TrajectoryBot — differentiable-simulation RL for orbital maneuvers

A from-scratch orbital-dynamics stack (no Basilisk, no poliastro) and a policy-gradient agent that learns spacecraft maneuvers by backpropagating through the physics, benchmarked against analytic transfers — with every claim re-verified at high fidelity before it's stated.

The agent is a small MLP at the decision layer only: every 200 s it emits a thrust direction (in the orbit frame) and a throttle; a deterministic pointing controller slews the spacecraft and a quaternion rigid-body integrator does the physics. The policy never touches attitude directly — burn planning is learned, burn execution is classical GNC.

flowchart LR
    O[observations<br/>r, v, elements, fuel] --> P[policy MLP<br/>13 → 128 → 128 → 4]
    P -->|"direction (orbit frame) + throttle"| C[pointing controller<br/>rate command]
    C --> D[quaternion rigid-body dynamics<br/>RK4, dt = 10 s]
    D -->|"1200+ substeps, fully differentiable (JAX)"| L[loss: terminal orbit error + Δv<br/>+ Δv-to-go potential shaping]
    L -.->|"∂loss/∂θ through the whole rollout"| P

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The whole policy is a tiny 13 → 128 → 128 → 4 tanh MLP — three weight matrices, trained end-to-end through the physics:

Verified results

Claim	Number	How it's verified
Success (5% tolerance terminal set, 3D)	92.3%	fresh 4096-episode set, never in-run telemetry
Fuel vs the impulsive analytic optimum	1.03× median (best-fuel policy, ~92% success)	float64 re-flight at dt = 1 s, clean episodes only, closed-form baseline (scripts/verify_probe.py)
Oracle it improves on	scripted analytic expert imitated at 79.9%	same fresh set
Sim gaming ruled out	0 of 4096 episodes beat the admissible tolerance-box bound	same probe, both baselines

Honest framing: the agent matches the analytic transfer's fuel cost while running the full closed-loop attitude + finite-burn pipeline; it does not yet beat it. The tolerance box admits solutions up to ~15% cheaper than exact circularization — that quantified headroom is the open research target, and the verification harness exists precisely so any future "beats the baseline" claim survives scrutiny (integrator-energy audit, float64 re-flight, clamp-region exclusion, per-geometry closed-form baselines).

Scope: the headline policy above circularizes at its own apoapsis (target radius = initial apoapsis). Generalizing across commanded target radii — a degeneracy where that specialist collapses out-of-distribution (~18% success once the target leaves its trained radius) — is solved separately. A target-conditioned scripted expert (a two-apse tangential controller that drives both apses to the commanded radius) DAgger'd into the same 13→128→128→4 network reaches ~99% success across commanded radii spanning ±15% of apoapsis on fresh 4096-episode sets. The cause was not network capacity or optimization but the imitation source — the specialist lineage was cloned from a fixed-target expert and had never imitated tracking. See scripts/dagger_target_jax.py.

It isn't one lucky episode — the final policy solves the distribution. Forty random start orbits, each flown to termination, coloured by whether the finish landed inside the 5% tolerance box:

Why differentiable simulation

Model-free RL was given every chance and walled out; exploiting the known, exactly-differentiable dynamics wins by an order of magnitude (2-D milestone, identical env):

Method	Success	Δv vs optimal
Scripted analytic expert	100%	1.00
Cold PPO (model-free, 8 runs)	0–3%	—
Behavior cloning	~16%	~1.37
DAgger	~45%	~1.5
Diff-sim policy gradient	81%	1.26

In 3-D, differentiable-sim refinement then climbs past the imitation oracle it started from — each point is the fresh 4096-episode success of a checkpoint along the campaign:

The 3-D stack ports the hot path to JAX/XLA (scripts/jaxsim.py): lax.scan + jit(value_and_grad) over the full 1200-substep rollout, numerically exact against the torch reference and ~50× faster on a consumer GPU — which is what made the research loop below possible.

The part that was actually hard

Backprop-through-physics gradients are heavy-tailed: one episode in a few hundred carries a gradient norm of 1e12–1e19 (finite, not NaN) and a single Adam step can erase 12 points of success. Getting from "imitates the oracle at 80%" to "92% and stable" was optimizer forensics, run as pre-registered hypothesis-refutation rounds (30+, logged verbatim):

Same start checkpoint, same seed — only the gradient aggregation differs.

And here is what that refinement buys on a single episode — the same start orbit flown by four training stages, imitation → refined, cycling so you can watch the path tighten onto the target ring:

The playbook that survived: measure the per-episode norm distribution, delete the monster tail (trimmed mean), clip survivors at the measured p90, bank progress with an EMA policy, polish at low lr. The failure modes en route (truncation bias in short-horizon BPTT, absorbing-state mismatches, potential-shaping traps that pay for zero progress, a normalize-epsilon that seeded 1e6 gradients at every coast decision) are documented in docs/EXPERIMENTS_3D.md (3-D campaign) and docs/EXPERIMENTS.md (2-D milestone).

Beyond circularize: the research frontier

The same backprop-through-physics approach extends to multi-body dynamics and to maneuvers where a fidelity term the textbook ignores changes the optimal strategy. Two recent threads (full methodology and honest verdicts in docs/ROADMAP.md):

Ballistic capture at the Moon (CR3BP). A hand-rolled differentiable circular-restricted three-body engine (rotating Earth–Moon frame, Jacobi constant conserved to ~1e-7), the stable manifold of an L2 Lyapunov orbit computed from its monodromy matrix (symplectic, det = 1), and a manifold-seeded transfer that arrives captured at the Moon — Moon-relative energy < 0, staying bound for 4.6 lunar revolutions (~26 days, verified at dt = 5e-5) with no capture burn — where a naive departure-burn search finds none.

Rediscovering J2 nodal-drift phasing. For a RAAN (orbital-plane) change, the textbook impulsive plane change is J2-blind — but J2 oblateness precesses the node for free, faster at lower altitude. A diff-sim policy minimizing true Δv over J2-on dynamics, with no maneuver structure baked in, rediscovers the operational phasing technique: dive to a lower altitude, let the node drift faster, return. It reaches the target node for ~0.88× the Δv of naive passive waiting at 30°, falling to a quarter–half at 60–90° (the bigger the node change, the more the dive pays) — and lands within ~10–15% of an analytic optimization of that same dive-drift strategy (which is slightly cheaper still). So this is autonomous rediscovery of a known technique from the raw objective, not a novel beat — the same genre as the agent rediscovering the raise-to-plane-change trick elsewhere in the project.

These are the honest positives at the frontier, with the deflations kept in view: the capture is in the idealized CR3BP (not real JPL ephemerides yet); the J2 result is a rediscovery that an analytic dive beats, and its low-thrust Δv is idealized (impulsive-per-step). The regimes where the savings vanish (small node angles, budgets so long that passive is free) are recorded per build — no claim outruns its verification.

Quickstart

uv sync --extra dev            # Python 3.12+, from pyproject/uv.lock
uv run pytest                  # physics, baselines, envs, solvability
uv run pyright                 # strict typing on the shipped library

# 2-D milestone (torch)
uv run python scripts/train_circularize2d.py

# 3-D JAX training run (GPU; CPU works, slower)
uv run --with "jax[cuda12]" python scripts/jaxsim.py \
  --init models/dagger_jax.npz --iters 3000 --chunk 60 --lr 1e-4 \
  --absorb --phi-dv --d-eps 1e-4 --trim-ep 16 --clip-ep 20000 --ema 0.995

# verify a fuel claim at high fidelity (float64, dt=1 s, both baselines)
uv run --with jax python scripts/verify_probe.py models/<ckpt>.npz

# regenerate the README figures
uv run --with jax --with matplotlib --with pillow python scripts/viz_readme.py models/<ckpt>.npz <logdir>
uv run --with jax --with matplotlib --with pillow python scripts/viz_readme_extra.py  # progression / weights / generalization / learning gif
uv run --with jax --with matplotlib --with pillow python scripts/viz_tier3.py          # CR3BP capture + J2-beat frontier (no checkpoint needed)
uv run --with jax --with matplotlib --with pillow python scripts/viz_lowthrust.py # low-thrust spiral (flies the E1 lt_2e-4 specialist)

Checkpoints and run logs are not committed (they regenerate by training); the circularize-lineage checkpoints behind the figures are published as a GitHub release. docs/media/ holds the small rendered figures only.

Repository map

Path	What it is
tbot/	The shipped library: quaternions, 2-D/3-D dynamics, orbital elements, attitude controller, Gymnasium envs. pyright-strict.
scripts/jaxsim.py	JAX/XLA 3-D diff-sim trainer (the research workhorse) with the full knob set.
scripts/verify_probe.py	float64/dt=1 s claim-verification harness (exact + tolerance-box baselines).
scripts/eval_probe.py, norm_probe.py, step_probe.py, …	The measurement toolkit the optimizer forensics ran on.
docs/EXPERIMENTS_3D.md, docs/EXPERIMENTS.md	The optimizer-forensics campaign (3-D) and the 2-D milestone methodology.
docs/ROADMAP.md, docs/AUDIT.md	Target maneuvers and the audit of the 2021 code.
v2/, archive/	The 2021 course project, kept as the honest "before" picture (excluded from CI/typing).

Roadmap

Circularize (3-D, done) → plane change → combined LEO→GEO transfer → low-thrust (Edelbaum spiral) → multi-body with real JPL Horizons ephemerides (Earth–Moon, Earth–Mars, capture) → benchmark against historically flown trajectories. The N-body tier reuses the 2021 project's Horizons stack. For any N-body fuel comparison, results must additionally be tested across solar-system phases (syzygy effects are real physics but epoch-specific).

Provenance

Started in 2021 as a graduate astrodynamics course project that trained but never converged — the original report and code are preserved in docs/final-report.md, v2/, and archive/, and the revival began by auditing why it failed (docs/AUDIT.md). Everything physics is hand-rolled on purpose: the point is to own the whole stack from the RK4 up.

MIT licensed. See CONTRIBUTING.md for how changes are evaluated (pre-registered experiments, verification-fidelity claims).