⚡ electrical engineering

Consensus Based Task Allocation for Angles-Only Local Catalog Maintenance of Satellite Systems

This paper presents a decentralized task allocation algorithm that enables communicating satellites to efficiently maintain local catalogs of space objects using angles-only measurements, significantly outperforming existing methods in balancing fuel usage and catalog uncertainty.

Original authors: Harrison Perone, Christopher W. Hays

Published 2026-02-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Harrison Perone, Christopher W. Hays

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are the captain of a small fleet of satellites orbiting Earth. Your job isn't just to fly; it's to keep a perfect, up-to-date "watch list" of everything else in the neighborhood—other satellites, space junk, and debris. If you don't know exactly where a piece of junk is, you might crash into it.

The problem? Your eyes (sensors) can only see a tiny slice of the sky at once, like looking through a drinking straw. You can't see everything at once. Also, you can't just sit still and stare; you have to turn your head (use fuel) to look at different things. If you stare too long at one thing, your "uncertainty" about where other things are grows, and you might miss a collision.

This paper is about teaching these satellites how to decide who looks at what, and when to switch their gaze, without needing a boss on Earth to tell them what to do.

Here is the breakdown of their solution using simple analogies:

1. The Problem: The "Blind Spot" Dilemma

Imagine you and three friends are in a dark room full of floating balloons (the space junk). You all have flashlights, but your flashlights are narrow beams.

The Goal: Everyone needs to know exactly where every balloon is.
The Catch: If you stare at one balloon for too long, you lose track of the others. If you switch too often, you waste energy spinning your flashlight around.
The Old Way: The previous method was like a strict rule: "Stare at a balloon until you are 100% sure of its location, then wait a fixed amount of time before looking at something else." This was okay, but it often made the satellites spin around unnecessarily, wasting fuel, or let some balloons get too "foggy" (uncertain) in their minds.

2. The Solution: A Decentralized "Group Chat"

The authors propose a new system based on something called CBBA (Consensus-Based Bundle Algorithm). Think of this as a group chat where the satellites talk to each other to make a plan, but without a leader.

Here is how their new "smart scheduler" works:

A. The "Scorecard" (Not just looking, but looking smart)

In the old days, satellites just picked the balloon that was the "foggiest" (most uncertain). But the new system uses a Scorecard.

Distance matters: It's easier to get a clear picture of a balloon that is close to you than one far away.
Angle matters: If a balloon is right in front of your flashlight, you get a great picture. If it's off to the side, the picture is blurry.
The Math: The satellite calculates a "Score" for every balloon. A high score means: "Hey, I'm close to this one, it's right in my view, and I'm not sure where it is yet. I should look at this one!"

B. The "Switching Rule" (When to stop staring)

This is the cleverest part. In the old system, you switched targets based on a timer or a fixed rule. In the new system, the satellite asks: "Is my view of this object getting better fast enough?"

Imagine you are trying to read a sign while driving. If the sign is getting clearer very quickly, you keep looking.
But if the sign is getting clearer very slowly (maybe it's far away or the angle is bad), the satellite says, "This isn't worth my time anymore. I'm going to switch to a different target that I can learn about faster."
This prevents the satellites from wasting fuel spinning around to look at things that are too hard to see.

C. The "Blacklist" (Don't look at what you already know)

If a satellite has figured out exactly where a piece of junk is, it puts that junk on a "Blacklist." It won't waste time looking at it again until the junk starts moving or becomes uncertain again. This stops the satellites from staring at the same thing over and over.

3. The Results: Saving Fuel and Seeing Better

The researchers ran computer simulations (like a video game for space) to test this new method against the old one.

The Old Way: Created a trade-off. You could either save fuel (by staring at one thing for a long time) OR keep the map clear (by switching often), but you couldn't do both.
The New Way: By using the "Scorecard" and the "Switching Rule," the satellites found a "sweet spot." They managed to keep the map of space very clear AND use significantly less fuel to do it.

The Bottom Line

Think of this new algorithm as upgrading from a strict teacher who says "Sit still for 5 minutes, then move" to a smart coach who says, "Look at the player who is closest to you and easiest to see, but if you stop making progress, switch to someone else immediately."

This allows the satellite fleet to work together like a well-oiled machine, keeping the space around them safe without burning through their fuel tanks. It's a big step toward making space travel safer and more autonomous.

1. Problem Statement

As the number of objects in Low Earth Orbit (LEO) increases, maintaining accurate relative state information (position and velocity) and covariance (uncertainty) for neighboring objects is critical for collision avoidance and close-proximity missions (e.g., formation flying, inspection). Ground-based tracking often lacks the required accuracy for these close-range operations.

The specific problem addressed is Local Catalog Maintenance using a decentralized network of communicating satellites equipped with angles-only sensors (limited Field of View, FOV).

Goal: Each agent must maintain a local catalog where the uncertainty (Shannon Entropy of the covariance matrix) of all objects remains below a predefined threshold.
Challenges:
- Dynamic Environment: Object states and uncertainties change over time.
- Task Definition: It is unclear when an observation task is "complete" because uncertainty naturally grows over time; a task completed today may need re-observation tomorrow.
- Inter-Agent Dependency: When one agent observes an object, the uncertainty decreases for all agents in the network due to data sharing.
- Resource Constraints: Agents must minimize fuel expenditure (control effort) while maximizing information gain.
- Sensor Limitations: Angles-only measurements result in range-dependent positional uncertainty, and the sensor has a limited FOV.

2. Methodology

The authors propose a decentralized task allocation algorithm based on the Consensus-Based Bundle Algorithm (CBBA), enhanced with specific modifications for orbital dynamics and angles-only sensing.

A. System Dynamics & Modeling

Relative Motion: Uses Clohessy-Wiltshire-Hill (CWH) equations to model relative orbital dynamics in the Hill frame.
Attitude Control: Agents use a proportional controller with a damping term (rather than computationally expensive Model Predictive Control) to point sensors at targets. The control law tracks the target's apparent angular velocity to minimize steady-state error.
State Estimation: A Networked Distributed Kalman Estimator is used, fusing measurements via Inverse Covariance Intersection (ICI) to maintain state omniscience across the network.

B. The Scoring Function (Key Innovation)

The paper introduces a new scoring metric ( $S$ ) to evaluate the value of observing a specific target. Unlike previous methods that relied solely on Shannon Entropy, this metric accounts for:

Uncertainty Magnitude: Higher variance ( $\lambda_k$ ) yields higher scores.
Observability Geometry: The angle ( $\theta_k$ ) between the target's principal axes of uncertainty and the line-of-sight vector. Observations are most valuable when the line of sight is perpendicular to the major axis of the uncertainty ellipsoid.
Range: Positional uncertainty for angles-only sensors scales with range ( $1/||r||$ ). Closer targets receive higher scores.

The score is calculated as:
$S = \sum_{k=1}^{6} \frac{\lambda_k \sin(\theta_k)}{||r||}$
Where $\lambda_k$ and $u_k$ are eigenvalues and eigenvectors of the covariance matrix, and $\theta_k$ is the angle between the line-of-sight and the principal axis.

C. Task Allocation & Switching Logic

The algorithm operates in a decentralized manner:

Bundle Construction: Agents build a path of tasks using CBBA, maximizing the sum of path scores.
Path Scoring: The total path score is discounted by the angular distance traveled to reach each task ( $e^{-L_i \mu}$ ), penalizing long, fuel-intensive maneuvers.
Target Switching Criteria: An agent switches targets if:
- The current target falls below the entropy threshold ( $\epsilon$ ) and is added to a "blacklist."
- The current target is out of the sensor's FOV (preventing unnecessary switching during rotation).
- The rate of decrease of the new target's score ( $D_t$ ) falls below a threshold relative to the current target's score, indicating diminishing returns.
Conflict Resolution: Agents communicate to resolve task overlaps. If a target switch occurs, the agent triggers a re-planning phase for the network.

3. Key Contributions

Novel Scoring Metric: Developed a physics-based scoring function that integrates covariance geometry, range, and sensor FOV constraints, moving beyond simple entropy minimization.
Decentralized CBBA Adaptation: Successfully adapted the CBBA algorithm for the specific constraints of catalog maintenance, including a dynamic "blacklist" mechanism to prevent redundant observations of well-known objects.
Fuel-Efficient Switching Logic: Introduced a switching criterion based on the rate of decrease of the observation score, preventing premature target switching and reducing fuel consumption.
Performance Benchmarking: Demonstrated that the new method outperforms the existing "hysteresis-based" approach (which uses fixed time delays) on the Pareto frontier of fuel usage vs. uncertainty maintenance.

4. Results

The algorithm was evaluated via numerical simulation in Python with two agents and eight target bodies over 200 seconds.

Parameter Sensitivity:
- Planning Depth: Increasing the number of tasks planned ahead had no statistically significant impact on performance. This is because the system frequently re-plans, and once targets are below the threshold, the "blacklist" limits available tasks regardless of depth.
- Discount Factor ( $\mu$ ): A value of 0.1 was optimal. It balanced the trade-off between observing high-value (distant) targets and minimizing fuel costs (angular distance).
- Switching Threshold ( $\alpha$ ): A value of 0.1 provided the best balance. High $\alpha$ caused frequent switching (high fuel, low uncertainty); low $\alpha$ caused agents to stay on targets too long (low fuel, high uncertainty).
Comparison to Baseline:
- The proposed CBBA-based method achieved a Pareto frontier superior to the hysteresis-based approach.
- It simultaneously achieved lower fuel expenditure and lower clipped integral uncertainty (a metric measuring how much time objects spend above the uncertainty threshold) compared to the best-tuned hysteresis configurations.
- The improvement is attributed to the angular distance weighting in the path score and the geometry-aware scoring function.

5. Significance and Future Work

Significance: This work provides a robust, decentralized solution for autonomous satellite systems to maintain situational awareness without ground intervention. It proves that CBBA can be effectively adapted for complex, time-varying orbital tasks where observation value is non-linear and dependent on geometry.
Future Directions:
- Multi-Target Observation: Scoring and observing multiple targets simultaneously within the sensor's FOV.
- Dynamic Thresholds: Moving away from fixed uncertainty thresholds to purely information-vs-fuel tradeoffs.
- Asynchronous Communication: Implementing ACBBA (Asynchronous CBBA) to handle real-world communication delays and time-varying network topologies.
- Machine Learning: Exploring ML approaches for task allocation and control to handle complex, non-explicit behaviors.

In conclusion, the paper presents a significant advancement in autonomous satellite operations, offering a method that is more fuel-efficient and effective at maintaining catalog accuracy than current state-of-the-art heuristics.