ordering constraints only set the order in which two time points occur, but do not establish a causal relationship between them.

[0050] S3: Planning to process numerical variables and expand nodes by searching A*;

[0051] Search from an initial plan Initially, the plan contains only one dummy action for the initial state , about the goal ,When a solution plan is found, a dummy action can be inserted into the plan;

[0052] By adding actions to support All possible actions and corresponding defects to expand a given node ;

[0053] Therefore, if the following conditions are met, it is considered yes The subexpression is: Towards Add a new action ,Right now, ; By inserting the corresponding causal relationships, all All conditions support Actions; All defects in are addressed by adding new sorting constraints, either by promotion or demotion.

[0054] To select the next node to expand, a standard heuristic function is applied to estimate the probability of Part of the plan to reach the goal The cost of , the heuristic function is: Among them, the plans in the open node list are Value descending order, component It is the arrival node The cost of It is measured by the number of actions planned in the component It is a slave node Planned arrival An estimate of the cost of , expressed in number of actions;

[0055] Moreover, using the state-based heuristic, the node The boundary states of the partial order programming in order to be able to apply ;

[0056] Next, we will focus on how to calculate the boundary state of planning;

[0057] For the boundary state, it is the variable Assignment of

[0058] Among them, the proposition variable Assign Boolean values ​​to numeric variables Assigned to interval ;

[0059] Given a partial order program: in, Boundary State In topological order The state resulting from applying the effect at each point in time, yes A set of actions in yes A set of ordering constraints on the action time points in , It is a set of cause-effect relationships;

[0060] The initial state of the planning problem Modeled as an unconditional virtual action, its ending effects include Facts, problem goals It is also a virtual action with no effect. Its starting condition is The conditions specified in;

[0061] Time , is ordered before another point in time ;

[0062] When (1) there is a causal relationship , or (2) there is a sequence , or (3) and They are the beginning and end of the same action respectively.

[0063] Although various topological orders are valid, it is not possible to obtain different boundary states for the same plan. Using numerical variables, whether in duration specifications, conditions, or effects, requires establishing causal relationships with the actions and time points required to generate the variable values. Topological sorting must follow causal relationships and ordering;

[0064] The boundary state is calculated by applying the effects specified at the time points in the topological order in sequence. The first time point represents the virtual action of the initial state, and its effect is applied to obtain the first state Equal to the initial state , proceed to the next time point in linear order and apply its effects to obtain a new state Generally speaking, at a given time point Status The effect is:

[0065] The effect of negating a proposition is assigned a false The values ​​are: The effect of the positive proposition is assigned a true The values ​​are: Numerical Effects ,renew Medium Variable The upper and lower bounds of use interval-based arithmetic where according to Update the interval value, The variable values ​​in If these numerical variables appear in middle, exist The values ​​in represent duration-dependent effects;

[0066] The resulting state after applying the effect of the last time point in the topological order is the planned boundary state .

[0067] S4: After explaining how to calculate the boundary state of the heuristic function node, we will introduce the design of the heuristic function, which is called ;

[0068] Using heuristic functions , estimated node The cost of The boundary state reaches the target problem Measured by the number of moves required;

[0069] Therefore, the temporal dimension of the planning problem is ignored. Heuristic approaches to temporal planning attempt to minimize the maximum makespan of a plan (the duration from the start of the first action to the end of the last action), particularly in optimal time planning. This patent devises a heuristic approach that focuses on the numerical characteristics of the problem and estimates the plan length based on the number of plan actions extracted from the propositional relaxation plan graph. Using the number of actions is often a more informative search guide than the total time span of the plan. The calculation of is divided into two stages, namely, the heuristic function Divided into:

[0070] S41: Establish a relaxation planning graph;

[0071] planning The RPG from its borderline state Construction,RPG is a graph of a relaxed version of the planning problem, ignoring deletion effects, a fact layer containing Positive propositions about variables in , and The value interval of the numeric variable in, an action layer contains actions;

[0072] The structure of RPG is as follows: The first fact layer It is a boundary state , action layer Contains all actions ,in, The propositional conditions are included in In the fact layer Depend on Determine, among which, The proposition in is All the propositions in The propositions added by the action are calculated in two steps The values ​​of the numeric variables in :

[0073] S421: The value of a numeric variable is set to The values ​​of corresponding variables in are equal;

[0074] S422: The value range of each variable is expanded to include all The values ​​obtained by the maximum and minimum assignment effects in ;

[0075] set up For a node in the search tree, if one of the following two conditions is met, the node The structure of RPG will be based on The layer fails and terminates;

[0076] Since the deletion effect of the action is ignored, a layer Indicates that the state may contain All facts actions. An action layer It also includes no-operation actions, indicating the previous fact layer For each fact, keep the same fact to the next fact layer , meaning that there is no operation on these facts. , Included in the application All possible facts that can be realized after the actions in the game, including propositions and numerical variables. Therefore, it is easy to see that RPG is monotonically growing.

[0077] S4111: The value is equal to the previous fact layer Neither new facts nor new numerical variables can be realized in the future. When the graph expansion stagnates, the relaxation problem is unsolvable;

[0078] S4112: Contains The same proposition, and , yes The parent node of

[0079] The rationale behind this is that since the plans extracted from the RPG contain at least one action in each layer, Therefore, when When established, The heuristic value of will never improve the heuristic value of its parent node. This stopping criterion is imposed to avoid infinite expansion when the numerical goal cannot be achieved.

[0080] In the S4112, when the node The number of RPG layers relative to its parent node The number of layers has increased a lot, at the node Planning in the solution leads to a better solution than planning The reachable solutions in are longer, or the nodes The plan in produces a high-quality solution, but the heuristic function is not informative and returns a higher value than it should, making the relaxation unsolvable.

[0081] Because the problem target may also be from the node Therefore, the node cannot be discarded. Assign a high heuristic value to give it the lowest priority in the search. Under the above criteria, the expansion of the RPG is guaranteed to be complete.

[0082] When the goal is reached, the expansion of the RPG ends. Otherwise, if the problem does not contain numerical variables, a level is reached where no more propositions can be added (because the number of propositions is finite). This level is called a fixed point. The expansion ends at the fixed point. When completing the RPG expansion, problems with infinite domain numerical variables may arise. If the node If the fixed point is not reached, set the maximum number of layers to ensure termination. The value of this limit will be the parent node because the goal is to keep searching for nodes with better heuristic values ​​(finally searching for nodes that make their parent's heuristic value worse).

[0083] After successfully expanding the RPG, extract the relaxed solution plan and define the function as: in, The first appearance of the factual hierarchy in an RPG;

[0084] Define the function as: Among them, given a variable and a numerical condition ,in Used to check if a higher or lower value to satisfy the condition, which can be easily obtained from Using comparators and The comparison side is calculated. For equality or not equal This function returns the sign of , indicating that both high and low values ​​can satisfy the condition;

[0085] Define the function as: Where, given a numerical variable , a preferred boundary, and an index at the fact level, which returns The preferred boundaries are updated in The last level before;

[0086] Computational Planning Heuristic value of Based on the information obtained from RPG, initially, the problem goals are stored in a priority queue. The goals can be propositions, pairs (proposition, level) or numerical triples (variable, preferred bounds, level). Then, these tuples are extracted from the queue (higher level tuples are extracted first). To achieve a subgoal, a producer action is selected from the corresponding action level and the condition of this action is introduced into the queue. The same proposition cannot be inserted into the queue multiple times. A numerical variable can be included multiple times, but the preferred limits or levels must be different. When the queue is empty, the process ends. The heuristic value is equal to the number of actions of the relaxed plan.

[0087] S5: Use Z3 to verify the consistency of the plan and assign the most appropriate value to the numerical variable in its interval value;

[0088] Once a solution is found, Z3 is called to check its consistency, which means checking: There exists a valid schedule of actions. To do this, it is necessary to choose the start times and durations of the actions such that all causal relationships and orderings are satisfied. There exist valid values ​​of the control parameters and action durations that allow to satisfy the numerical conditions of other actions. Among these possible values, Z3 will choose the one that minimizes the schedule makespan;

[0089] Z3 is used to solve nonlinear fixed point optimization problems. To model a plan: In Z3, real fixed point variables with three decimal places are defined as: ,action The start time of ,action End time of ,action Duration of ,action The control parameter value of , which can be defined as an integer or a real number, so the type of this variable will be defined accordingly; , the value of the variable In Action Update after the start time of ; , the value of the variable In Action Update after the end time of

[0090] Also, define the following constraints:

[0091] Initial virtual action, action Indicates the initial state , the end time is 0, with duration, is a small interval,

[0092] Each sequence or The causal relationship in an action The beginning or end of another action An order is established between the start or end of the , which is transformed into a constraint: For each action , the following constraints are defined: The constraint is defined as ;

[0093] The relationship between the start and end of an action is also modeled as ; The numerical condition for .

[0094] These constraints involve numerical variables, control parameters, and action durations. The values ​​of the variables are taken from the last time they were updated (information stored in digital causality). For example, if the variable The required conditions are and Then, yes The value of is used to evaluate Medium condition. The numerical effect of As with numerical conditionals, the previous value of the variable is obtained from the causal relation.

[0095] Among them, Z3 is only run on the search space nodes that contain solutions to check their consistency. Z3's lazy execution allows large parts of the search space to be pruned without running Z3 on every node in the search space, which would otherwise result in excessive overhead. The plan algorithm pruning works as follows: plans detected as inconsistent by Z3 are pruned; the solver then checks whether the parent plan node is also inconsistent, in which case it is also deleted along with all its successors; the process continues upward in the search tree until a valid plan is found.

[0096] S6: Output the final planning result and complete the mission planning of satellite to avoid threats;

[0097] The planning algorithm has theoretical properties in terms of robustness and completeness. The partial order planning algorithm has completeness and reliability. This patented algorithm uses standard partial order mechanisms to ensure the correctness of the solution. Effects and conditions are linked by causal relationships, and any conflicts that undermine the integrity of the plan are resolved through traditional defect resolution mechanisms (promotion or demotion). In addition, Z3 is used to perform timing scheduling and numerical constraint verification of the plan.

[0098] For completeness, the algorithm uses the standard Search, on a finite graph with non-negative edge weights, the search is guaranteed to terminate and be complete.

[0099] Through a basic plan The method to generate the successor plan is:

[0100] When action Can be added to hour, The conditions must be passed To support the existence of actions in is The last action inserted in The effect is not supported Any condition indicates that Has been inserted into In the previous planning, therefore, Will also appear in In some other plans, The successor planning constraint is to a node, which is introduced by Supported actions, and introduction The last action of the sibling nodes in and their causal links and ordering.

[0101] Through the above steps, the final planning result is output, and the mission planning of satellite evasion threat is completed. In order to prove the effectiveness and feasibility of the above steps, this technical solution discloses a simulation experiment, which is as follows:

[0102] Simulation settings:

[0103] In the space environment, there are three lighting conditions, including front lighting, back lighting, and ground shadow. When the satellite encounters an orbital threat, different combinations of four sensors are selected to perceive the threat target according to the illumination. Table 2 shows the sensors used in the three types of illumination. The actions of each subsystem in the spacecraft are performed autonomously to avoid orbital threats. The subsystem names and functions are shown in Table 1.

[0104] Table 2: Data acquisition sensors under three lighting conditions;

[0105] All steps in the simulation are implemented in Ubuntu operating system using C++ programming language, with computer memory limited to 8GB and frequency of 3.60GHz.

[0106] Simulation results analysis:

[0107] Figure 1The task planning solution for autonomous avoidance of orbital threats by spacecraft under front-light conditions is shown. Table 3 explains the meaning of the symbols in the planning results. The global camera is always turned on when performing observation tasks, and the threat target is found at 2s; because the spacecraft is currently in a front-light environment, two other sensor devices are used to collect threat data; when the distance requirements are met, the visible light camera is also used for data collection; after the threat data is collected, data fusion and software action decision-making are performed in the intelligent computing unit to analyze the threat target. Since the threat intention of the enemy spacecraft is analyzed to image our spacecraft. Therefore, the decision to perform attitude maneuvers to hide the payload can achieve threat avoidance. Finally, the attitude of the spacecraft is adjusted by the attitude system to avoid the threat. Figure 2 A diagram showing the resource consumption of the satellite in response to orbital threats. During the avoidance process, the satellite's fuel resources were not consumed because there was no orbit change maneuver. Electric power resources were consumed as the avoidance action was executed, while computing power resources were occupied and released according to the software actions;

[0108]

[0109] Table 3: Planning results Figure 2 The meaning of the symbols in ;

[0110] from Figure 1 and 2 It can be seen that the spacecraft can autonomously plan a series of onboard action sequences from threat target detection to collision avoidance. Through the proposed autonomous mission planning strategy, the spacecraft can plan a series of threat avoidance actions. In the absence of ground measurement and control, the spacecraft can autonomously respond to orbital threats.

[0111] The simulation results show that the spacecraft can perform autonomous onboard collision avoidance when it is threatened by an orbit. The entire planning result derives the action sequence between the spacecraft subsystems and software modules, and coordinates a series of actions of the spacecraft in response to threats. The effectiveness and advantages of the strategy have been verified.

[0112] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims

1. A spatial hostile target avoidance interval relaxation planning method for action conflicts, characterized in that: include Follow these steps: S1: Define the mission planning problem of satellite threat avoidance; The satellite threat avoidance mission planning problem in S1 is a tuple , expressed as: in, is a set of satellite facts, a propositional Boolean variable, is a collection of satellite real-valued numerical resource variables, is the initial state of the threat under the orbital threat, and is the variable Partial assignment of is the target condition for the satellite to avoid the satellite, a set of propositional conditions and / or conditions on numerical variables; is a collection of continuous actions in the form of: in, Is a value between the upper and lower limits, indicating the action a Duration of action a The duration defines a time interval , which corresponds to the start of the action execution and end Time point, The value is the interval Length; It is necessary to A set of conditions that hold true, is a set of The end condition, yes A set of invariant conditions must be Maintained during execution, that is, throughout the interval Keep; yes A set of effects produced, and yes A set of effects produced; Describe the specified action The control parameters in is a numeric variable and is equated with the numeric variable ,therefore, The variables involved in the numerical expression and The variables defined in are used to model and the conditions or effects of action Duration Combined with the time constraint and constrained to a certain interval, the duration constraint is expressed as: in, , is a Contains arithmetic operators For expressions involving numeric constants and variables, The value represents the interval The time that has passed in action The condition set , is a set of propositional or numerical conditions. Propositional conditions are of the form The text of , or the form Negative text of ; The numerical conditions are expressed as: The numerical constraints are expressed as ,and Same, one action The effect set, , It is propositional or numerical; Satellite threat avoidance mission planning problem The solution to is a time-stamped sequence of actions, with associated durations, that transforms the initial state to a state that satisfies the goal, subject to all imposed conditions. The solution is defined as: in, and ; Action specifications are satisfied by different duration values, so the duration of the action is clear and the problem The solution is necessary to include the specific values ​​of the control parameters of the action in the timestamp sequence; S2: The structure of the planning algorithm. In the planning search, the concurrency problem and the numerical variable problem are handled by introducing numerical causality and interval-based numerical variable representation, action duration and control parameters. The planning algorithm uses the Z3 theorem prover to assign numerical variables and verify the consistency of the plan. In S2, an action It consists of two time points, the start time point and end time point , in addition, the invariant condition It needs to be held within the open interval defined by the start and end of the movement; When performing runtime numerical planning, the following two key operations are required: S21: Introduce an action into the plan to satisfy the prerequisite of another action; set up and are two actions in a plan, and causality is two actions at a point in time. and The relationship between , expressed as , which means the condition Depend on Effect support in action is called a producer action, It is called consumer action; S22: Resolving conflicts between actions in the plan; There is a conflict between a certain time point in the plan and the causal relationship, which is called a defect. , In causal relationship If the defect is caused Relative to and is unordered, and For the positive proposition and ,Right now: Proposition At the point in time is deleted, or To negate the proposition and ; That is, the proposition At the point in time is added, or is a numeric variable and is Update its value; S3: Planning to process numerical variables and expand nodes through search; In S3, the search starts with an initial plan Initially, the plan contains only one dummy action for the initial state ; By adding actions to support All possible actions and corresponding defects to expand a given node ; To select the next node to expand, a standard heuristic function is applied to estimate the probability of Part of the plan to reach the goal The cost of , the heuristic function is: Among them, the plans in the open node list are Value descending order, component It is the arrival node The cost of It is measured by the number of actions planned in the component It is a slave node Planned arrival An estimate of the cost of , expressed in number of actions; Moreover, using the state-based heuristic, the node The boundary states of the partial order programming in order to be able to apply ; For the boundary state, it is the variable Assignment of Among them, the proposition variable Assign Boolean values ​​to numeric variables Assigned to interval ; Given a partial order program: in, Boundary State In topological order The state resulting from applying the effect at each point in time, yes A set of actions in yes A set of ordering constraints on the action time points in , It is a set of cause-effect relationships; The initial state of the planning problem Modeled as an unconditional virtual action, its ending effects include Facts, problem goals It is also a virtual action with no effect. Its starting condition is The conditions specified in; Time , , is ordered before another point in time ; The boundary state is calculated by applying the effects specified at the time points in the topological order in sequence. The first time point represents the virtual action of the initial state, and its effect is applied to obtain the first state Equal to the initial state , proceed to the next time point in linear order and apply its effects to obtain a new state , given a time point Status The effect is: The effect of negating a proposition is assigned a false The values ​​are: The effect of the positive proposition is assigned a true The values ​​are: Numerical Effects ,renew Medium Variable The upper and lower bounds of use interval-based arithmetic where according to Update the interval value, The variable values ​​in If these numerical variables appear in middle, exist The values ​​in represent duration-dependent effects; The resulting state after applying the effect of the last time point in the topological order is the planned boundary state ; S4: Using heuristic functions , estimated node The cost of The boundary state reaches the target problem Measured by the number of moves required; In S4, the heuristic function Divided into: S41: Establish a relaxation planning graph; planning The RPG from its borderline state Construction,RPG is a graph of a relaxed version of the planning problem, ignoring deletion effects, a fact layer containing Positive propositions about variables in , and The value interval of the numeric variable in, an action layer contains actions; First level of facts It is a boundary state , action layer Contains all actions ,in, The propositional conditions are included in In the fact layer Depend on Determine, among which, The proposition in is All the propositions in The propositions added by the action are calculated in two steps The values ​​of the numeric variables in : S421: The value of a numeric variable is set to The values ​​of corresponding variables in are equal; S422: The value range of each variable is expanded to include all The values ​​obtained by the maximum and minimum assignment effects in ; set up For a node in the search tree, if one of the following two conditions is met, the node The structure of RPG will be based on Termination due to failure at layer: S4111: The value is equal to the previous fact layer , neither new facts nor new numerical variables can be realized in the future. When the graph expansion stagnates, the relaxation problem is unsolvable. S4112: Contains The same proposition, and yes The parent node of In the S4112, when the node The number of RPG layers relative to its parent node The number of layers increases a lot, at the node Planning in the solution leads to a better solution than planning The reachable solutions in are longer, or the nodes The plan in produces a high-quality solution, but the heuristic function is not informative and returns a higher value than it should, making the relaxation unsolvable. After expanding RPG, the relaxed solution plan is extracted and the function is defined as: in, The first appearance of the factual hierarchy in an RPG; Define the function as: Among them, given a variable and a numerical condition ,in Used to check if a higher or lower Value to satisfy the condition; Define the function as: Where, given a numerical variable , a preferred boundary, and an index at the fact level, which returns The preferred boundaries are updated in The last level before; Computational Planning The heuristic value of is based on the information obtained from RPG; S5: Use Z3 to verify the consistency of the plan and assign the most appropriate value to the numerical variable in its interval value; In S5, Z 3 is used to solve nonlinear fixed point optimization problems, in order to model a plan as: In Z3, real fixed point variables with three decimal places are defined as: ,action The start time of ,action End time of ,action Duration of ,action The control parameter value of , the value of the variable In Action Update after the start time of ; , the value of the variable In Action Update after the end time of Also, define the following constraints: Initial virtual action, action Indicates the initial state , the end time is 0, with duration, is a small interval, Each sequence or The causal relationship in an action The beginning or end of another action An order is established between the start or end of the , which is transformed into a constraint: For each action , the following constraints are defined: The constraint is defined as ; The relationship between the start and end of an action is also modeled as ; The numerical condition for ; S6: Output the final planning result and complete the mission planning of satellite to avoid threats; The S6, basic planning The method to generate the successor plan is: When action Can be added to hour, The conditions must be passed To support the existence of actions in is The last action inserted in The effect is not supported Any condition indicates that Has been inserted into In the previous planning, therefore, Will also appear in In some other plans, The successor planning constraint is to a node, which is introduced by Supported actions, and introduction The last action of the sibling nodes in and their causal links and ordering.

2. The planning method according to claim 1, characterized in that: In S21, The effects in support an invariant global condition , two causal relationships are necessary, one is the start of the action, which is: One is the end of the action: Ensure that the condition is in action Valid for the entire duration of In said S22, the defect is determined by raising or lowering the defect time point. To solve this, lifting means introducing a sorting constraint of the form , reducing means introducing order constraints .

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