V-BAR: Verified Benchmark for Autonomous Rendezvous

V-BAR is a headless Python benchmark for spacecraft rendezvous and proximity-operations controllers. Classical guidance laws, reinforcement learning agents and LLM agents fly the same scenarios and are scored with the same metrics.

The PD baseline reaches the hold point from behind the target (blue) but flies through the keep-out zone from ahead of it (orange), closing to 14.4 m.

Status: early development (0.6). The dynamics, spacecraft, sensor and constraint layers are validated (see Tests). Version 0.3 added the metrics, agent tools (remote and ONNX policy agents, the sign check, reward and training interfaces), a scenario catalogue and vbar.solvers (command projection and horizon quadratic programs). Version 0.4 adds the classical baselines and fuel oracles, the evaluation harness, comparison tasks rebuilt from published benchmarks, agreement checks against Basilisk and Orekit, pursuit-evasion in KSPDG's format, replay export to Rerun, fault injection, mission reconstructions and a tumbling-capture scenario. Version 0.5 adds the safety filters (barrier, backup, predictive, corridor and run time assurance filters, and an audit of the certified ones), LLM agents for every task kind and a supervisory channel for LLM and rule supervisors, KSPDG's pe1 evader bots and starts with a kspdg import alias, one-command reproduction of the published tables and figures, and a Colab quickstart; 0.5.0 was not published to PyPI, so these ship in 0.6. Version 0.6 adds Holm and Benjamini-Hochberg corrections and a paired sign-flip test, a call and dollar cap for LLM agents, and repair counts for the LLM supervisor. The LLM supervisor study is in progress, and interfaces may change before 1.0.

Why

KSPDG, the main existing environment for this kind of work, runs on Kerbal Space Program in real time and needs a copy of the game. V-BAR is a plain Python package that runs much faster than real time on Linux, macOS and Windows, so experiments with hundreds of seeds and many controllers are practical. Its physics is checked against closed-form solutions and published textbook examples, so a result reflects the controller and not a simulator error.

Install

pip install vbar

Python 3.12 or later. The core dependencies are numpy, scipy and gymnasium. Plotting needs the plot extra: pip install "vbar[plot]"; ONNX policy export and inference need the onnx extra: pip install "vbar[onnx]"; replays for the Rerun viewer need the replay extra: pip install "vbar[replay]". The agreement checks against Basilisk and Orekit need the basilisk extra, pip install "vbar[basilisk]", and the orekit extra, pip install "vbar[orekit]" with a Java runtime (11 or later) on JAVA_HOME. To work on V-BAR itself, see CONTRIBUTING.md.

Quickstart

from vbar import ApproachConfig, ApproachEnv, run_episode
from vbar.agents import PDAgent

env = ApproachEnv(ApproachConfig(start_state=(0, -400, 0, 0, 0, 0)))
result = run_episode(env, PDAgent())
print(result["captured"], result["keep_out_violated"], result["dv_used_mps"])

This flies the PD baseline from 400 m behind the target to the hold point 100 m behind it, about 620 s of flight, and prints True False 2.41...: it arrived, it never entered the keep-out zone, and it used 2.4 m/s of delta-v.

The quickstart notebook runs without a local install. It installs the package from PyPI, flies this baseline, prints its metrics and rebuilds a two-episode results table with the evaluation harness (docs/evaluation.md).

Benchmarks need many runs, not one. With the default random starts, which put the chaser 200 to 600 m ahead of the target so the target sits between it and the hold point:

import numpy as np
from vbar import ApproachEnv, run_many
from vbar.agents import PDAgent

results = run_many(ApproachEnv(), PDAgent(), seeds=range(100))
print(np.mean([r["captured"] for r in results]), np.mean([r["keep_out_violated"] for r in results]))

The PD baseline reaches the hold point and flies through the keep-out zone on every default seed, because it ignores the target. That gap is what safety filters and better controllers are measured against. In a clone of the repository, python examples/v0_demo.py shows both cases and saves a plot to outputs/ (needs the plot extra).

The orange run animated: it spends about 2.3 minutes inside the keep-out zone.

python examples/readme_figures.py regenerates this animation and the figure above (docs/viz.md).

Frame and units

Everything is in the target's Hill frame (also called RIC, RSW or RTN), centred on the target and rotating with its orbit:

• x: radial, pointing away from Earth (the R-bar)
• y: along-track, the direction the target is moving (the V-bar); "behind the target" is -y
• z: orbit normal, completing a right-handed frame

States are [x, y, z, vx, vy, vz] in metres and metres per second, with velocities measured in the rotating frame. All units are SI and angles are in radians. The ISS-style LVLH frame used in much of the operations literature orders and signs the axes differently; vbar.conventions.hill_to_iss and iss_to_hill convert between the two.

The scenario: approach to a hold point

The chaser must reach a hold point 100 m behind the target and stop there without entering a 50 m keep-out sphere around the target. The target is on a circular 500 km orbit. Defaults, all set in ApproachConfig:

Each run reports whether it captured, whether and in how many steps it entered the keep-out zone, the minimum range to the target, the final distance to the hold point, delta-v used (each step's delta-v summed, the usual proxy for propellant), flight time and wall-clock time, plus the intervention count when a safety filter wraps the agent. run_episode also returns the full true state and action history and the seed of the agent's random stream. Propellant used, mass and the certified bound on the keep-out margin are in info.

The environment propagates with Clohessy-Wiltshire dynamics by default; ApproachConfig(dynamics="twobody") or "twobody_j2" selects one of the nonlinear models below.

Scoring

vbar.metrics.record_episode(env, agent, seed) records a run and vbar.metrics.evaluate(episode) scores it from the true trajectory in continuous time: mission (success, terminal errors, time, progress, docking contact, hold dwell), efficiency (delta-v in both norms, propellant, burns, duty cycle, chatter, the optimality gap against oracle bounds), constraint margins with violation depth and duration, passive safety and collision-avoidance availability, thruster plume, safety-filter and agent metrics, a composite score with its breakdown, and a failure label for failed runs. These are the benchmark's scores; the keys run_episode returns are a quick check of one run.

from vbar import ApproachConfig, ApproachEnv
from vbar.agents import PDAgent
from vbar.metrics import evaluate, record_episode

env = ApproachEnv(ApproachConfig(start_state=(0, -400, 0, 0, 0, 0)))
m = evaluate(record_episode(env, PDAgent()))
print(m["success"], m["composite_score"], m["failure_label"])  # True 1.0 None

Definitions, tests and one card per metric are in docs/metrics.md.

A whole suite is run and reported with vbar.eval: every (scenario, seed) of the suite in parallel, one JSON-lines result per run with a provenance hash, and a report that refuses a partial suite and gives success rates with exact intervals, interquartile means with stratified bootstrap intervals and safety metrics by their unsafe tails. The core suite core-v1 holds the headline benchmark: the V-bar and R-bar approaches, the on-axis docking, the run time assurance docking and the inspection, each with and without navigation noise.

python -m vbar.eval run --suite core-v1 --agent vbar.agents:DriftAgent --workers 8 --out drift.jsonl
python -m vbar.eval report drift.jsonl --markdown drift.md

See docs/evaluation.md.

Writing a controller

Any object with a name, a reset(view, rng) method and an act(obs, info) method that returns three numbers in [-1, 1] is an agent:

import numpy as np

from vbar import ApproachConfig, ApproachEnv, run_episode
from vbar.agents.sign_check import sign_check


class SpringAgent:
    name = "spring"

    def reset(self, view, rng=None):
        self.max_accel = view.max_accel
        self.hold_point = np.array(view.goal["hold_point"])

    def act(self, obs, info):
        # Critically damped at 0.01 rad/s, nine times the orbital rate, so the CW terms are small.
        a = 1e-4 * (self.hold_point - obs[:3]) - 0.02 * obs[3:6]
        return np.clip(a / self.max_accel, -1.0, 1.0)


print(sign_check(SpringAgent()).passed)  # True
env = ApproachEnv(ApproachConfig(start_state=(0, -400, 0, 0, 0, 0)))
print(run_episode(env, SpringAgent())["captured"])  # True

reset receives a read-only AgentView with the scenario's public description (time step, mean motion, actuator limits, goal and constraints) and a random stream for the agent's own use. obs comes from the navigation sensor and info holds only the time, so a controller never sees the true state. The agent's stream is seeded by run_episode(env, agent, seed, agent_seed) independently of the episode seed. Seeds not given are drawn (128 bits) and returned in the result, so the run can be repeated; scored comparisons keep them drawn, since an agent can find a small seed by matching its first observation against the public scenario (docs/environment.md).

Classical baselines

vbar.agents includes classical controllers to compare against. Each page gives the method, its limits and how it is tested.

Mutant(agent, kind, severity) wraps any of them with one deliberate defect, to check that the metrics catch it (mutants.md).

vbar.oracles gives what the baselines are scored against: certified fuel bounds from the primer vector and a finite-thrust dual bound (FuelOracle, bounds_for), primer-vector certificates, the minimum-time and passing-side oracles, and OracleAgent with expert_dataset for expert trajectories (oracles.md, oracle-certificates.md, minimum-time-oracle.md, passing-side-oracle.md, expert-datasets.md).

LLM agents

LLMAgent wraps any model through a function that takes the decision's messages and the tools offered and returns the reply; text_model adapts a plain prompt-to-text function:

from vbar import ApproachConfig, ApproachEnv, run_episode
from vbar.agents import LLMAgent, Price, Reply, text_model


def complete(messages, tools):
    """Send the conversation to any hosted or local model and return its reply."""
    return Reply('{"ax": 0.0, "ay": 0.0, "az": 0.0}', input_tokens=900, output_tokens=20)


env = ApproachEnv(ApproachConfig(start_state=(0, -400, 0, 0, 0, 0)))
agent = LLMAgent(complete, name="my-model", price=Price(3.0, 15.0))
result = run_episode(env, agent)
print(agent.usage())  # decisions, model calls, tokens, cost and parse failures

plain = LLMAgent(text_model(lambda prompt: '{"ax": 0.0, "ay": 0.0, "az": 0.0}'))

Each step's prompt gives the frame, the mean motion, the task's goal and constraints in words, the current state measured against them (offsets from a docking port's axis, coverage of an inspection) and the thrust limit, and asks for a JSON reply such as {"ax": 0.1, "ay": -0.5, "az": 0.0}; the agent flies every task kind of the catalogue. A reply that cannot be parsed counts as a parse failure and the spacecraft coasts for that step. The prompt is configurable, the agent can offer tools (coast and transfer predictions from its own observation), every run can be recorded and replayed without the model, and an optional belief check measures whether the model's stated reasoning matches its inputs (docs/llm-agents.md). The simulation clock is paused while the model answers, unless the run is in real time.

Agents can also run in another process or language through the agent server (with Python and MATLAB clients), LLM harnesses can fly episodes through a Model Context Protocol tool server (docs/remote-agents.md), and planners can submit whole plans to an external verifier (docs/agents.md). Every agent should pass the sign-convention check, vbar.agents.sign_check.sign_check(agent), before it is scored.

Reinforcement learning

ApproachEnv follows the Gymnasium API (reset(seed=...), step(action)), by default with a Box(-1, 1, (3,)) action space and a 6-element observation, and passes Gymnasium's environment checker, so it works with standard RL libraries. Importing vbar registers it:

import gymnasium as gym

import vbar  # noqa: F401

env = gym.make("vbar/Approach-v0")
obs, info = env.reset(seed=0)
obs, reward, terminated, truncated, info = env.step(env.action_space.sample())

Train with a library reward, whose terms follow the benchmark metrics and whose discount is declared per second, so the task does not change with the step length (docs/rewards.md):

from vbar import ApproachConfig, ApproachEnv
from vbar.rewards import Reward

reward = Reward(tau=3600.0, success_bonus=10.0, fuel_weight=1.0, entry_weights={"keep_out": 5.0})
env = ApproachEnv(ApproachConfig(reward=reward, training=True))
obs, info = env.reset(seed=0)
obs, r, terminated, truncated, info = env.step([0.0, -0.1, 0.0])
print(round(info["discount"], 6))  # discount this transition by exp(-dt / tau)

Without reward the scenario returns its legacy shaped reward (progress toward the hold point, minus delta-v, minus a penalty for each step in the keep-out zone, plus a bonus on capture), which is not aligned with the metrics and is not the benchmark score; score agents with vbar.metrics. ApproachVectorEnv steps many copies as one batch (docs/vector-env.md); the discrete bang-off-bang and burn-and-coast action modes, training-only starts and a safety filter in the training loop are on docs/training.md, and trained networks export to ONNX with their normalization built in (docs/policy-export.md). Rewards and info come from the true state, so fly trained policies for scoring through run_episode or vbar.metrics.record_episode, which pass them only the observation and the time and refuse environments built for training.

Dynamics

The dynamics can be used without the environment:

import numpy as np
from vbar.dynamics import make_dynamics

dyn = make_dynamics("twobody_j2", altitude=500e3, inclination=np.radians(51.6))
dyn.reset([0.0, -200.0, 0.0, 0.0, 0.0, 0.0])  # Hill-frame state, m and m/s
x, _ = dyn.advance([0.0, 0.0, 0.0], 600.0)  # hold zero acceleration for 600 s

Also included, each documented in docs/:

• differential drag and solar radiation pressure with Earth shadow for the two-body model (vbar.dynamics.perturbations), and elliptic or phased target orbits;
• the Yamanaka-Ankersen elliptic model, curvilinear Clohessy-Wiltshire and linearized two-body motion with J2 (vbar.dynamics.relative); transition matrices from the variational equations; model-error measures between models (vbar.dynamics.fidelity);
• Earth-Moon three-body models: the circular restricted problem, linear models about libration points and periodic orbits, and the bicircular Sun perturbation (vbar.dynamics.cr3bp), with halo-orbit seeds, correctors, continuation and Floquet analysis (vbar.dynamics.periodic_orbits);
• Kepler propagation for any conic (vbar.dynamics.kepler), conversion between states and classical elements for elliptic orbits, and J2 secular rates with a first-order mean-osculating element map (vbar.dynamics.mean_elements);
• a replay of flown orbits through these models (vbar.flightdata): GRACE-FO's two satellites on 3 December 2019, 182 km apart, stay inside an error bound stated before the run over ten orbits on the J2 and drag rungs, a check of the nonlinear models, not of Clohessy-Wiltshire.
• published results rebuilt from their papers (vbar.reproductions): Ariba et al.'s minimum-fuel V-bar glideslope by linear programming (vbar.agents.glideslope_lp) on Hablani's case, compared number by number with python -m vbar.reproductions.

Earth uses the WGS 84 constants; a Kerbin body with KSP's values is available for comparison with KSPDG.

Pursuit-evasion in KSPDG's format

vbar.games rebuilds KSPDG's pe1 pursuit-evasion problem on two-body dynamics, with KSPDG's observation list, action dictionary and agent interface, so an agent written for KSPDG runs unchanged, headless, faster than real time and in parallel. The four starts are KSPDG's mission saves; the evaders are V-BAR's versions of KSPDG's public evaders.

from vbar.games import PE1_E3_I3_Env, AgentEnvRunner
from vbar.games.pursuers import VelocityMatchingPursuer

results = AgentEnvRunner(VelocityMatchingPursuer(), PE1_E3_I3_Env, {"episode_timeout": 30.0}).run()
print(results["agent_env_results"]["weighted_score"])

A KSPDG agent file runs with no change at all through python -m vbar.games.compat my_agent.py, which gives KSPDG's import names to V-BAR's classes in that process. The scenarios are also Gymnasium environments (vbar/PursuitEvasionE3I3-v1 and the others); see docs/pursuit-evasion.md.

Scenario catalogue

Beyond the approach above, vbar.scenarios holds twenty-three scenarios built from specs: the V-bar, R-bar and orbit-normal approaches with a dwell at the hold point, docking as a contact event with mechanism windows and corridors (with on-axis, Shuttle-corridor and Sun-window variants), an offset port, an inertially pointing target, the run time assurance docking task, inspection under lighting and shadow, the ISS-class closing and R-bar acquisition, a berthing box, and the Shuttle's flown profiles (ORBT, the pitch-manoeuvre hold, the twice-orbital-rate transition, the V-bar final approach, the HST grapple approach and the separation fly-around), four comparison tasks rebuilt from their papers (the AFRL docking and illuminated inspection, the SpaceGym docking and rendezvous), a departure from an aft port, and the capture of a tumbling upper stage with five tumble presets (flat spin, coning, near the separatrix, next to the intermediate axis, a dead stage librating in the gravity gradient). Each has a Gymnasium ID, and all but the comparison tasks, the departure and the capture have :nav1 and :nav2 variants:

import gymnasium as gym

from vbar.scenarios import SCENARIOS, make, seeds

print(sorted(SCENARIOS))
env = make("docking:axis")
print(env.scenario_id)
env.reset(seed=seeds("docking:axis", "validation", 10).seed(0))
env = gym.make("vbar/ApproachRbar-v1")

Identifiers name every option that changes a result, seeds come in train, validation and hidden test splits, and suites list the runs a report must cover in full (docs/scenarios.md).

Three real rendezvous events are rebuilt from public reports with their failures as fault models: the Progress M-34 collision with Mir, the ETS-VII thruster anomaly and the DART collision, each with a :nominal variant without the failure (docs/reconstructions.md).

Documentation

How each part is built, with its equations, methods, assumptions and limits, is in docs/, one page per part: frames, dynamics, perturbations, relative-motion models, flight-data replay, transition matrices, three-body models, spacecraft, sensors, faults, constraints, the environment, scenarios, reconstructions, reproduced results, metrics, rewards, training interfaces, the vectorized environment, agent tools, LLM agents, remote agents, policy export, solvers, the evaluation harness, the external propagators, the classical baselines, pursuit-evasion in KSPDG's format and validation.

Tests

python -m pytest -q          # the default run, without the whole-episode audits
python -m pytest -q -m slow  # the whole-episode scenario audits

The models are tested against closed-form solutions, an independent integrator and published textbook examples (listed in the validation page). CI runs the tests on Linux, macOS and Windows.

Contributing

See CONTRIBUTING.md.

Citation

If you use V-BAR in your work, please cite it using the metadata in CITATION.cff (GitHub's "Cite this repository" button gives BibTeX and APA). Each release is archived on Zenodo; the DOI 10.5281/zenodo.23632751 always resolves to the latest version, and each version has its own DOI on that page.

License

MIT