Towards Realistic Earth-Observation Constellation Scheduling: Benchmark and Methodology
Authors: Luting Wang
Yinghao Xiang
Hongliang Huang
Dongjun Li
Chen Gao
Si Liu
Venue: NeurIPS 2025 poster ()
Keywords: Task Scheduling
Satellite Constellation
Realistic
Benchmark
Transformer
Primary area: applications

Abstract: Agile Earth Observation Satellites (AEOSs) constellations offer unprecedented flexibility for monitoring the Earth’s surface, but their scheduling remains challenging under large-scale scenarios, dynamic environments, and stringent constraints. 
  Existing methods often simplify these complexities, limiting their real-world performance. 
  We address this gap with a unified framework integrating a standardized benchmark suite and a novel scheduling model.
  Our benchmark suite, AEOS-Bench, contains $3,907$ finely tuned satellite assets and $16,410$ scenarios.
  Each scenario features $1$ to $50$ satellites and $50$ to $300$ imaging tasks.
  These scenarios are generated via a high-fidelity simulation platform, ensuring realistic satellite behavior such as orbital dynamics and resource constraints.
  Ground truth scheduling annotations are provided for each scenario.
  To our knowledge, AEOS-Bench is the first large-scale benchmark suite tailored for realistic constellation scheduling.
  Building upon this benchmark, we introduce AEOS-Former, a Transformer-based scheduling model that incorporates a constraint-aware attention mechanism. 
  A dedicated internal constraint module explicitly models the physical and operational limits of each satellite.
  Through simulation-based iterative learning, AEOS-Former adapts to diverse scenarios, offering a robust solution for AEOS constellation scheduling.
  Experimental results demonstrate that AEOS-Former outperforms baseline models in task completion and energy efficiency, with ablation studies highlighting the contribution of each component.
  Code and data are provided in https://github.com/buaa-colalab/AEOSBench.

Towards Realistic Earth-Observation Constellation Scheduling: Benchmark and Methodology
Luting Wang" Yinghao Xiang*
Hongliang Huang
Dongjun Li Chen Gao
Si Liut
Beihang University
Abstract
Agile Earth Observation Satellites (AEOSs) constellations offer unprecedented flexibility for monitoring the Earth's surface, but their scheduling remains chal- lenging under large-scale scenarios, dynamic environments, and stringent con- straints. Existing methods often simplify these complexities, limiting their real- world performance. We address this gap with a unified framework integrating standardized benchmark suite and a novel scheduling model. Our benchmark suite, AEOS-Bench, contains 3, 907 finely tuned satellite assets and 16, 410 sce- narios. Each scenario features scenarios are generated via high-fidelity simulation platform, ensuring realis- tic satellite behavior such as orbital dynamies and resource constraints. Ground truth scheduling annotations are provided for each scenario. To our knowledge, AEOS-Bench
50 satellites and 50 300 imaging tasks. These
first large-scale benchmark suite tailored for realistic constel- lation scheduling. Building upon this benchmark, we introduce AEOS-Former a Transformer-based scheduling model that incorporates a constraint-aware atten- tion mechanism. A dedicated internal constraint module explicitly models the physical and operational limits of each satellite. Through simulation-base itera- tive learning, AEOS- Former adapts to diverse scenarios, offering robust solution for AEOS constellation scheduling. Experimental results demonstrate that AEOS- Former outperforms baseline models in task completion and energy efficiency, with ablation studies highlighting the contribution of each component. Code and data are provided in htttp:://gii com com///oaaa-
1 Introduction
Agile Farth Observation Satellites (ABOSs) 32 7 21 have emerged as transformative technology remote sensing, enabling rapid and flexible monitoring of the Earth's surface. By operating co- operatively in constellations [44] [4] 40 39 42], multiple AEOSs can dramatically increase revisit frequency and broaden coverage beyond the capability of single satellite. As shown in Fig. [ the AEOS constellation scheduling problem seeks to optimally assign imaging tasks across satellites to maximize task completion while minimizing time and resource expenditure [15 41) all within real- world constraints. Robust scheduling models empower faster and more informed decision-make for applications such disaster response [5] 26), environmental monitoring (3] and resource man-
agement 33
The challenge of AEOS constellation scheduling stems from three core factors. First, modern stellations may comprise dozens satellites tasked with hundreds of imaging requests ( This
"Equal contribution. Email: @ htw.tutiiin@uuaauuuuu.. xiangyinghao www.a.du..co 'Corresponding authors. Email: gaochen.aiieeooo @ @iai@@@gmmacooo gmail.com
liusi buaa.cdu.cn
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Illustration of AEOS constellation scheduling over four timesteps. At each timestep, satellites adjust their attitude to image ground targets, consuming battery energy while charging via solar panels. Tasks can be published or expired. Multiple satellites can cooperate complete tasks.
Figure 1:
scale renders exhaustive searches infeasible and strains both heuristic algorithms and reinforcement- learning methods [15]. Second, the operating environment is highly dynamic: new tasks can appear expire at any moment, satellite positions and attitudes are continuously changing. batteries cycle through charge and discharge, and satellites may even join or leave the constellation. Scheduling algorithms must adapt the fly without foreknowledge of these changes. Third, every assignment of tasks must respect strict constraints, such as the available battery energy, the sensor field of view (FOV), and the allowable time window for each task, or the imaging request cannot be fulfilled.
Any practical scheduling model must simultancously scale to large constellations, adapt in real time, and respect every operational constraint. However, most existing methods compromise one or more of these goals. For example, REDA (IS) tailored to a fixed set satellites and tasks under abstracted constraints, while EOSSP- RCS on simplified benchmarks, their performance degrades sharply in realistic scenarios. Moreover, the absence of common benchmark prevents fair comparison across scheduling models.
23 targets small constellations. While effective
To bridge this gap, we present a unified framework for the AEOS constellation scheduling, com- prising a standardized benchmark suite and a novel scheduling model. Our benchmark is built simulation platform powered by the Basilisk engine [9), which accurately models each satellite's orbital dynamics, attitude control, and other physical characteristics. We provide 3, 907 satellite assets, each with fine-tuned control parameters to ensure stability during task execution. AEOS- Bench, our benchmark suite, is distinguished by four key features: 1) Large-Scale. includes 16, 410 scenarios, each featuring to 50 satellites, 50 to 300 imaging tasks, and 3, 600 timesteps. 2) Realism. All scenarios generated and evaluated on simulation platform, ensur- ing physically accurate satellite behavior. The test split incorporates real satellite data from publicly available sources"] enabling evaluation authentic data. 3) Comprehensiveness. AEOS Bench evaluates six metrics, including task completion rate, turn-around time, and power consumption. 4) Open-Accessible Data. Every scenario is annotated with ground truth assignments through rigorous pipeline. All benchmark data and annotations are publicly accessible. To our knowledge, AEOS-Bench is the first large-scale benchmark for realistic AEOS constellation scheduling.
We further introduce AEOS-Former, a Transformer-based (28) scheduler engincered for AEOS con- stellations. At its core lies a dedicated internal constraint module that explicitly models each satel- lite's 's physical and operational limits, including sensor field of view, battery state, and attitude con- trol time. By predicting a feasibility probability and minimal control time, this module produces a constraint-driven attention mask to guide scheduling. AEOS-Formes begins by embedding static attributes (e.g., orbital parameters, target location) and dynamic states (e.g., current attitude, task progress). A transformer encoder ingests task embeddings to produce contextual task features. Con- currently, the decoder takes satellite embeddings and attends the task features under the constraint.
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Table 1: Comparison of existing benchmarks. Our JEOS-Beenh incorporates 16k scenarios with
realistic physics simulator and ground truth annotations.
Setting
Benchmark
#Scene
#Sat
#Task
Traj. Len.
Phy. Sim.
Ann.
Eddy al. [
30
200~22000
500s
X
X
Single
Hermann al. 14
45k
135
4.5h
Satellite
H-PPO 34
5
100~~2000
30m
X
TRM-TE 23
100k
50~~200
x
x
EHE-DCF 136
8
10
200~~
Ih
x
x
SFMODBO 330
4
50~2000
3h
X
X
Multiple
SatNet [1]
5
29-033
257~333
168h
Satellites
REDA
15
1
324
450
100m
X
AEOS-Bence (Ours)
16k
1~-50
50~300
1h
mask, yiclding assignment matrix. To extend beyond purely supervised learning, AEOS-Former integrated in a simulation-bas based iterative learning loop. After pretraining on AEOS-Bench anno- tations, it is deployed in simulator explore random scenarios. Schedules exceeding a preset performance threshold are merged back into AEOS-Bench for retraining. Through iterative cycles of constraint-driven attention and iimulator-guide exploration, AEOS-Formed converges on high- value scheduling strategies that generalize across diverse scenarios.
To evaluate the effectiveness of ABOS-Former, we conduct a series of comparison experiments against several baseline models, using six metries that encompass task completion, timeliness, and energy efficiency. On the val-unseen split, AEOS-Former achieves completion rate of 35.42% with a power consumption of only 68.99 Wh, outperforming the baseline (35.35% completion rate and 140.83 Wh power consumption). Moreover, AEOS-Former surpasses all baselines across all splits in terms the comprehensive score. Ablation studies further confirm the contribution each component in AEOS-Former By providing the AEOS-Bench and AEOS-Formed we hope this work will inspire novel methods AEOS constellation scheduling.
Related Work
To solve the constellation scheduling problem, researchers have developed various benchmarks and methods. Methods can be broadly classified as optimization-ban based neural-networr--baseee
Benchmarks. As summarized in Tab. [ most existing benchmarks for multi-satellite scheduling include fewer than 10 scenarios, limiting their diversity and generalizability. In contrast, AEOS- Bench offers 16, 410 diverse scenarios. Unlike prior benchmarks, AEOS- Benchh further leverages high-fidelity simulation platform with expert-generated ground truth annotations. These features ensure both realistic constrains and reliable evaluation metrics for real-world applicability.
Optimization-bann based Methods. Early studies rely on exact solvers to optimize satellite assignments. Lemaître al. [1] adopt a constraint programming framework for agile satellite scheduling. Sin et al. 27 uses sequential convex programming to accelerate target acquisition. Although these methods guarantee optimality, their computational cost escalates sharply with the problem scale. Subsequent heuristic methods aim to improve scalability [1 6
12
37
38 25
HAAL [66 bal-
ances performance and runtime via handover-aware task allocation. MSCPO-SHCS
employs
stochastic hill-climbing strategy for timely assignment optimization. Other approaches include [17], evolutionary algorithm [10], and genetic algorithm (2]. While these
Ant Colony Optimization methods offer faster runtimes, their performance diminishes with large-scale or dynamic scenarios.
Neural-Network-Bn based Methods. The robust fitting capabilities of neural networks have driven breakthroughs across diverse domains [4] 20 22). including constellation scheduling 35 43 Her-
rmann al. 13 formulates the problem Markov decision process (MDP) and adopts reinforce- ment learning for scheduling. Pointer Networks (29 provide sequence-to-sene to-sequence formulation
for combinatorial assignments. EOSSP-RCS (33 proposed Transformer-based encoder-decoder architecture with temporal encoding model and achieved relatively good performance. Infantes et al. [18] adopts GNN Deep Reinforcement Learning to the Earth Observation Satellite Plan- ning problem with very competitive performance. REDA [1] combines multi-agent RI with

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Campletion Rate Check
3t Human Quality Check
Tabe med
Summary X Reject
Summary
Suspicious
47.5%5
Accept
① Empirical Formula
Satellite Awets
Yuer 23x
0.10
Place (ity
2)
Regenceate MRP
Jear
Jusa SX Rl where a.8.y.8-000.3)
Figure 2: The generation process of satellite assets, which incorporates an empirical formula and multiple checks to ensure stable attitude control for each asset.
polynomial-time greedy solvers balance assignment quality and speed. Despite promising sults, many these methods simplify key physical constraints. contrast, our AEOS-Forme in- tegrates an intrinsic constraint module that explicitly enforces physical and operational limitations, substantially improving the feasibility and fidelity of generated schedules.
The AEOS-Bench Suite
Initial
In this section, we first define the problem setup of AEOS constellation scheduling. Next, we describe the process generating satellite assets and ground truth scheduling annota- tions for AEOS-Bench. Finally, we provide analysis of JEOS-Bench
Greeds Inittative
Scarrrio
To
Elurative plice
Satellite Assess
Trajectry
3.1 Problem Setup
Figure 3: The annotation pipeline for AEOS-Bench
Scenario Modeling, To capture the essential physics that determines task feasibility, we model each satellite a composition of four core subsystems: orbital dynamics, attitude control, power system, and sensor payload. Satellites occupy low-Earth orbit (LEO), with parameters like orbital elements, mass properties, and moments of inertia sampled uniformly from representative ranges (details in Appendix C. Attitude control employs the Modified Rodrigues Parameters (MRP) for- malism, with control gains and acutator limits specified per satellite Sec. [.22] We collect the satellite characteristics into a matrix S* Nexe, where Ns denotes the number satellites and ds the feature dimension. Imaging tasks arrive dynamically, each defined by a release time, due time, required observation duration, and the ground-targe coordinates. These task descriptors form matrix T R Xd' with Nr tasks and dz task attributes.
Action Space. We adopt a two-tier action abstraction to separate high-level scheduling from low- level control. The low-level action space comprises power-on/off commands and prrnuud-ppiinting directives, which are dispatched directly to the Basilisk engine to simulate battery cycling, sensor activation, and MRP- attitude maneuvers. While this affords maximal control flexibility, it imposes excessive complexity on scheduling models. Instead, our high-level action space consists of task-assignment commands. The scheduler outputs
assignment vector [d, ......... &Ng). A value of a; = 0 directs satellite i to power down its sensor,
where each 0g E 1.... ). while any a, 0 instructs it activate the sensor and reorient to service task a, The platform automatically converts these high-level assignments into low-level commands, allowing scheduling models to concentrate purely on task selection and timing.
Constraints. Real-world ABOS constellation scheduling is governed by multiple constraints. We enforce 5 constraints in our platform: dynamics, energy, FOV, continuity, and time window (de-

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2003
atraleeturkes
200
(a)
(b)
(c)
(d)
Figure 4: Statistical analysis of ABOS-Benche (a) and (b) show the distribution of trajectories w.r.t the semi-major axis and eccentricity of satellite orbits, respectively. (c) and (d) illustrate the distribution trajectories w.r.t. the number of satellites and tasks, respectively.
Any high-level assignment that violates these constraints is rejected by the simulator, and only successful observations are recorded for downstream benchmarking.
tails in Appendix C
3.2 Data Collection
The attitude control system in our simulation platform uses the MRP method, whose performance relies on several key parameters: control gains and actuator limits. These parameters govern the speed and precision that satellite can adjust attitude. Low control gains result slow attitude adjustments, while overloaded actuators destabilize the satellite, risking task failures. To ensure dependable performance under these conditions, we repeat the cycle Fig. until we accumulate 3, 907 satellite assets, each proven to deliver reliable on-orbit performance.
While our platform supports closed-loop simulation, training scheduling models from scratch via simulator roll-outs is computationally expensive. To bootstrap learning, we curated AEOS-Bench: large dataset with constellation scheduling annotations. As shown in Fig. [3] each REOS-Bench scenario begins with distance-based initialization. While simple and intuitive, this method often assigns tasks that lie too close to the satellite, leading to attitude control failures. Therefore, we introduce the iterative filter stage and human quality review. Through this process, AEOS-Bench delivers reliable scheduling data for training schedulers.
3.3 Data Analysis
We partition AEOS-Bench into four splits. The train split consists of 16, 218 trajectories with 2, 907 satellite assets. The val-seen split includes 64 scenarios using the same satellites as the train split. The val-unseen split features 64 scenarios with 500 satellites present in the train split. The test split contains 64 scenarios with 500 satellites, each having realistic properties sourced from the web.
As shown in Fig. 4 the orbital parameters of each satellite asset follow approximately random distribution within specific ranges. Scenarios with smaller constellations or a larger number of tasks more frequent in AEOS-Bas Bennch. This may be because generating high-quality assignments is easier when there are fewer satellites and more tasks.
4 The AEOS-Former Model
This section begins with the dynamic data processing pipeline in Sec. 4.1 Next, Sec. 4.2 introduces internal constraint module for the prediction of feasibility and control time. In Sec. 4.3 detail the transformer-basee satellite-task matching architecture. Finally, Sec. p.4]peenttt our simulation- driven iterative learning pipeline. The architecture of AEOS-Forme demonstrated Fig.
4.1 Dynamic Data Processing
As demonstrated in Sec. 3.1 each scenario in the AEOS- Bench is defined by static satellite matrix S and static task matrix T which capture time-independent properties. Dynamic properties, such as task progress and satellite attitude, are not contained within these static matrices. Enabling
5

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X
hs
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Es
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Figure 5: Architecture of AEOS-Formed Static and dynamic data of satellites and tasks are first concatenated and embedded. A transformer encoder processes task features, and decoder attends to satellite embeddings under constraint-derived cross-attention mask. The internal constraint module then predicts feasibility logits and required control times, guiding action selection.
the scheduling model infer dynamic states from static properties and past decisions would sub- stantially increase complexity without clear benefit. Instead, we query our simulator at each timestep to retrieve the current dynamic satellite and task properties.
The full input matrices are formed by concatenating static and dynamic components:
= "S"::" E Naxs
T T E Nexdr
where Sd E Naxx is the dynamic satellite matrix, T E Nr is the dynamic task matrix, ds d's + d and dr di + d4.
To embed temporal context into AEOS-Formen we incorporate a sinusoidal time embedding E, at the current timestep t. Task release and due times converted into relative time offsets w.r.t. t. Finally, we normalize both S and using statistics computed over the entire AEOS-Bench dataset.
4.2 The Internal Constraint Module
To explicitly model the constraints inherent in our platform, we introduce an internal constraint module C. For satellite-task pair (i,j), C predicts the feasibility of satellite performing task j::
f. C(S;;))))
i < Ns. 1 1 < Nr;
where fig = [Sis $r,5l E R²2 comprises two components: $..j the predicted logit indicating the feasibility of satellite i completing task j. and f., is the estimated time for attitude adjustment.
Ideally, ground truth labels si.j E (0.1) 1) would be available supervise &. However, in AEOS- Bench, many tasks are accomplished through the collaboration multiple satellites, making challenging to attribute task completion individual satellites directly. Determining 8i,j would necessitate dedicated simulations, which are computationally intensive.
To address this, we define approximate label Bi,; E {0, 1}, which can be easily obtained from AEOS-Bench. We set 8i,j = 1 satellite contributed to task j for at least n consecutive timesteps and the task is completed in the trajectory. The loss function is defined using binary cross-entropy:
C,
DCC(S,,,,8L..
N
To further guide C in internalizing constraints, we introduce time supervision. If 8i.j = 1, we denote Egg the minimal time offset At from the current timestep such that satellite begins continuous

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contribution to task j.
The corresponding loss function is:
NT Bi,j MSE((,,; (45)
Nr
L
8i.
(4)
This dual supervision strategy enables C to learn both the feasibility and temporal aspects of satellite- task assignments, effectively capturing the constraints present in AEOS-Besd scenarios.
Satellite- Tasii Matching
To match satellites with tasks, we employ an encoder-decoder architecture that jointly processes satellite and task embeddings, guided by our internal constraint module.
First, we project S and T into embedding space and append a sinusoidal timestep embedding E,: Es- (S) Ex), Ey = [&T (T); Ex),
(5)
where Eg and Êr are the embedding modules. Categorical data (e.g., sensor modes) looked up in embedding matrices, while continuous ones (e.g., mass, progress) use linear projections.
We encode task features with transformer encoder E: hT (ET)) Then, decode satellite features via a transformer decoder D, attending to tasks under a mask M: hg = D(Es, hT, M). The cross cross- attention mask M R NN x NNr is derived from the constraint logits: M.j x 8 bb, with w, initialized to 0 for stable training. We compute an assignment score matrix A:
A hy [hr: hr]
IR (e
(6)
where h a trainable vector representing the null assignment. The loss function is defined as:
1
Σ No
Nr
Ca
CE(A,a+1))
Ns
j=1
where a is the ground truth assignments in Sec. 3.1 the constraint logits before sampling from A:
At test time, we filter out infeasible pairs via
à + arg max15JeN; 1 (o(()))) r²) Ar,;
where 1|-} is the indicator function, is the sigmoid function, $1,j is the predicted logits of task completion, and T. is predefined feasibility threshold. This design tightly integrates learned con- straints with feature matching, enabling efficient satellite-task assignments.
4.4 Simulation- based Iterative Learning
Stage
Supervised Pretraining
To fully leverage simulator platform, introduce iterative learning pipeline as demonstrated in Fig.
In the supervised pretraining stage, we initialize THOS-Former with random weights and train it on the annotated trajectories in AEOS-Bende The overall loss is weighted sum of feasibility, timing, and assignment objectives:
AEOS-Bench
AEOS-Former
Pretrained Weight
High Quality Trajectories
= W. L. + Wi La + Wa Lar
(9)
where Wr. and balance the three components. This stage bootstraps the model with basic scheduling strategies learned from expert annotations.
In the subsequent simulation-driven exploration stage, we gener- ate new scenarios and use the pretrained AEOS-Former to pro- pose schedules. Each generated trajectory evaluated by a com- prehensive score as defined in Eq. (TO). We then collect only those trajectories whose performance exceeds predefined threshold These high-quality schedules are added back into the AEOS- Bench training set. We repeat this loop until convergence. In this way, AEOS-Former continually refines its policy, discover- ing novel strategies beyond the original annotations and adapting to increasingly diverse scenarios.
Simulation
AEOS-Former
Platfurm
Stage 2
Simulation Explecation
Figure 6: The iterative learning framework with two stages: supervised pretraining and simulation-dris exploration.
7

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Table 2: Performance Comparison between ALEOS-Formee and Baseline Scheduling Models.
Split
Method
CS +
CR/%
PCR/%
WCR/%
TAT/h +
PC/Wh +
Random
116.81
0.83
0.99
0.83
0.20
136.92
HAAL
[16
101.09
0.98
1.09
0.97
0.23
148.02
Val Seen
REDA
15
31.60
3.80
3.15
0.74
147.09
MSCPO-SHE SHCS
9
5.85
28.77
32.93
28.23
7.75
135.93
JEOS-Formes (Ours)
5.00
30.47
33.68
30.05
7.50
71.27
Random
90.27
1.08
1.33
1.02
0.17
142.27
HAAL 16
77.17
1.28
1.46
1.28
0.25
155.36
Val
REDA 15
21.54
4.83
5.75
4.85
0.71
153.95
Unseen
MSCPO-SHE
9
5.21
35.35
39.45
34.85
7.27
140.83
AEOS-Former (Ours)
4.43
35.42
38.93
35.14
6.78
68,99
Random
113.53
0.85
1.02
0.88
0.17
150.54
HAAL [I6
94.83
1.05
1.17
1.03
0.25
155.56
Test
REDA
15
28.21
3.65
4.27
3.58
0.73
154.49
MSCPO-SHCS 9
7.33
19.44
24.00
18.71
6.23
149.20
AEOS-Former (Ours)
6.28
19.25
22.31
18.73
5.67
40.91
Experiments
This section begins with the implementation details of AEOS-Forme Next, we introduce the met- rics used to evaluate AEOS-Former and baselines. Sec. 5.3 presents the comparison experiments and ablation studies. Sec. 5.4 provides a performance analysis of THOS-Former through visualization.
5.1 Implementation Details
The internal constraint module C is implemented as multi-layer perception (MLP) with two hidden layers of width 1024. The transformer encoder & and decoder are configured with width of 512, a depth of 12, and 16 attention heads. All loss weights are assigned as w, = w/
= 1.
Training conducted with the AdamW optimizer [24] with a base learning rate of 10-4 0.9, B2 = 0.98, and weight decay 10-4, Each training batch contains 48 timesteps uniformly sampled from a trajectory. The supervised stage spans 30, 000 iterations, with linear warm-up of the learning rate from 10 to 10-4 over the first 10, 000 iterations. The complete iterative pipeline comprises three supervised stages, culminating in total of 90, 000 iterations.
Both training and evaluation are performed on a Linux server with 256 CPU cores, 984 GB RAM, and 8 RTX 4090 GPUs. The training process demands approximately 48 GPU-hours. Evaluation is executed over 96 parallel simulator environments and completes in about 30 minutes.
5.2 Evaluation Metrics
We evaluate schedulers using six metrics including task completion, timeliness, and energy effi- ciency. Completion rate (CR) measures the proportion of completed tasks out of all. Partial comple- tion rate (PCR) assesses the ratio of the maximum progress the total required duration. Weighted completion rate (WCR) is weighted version CR, considering task durations. Turn-aruund time (TAT) calculates the average time taken complete tasks, reflecting scheduling efficiency. Power consumption (PC) quantifies the total energy consumed by the satellite sensors during imaging. Finally, the comprehensive score (CS) aggregates these metrics into a single performance indicator:
CS (WCR CR WPCR PCR WWCR WCR) + WTAT TAT WpC PC,
(10)
where WCR
0.6, WPCR 0.2, WWCR 0.2, WTAT 1/7, and uPc 1/100.
5.3 Main Results
We benchmark our AEOS-Former with several scheduling models. HAAL and MSCPO-SHCS are optimization-based scheduling models, while REDA adopts the multi-agent reinforcement learn-

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Table 3: Ablation study on AEOS-Former.
Constraint Module C
Iterative Training
Split
CS 4
CR/%
PCR/%
WCR/%
TAT/h + PC/Wh
5.85
27.47
30.88
27.16
6.56
135.94
Val Seen
5.27
28.06
30.84
27.82
7.54
69.76
5.28
34.25
38.04
33.80
7.44
135.90
5.00
30.47
33.68
30.05
7.50
71.27
5.17
34.05
37.83
33.60
6.21
140.84
Val Unseen
4.51
33.71
36.79
33.57
6,43
67.84
4.72
40.88
46.72
40,58
6.55
140.87
4,43
35.42
38.93
35.14
6.78
68.99
9.31
13.26
15.83
12.92
3.67
149.28
7.02
16.44
18.64
16.30
5.11
36.57
Test
6.29
24.67
28.85
24.21
6.01
149.26
6.28
19.25
22.31
18.73
5.67
40.91
0
C677
CRIN
12.30
A6
16
Ny
(a)
(b)
(c)
(d)
Figure 7: Distribution of CS and CR metrics across varying values of Ns and Ny. the test split.
ing approach. These models were originally designed for simplified environments and do not di- rectly accommodate the comprehensive constraints of our AEOS-Bench setup. Therefore, we have adapted their formulations to ensure compatibility. Additionally, we include random scheduling model to provide a baseline performance measure. As shown in Tab. 2 AEOS-Former outperforms all baselines across all splits. Notably, the test split, AFOS-Former achieves 6.28 CS, surpass- ing MSCPO-SHCS by 16.7%. Thanks to our integrated constraint module and iterative learning paradigm, our model achieves better balance between CR and PC.
To assess the impact of each component within AEOS-Former, an ablation study conducted, as shown in Tab. On the val-seen split, incorporating the constraint module enhances both CR and PC, increasing CR from 27.47 to 28.06 and reducing PC from 135.94 to 69.76. Iterative training further boosts CR to 30.47. Due to the conflict between CR and PC, the final CR is lower than the CR achieved by sole iterative training. Nonetheless, the CS still improves by more than 0.27.
5.4 Analysis
The baselines include both optimization- and learning- based methods. Specifically, HAAL and MSCPO-SHCS are optimization- based approaches, while REDA is neural network-basee based method.
As shown in Fig. [ as Ns increases from to 50, the CS metric initially decreases before stabilizing between 31 and 40, while the CR metric con- sistently increases. This suggests
Figure 8: Scheduling visualization of AEOS-Former.

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trade-off between task completion and resource consumption. Regarding Nr, an increase in the number of tasks leads to lower completion rates and more resource consumption, with the CS metric slightly increasing and the CR metric slightly decreasing.
We also visualize the scheduling of AEOS-Former with Unity3D. In the highlighted areas of Fig. satellite collaborations are observed.
Conclusion
This work introduces a comprehensive framework for Agile Earth Observation Satellites (AEOS) constellation scheduling. We present AEOS-Bench, a standardized benchmark with 3, 907 satel- lite assets and 16, 410 scenarios, enforcing realistic constraints and providing ground truth annota- tions. To our knowledge, AEOS-Benc is the first large-scale benchmark for realistic constellation scheduling. We also propose AEOS-Former, a Transformer-based scheduler featuring a novel con- straint module. Through simulation-baan baaed iterative learning, ABOS-Former outperforms baselines across diverse scenarios, with ablation studies validating the effectiveness each component. We hope AEOS-Bench and AEOS- AEOS-Former will drive innovations in AEOS constellation scheduling.
Acknowledgement
This research is supported in part by National Key R&D Program of China 00222/D01155022 Na- tional Natural Science Foundation of China (No. 62461 160388, U23B2010), "Pioneer" and "Lead- ing Goose" R&D Program of Zhejiang (No. 2024C01 161), Beijing Natural Science Foundation (QY25227), Ningbo Science and Technology Innovation 2025 Major Project (2025Z034), NSFC- RGC Project (N.CH4.492244).
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Power output
Power output
Battery
Sensor
Power input
Solar Panel
Reaction
Wheel
Light
RW0
Reaction Wheel
Gravitation
Planetary
Navigation
Control
Environment
RWI
Attitude
Location
Sun
Earth
RW2
Angular Speed
Attitude Tracking Error
Attitude
Target
MRP Control
Guiding
Location
Figure 9: Architecture of the simulation platform used in AEOS-Bench.
A Limitations
our AEOS-Bench, each task is represented as single location point. the future, we plan to propose a new task to incorporate area-based task representations, allowing each observation request to span a defined region. This would enable the evaluation of scheduling algorithms under more realistic constraints, such partial area coverage, time-window flexibility, and spatial prioritization.
B Broader Impacts
AEOS-Bench an open-source suite for AEOS constellation scheduling research, enabling re- searchers to develop more effective models and conduct fair comparisons. Enhanced scheduling models for AEOS constellations offer several societal benefits. In disaster response, optimized task assignment delivers timely data first responders, improving search and rescue operations, damage assessment, and resettlement planning. In environmental protection, high-quality imagery data enables early detection of threats such as illegal logging and industrial pollution, strengthening ecosystem oversight and facilitating rapid intervention.
C Scenario Modeling
Fig. demonstrates the architecture of our simulation platform. The green modules simulate satellite components, including reaction wheels, batteries, sensors, and solar panels. Reaction wheels and sensors draw power from batteries, while solar panels recharge those batteries. The blue modules handle satellite dynamics. A planetary environment, including the Sun and the Earth, supplies the solar incidence angle for the solar panels and simulates gravitational forces. Closed-loop attitude control is achieved by the navigation module, the attiuud-guiding module, the MRP control module, and the reaction-wheel control module. The MRP algorithm adjusts the orientation of satellites to keep target locations in view.
Parameters for the simulation platform are summarized Tab. 4 The range for each parameter is also specified to facilitate random scenario generation. Task parameters are listed in Tab. 5
21

---

Table Satellite parameters.
Index
Description
Range
Unit
scaled moment of inertia
50 I3 200 I3
kg m
scaled mass
50 200
kg
-880 180
direction of solar panel
deg
-90 ~ 90
1880 ~ 180
scaled area of solar panel
5 ~ 10
m²
half field of view (FOV) of sensor
0.5 1.5
rad
power of sensor
W
power status of sensor
{0, 1]
battery capacity
8,000 30,000
mA
battery percentage
0 ~ 100
%
10
maximum angular momentum of reaction wheels
10 ~ 100
kg m²/s
180 ~ 180
direction reaction wheels
deg
-90 ~ 90
180 180
12
angular speed of reaction wheels
6,000 6,000
rpm
power of reaction wheels
W
power efficiency of reaction wheels
0.1 ~ 0.5
MRP control parameter k
~
15
MRP control parameter ki
0.0 ~ 0.1
MRP control parameter
6 ~ 12
MRP control parameter integral limit
0.0 ~ 0.5
16
orbital true anomaly
0 ~ 360
deg
17
orbital eccentricity
0 0.005
18
orbital semi-major axis length
6,800 8,000
km
19
orbital inclination
0 ~ 180
deg
20
orbital right ascension of the ascending node
0 ~ 360
deg
21
orbital argument of perigee
0 ~ 360
deg
Table 5: Task parameters
Index
Description
Range
Unit
minimum time of consecutive observation for a task to be considered completed
15 60
2
release time
0 3,600
3
due time
0 3,600
latitude of the target location
-90 90
deg
4
longitude of the target location
180 180
dog
22


Reviews:
[{"review_id": "cDxXFfhSwA", "reviewer": "Reviewer_ACJP", "summary": "The paper presents a comprehensive framework for scheduling constellations of Agile Earth Observation Satellites (AEOSs), addressing the challenge of efficiently assigning imaging tasks to multiple satellites under dynamic conditions and stringent constraints. The authors introduce AEOS-Bench, a large-scale benchmark suite containing 3,907 satellite assets and 16,410 scenarios, generated through high-fidelity simulations to ensure realistic satellite behavior and operational constraints. Each scenario includes ground truth scheduling annotations. Building on this benchmark, they propose AEOS-Former, a Transformer-based scheduling model with a constraint-aware attention mechanism. This model incorporates an internal constraint module that explicitly models each satellite's physical and operational limits, such as battery state and sensor field of view. AEOS-Former is trained through a simulation-based iterative learning process, adapting to diverse scenarios and improving scheduling robustness.", "questions": "1. How to extend the proposed solution to new constellations and tasks?\n2. How to quantify the computational cost?\n3. Any optimality or convergence properties of the proposed model?", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "# Strengths\n1. The paper introduces AEOS-Bench, a large-scale benchmark suite with 16,410 scenarios and 3,907 satellite assets, generated using a high-fidelity simulation platform. This ensures realistic satellite behavior, including orbital dynamics and resource constraints. The inclusion of ground truth scheduling annotations further enhances its utility.\n2. The benchmark is diverse, covering a wide range of satellite and task configurations (1 to 50 satellites and 50 to 300 tasks). It is publicly accessible, allowing researchers to evaluate and compare different scheduling models under realistic conditions.\n3. The use of a Transformer-based architecture allows the model to effectively capture contextual relationships between satellites and tasks. The constraint-driven attention mechanism guides the scheduling process, improving both efficiency and feasibility.\n# Weaknesses\n1. The training process of AEOS-Former requires significant computational resources (approximately 48 GPU-hours).\n2. While the model demonstrates strong performance on the provided benchmark, its scalability to even larger constellations or more complex scenarios is not fully explored. The computational cost may increase prohibitively with larger problem sizes.\n3. The Transformer-based architecture, while powerful, may lack interpretability compared to simpler heuristic or optimization-based methods.\n4. The paper does not provide theoretical guarantees or proofs regarding the optimality or convergence properties of the proposed model.", "was_revised": true, "final_justification": "Based on the author rebuttal for all reviewer comments, I think they further clarified my previous concerns and I would vote for an acceptance.", "rebuttal": "Thank you for your thoughtful feedback and the recognition of our work. Below we address specific questions.\n\n# 1. Computation Cost for Training\nWhile AEOS‑Former requires approximately 48 GPU-hours to train ($6$ hours on $8$ RTX 4090 GPUs), we believe this cost is justified given the complexity of the AEOS constellation scheduling task and the significant generalization benefits it enables.\nFollowing the scaling law of Transformers [1], model performance improves with increased model size, dataset size, and training cost. In the AEOS constellation scheduling problem, inference latency is strictly constrained, thus limiting the model size. Therefore, **we scale up the dataset size to cover a wide diversity of scenarios and prolong the training process to better optimize the model.**\n\nWhile the training cost is more expensive than some heuristic or optimization-based methods, it is a **one-time cost**. The resulting model exhibits **robust generalization to unseen or changing scenarios** (e.g., a satellite malfunctions) without retraining, enabling real-time scheduling (latency in milliseconds). In contrast, prior methods are often tailored to fixed scenarios; when the scenario changes, re-running the optimization procedures (taking minutes to hours) is required, which severely hinders real-time responsiveness.\n\nTo further investigate the trade-off between training cost and performance, we conducted a small-scale ablation. As summarized in the table below, **AEOS‑Former retains high performance even under reduced training budgets**:\n\n| GPU-hours | CS $\\downarrow$ | CR/% | PCR/% | WCR/% | TAT/h $\\downarrow$ | PC/Wh $\\downarrow$ |\n|---|---|---|---|---|---|---|\n| 16 (30k iters) | 4.67 | **38.17** | **41.52** | **38.22** | 7.82 | 97.68 |\n| 32 (60k iters) | 4.55 | 37.62 | 41.13 | 37.31 | 7.82 | 82.34 |\n| 48 (90k iters) | **4.43** | 35.42 | 38.93 | 35.14 | **6.78** | **68.99** |\n\nTo lower the computational barrier for the community, we will release both the AEOS-Bench dataset and the pretrained AEOS-Former model. This allows researchers to finetune or directly deploy the model, mitigating the need for expensive pretraining.\n\n[1] Scaling laws for neural language models. arXiv: 2001.08361.\n\n# 2. Scalability to More Complex Scenarios\nSince AEOS‑Former formulates scheduling as a matching problem between satellites and tasks, it extends seamlessly to arbitrary new constellations and task sets. Currently, each scenario in AEOS-Bench contains $1$-$50$ satellites and $50$-$300$ tasks. To test the scalability of AEOS-Former, we evaluate the pretrained model on more complex scenarios that lie outside the original range of AEOS-Bench. The results are summarized below: \n\n| #Satellites | #Tasks | CS $\\downarrow$ | CR/% | PCR/% | WCR/% | TAT/h $\\downarrow$ | PC/Wh $\\downarrow$ |\n|---|---|---|---|---|---|---|---|\n| 1-50 | 50-300 | 4.43 | 35.42 | 38.93 | 35.14 | 6.78 | 68.99 |\n| 50-100 | 100-300 | 5.38 | 64.71 | 69.73 | 64.51 | 12.14 | 212.13 |\n| 1-50 | 100-600 | 6.62 | 24.30 | 27.69 | 23.93 | 11.98 | 89.38 |\n\nWhen we increase the number of satellites to $50$-$100$, CR jumps from $35.42$ to $64.71$, indicating that AEOS‑Former effectively leverages additional resources without retraining. With more tasks ($100$-$600$), CR drops to $24.30$ since the task load exceeds the satellite resources. These experiments demonstrate that AEOS-Former retains strong generalization when facing complex scenarios **beyond its training distribution**.\n\n# 3. Computation Cost for Inference\nWe sincerely appreciate you for emphasizing this critical concern about computational scalability. We have quantified the computational cost through two key metrics: arithmetic complexity (GFLOPS) and inference latency (to directly reflect real-time feasibility).\n\nWe use the `calflops` tool to measure the GFLOPS across varying scenario sizes (the number of satellites and tasks). While Transformer modules theoretically exhibit quadratic complexity, it contributes only $10%$ in the total GFLOPS of AEOS-Former. The remaining $90%$ stems from our constraint module, which scales linearly with the scenario size. As shown below, the GFLOPS of AEOS-Former grows linearly with the scenario size:\n\n| #Satellites | 10 | 50 | 100 | 1000 | 50 | 50 | 50 |\n|---|---|---|---|---|---|---|---|\n| #Tasks | 300 | 300 | 300 | 300 | 50 | 100 | 1000 |\n| GFLOPS | 54.29 | 165.25 | 303.94 | 2800.50 | 31.24 | 58.04 | 540.47 |\n| Latency (ms) | 1.376 | 1.796 | 2.286 | 11.577 | 1.385 | 1.454 | 2.878 |\n\nWe benchmark the inference latency over $1,000$ runs on an RTX 4090 GPU to assess real-world performance. Even at the largest scale ($1,000$ satellites + $300$ tasks), AEOS‑Former completes in $11.58$ ms. For smaller scenarios (e.g., $100$ satellites + $100$ tasks), latency drops to under $3$ ms. Since our scheduling system operates at a $1$ Hz update rate, these latencies **leave ample margin** for real‐time operation.\n\n# 4. Interpretability of AEOS-Former\nTraditional heuristic or optimization-based schedulers provide full transparency by applying explicit decision rules or optimizing known objective functions at each step. In contrast, neural network (NN) models, including AEOS-Former, are inherently \"black boxes\". It is challenging to trace exactly how individual scheduling decisions arise. This lack of transparency is a general limitation of NN-based methods. \n\nTo improve interpretability, we introduce an internal constraint module that explicitly predicts the feasibility of each satellite-task pairing. By exposing these feasibility scores, users can observe which assignments are permitted or filtered out. While this does not fully reveal the model’s internal reasoning, it introduces a verifiable layer that partially bridges the interpretability gap between AEOS-Former and traditional heuristic or optimization-based approaches.\n\n# 5. Convergence of AEOS-Former\nOptimization-based methods perform iterative optimization for specific scenarios, attempting to find optimal solutions. As the number of iterations increases, the probability of finding the optimal solution becomes higher. Our method directly takes scenario information as input and outputs task assignment without any iterative process. Therefore, the performance of our method primarily depends on the degree of fitting to the training set and the generalization error. Quantitative research on the fitting degree and generalization error of deep neural networks is still in a relatively foundational stage. Some studies have achieved global convergence of encoder-only shallow transformers [1]. However, we acknowledge that the performance of deep neural networks, compared to optimization-based methods, lacks theoretical guarantees and mainly relies on statistical results on test data to qualitatively demonstrate effectiveness. In future work, we will attempt to integrate deep neural networks with optimization-based methods to achieve stronger theoretical guarantees. \n\n[1] On the convergence of encoder-only shallow transformers. NeurIPS."}, {"review_id": "GcrVvhqkB3", "reviewer": "Reviewer_FRRA", "summary": "The authors tackle the problem of large-scale satellite constellation scheduling. They introduce a new benchmark (AEOS-Bench) obtained through high-fidelity simulations. Further, a new architecture is proposed (AEOS-Former) which is a Transformer-based scheduling model featuring a constraint-aware attention mechanism and a dedicated internal constraint module that explicitly models the physical and operational limits of each satellite. This model is compared on the proposed benchmark to various baselines and demonstrates superior performance.", "questions": "* Are all of the presented baselines neural network based? \n* Were also Optimization-based Methods evaluated on the benchmark?\n* How do you make sure that the sequences from the simulation in the data gathering phase are not present in the evaluation phase as it uses the same simulator?", "limitations": "No Limitations section and not really discussed in the Conclusion.", "rating": 5, "confidence": 1, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n* The paper is well written and the methods are explained comprehensively.\n* The introduced benchmark is a nice contribution to the community surpassing earlier benchmarks quite significantly by e.g. number of scenes (Table 1).\n* The authors provide an extensive ablation study on the individual components of AEOS-Former.\n\n\n**Weaknesses**\n\n* Experiments are only performed on the introduced new benchmark. It would be helpful to also evaluate the model on some of the other benchmarks presented in Table 1 to get an understanding whether the method is specially tuned for this particular benchmark.\n* A bit more context on the different baselines would have made it easier to understand the improvement and how the method compares to earlier methods.", "was_revised": true, "final_justification": "The authors addressed all my questions and concerns by their response.", "rebuttal": "Thank you for your meticulous review and constructive comments. Below we address specific questions.\n\n# 1. Experiments on Previous Benchmarks\nWe agree that testing AEOS-Former on external benchmarks is important to demonstrate its broader applicability. To that end, we directly evaluated our pretrained AEOS-Former on the REDA benchmark, which comprises a single scenario with $324$ satellites and $450$ tasks. Unlike AEOS-Bench, REDA does not simulate attitude dynamics. Instead, it measures reward solely based on the proximity between satellites and task locations. Since AEOS-Former relies on attitude information as part of its input, we use the AEOS-Bench simulator to generate the necessary attitude information for each REDA satellite.\n\nIntroducing these attitude constraints naturally prevents AEOS-Former from selecting some task assignments that would maximize the reward metric. Nevertheless, even under this more restrictive regime, AEOS-Former achieved a total reward of $17,325$, outperforming REDA’s score of $11,094$ by a wide margin.\n\nThis result shows that AEOS-Former is not over-fitted to AEOS-Bench but can also generalize to much larger constellations and different evaluation criteria. We will include these cross-benchmark results in the revised manuscript to underscore the versatility and robustness of our approach.\n\n# 2. Context on Baselines\nThe baselines presented in our paper include both optimization-based and learning-based methods. Specifically, **HAAL** and **MSCPO-SHCS** are optimization-based approaches. HAAL formulates the scheduling problem as an integer-constrained optimization task, solving it using traditional planning solvers. MSCPO-SHCS adopts a stochastic hill-climbing strategy to iteratively refine scheduling decisions in a time-efficient manner. In contrast, **REDA** is a neural network-based method that combines multi-agent reinforcement learning with polynomial-time greedy solvers to strike a balance between solution quality and computational speed.\n\nAs shown in Table 2 of the manuscript, we evaluated all of these methods on AEOS-Bench. Our AEOS-Former demonstrates consistent improvements over both optimization-based and learning-based baselines. We will expand the background and clarify the distinctions between baseline methods in the revised version to improve readability and context.\n\n# 3. Uniqueness of Scenarios\nEvery scenario in AEOS-Bench is guaranteed to be unique. Even across different splits, no two scenarios share the same constellation or task set. During simulation, the AEOS-Bench simulator first loads the scenario to initialize the constellation, then steps through time. At each subsequent timestep, the simulator applies the high‑level scheduling commands, updates the constellation state, and records task progress until the scenario concludes. When gathering training data and when running evaluations, the simulator is indeed the same, but the scenarios are always different. As the simulator steps through time, it produces a distinct trajectory of constellation states and task progress for each scenario.\n\nSince the train, val-seen, val-unseen, and test splits are disjoint pools of scenarios, no exact sequences from data collection appear during evaluation. This prevents the model from memorizing specific simulation runs, forcing it to learn scheduling strategies that generalize to **entirely new** constellations and task sets.\n\n# 4. The Limitations Section\nA dedicated limitations section in the main text is omitted due to page limits. The discussion is included in Sec. 1 of the supplemental material. In the final manuscript, we will move the limitations section back to the main text."}, {"review_id": "7LMvhOE6mY", "reviewer": "Reviewer_fTGm", "summary": "This paper addresses the scheduling challenges faced by Agile Earth observation satellite (AEOS) constellations in large-scale and dynamic scenarios.  \nThe authors propose a dual innovation strategy by integrating a standardized benchmark and a novel scheduling model to alleviate these challenges. \nThe key contributions are as follows: \n1. AEOS-Bench Benchmark: \nThe authors introduce AEOS-Bench, the first large-scale, high-fidelity scheduling benchmark consisting of 3,907 satellite assets and 16,410 dynamic scenarios (ranging from 1–50 satellites and 50–300 tasks). The dataset is generated using a physics-based simulation platform (Basilisk engine), providing realistic orbital dynamics and energy constraints along with labeled scheduling data. \n2. AEOS-Former Scheduling Model: \nA Transformer-based model, AEOS-Former, is proposed with a novel internal constraint module. This module explicitly encodes physical limitations of satellites (e.g., sensor field of view, battery status), and uses a constraint-driven attention mechanism to generate feasible scheduling policies. Further, the model is trained using a hybrid learning framework that combines supervised pre-training with simulation-based self-optimization, leading to significant improvements in task completion rate and energy efficiency.", "questions": "**Questions**\n\n- The paper does not elaborate on the benchmark’s use cases in sufficient detail. Could the authors clarify their choice of track, and explain why the benchmark/dataset track was not considered more appropriate for this submission?\n\n**Suggestions**\n\n- Generalization to Unseen Scenarios: While the model performs reasonably well under the val-unseen split setting, its completion rate and partial completion rate on the test split fall below those of some baseline methods. This suggests that the model’s generalization to truly unseen scenarios remains limited. The authors are encouraged to further analyze this performance gap and consider possible enhancements to improve adaptability in novel or out-of-distribution environments.\n- Scalability to Large-Scale Constellations: While the current setup supports up to 50 satellites, many operational constellations (e.g., Starlink, OneWeb) involve hundreds or thousands of satellites. The authors are encouraged to strengthen their evaluation or at least discuss the potential scalability of their approach under such large-scale constellation settings.  \n- Impact of High-Level Scheduling Decoupled from Low-Level Control: The proposed method generating high-level scheduling commands, which are then translated into low-level control actions (e.g., attitude maneuvers) by downstream systems. However, it remains unclear whether this decoupling between high-level scheduling and low-level execution might introduce inaccuracies or latency during real-world operations. A brief discussion on this potential issue—such as how the system ensures feasibility and timing alignment—would strengthen the clarity and completeness of the system design.  \n- Temporal Granularity and Feature Fusion:  \nThe model jointly embeds static orbital parameters and dynamic satellite states (e.g., real-time attitude). However, orbital dynamics typically evolve over hour-level timescales, whereas attitude control changes on the order of seconds. This significant mismatch in temporal granularity might require a hierarchical or decoupled processing scheme. The authors are encouraged to discuss whether such a temporal difference affects decision-making and how it is handled in the current model.", "limitations": "- Lightweight Deployment on Resource-Constrained Platforms.  Given that satellites typically operate in resource-constrained environments, it would be valuable for the authors to explore lightweight inference or training strategies suitable for deployment on onboard SoC (COTS) platforms. Discussing techniques such as model pruning, quantization, or knowledge distillation would enhance the practical applicability of the proposed method (in the future work).", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n- High-Fidelity Benchmark Construction: \nThe authors leverage a physics-based simulation engine to model orbital dynamics, energy cycles, and other physical constraints with expert-reviewed realism. The benchmark scenarios are diverse, covering a wide range of orbital parameters and task loads. \n\n- Scalability and Robustness: \nThe proposed model supports scheduling for 1–50 satellites and demonstrates strong robustness in the presence of dynamic task arrivals and fluctuating onboard resources. This reflects good scalability toward real-world AEOS operations. \n\n- Integration of Learning and Constraint Modeling: \nThe work tightly integrates benchmark construction, explicit constraint modeling, and reinforcement learning. The AEOS-Former achieves superior performance across multiple metrics compared to baseline approaches. \n\n**Weaknesses and concerns**\n- High Computational Cost: \nTraining AEOS-Former requires 8 RTX 4090 GPUs and nearly 48 GPU-hours, which raises concerns about computational efficiency. This cost may hinder real-time deployment in resource-constrained onboard environments. \n\n- Limited Validation on Truly Large-Scale Constellations: \nWhile the model supports up to 50 satellites, many real-world constellations involve significantly more satellites (e.g., hundreds or thousands). It would strengthen the work to evaluate or at least discuss scalability and limitations in truly large-scale constellations. \n\n- Execution Interface and Control Fidelity: \nThe current model outputs high-level scheduling commands, which still depend on downstream attitude control systems for actual execution. This raises a question: could the decoupling from low-level control introduce execution inaccuracies or delays?", "was_revised": true, "final_justification": "The authors' detailed response has addressed most of my concerns. It may be worthwhile to explore scalable system designs that can support such expanded deployments.", "rebuttal": "We appreciate your detailed review and constructive feedback very much. We provide our response to your review as follows.\n\n# 1. Computation Cost and Deployment\nAlthough our model requires $6$ hours for training completion (with $8$ RTX4090 GPUs), the training cost is incurred only once. Upon training completion, the model can **directly** perform inference on new scenarios. Consequently, deployment in real-world applications does not necessitate substantial computational resources for retraining, but rather enables deployment through invocation of the pre-trained model. Moreover, **this training cost can be further reduced**. Our $6$-hour training duration is implemented to achieve superior performance. As demonstrated in the table below, the model exhibits satisfactory convergence after $2$ hours of training on $8$ RTX4090 GPUs, achieving a CS score of $4.67$.\n\n| GPU-hours | CS $\\downarrow$ | CR/% | PCR/% | WCR/% | TAT/h $\\downarrow$ | PC/Wh $\\downarrow$ |\n|---|---|---|---|---|---|---|\n| 16 (30k iters) | 4.67 | **38.17** | **41.52** | **38.22** | 7.82 | 97.68 |\n| 32 (60k iters) | 4.55 | 37.62 | 41.13 | 37.31 | 7.82 | 82.34 |\n| 48 (90k iters) | **4.43** | 35.42 | 38.93 | 35.14 | **6.78** | **68.99** |\n\nRegarding deployment challenges under resource-constrained conditions, as illustrated in the table below, the model's required FLOPS do not operate at an excessively high level. Taking the RK3568, a commonly employed Commercial Off-The-Shelf (COTS) platform for satellite deployment, as an example, its FP32 computational capacity approximates $500$ GFLOPS, which is sufficient to achieve second-level task allocation for the majority of scenarios presented in the table. Since constellation scheduling constitutes a high-level task, frequent execution at millisecond granularity does not impact allocation outcomes but with higher power consumption. Therefore, **second-level allocation is entirely adequate for constellation mission planning applications**. That said, we agree that model compression techniques can further boost the performance. In future work, we will implement model quantization and pruning to better accommodate the demands of larger-scale constellation planning over the coming decades.\n\n| #Satellites | 10 | 50 | 100 | 1000 | 50 | 50 | 50 |\n|---|---|---|---|---|---|---|---|\n| #Tasks | 300 | 300 | 300 | 300 | 50 | 100 | 1000 |\n| GFLOPS | 54.29 | 165.25 | 303.94 | 2800.50 | 31.24 | 58.04 | 540.47 |\n| Latency (ms) | 1.376 | 1.796 | 2.286 | 11.577 | 1.385 | 1.454 | 2.878 |\n\n\n# 2. Scalability to Large-Scale Constellations\nAs mentioned in the table below, this model can be applied to larger-scale constellations without additional training and can essentially cover larger-scale real-world constellations. Regarding satellite internet constellations such as Starlink, although they contain massive constellations (typically thousands of satellites in different orbits), they differ fundamentally from the remote sensing satellites targeted in this paper: internet constellations focus on providing continuous services to broader regions and generally do not concern themselves with signal directionality, meaning they only need to consider satellite coverage of ground areas. In contrast, remote sensing satellites face extensive remote sensing demands across various regions and require specialized scheduling for specific locations. Moreover, due to the difficulty in miniaturizing the optical equipment they carry, it is challenging to launch multiple satellites simultaneously. This indirectly results in remote sensing constellations being at most in the hundreds scale, even when not small in size. Most remote sensing constellations planned for the next decade are around the scale of $100$ satellites. Therefore, this model possesses good scalability for constellations that require constellation planning of this type.\n\n| #Satellites | #Tasks | CS $\\downarrow$ | CR/% | PCR/% | WCR/% | TAT/h $\\downarrow$ | PC/Wh $\\downarrow$ |\n|---|---|---|---|---|---|---|---|\n| 1-50 | 50-300 | 4.43 | 35.42 | 38.93 | 35.14 | 6.78 | 68.99 |\n| 50-100 | 100-300 | 5.38 | 64.71 | 69.73 | 64.51 | 12.14 | 212.13 |\n| 1-50 | 100-600 | 6.62 | 24.30 | 27.69 | 23.93 | 11.98 | 89.38 |\n\n# 3. Accuracy and Timeliness of Low-Level Attitude Control \nWe appreciate your insight regarding the low‑level attitude control. In our framework, AEOS‑Former outputs only the high-level task assignments (specifying which satellite observes which target) at each timestep, while the AEOS-Bench simulation handles low-level attitude control for each satellite. As detailed in Fig. 1 of the supplemental materials, the simulator first computes the attitude tracking error (the angular separation between the satellite's current attitude and the task's line of sight). Then, the Modified Rodrigues Parameters (MRP) feedback control algorithm [1] adjusts the angular velocities of reaction wheels to control the attitude. MRP, much like a PID controller but tailored for spacecraft attitude, is carefully tuned to optimize operational accuracy and timeliness. As long as the high‑level commands generated by AEOS‑Former respect the constraints of the satellite, the MRP controller can execute these commands without introducing additional latency or inaccuracy.\n\nThis decoupled architecture, where a task planner issues high-level commands and a specialized controller executes them, is widely used in Embodied AI and robotics [2, 3]. This separation allows the planner to operate at a lower frequency that is sufficient for strategic scheduling, while the low‑level controller runs at high rates to ensure stable and precise attitude control. **By delegating low-level control to MRP, AEOS‑Former can focus on optimizing task assignments, which leads to better scheduling performance and more accurate evaluation.**\n\nWe agree that an end‑to‑end co‑optimization of scheduling and control could yield further gains, as the model would have direct influence over reaction wheels. Investigating such integrated approaches, potentially via a hierarchical design, is an exciting direction for future work.\n\n[1] Analytical Mechanics of Space Systems. AIAA. DOI: 10.2514/4.102400.\n\n[2] Helix: A Vision-Language-Action Model for Generalist Humanoid Control. Figure.\n\n[3] Agent as cerebrum, controller as cerebellum: Implementing an embodied lmm-based agent on drones. arXiv: 2311.15033.\n\n# 4. Choice of Track\nWe carefully considered submitting to the dataset/benchmark track before deciding on the main track. Our primary goal was to present a complete solution to the realistic AEOS constellation scheduling problem, one that not only provides a realistic benchmark but also introduces a novel constraint‑aware Transformer architecture and training pipeline. \n\nExisting benchmarks either focus on toy scenarios or omit critical constraints, failing to support the training and rigorous evaluation of scheduling models for real-world deployment. Therefore, we develop AEOS-Bench as an essential component for solving the realistic AEOS constellation scheduling problem, though it is not an end in itself. While we believe AEOS‑Bench will be a valuable resource for the community, our contribution also lies in the methodological innovations of AEOS-Former.\n\nSubmitting to the main track allows us to present the **full narrative**: from problem formulation to network design and training. We believe this integrated presentation better reflects the breadth and depth of our contributions and will more effectively inspire future work.\n\n# 5. Completion Rate on the Test Split\nThe reduced CR metric on the test split is primarily driven by its internal constraint module $\\mathcal{C}$, which filters out satellite-task pairs deemed infeasible. On both the val-seen and val-unseen splits, the PC metric remains around $70$ Wh, but on the test split, PC falls to $40.91$ Wh, indicating that $\\mathcal{C}$ rejects a substantially larger fraction of assignments. The underlying cause is a sim-to-real gap. The satellite parameters in AEOS-Bench are uniformly sampled (Tab. 1 of the supplemental material), while real-world satellite parameters often follow different distributions. As a result, the feasibility checks of $\\mathcal{C}$ are overly conservative on the test split.\n\nAn immediate remedy is to adjust the feasibility threshold $\\tau$ of $\\mathcal{C}$. In Tab. 3 of the supplemental material, lowering $\\tau$ from $1 \\times 10^{-3}$ to $5 \\times 10^{-4}$ increases test-split CR from $19.25$ to $20.37$, surpassing the MSCPO-SHCS baseline ($19.44$ CR) and reduces CS from $6.35$ to $6.18$. This simple tuning **recovers** much of the lost performance.\n\n# 6. Temporal Granularity\nIn astronautics, the orbital dynamics of a satellite are affected by the orbital altitude. Our research focuses on AEOS satellites, which typically operate in Low-Earth Orbit (LEO), with altitudes ranging from $200$ km to $2000$ km. At these altitudes, LEO satellites travel at approximately 7.9 km/s and complete an orbit around the Earth in merely $90$-$120$ minutes. As a result, their orbital state evolves significantly in the order of seconds. This temporal granularity aligns closely with that of attitude control.\n\nAt each timestep, we feed the full satellite state (including both orbital parameters and attitude parameters) into AEOS-Former to make task assignments."}, {"review_id": "iw46gLBioL", "reviewer": "Reviewer_Tcxm", "summary": "This work addresses the challenge of scheduling Agile Earth Observation Satellites (AEOSs) under complex, large-scale, and dynamic conditions. The authors introduce AEOS-Bench, the first large-scale, realistic benchmark suite for satellite constellation scheduling, featuring over 16,000 scenarios and 3,900+ satellite assets with ground truth annotations. They also propose AEOS-Former, a Transformer-based model with a constraint-aware attention mechanism and a dedicated module for modeling satellite limitations. AEOS-Former uses simulation-based iterative learning to adapt to diverse scenarios and outperforms existing baselines in both task completion and energy efficiency.", "questions": "Who were the experts who annotated the dataset?  Were they subject experts? \n\nWhat is a scenario? What is an asset?", "limitations": "The authors did not discuss any limitations or potential negative societal impact of their work. Can this work be used to create more powerful surveillance systems? How about licensing the code, data or using export controls?", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths- \n\nThe paper proposes a new scheduling model and a benchmark with 16k scenarios.  The AEOS-Bench and AEOS-Former models are highly useful for real-time, multi-satellite scheduling in Earth observation applications, including disaster response systems.  \n\nThe solution employs mathematical equations for scenario modeling and multiple constraints to obtain accurate simulation and scheduling. Furthermore, the work introduces a Transformer-based architecture customized with an Internal Constraint Module to predict feasibility and control time, and Cross-attention masking based on learned constraints. The individual ML components (Transformers, iterative learning, attention masking) exist elsewhere. But the cohesive integration of these techniques for the complex, real-world domain of satellite scheduling is interesting. \n\nGood ablation studies. \n\nThe performance improvements are marginal when compared to SOTA. The major highlight is the total energy consumed by the satellite sensors during imaging, which is good, as the onboard energy resources on a satellite are a precious commodity.  \n\nThe writing is good with a clear structure from motivation to results. \n\nThe code is provided in the appendix. \n\nWeaknesses - \n\nSome of the concepts are unclear. For example, what is a scenario? What is an asset? \n\nHow much energy is saved in doing ML-related tasks on the satellites if the proposed method is used? This is not evaluated. \n\nAll loss weights are assigned as ws = wt = wa = 1. Then what is the purpose of these weights in equation (9)? How were these values selected, and what will be the impact on performance if these values are varied? Similarly, how were values for wCR, wPCR, wTAT, etc were selected? \n\nThe paper makes two claims: In section 1, it mentions \"While effective on simplified benchmarks, their performance degrades sharply in realistic scenarios.\", and in Section 2, \"While these methods offer faster runtimes, their performance diminishes with large-scale or dynamic scenarios,\" without backing them up. \n\nThere are no details present on tasks like what the tasks were, how they were introduced into the system - randomly, uniformly, what their deadline was. \n\nMinor issues - \n\nSome types, such as out instead of ours.", "was_revised": true, "final_justification": "I have read the rebuttal, and the authors have addressed my concerns and questions. I think the paper should be written more clearly for a better understanding in the next version. The paper makes an important contribution, and it can be accepted.", "rebuttal": "Thank you for your detailed review and insightful questions about our work. Below we address specific questions.\n\n# 1. Concept Clarification\nWe apologize for the ambiguity around these terms and appreciate the opportunity to clarify. In our work, a scenario refers to a scheduling problem instance at timestep $0$, which comprises the constellation state (positions, attitudes, remaining resources) and a set of tasks (target coordinates, time windows). During inference, the AEOS-Bench simulator first loads the scenario to initialize the constellation, then steps through time. At each subsequent timestep, the simulator applies the high‑level scheduling commands from AEOS‑Former, updates the constellation state via the MRP controller, and records task progress until the scenario concludes.\n\nAn asset denotes a satellite eligible for inclusion in AEOS-Bench. As shown in Fig. 2 of the manuscript, we generate a large pool of assets by sampling satellite properties, computing corresponding MRP parameters via an empirical formula, and then filtering through a completion rate check and a human quality check. The surviving satellites become part of the asset pool. When constructing scenarios for AEOS-Bench, constellations are formed by random sampling from the asset pool.\n\nWe will incorporate these definitions of \"scenario\" and \"asset\" into the revised manuscript to eliminate any remaining confusion.\n\n# 2. Power Consumption \nWe presume the \"energy\" is referring to the **onboard power consumption** of satellites during task execution. As shown in Tab. 2 of the manuscript, AEOS-Former achieves a significant reduction in power usage compared to baseline methods. For example, on the **val-unseen** split of AEOS-Bench, our method reduces power consumption from **140.83 Wh** (MSCPO-SHCS) to **68.99 Wh**, representing an approximate 50% reduction.\n\nAlthough satellites are typically equipped with solar panels for recharging, minimizing power consumption has clear benefits: it enables more flexible maneuver and reduces wear on high-power components—ultimately helping to extend satellite lifespan without requiring additional hardware robustness.\n\n# 3. Ablation Study on Loss Weights\nThe loss weights $(w_s, w_t, w_a)$ in Eq. (9) are designed to balance the contributions of feasibility loss, timing loss, and task assignment loss. We selected $ws=wt=wa=1$ based on preliminary experiments, where an ablation study (summarized in the table) showed that AEOS-Former is robust to the loss weights and setting $w_s = w_t = w_a = 1$ achieves **better performance**, which is shown below:\n\n| $w_s$ | $w_t$ | $w_a$ | CS $\\downarrow$ | CR/% | PCR/% | WCR/% | TAT/h $\\downarrow$ | PC/Wh $\\downarrow$ |\n|---|---|---|---|---|---|---|---|---|\n| 1.0 | 1.0 | 1.0 | **4.43** | **35.42** | **38.93** | **35.14** | 6.78 | 68.99 |\n| 0.5 | 1.0 | 1.0 | 4.74 | 31.71 | 34.57 | 31.65 | 6.91 | 65.31 |\n| 1.5 | 1.0 | 1.0 | 4.79 | 31.41 | 34.26 | 31.37 | 7.05 | 65.58 |\n| 1.0 | 0.5 | 1.0 | 4.65 | 32.47 | 35.38 | 32.40 | 6.75 | 66.17 |\n| 1.0 | 1.5 | 1.0 | 4.68 | 32.03 | 34.75 | 31.97 | 6.67 | 65.79 |\n| 1.0 | 1.0 | 0.5 | 4.84 | 30.55 | 33.30 | 30.82 | 6.83 | **65.02** |\n| 1.0 | 1.0 | 1.5 | 5.49 | 24.58 | 27.37 | 24.53 | **5.82** | 67.48 |\n\nWe did not perform an extensive hyperparameter sweep over the three loss weights. Thus, in future work, we plan to conduct more systematic hyperparameter searches to determine whether alternative weight combinations can yield further improvements.\n\n# 4. Rationale of the CS Definition\nWe define CS as a **comprehensive metric** that balances completion rate metrics (CR, PCR, WCR) with efficiency metrics (TAT, PC). To do so, we first aggregate the three completion rate metrics into a single completion ratio, and then combine this with normalized versions of TAT and PC.\n\nSpecifically, we compute the completion ratio as a weighted average of CR, PCR, and WCR. The weights ($w_\\text{CR} = 0.6, w_\\text{PCR} = 0.2, w_\\text{WCR} = 0.2$) reflect our prioritization of CR over PCR and WCR. This aggregated ratio naturally lies in $[0, 1]$, where higher is better. In contrast, TAT and PC are unbounded positive quantities that we wish to minimize. To align all components, we take the reciprocal of the completion ratio, mapping it to $[1, \\infty)$. \n\nThen we normalize TAT and PC with their respective normalization weights. To choose the values for $w_\\text{TAT}$ and $w_\\text{PC}$, we examined the typical ranges of these metrics. We observed that TAT hovers around $7$ hours and PC around $100$ Wh. Setting $w_\\text{TAT} = 1/7$ and $w_\\text{PC} = 1/100$ therefore brings these terms into the same order of magnitude (around $1$), so that no single metric overwhelms the overall score. Random, HAAL, and REDA were omitted from this calibration because their completion rate metrics were anomalously low and would skew the normalization.\n\nThis formulation ensures that CS accounts **fairly** for both coverage performance and resource efficiency, with no undue bias toward any single metric.\n\n# 5. Performance of Prior Works\nThank you for pointing out the need for concrete evidence behind these two claims.\n\nFirst, regarding \"While effective on simplified benchmarks, their performance degrades sharply in realistic scenarios,\" Tab. 2 of our manuscript shows that REDA achieves 21.54 CS on the val‑unseen split, whereas AEOS‑Former achieves 4.43 CS. On the original REDA benchmark (which ignores attitude control, sensor FOV, etc.), REDA and AEOS‑Former score $11,094$ and $17,325$ in total return, respectively. Although REDA still falls short there, the performance gap shrinks on the simplified benchmark. This contrast confirms that the performance of REDA degrades much more severely when faced with the realistic dynamics and constraints embedded in AEOS‑Bench.\n\nSecond, for \"While these methods offer faster runtimes, their performance diminishes with large‑scale or dynamic scenarios,\" we performed a scenario‑level analysis comparing MSCPO‑SHCS and AEOS‑Former. We found that MSCPO‑SHCS outperforms AEOS‑Former only on scenarios with an average of 168.8 tasks, whereas AEOS‑Former takes the lead on scenarios averaging 191.3 tasks. This pattern demonstrates that while MSCPO‑SHCS may be competitive on smaller task sets, AEOS‑Former’s learning‑based approach scales gracefully to higher task densities.\n\n# 6. Task Definition\nTasks in AEOS-Bench are defined as satellite observation missions, each characterized by key parameters: minimum continuous observation duration, release time, due time, and target coordinates. In AEOS-Bench, these parameters are sampled independently and uniformly from predefined ranges, as fully specified in Tab. 2 of the supplemental material.\n\n# 7. Typos\nThank you very much for pointing out our typo. We will strive for excellence and correct all typos in the revised manuscript.\n\n# 8. Data Annotation\nAnnotating ground‑truth schedules by hand is laborious. Annotating a single scenario with $10$ satellites and $50$ tasks can take an expert nearly $40$ minutes. To streamline this, we developed the pipeline in Fig. 3 of the manuscript: an iterative algorithm proposes candidate schedules, and human reviewers simply verify them rather than building them from scratch. Because reviewers only need to confirm rationality, this task requires **minimal** specialized astronautics knowledge.\n\nAll human validation was performed by the paper’s authors. In future work, we plan to expand our annotation effort via crowdsourcing to scale AEOS‑Bench even further while maintaining high quality.\n\n# 9. Limitations and Broader Impacts\nDue to page limits of the manuscript, we provide detailed discussions of limitations (Sec. 1) and broader impacts (Sec. 2) in our supplementary materials. \n\nOur work is designed with socially beneficial applications in mind, such as ecological monitoring and disaster response of AEOS constellations. While it is possible that the scheduling technology could be applied in surveillance contexts, we strongly oppose any misuse. Importantly, the **Outer Space Treaty** adopted by the United Nations prohibits harmful interference and hostile activities in space, including unlawful surveillance, providing a legal framework that governs responsible use of space technologies worldwide.\n\nTo further mitigate risks, our source code is licensed under Apache 2.0, but we plan to introduce additional restrictions, including provisions that explicitly limit downstream misuse. For AEOS-Bench, access will require submission of an application form and approval by the authors. Redistribution of the dataset will be strictly prohibited without explicit permission.\n\nWe take the potential for negative societal impact seriously and are actively incorporating safeguards into both our licensing and data access policies to ensure that our work is used ethically and in accordance with international norms."}, {"review_id": "pLXcKcOLti", "reviewer": "Reviewer_W3g8", "summary": "The authors make two contributions towards the scheduling of a constellation of agile earth observation satellites: 1) a benchmark suite including a simulator which is more detailed and contains more and larger instances, and 2) a novel transformer-based method for finding solutions to this type of scheduling problems. The new approach scores better than the four baselines (inc. random).", "questions": "1. In the introduction it says \"the operating environment is highly dynamic: new tasks can appear or expire at any moment, satellite positions and attitudes are continuously changing, batteries cycle through charge and discharge, and satellites may even join or leave the constellation. Scheduling algorithms must adapt on the fly without foreknowledge of these changes.\". Which of these changes are under control or at least partially influenced by the scheduling algorithm and which uncertainty is completely external?\n2. \"To bootstrap learning, we curated AEOS-Bench: a large dataset with constellation scheduling annotations.\" Where does the dataset of tasks come from? And where do the scheduling annotations come from? How has been decided which instances to include and which to exclude?\n3. What are the limitations of AEOS-Former? For how many instances does one of the other methods score better? Is there a pattern here, e.g. what properties do those instances have (e.g. considering size)?", "limitations": "The limitations are not really discussed nor analyzed. See question 3 above.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\n- two good quality contributions\n- the benchmark framework may bring more maturity to the field of multi-satellite scheduling\n- the transformer-based approach appears to be novel\n\nWeaknesses:\n- the description in the paper provides limited understanding as to why certain design choices of the transformer-based method are taken, and what alternative choices are\n- the experiments provide no understanding of which instances work better with which of the baselines, or what the limitations of the transformer-based method are", "was_revised": true, "final_justification": "In the rebuttal, the authors write that the plan is to include in the revised manuscript:\n- a concise discussion of the design alternatives and their rationale\n- an analysis to provide a clearer understanding of which instances favor which method\nWith these additions, I believe this is a good contribution.\n\nFor further improvements, the authors could also consider separate experiments to evaluate the learning success with regard to learning physical laws vs dealing with the uncertainty.", "rebuttal": "Thank you for the valuable comments and the recognition of our contributions. Below we address specific questions.\n\n# 1. Design Choice of AEOS-Former\nWe appreciate your suggestion to better articulate the motivations behind our design choices. At its core, the AEOS scheduling problem asks: \"Which satellite should service which task, subject to constraints?\" We frame this as a matching problem under constraints, where satellites and tasks are two sets of “tokens” whose pairwise affinities must respect feasibility. \n\nThis formulation naturally leads to the choice of **Transformer**, which can ingest variable-sized inputs and excel at reasoning through the attention mechanism. That said, a vanilla Transformer is essentially a black box. Learning to perform task assignments while conforming to all constraints would require massive datasets and prohibitively large compute budgets. \n\nTo avoid this, we introduce an **internal constraint module** that explicitly predicts the feasibility of every satellite–task pair. This separation lets the Transformer focus on high-level reasoning, while the lightweight constraint checker guarantees that only physically possible assignments are considered.\n\nAlternative design choices were also considered. A simple **MLP** would fail to handle dynamic input sizes without padding or truncating the inputs. **Graph neural networks** (GNN) over a bipartite satellite-task graph could capture pairwise interactions, but the message-passing schemes would complicate both model design and training, and still leave constraint learning implicit. \n\nBy contrast, our matching-based Transformer, augmented with an internal constraint module, strikes the right balance. It naturally accommodates any number of satellites and tasks, leverages powerful attention-driven reasoning, and enforces real-world operational constraints without inflating the training cost. We will include a concise discussion of these design alternatives and our rationale in the revised manuscript.\n\n# 2. Detailed Comparison with Baselines\nAmong all baseline methods, MSCPO-SHCS performs closest to our approach. On the **val-unseen** split, it outperforms AEOS-Former on $15$ out of $64$ scenarios. To better understand this, we conducted a statistical analysis comparing the scenarios where each method performs best.\n\nThe key differentiating factor appears to be task volume. In scenarios where MSCPO-SHCS outperforms AEOS-Former, the average number of tasks is $168.8$. In contrast, for the remaining scenarios where AEOS-Former performs better, the average number of tasks is $191.3$. This suggests that MSCPO-SHCS is more competitive in smaller-scale settings, likely due to its local search nature being more effective when the solution space is limited. On the other hand, AEOS-Former scales more robustly to high-task-density scenarios, where optimization-based methods tend to struggle with increasing combinatorial complexity.\n\nWe will include this analysis in the revised manuscript to provide a clearer understanding of which instances favor which method.\n\n# 3. Limitations\nDue to page limits of the manuscript, we included the limitations section in Sec. 1 of the supplementary materials. In the final manuscript, we will move the limitations section back to the main text.\n\n# 4. Clarification on the Problem Setting \nWe appreciate your meticulous review of our manuscript. All of the dynamics mentioned in the introduction (including tasks, satellites, and batteries) are governed by the simulator, instead of the scheduling algorithm. However, not all of these factors are equally uncertain. \nSome properties, such as satellite positions and battery levels, evolve according to physical laws and are therefore predictable given the current state. In contrast, the emergence of new tasks represents true external uncertainty. For example, a task may request observation of a region affected by a sudden natural disaster, something that cannot be predicted in advance. The scheduling algorithm has no prior knowledge of when or where such tasks will be released.\nA central goal of AEOS-Former is to handle this mix of predictable dynamics and unpredictable events in a unified framework. Traditional methods often require re-optimization when the environment changes, which introduces latency. AEOS-Former, by contrast, adapts to all changes without retraining.\n\n# 5. The Data Generation Process\nAll tasks in AEOS-Bench are randomly sampled from predefined ranges, as detailed in Tab. 2 of the supplemental material. Each scenario comprises a randomly sampled constellation and task set. Scheduling annotations are then generated using the pipeline described in Fig. 3 of the manuscript: an iterative algorithm proposes candidate schedules, and human reviewers verify their correctness. Only annotations that pass the verification are included in AEOS-Bench.\n\nThere are two key stages in our data generation process that involve human oversight. First, during satellite asset generation (illustrated in Fig. 2 of the manuscript), human reviewers filter out satellites with unstable or inefficient attitude control. Only satellites with smooth and reliable pointing behavior are retained as valid assets. Second, during the data annotation phase (as shown in Fig. 3 of the manuscript), human reviewers check for irrational scheduling behavior, such as observations of the same task by multiple satellites. \n\nThis pipeline allows us to curate a high-quality dataset of realistic task assignments, while minimizing the burden on human annotators by delegating most of the heavy lifting to automated methods.\n\n# 6. Paper Formatting Concerns\nWe appreciate your careful reading and constructive feedback. We will correct the label in Fig. 5 to “Constraint Model.” As for the spacing problem of separators, we have reviewed all mathematical expressions and will address any inconsistent spacing between symbols and numbers during final typesetting. Finally, “w.r.t.” is an abbreviation for “with respect to”, which is widely used in mathematical contexts. We will spell it out to improve readability."}]

Author rebuttal:

Meta-review: This paper proposes a framework to schedule Agile Earth Observation Satellites (AEOSs) constellations. The reviewing team was overwhelmingly positive about the submission, mentioning only relatively minor issues, which could be addressed for the camera-ready.
Please incorporate all the feedback received from the reviewers in the revised version.
Decision: Accept (poster)