🚀 How to avoid crashing a spacecraft

From: Collision Avoidance Manoeuvres Optimisation in the Presence of Multiple Encounters

The Problem

Spacecraft are facing increasing risks from space debris (non-functional, human-made objects in space like dismissed satellites), especially in popular orbital zones like the geostationary orbit (GEO) and low Earth orbit (LEO).

To avoid collisions, spacecraft operators perform Collision Avoidance Manoeuvres (CAMs), which are adjustments to the spacecraft's path to steer clear of potential collisions. This paper aims to optimise CAMs in scenarios where there are multiple encounters while minimising fuel consumption.

The Solution

Imagine you're driving on a busy highway, trying to avoid other cars (space debris) while saving fuel. You need a plan to change lanes or speed up without crashing. This is similar to how spacecraft avoid collisions.

The big problem is planning your entire trip with many cars potentially in your way. You need to:

• Avoid crashes.

• Use the least fuel.

• Deal with many possible near-crashes, not just one.

To solve this, scientists break it into smaller, easier steps using Sequential Convex Programming (SCP).

Steps

1. Initial Guess:

   • Start with a rough idea of your path, like drawing a simple route on a map.

2. Refine the Path:

   • Gradually adjust the path to avoid cars more efficiently and use less fuel.

What is actually used:

1. Sequential Convex Programming (SCP): Breaks down the complex problem into simpler, more manageable sub-problems.

2. Second-Order Cone Programming (SOCP): Ensures that the adjustments to the path are within realistic and safe limits.

3. Differential Algebra (DA): Predicting future changes based on current conditions. Handles the nonlinearities and uncertainties in the spacecraft's position and velocity.

4. Gaussian Mixture Model (GMM): The positions of other cars (debris) are uncertain, we don’t always know where they are. GMM breaks this uncertainty into smaller parts, making it easier to predict their positions.

Conclusion

The proposed method effectively generates fuel-efficient CAMs while considering multiple encounters, offering a reliable solution for future space operations in increasingly crowded orbits.