A Multi-satellite Scheduling Method for Emergency Observation Mission Based on Hierarchical Planning Strategy

Emergency observation tasks involve Earth imaging activities by satellites to aid in emergency scenarios like disaster relief, emphasizing promptness and unpredictability. Multi-satellite collaborative planning for several emergency tasks faces issues like high computational complexity, slow processing, and numerous optimization considerations. This paper introduces a hierarchical planning approach and designs an algorithm for collaborative task planning across multiple emergencies and satellites. The algorithm’s computational efficiency and planning effectiveness are later confirmed through a case study.


Introduction
Multi-satellite cooperative task planning is intricate, aiming to find optimal solutions given constraints like limited resources, time, and space.With various imaging satellites and task types, specific planning models and algorithms are essential.Emergency observation tasks, characterized by immediacy and unpredictability, differ from conventional multi-satellite cooperative missions.These missions require swifter responses, strict timeliness, and the ability to integrate emergency tasks into existing schedules without disrupting them.Existing methods either prioritize emergency task revenues without considering existing satellite schedules or focus excessively on merging emergency tasks with routine plans.This paper proposes a swift emergency task scheduling method using a hierarchical approach that balances emergency task benefits with the implications of adjusting routine Keywords: Multi-satellite Scheduling Method; Emergency Observation Mission; 2 Equipment Department of Aerospace Systems Department, Beijing 100090，China Email: Abstract.Emergency observation tasks involve Earth imaging activities by satellites to aid in emergency scenarios like disaster relief, emphasizing promptness and unpredictability.Multi-satellite collaborative planning for several emergency tasks faces issues like high computational complexity, slow processing, and numerous optimization considerations.This paper introduces a hierarchical planning approach and designs an algorithm for collaborative task planning across multiple emergencies and satellites.The algorithm's computational efficiency and planning effectiveness are later confirmed through a case study.

Problem description and basic assumptions
The multi-satellite planning issue for emergency tasks seeks to select an observation meta task for each emergency target, optimizing the collective revenue.Assumptions include:. All emergency targets are point targets. All scheduled satellites are low-Earth orbit remote sensing satellites. Each emergency target has its own time constraints.; Multi-satellite scheduling can address multiple emergency targets simultaneously. Each satellite has a single payload involved in planning. Satellites can only observe one target at once. Satellite attitudes remain unchanged during an observation mission. Emergency targets require a single observation. Each task has its own weight.

Planning constraint modeling
Task planning constraint processing is an important part of task planning.Its function is to ensure that the results of task planning meet the corresponding constraints and have practical feasibility.For emergency tasks, planning constraints can be divided into two categories: One type is the constraints that relate only to the task itself, which is recorded as limit {visual, sensor, image}.Among them, visual is the visibility constraint, sensor is the sensor type constraint, and image is the image quality constraint, that is, the minimum resolution constraint.The other type is the related constraints between tasks, that is, the constraints representing the conflict between tasks.It is recorded as limit {maneuver, payload, energy, capacity, command}.Maneuver is the constraint related to attitude maneuver; payload refers to payload related constraints, mainly refers to the use constraints of the on-board cameras; Energy is the energy constraint, which is mainly reflected in the balance of energy.Capacity is the storage capacity constraint, including the maximum capacity of memory, the amount of data generated by load observation, data transmission rate, etc; In addition, the constraints related to command operations need to be considered in emergency task planning are related constraints too, which.include whether the satellite supports the operation of deleting a single old command and inserting a new command, or only supports the operation of updating all command in batches, etc.

Design of eigenvalue function
For each emergency target, the optimization factors that need to be considered in the task planning are: the observation time should be as early as possible, the observation data should be obtained as soon as possible, the imaging quality should be as high as possible, and the conflict cost with the existing routine plan should be as low as possible.For multiple emergency targets, the optimization factors of task planning also need to consider that the comprehensive value of conflict cost among multiple emergency tasks should be as low as possible.
The above optimization goals are difficult to achieve the best, and the urgency of each aspect of optimization needs is different due to different tasks.Therefore, it is necessary to design a set of objective function of comprehensive optimization, so that the planning results can not only highlight the optimization indexes most concerned by users, but also take into account other optimization goals.
This paper assumes that TT & C and data transmission resources are sufficient, so only the observation task planning of emergency tasks is considered.In terms of solving ideas, we transform the optimization problem of multiple emergency tasks collaborative planning into the problem of making each emergency task plan optimal.Therefore, we design a eigenvalue function for the emergency observation meta task.Considering the window time, imaging quality and conflict cost with other tasks, the eigenvalue function of the observation meta task is defined as follows: In function (1), the definitions of Mathematical Variables are as follows:  J :Comprehensive eigenvalue of the current meta task, indicating features like timing, imaging quality, and task conflict levels.  ,  ，  ：Weighted coefficients.

Design of optimization algorithm
Unlike traditional multi-satellite cooperative task planning, each emergency task possesses unique timeliness requirements due to the urgent nature of emergency tasks.When planning, conflicts between emergency observation tasks and existing satellite plans must be addressed.
In theory, based on the observation meta task's eigenvalue definition, if all meta tasks are arranged by eigenvalues from smallest to largest, the optimal meta task for each emergency task can be identified by selecting the tasks with the minimum eigenvalue.However, this approach has its drawbacks.It demands the calculation of eigenvalues and constraint checks for every potential meta task.Furthermore, while conflicts between emergency meta tasks and existing routine tasks can be straightforwardly resolved by eliminating the routine task, conflicts among emergency meta tasks require a more nuanced approach, weighing which task offers greater comprehensive value.
Given the extensive constraints in emergency task planning and the multifaceted considerations in eigenvalue calculations, this approach's efficiency decreases with a higher number of alternative meta tasks.This is not conducive to quickly determining an optimal solution for urgent tasks.
To address this, our paper introduces an optimization algorithm based on a hierarchical strategy.This method divides the eigenvalue calculation process into two stages: intrinsic eigenvalue optimization and correlation eigenvalue optimization.Initially, meta tasks are optimized based on their intrinsic eigenvalues.Subsequently, the final optimization of meta tasks is performed using their correlation eigenvalues.This two-tiered approach substantially reduces computational overhead, accelerating the solution process.
The intrinsic attributes of an observation meta task, such as timing and imaging quality, are termed as intrinsic feature sub-items.The function representing these attributes is named the intrinsic sub-eigenfunction, given by the following function: In function (2), the definitions of Mathematical Variables are as follows: The conflict generation value between the current emergency observation meta task and other emergency observation meta tasks and existing conventional plans on the satellite is called the related feature sub term, and the function representing such information is called correlation sub-eigenfunction.The function is as follows: In function (3), the definitions of Mathematical Variables are as follows: : Inter-task correlation eigenvalue, denoting the conflict resolution cost with other meta tasks;  The definitions of other variables are the same as those in function (1).
The intrinsic eigenvalue of the meta task is only related to the current meta task itself.Except for the weighting coefficients, this value can be obtained at the same time that the candidate meta task is generated by task preprocessing.
However, the calculation of the inter-task correlation eigenvalues is more complex.The conflict terms include time conflict, energy conflict and memory capacity conflict.In addition, The support degree of satellite itself for emergency mission insertion operation is also a very important indicator.
Therefore, the processing of the inter-task correlation eigenvalue sub-items, which are very complicated in calculation, is bound to be very different from the processing of the intrinsic eigenvalue sub-items.
The specific steps of the algorithm are as follows: first, considering the inherent constraints of the emergency meta tasks, according to the inherent characteristic sub-function, the inherent characteristic value of each meta task is obtained, which can be obtained at the same time of calculating the visibility window.Selected the meta tasks with intrinsic eigenvalues in the first 30% for emergency targets, and record them as a set of candidate meta taks for next planning step.If the number of the first 30% meta tasks of one emergency target is less than 2, the first 2 meta tasks are taken.In the second step, the set of alternative meta tasks obtained in the previous step is further optimized to achieve multi-satellite collaborative planning of multi emergency tasks.Considering the correlation constraints between tasks, the conflict preprocessing is carried out according to the principle of minimizing the cost of conflict resolution, and the correlation eigenvalues of alternative meta tasks are calculated.Combined with the existing inherent eigenvalues, the comprehensive eigenvalues of each alternative meta task are obtained.These meta tasks are sorted according to the comprehensive eigenvalues, and the optimal meta tasks are determined according to the comprehensive eigenvalues.Specifically, determine one preferred meta task at a time, and at the same time, the other meta tasks corresponding to the same emergency target as the selected meta task are deleted from the set of candidate meta tasks, and the conflict preprocessing scheme corresponding to the selected meta task is confirmed.If only one candidate meta task is left for an emergency target in the optimization process, the meta task is directly determined as the optimization meta task.Repeat the above operations until the observation scheme of all emergency targets are arranged, or the set of candidate meta tasks is empty.Then, an emergency mission observation scheme is obtained, which takes into account three key factors: observation time factor, imaging quality factor, and impact factor on routine plans.

Simulation Results and Analysis
A simulation with 100 low orbit remote sensing satellites and 20 emergency targets within 24 hours was set.The eigenvalue function's weighting coefficients were set as :  =4 ,  =2,  =4.The simulation results are as follows in Table 1 The results showed that the hierarchical strategy significantly reduced computation time compared to the global search strategy without compromising solution quality.

Concluding Remarks
In this paper, the problem of multi satellite cooperative task planning for multiple emergency point targets is studied.In view of the characteristics of high response speed of emergency mission planning, planning needs to consider conflicts with existing conventional missions on the satellite，the planning constraint modeling is carried out, According to the characteristics of the emergency observation meta tasks, two kinds of eigenvalues are extracted, which are the intrinsic eigenvalue sub items only related to the current meta task and the inter-task correlation eigenvalue sub items related to other meta tasks on the satellite.A set of eigenvalue functions are designed by weighting, Finally, through the strategy of hierarchical programming, the calculation amount of the most tedious related eigenvalue sub items is reduced, so that the operation speed is improved while the optimal meta tasks are guaranteed.

:
Start time of the current emergency observation meta task.Start of the valid time frame for the emergency target observation task linked to the current meta task.：End of the valid time frame for the emergency target observation task linked to the current meta task.;  vs R ：Initial resolution at the start of the current emergency observation meta task.required for the emergency observation task linked to the current meta task. N ：Total count of conflicting meta tasks with the current one, which includes conflicts with existing planned observation tasks and other emergency observation meta tasks. i W ： Weight of the ith meta task that conflicts with the current task ;  max W :Weight of the emergency target corresponding to the current emergency observation meta task.

:
Intrinsic eigenvalue of the current meta-task, representing intrinsic qualities such as time and imaging quality. The definitions of other variables are the same as those in function(1).

Table 1 .
: The calculation time for two planning strategy types