💻 computer science

Adaptive Relative Orbit Control Considering Laser Ablation Uncertainty

This paper proposes and validates an adaptive relative orbit control law utilizing Gaussian process regression to effectively manage uncertainties in laser ablation and atmospheric drag for laser-based space debris removal missions.

Original authors: Shun Isobe, Yasuhiro Yoshimura, Toshiya Hanada, Yuki Itaya, Tadanori Fukushima

Published 2026-08-18

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CC BY 4.0

Original authors: Shun Isobe, Yasuhiro Yoshimura, Toshiya Hanada, Yuki Itaya, Tadanori Fukushima

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

Space is becoming increasingly crowded, not with stars, but with the silent, speeding remnants of human activity. Old satellites, spent rocket stages, and fragments from collisions drift in orbit, posing a constant threat to active spacecraft. To keep space usable, engineers must find ways to remove this debris. One promising method involves using powerful lasers to nudge debris out of the sky without ever touching it. A spacecraft would fire laser pulses at a piece of junk, heating its surface just enough to vaporize a tiny amount of material. As this vapor shoots away, it creates a gentle push that slowly lowers the debris's orbit until it burns up in the atmosphere. However, for this to work, the laser-firing spacecraft must stay in a precise, fixed position relative to the drifting target. If the debris moves unexpectedly or the laser push is weaker than predicted, the two spacecraft could drift apart, breaking the link needed to continue the job.

The challenge lies in the unpredictability of space. The force generated by the laser depends on the exact material of the debris and how the laser beam hits it, both of which are hard to know in advance. Furthermore, the thin atmosphere at low altitudes creates a drag force that varies as the Earth's atmosphere expands and contracts with solar activity. Traditional control systems, which rely on fixed mathematical models, struggle when these conditions change. They often leave a small but persistent error in the spacecraft's position, which could eventually lead to a collision or a failed mission. To solve this, researchers at Kyushu University and SKY Perfect JSAT Corporation have developed a new way for the spacecraft to learn and adapt in real time.

Instead of relying on a rigid set of rules, the team designed a control system that uses a learning technique called Gaussian process regression. Imagine the spacecraft's computer as a student who is constantly watching the environment. Every time the spacecraft fires its thrusters or feels a push from the atmosphere, the system records what happened. It then uses this history to predict what will happen next, adjusting its own behavior to cancel out the surprises. This approach allows the spacecraft to automatically compensate for the unknown strength of the laser push and the shifting drag of the atmosphere. The researchers tested this idea through detailed computer simulations, pitting their new adaptive system against a standard control method that does not learn from its mistakes.

The results of these simulations show a clear advantage for the learning system. When the researchers introduced uncertainties, such as variations in atmospheric density or unpredictable changes in the laser's pushing power, the standard system struggled to hold its position, drifting slightly off course. In contrast, the adaptive system successfully tracked the target, keeping the relative distance steady. The system learned to predict the disturbances and applied just the right amount of counter-force to neutralize them. In one test case, the researchers simulated a scenario where the laser-firing spacecraft had to stay exactly 100 meters ahead of the debris while the debris was being pushed down by the laser. Even when the laser's effect was modeled with random fluctuations and the spacecraft had to use simple on-off thrusters rather than smooth, continuous ones, the adaptive controller maintained the correct formation.

The study also explored how to make this learning system practical for real hardware. Since spacecraft thrusters often work by firing in short, fixed bursts rather than flowing continuously, the team developed a method to translate the smooth, continuous commands of their learning algorithm into these on-off pulses. The simulations confirmed that this translation worked effectively, allowing the spacecraft to maneuver frequently enough to correct its path without wasting fuel or losing precision. The researchers found that the system learned best when it focused on specific patterns in the data, particularly the position of the spacecraft relative to the sun and its location in its orbit, as these factors drive the changes in atmospheric drag.

This work suggests that future missions to clean up space debris could be much safer and more reliable if they use this type of adaptive control. By allowing the spacecraft to learn from the environment rather than guessing based on imperfect maps, the mission can continue even when conditions are uncertain. While the findings are currently based on computer simulations, they provide a strong foundation for building spacecraft that can handle the messy, unpredictable reality of low Earth orbit. The ability to maintain a precise formation without constant human intervention is a critical step toward making laser debris removal a viable solution for protecting our orbital environment.

Technical Summary: Adaptive Relative Orbit Control Considering Laser Ablation Uncertainty

Problem Statement

Active Debris Removal (ADR) missions utilizing laser ablation face significant challenges in maintaining the precise relative orbit required for continuous laser irradiation. In this scenario, a removal spacecraft (deputy) must track a target debris (chief) as the ablation force lowers the target's altitude. The primary difficulty lies in the uncertainties associated with the magnitude of the laser ablation force (dependent on target material and laser spot size) and external disturbances, particularly atmospheric drag.

Previous formation-keeping control laws for laser ADR were largely based on feedforward designs that failed to account for these uncertainties. Unmodeled disturbances can lead to increased relative position errors, creating a high risk of collision. While Model Reference Adaptive Control (MRAC) offers a solution for handling uncertainties, conventional implementations rely on parametric regression using assumed basis functions, which may not accurately capture complex, non-parametric disturbance characteristics without prior information.

Methodology

This study proposes a Gaussian Process Model Reference Adaptive Control (GP-MRAC) law to address these uncertainties. The methodology integrates the following components:

Relative Motion Dynamics: The system utilizes the Hill–Clohessy–Wiltshire (HCW) equations to model the relative motion between the deputy and chief spacecraft in a circular orbit. The state vector includes relative positions and velocities.
Model Reference Adaptive Control (MRAC) Framework:
- A reference model is designed to represent the ideal system dynamics without disturbances.
- The control law consists of a linear feedback part ( $u_{pd}$ ), a linear feedforward part ( $u_{crm}$ ), and an adaptive part ( $u_{ad}$ ).
- The goal is to drive the tracking error ( $e = x - x_{rm}$ ) to zero by adjusting the control gains and canceling the disturbance term $\Delta$ .
Gaussian Process (GP) Regression for Adaptation:
- Unlike traditional MRAC which uses parametric models (e.g., Radial Basis Function networks), this study employs GP regression for the adaptive part $u_{ad}$ .
- GP regression is a non-parametric, data-driven machine learning approach that learns the disturbance model directly from observed data without requiring prior information about the functional form of the uncertainty.
- The adaptive part $u_{ad}$ is set to the mean estimate of the GP, effectively canceling the uncertain disturbance acceleration (atmospheric drag and laser ablation thrust).
- To manage onboard computational resources, a sparse GP algorithm is implemented to restrict the number of training data points by deleting data with the highest Kullback–Leibler divergence.
Discrete Implementation:
- Since high-frequency acceleration measurements are noisy or unavailable, the disturbance acceleration is estimated using state vectors at discrete time intervals ( $t_i$ and $t_{i+1}$ ).
- For practical application, the continuous control signal generated by GP-MRAC is translated into ON/OFF thruster commands using a modulation method based on constant thrust magnitude and injection duration.

Key Contributions

Development of GP-MRAC for Laser ADR: The paper derives a relative orbit control law specifically tailored for laser debris removal missions that simultaneously accounts for laser ablation uncertainty and atmospheric drag.
Non-Parametric Uncertainty Cancellation: The study demonstrates the application of Gaussian Process regression within an MRAC architecture to cancel modeling errors without assuming a specific parametric basis function for the uncertainties.
Operational Feasibility: The research includes a modulation algorithm to convert the continuous GP-MRAC signal into ON/OFF thruster commands, addressing the constraints of actual spacecraft propulsion systems.
Input Selection Strategy: The paper identifies the mean argument of latitude and the sun phase angle as effective input parameters for the GP regression, leveraging the periodic nature of atmospheric drag relative to the Sun and Earth.

Results

Numerical simulations were conducted to compare the proposed GP-MRAC against a standard PD controller under two scenarios:

Atmospheric Drag Uncertainty:
- In a scenario involving differential drag, the GP-MRAC successfully learned the disturbance pattern.
- While both controllers maintained the desired relative orbit, the PD controller exhibited a steady-state deviation.
- The GP-MRAC adaptive part showed better performance in canceling the actual differential drag compared to the PD controller, though it exhibited overshoot at peak points. Consequently, the GP-MRAC excelled the PD controller in terms of tracking error.
Laser Ablation Uncertainty:
- Simulations modeled the ablation force with trigonometric uncertainties and assumed a stationary relative orbit requirement (100 m ahead of the target).
- Both the PD control and the GP-MRAC exhibited steady-state deviation in this case. However, the GP regression demonstrated better performance in canceling the actual differential drag and laser ablation thrust compared to the PD controller.
- The modulation method successfully translated the continuous control signal into ON/OFF thruster pulses, confirming the viability of the approach for practical spacecraft with constant-magnitude thrusters.

Significance and Claims

The authors claim that the proposed GP-MRAC control law contributes to the realization of safer and more secure missions, not only for laser debris removal but also for other on-orbit services. By enabling autonomous feedback control that adjusts to disturbances without manual adjustment, the method addresses the critical need for long-term mission reliability. The study concludes that the adaptive part of the GP-MRAC successfully improves the handling of laser ablation uncertainties and differential drag, leading to superior tracking performance compared to conventional PD control, despite residual steady-state deviations in the laser ablation case. Furthermore, the research highlights that effective regression of atmospheric drag can be achieved by selecting specific orbital and solar geometric parameters as training data, validating the data-driven approach for space environment modeling.