A research-grade, reproducible benchmark that puts classical, optimal, game-theoretic, and learned missile-interception guidance on the same field — identical dynamics, a shared scenario suite, shared metrics, and full seeded Monte-Carlo statistics.
I built INTERCEPT to answer a question the literature leaves scattered: on equal footing, which guidance paradigm actually wins, and at what cost? Every guidance law, evader, and allocator here runs against the same physics, so every difference you see is the algorithm — not the testbed.
Scope & ethics. INTERCEPT is a simulation-only, educational/research project. It uses point-mass / kinematic models and public, textbook-level guidance, estimation, and control algorithms (Zarchan, Siouris, Shneydor, Bar-Shalom, Isaacs). It contains no hardware integration, no real targeting or sensor data, no munitions/warhead modeling, and no detection-evasion tooling. The goal is to study and compare guidance and autonomy algorithms as a controls/robotics research and teaching artifact.
A benchmark framing I haven't seen elsewhere: every seeded engagement is a match (intercept ⇒ the guidance law wins; escape ⇒ the evader wins), and a Bradley-Terry fit over the full round-robin — every law vs every adversary on identical dynamics — puts both sides on one Elo ladder. It is, as far as I can find in the literature, the first skill-rating ladder for guidance laws.
| rank | participant | side | Elo |
|---|---|---|---|
| 1 | Sliding-mode | guidance | 2214 |
| 2 | optimal (anti-LOS) | evader | 2019 |
| 3 | Optimal (OGL) | guidance | 1917 |
| 4 | Augmented PN | guidance | 1871 |
| 5 | RL recurrent APN-residual | guidance | 1681 |
| … | (full 14-row ladder: results/p32_league.md) |
The ladder says in one glance what a dozen separate tables could not: robustness (sliding-mode)
wins the league, the game-theoretic evader out-rates every other guidance law (a target is
the #2 player overall), learned laws sit mid-table, and scripted evaders fall to the bottom. The fit
also predicts unplayed match-ups (elo_expected_score). Reproduce: python experiments/p32_league.py.
Comparisons between guidance paradigms — Proportional Navigation, optimal/geometric laws, differential-game strategies, and reinforcement learning — are scattered across single studies on different geometries and metrics, and most report only miss distance (ignoring control effort/efficiency, where learned methods often win). I could not find a clean, reproducible open-source benchmark that puts these paradigms on the same field, so I built one.
The design invariant that makes the comparison valid: every controller — guidance law, scripted
or RL evader, swarm allocator — is the same callable contract (t, own_state, world) -> control and
shares the same injected dynamics. No method gets a physics advantage; differences are the
algorithm, not the testbed.
Across six paradigms, three fidelity levels, 2-D and 3-D, single- and many-vs-many:
| Layer | Implemented |
|---|---|
| Guidance (9 laws / 6 paradigms) | Pure / True / ZEM Proportional Navigation · Augmented PN · Optimal LQ/ZEM (OGL) · Sliding-Mode · NMPC (CasADi/IPOPT, impact-angle, event-triggered) · RL (PPO) · Apollonius-circle geometric pursuit |
| Fidelity ladder (L0→L3) | PointMass2D/3D → AeroMissile2D/3D (gravity, parasitic + induced drag, g-limit, autopilot lag) → RealisticMissile2D/3D (ISA atmosphere, boost–sustain–coast propulsion + mass burn-off, Mach + induced drag, lift / dynamic-pressure-limited turning — turn capability emerges from physics, not a prescribed limit) |
| Estimation & sensing | Radar (range+bearing) & IR (angles-only) sensors with seeded noise · EKF (Joseph) · UKF · IMM · sense→estimate→guide closure |
| Game theory & adversaries | Apollonius dominance geometry · game-theoretic optimal (anti-LOS) evader · scripted weave/jink/bang-bang · reactive max-g break · 3-D barrel-roll / serpentine / intensifying terminal spiral |
| Multi-agent | Hungarian weapon-target assignment · N-vs-M area defense with live re-assignment · diverse-threat swarm raid (6 realistic trajectory profiles) · learned (MARL) cooperative allocation · coordinated swarm-penetration tactics (time-on-target / decoy-screen / saturation-point / waves) + asset-value layered-defense counter |
| Benchmark | YAML scenario suite (2-D and 3-D) · seeded Monte-Carlo (fairness invariant) · Wilson-CI metrics · paired-bootstrap significance · capture-region sweeps · publication-quality figures + animations |
199 unit/property/regression tests passing · ruff-clean · fully type-hinted (mypy runs in CI).
- Intelligence beats speed. On realistic evasive engagements, simple True PN collapses to P(intercept) 0.21–0.56 (reactive break / unpredictable jink), while Augmented PN, Optimal, and Sliding-Mode recover to 0.79–1.00 — prediction and robustness, not a speed margin.
- Speed parity, no artificial edge. Both missiles run on the full L3 plant; a ~Mach 3 threat flies a lofted serpentine + intensifying terminal spiral, and the interceptor wins with only a +37 % closing-speed margin — a propulsion sweep confirms that shrinking its motor turns the win into a miss, so the result is an algorithm win, not a thrust advantage. 60/60 robustness intercept across randomized geometry and maneuver parameters (P = 1.00, 95 % CI [0.94, 1.00]).
- Estimation matters. Against a maneuvering target, an IMM filter holds ~9 m tracking error where a single-model EKF diverges to ~350 m.
- Area defense. 8 interceptors vs an 8-threat fan → 8/8 intercepted, 0 leakers via Hungarian WTA with re-assignment; scaled up, a two-wave 12-threat raid is fully defeated 12/12.
- Beating a decoy-screen saturation raid. Against a coordinated raid that screens real threats with decoys, a naive time-minimizing defender wastes its magazine on chaff (1.7 real leakers); my asset-value defense — impact-point prediction plus a track-history decoy discriminator — spends every interceptor on real threats (0.0 leakers), and breaks even with the naive defender when there are no decoys to exploit — discrimination helps exactly where it should.
- Learned vs classical, at speed parity. With the interceptor only ~1.45× the target, from- scratch PPO collapses — so the policy instead learns a residual on a PN baseline, matching the classical laws (head-on / weave 1.00) and edging them on the crossing shot (0.82 vs 0.76) at higher control effort. A clean, reproducible learned-vs-classical comparison with the cost reported alongside the win.
- A learned guidance law that outperforms the PN family. From-scratch PPO collapses on the realistic (lagged + gravity) plant (~0–2 %). The residual parameterization — a bounded correction on a PN/APN baseline — restores it, and with an APN baseline + a recurrent (LSTM) policy it reaches 1.00 / 1.00 / 0.95 (crossing / weave / jink). On the unpredictable jink it beats True PN (0.81) and Augmented PN (0.93) at lower effort, trailing only sliding-mode (1.00) — a genuine learned win on the hardest realistic case.
- One fair benchmark, statistically grounded. The same seeded harness spans paradigm × fidelity (L0→L3) × dimension (2-D/3-D); pairwise differences use a paired bootstrap (the fairness invariant makes trials paired). E.g. on the 2-D L2 jink, Augmented PN beats True PN by +0.09 (95% CI [+0.03, +0.16], p = 0.009); in 3-D a barrel-roll defeats True PN (0.00) while Augmented PN holds 1.00.
Every engagement below is produced by a script in experiments/ and rendered with
the project's own dark/neon visualization layer. The full set lives in
gallery/.
Coordinated swarm penetration vs. the asset-value defense — a decoy-screen saturation raid (left) and a simultaneous time-on-target raid (right). The defender predicts each track's impact point and spends its magazine only on the threats that actually endanger the asset.
3-D area defense and complex-trajectory evasion — a 12-threat two-wave raid intercepted 12/12 (left), and a single ~Mach 3 interceptor running down a lofted, spiralling threat on the full aero-propulsive plant (right).
Cooperative and estimation-aware guidance — an impact-time-controlled salvo arriving together (left), a pincer pair covering both branches of an unpredictable break (centre), and mode-adaptive guidance whose colour tracks the IMM maneuver belief that arbitrates PN↔APN (right).
Classical vs. learned, 1-v-1 — True PN leading a crossing target while pure pursuit lags (left), the game-theoretic anti-line-of-sight evader stretching capture time (centre), and a trained RL evader exploiting a fixed pursuer (right).
Two interactive Plotly 3-D replays (
gallery/animations/*_interactive*.html) can be opened locally or served from the docs site — they render an orbitable, zoomable version of the 3-D engagements.
Scenario (YAML) → Simulation Core (dynamics · RK4 · engagement loop)
├── Sensors → Estimation/Tracking (EKF/UKF/IMM) ┐
├── Guidance/Control (PN·APN·OGL·SMG·MPC·RL·Game) ├→ Engagement → Result/metrics
└── Adversary (scripted · game-theoretic · RL) ┘
Experiment & Analysis: Monte-Carlo · benchmark harness · capture-region · viz · RL training
An algorithm-agnostic core, plug-in paradigms, and an experiment/analysis layer. The dimension-agnostic engagement loop runs L0–L3 and 2-D/3-D unchanged. See docs/index.md and the Architecture Decision Records for the rationale behind each design choice.
pip install -e ".[dev]" # core + dev tools (extras:.[rl].[mpc].[estimation])
pytest -q # 199 tests
ruff check intercept tests experiments # lint
python experiments/p2_benchmark.py # the centerpiece: PN-family Monte-Carlo + figures
python experiments/p8_realistic_benchmark.py # intelligence-beats-speed on realistic evaders
python experiments/p14_advanced_evasion.py # L3 complex-trajectory showcase + robustness (speed parity)
python experiments/p35_swarm_penetration.py # coordinated saturation tactics vs the asset-value defense
python experiments/p9_3d_demo.py # 3-D engagement + modern animation + interactive HTMLHeadless plotting (CI/automation): set MPLBACKEND=Agg. Experiments write figures to gallery/
and CSVs to results/.
intercept/ core · guidance · sensors · estimation · multiagent · adversary · envs · benchmark · viz
experiments/ runnable scripts (p0…p35) producing every figure/animation in gallery/
tests/ unit · property · regression (199)
scenarios/ YAML scenario suite (2-D and 3-D)
results/ benchmark CSVs + the League ladder (committed, so the numbers travel with the repo)
gallery/ publication-quality figures + cinematic animations
docs/ index · algorithms/ (governing equations + references) · benchmarks/ (methodology)
planning/ research foundation (state of the art) + design document / roadmap
A full mkdocs-material site (mkdocs.yml) collects the docs below; build it locally with
pip install -e ".[docs]" && mkdocs serve, or it auto-deploys to GitHub Pages via
.github/workflows/docs.yml once the repo is on GitHub. CI (.github/workflows/ci.yml) runs
ruff and pytest on Python 3.10–3.12, type-checks with mypy (advisory), and verifies the docs build.
- Results digest (headline findings + figures): docs/results.md
- Research foundation & roadmap: planning/00_RESEARCH_REPORT.md, planning/01_PROJECT_PLAN.md
- Algorithm notes (with governing equations + references): docs/algorithms/
- Benchmark methodology: docs/benchmarks/methodology.md
Python · numpy / scipy core · CasADi + IPOPT (NMPC) · Gymnasium + Stable-Baselines3 (RL) ·
Matplotlib (2-D/3-D viz + animations). Optional extras keep the core install light.
MIT.