There are approximately 3,000 derelict satellites in orbit right now. As massive mega-constellations such as Starlink and Project Kuiper come online, that number is only set to grow.

This rapid increase in satellites that no longer serve a purpose will require new methods to deal with them - most commonly through other satellites known as on-orbit servicers (OOSs). Depending on the mission requirements, these specialists can capture, repair, refuel or deorbit a satellite.

However, the hardware and software required to work with such a wide range of potential targets in such dynamic environments is complex. And when faced with the challenge of non-responsive or rogue satellites, it is a unique challenge.

Let’s dive into what makes it so.

What are OOSs?

Normal OOSs operations can be broken down into four distinct phases, each with its own requirements.

1. Long-range guidance
2. Final approach
3. On-orbit capture
4. Post-capture

Long-range guidance requires a wide array of sensors, from telescopes to star trackers, and a detailed understanding of orbital mechanics to plot a course from an OOS’s current position toward the target satellite. Adjusting orbits is increasingly done via onboard computers, which calculate trajectory differences using as many sensor inputs as possible and then feed them into a traditional controller. That controller uses the different thrusters and flywheels onboard the OOS to control its speed, orientation and ultimately, its orbital trajectory.

Once it nears the target satellite, the next phase begins: the final approach. This phase requires much finer-tuned control, as any misstep could prove disastrous for both the OOS and its target. This is where proximity detection sensors, such as lidar and ultrasonics, take over. The OOS issues minor adjustments in trajectory to get near, but not collide, with its target.

The success of orbit capture phase largely depends on the type of capture system the OOS is using. Common options include a grappling hook, a robotic arm, or a net. Older satellites don’t have a standardized interface for capture, such as a docking ring or something similar, though newer ones are typically designed with this in mind. However, for smaller satellites, like CubeSats, there is yet to be any standardization regarding a docking mechanism.

OOSs are typically designed and launched on a case-by-cases basis, as it is cheaper than building and launching a new satellites. However, this is a process that has only been completed successfully a few times, and only when the OOS and the target satellite cooperated.

There has yet to be an example of an OOS capturing an uncooperative satellite, meaning a satellite that is either damaged, unresponsive or unable to recognize that an OOS is attempting to capture it. This is in part due to the potentially unpredictable nature of satellite trajectories.

When satellites go uncooperative

Such random and dynamic environments present exciting challenges for control engineers. Many teams have developed models for everything from estimating a satellite’s inertia to calculating its rotational speed. These estimates are then fed into a control model, which helps provide key data points to the OSS for long-range, final approach and capture phases.

Once the satellite is captured, more interesting control problems arise. From an orbital mechanics and dynamics perspective, the two satellites are now one combined system. However, the target satellite has several unknown parameters, such as its mass or the presence of any local debris, which makes it tricky to control using traditional control theory.

An additional complication is that some satellites are programmed to resist manipulation. They may be designed to point in a specific direction and adjust their orientation based on control parameters. If the OOS attempts to change those parameters, and the satellite still has operational attitude control, it could actively resist the OOS.

All this makes the situation ideal for a machine learning model to manage—and that is precisely what Yuhan Liu of Eindhoven University of Technology and his colleagues explored in a recent paper. They employed a machine learning technique known as Gaussian process (GP) to create a dynamic model of the multi-spacecraft system, without the need to update training sets or conduct significant background calculations in real time.

Computational load is a major consideration for GP machine learning models, as they typically require a significant amount of training data and continuous updates based on new inputs. This would not work in the computationally constrained environment of an OOS satellite. Furthermore, transmitting new control commands from the ground would be too slow.

To address this, the team devised a way of adapting an online model that is designed more for making real-time decisions than for learning from an existing dataset. They used a sparse model to reduce computational demands, considering only a subset of the incoming data. They also made the model recursive, so new data updates the system rather than retraining it from scratch.

However, there are still limitations. These include the need to efficiently utilize the OOSs' onboard memory, as updating parameters can consume a significant portion of the system's working memory. Additionally, the algorithm must ensure that the solution converges to a stable point rather than introducing further chaos into an already unpredictable system.

To demonstrate, the authors ran it in a simulator designed to mimic the capture and attitude control of a non-cooperative satellite. They found that their solution performed significantly better than existing models. Stability was demonstrated by maintaining the final positioning of the attitude parameters of the OOS, thus avoiding the catastrophic failure of a runaway feedback loop, which is akin to microphone feedback.

Summary

Running such a controller in a simulator is one thing; doing so on an actual OOS satellite is quite another. Many companies are vying to manufacture the first OOS capable of adaptively capturing and controlling a non-cooperative satellite, including smaller players like Astroscale and industry giants like Maxar and Airbus.

As more test flights demonstrate increasingly effective systems for capture, control and eventually repair and refueling, the engineers tackling these challenging problems—whether in theory or practice—will continue to stay busy.