Method note
The problem, the method and the evaluation behind the interactive demo. The four sections below describe the method only; they introduce no new results.
The problem
A spacecraft in low Earth orbit can face several conjunctions within one or two orbital periods. Every avoidance burn costs propellant and changes the orbit itself, which shifts the geometry of all subsequent encounters. Treating each conjunction as an independent event and solving a sequence of impulsive manoeuvres often leaves no propellant by the third or fourth encounter.
The method
We formulate continuous low-thrust avoidance under cascaded conjunctions as a constrained Markov decision process: the state holds the orbital elements and relative geometry of the protected spacecraft and all debris objects, and the action is a three-axis velocity increment per control cycle.
The policy is a set-attention network — each debris object is encoded independently, a Transformer lets the objects attend to one another, and a threat-focused pooling layer concentrates weight on the few most dangerous targets. A single set of weights therefore handles one to ten debris objects without retraining.
Training uses safe reinforcement learning: collision probability enters as a constraint rather than a reward, adapted through a Lagrange multiplier, while SOCP expert solutions provide directional anchoring and action shielding so that early exploration cannot drag the policy off course.
Relation to the SOCP expert
The SOCP expert casts continuous-thrust avoidance as a convex program (corridor constraints with relaxation) and solves it once over a fixed time grid, yielding a globally optimal open-loop thrust sequence. Its cost grows with the number of debris objects (about 6 s for one object and 80 s for three on this machine). The policy instead closes the loop every control cycle with a forward pass of roughly 8 ms.
They are complementary: the expert supplies a verifiable benchmark, the network supplies a closed-loop controller that can run onboard.
Reading the demo
Blue is the closed-loop policy trajectory, the grey dashed line is the no-manoeuvre case, and orange is the SOCP expert. The ticks on the timeline mark each time of closest approach (TCA).