Astrogator: Navigation & Code Verification

• Astrogator is a dual-domain system that combines autonomous deep-space navigation with formal verification techniques for LLM-generated code.
• It employs methods such as nonlinear least squares, Extended Kalman Filters, and Ant Colony Optimization to optimize spacecraft trajectory and state estimation.
• Implementation focuses on high performance and reliability, achieving precise position estimations and verifying up to 83% of correct automation tasks.

Astrogator comprises two distinct but historically related domains: (1) the set of methods, architectures, and tools that support autonomous navigation of spacecraft across interplanetary and interstellar distances, and (2) in a recent extension, a system for the formal verification of code generated by LLMs. The term "astrogator" denotes both the human operator or software module responsible for strategic guidance, trajectory planning, and navigation in spacecraft operations, and in automation-era contexts, the algorithms, computational pipelines, and supporting instrumentation that deliver autonomous guidance solutions. The following overview surveys technical developments central to the operational and methodological foundations of astrogation, spanning deep-space navigation, trajectory optimization, in-situ state estimation, and correctness verification for human-in-the-loop automation.

1. Astrogator in Interstellar and Deep Space Navigation

The principal challenge addressed by astrogator systems in the context of relativistic and interstellar navigation is the autonomy of spacecraft navigation at distances where Earth-based radiometric tracking is infeasible or latent. Bailer-Jones (2021) formalizes a navigation protocol in which the spacecraft autonomously computes its Sun-centered inertial position $\mathbf{r}$ and velocity $\mathbf{v}$ by iteratively comparing measured angular distances between pairs of stars to their catalog values, robustly incorporating both parallax and special-relativistic aberration (Bailer-Jones, 2021).

The forward model predicts for each cataloged star $i$ its apparent direction $\mathbf{p}_i(\mathbf{x},\mathbf{v})$, including geometric parallax and velocity-induced aberration, with the following steps:

• Geometric line-of-sight: $$\mathbf{n}_i = (\mathbf{s}_i-\mathbf{r})/\|\mathbf{s}_i-\mathbf{r}\|$$
• Relativistic aberration:

$$\mathbf{p}_i(\mathbf{x},\mathbf{v}) = \frac{\mathbf{n}_i + (\gamma-1)(\mathbf{n}_i\cdot\boldsymbol{\beta})\boldsymbol{\beta}/\|\boldsymbol{\beta}\|^2 + \gamma\boldsymbol{\beta}}{\gamma(1+\mathbf{n}_i\cdot\boldsymbol{\beta})}$$

where $\boldsymbol{\beta}=\mathbf{v}/c$ and $\gamma=(1-\|\boldsymbol{\beta}\|^2)^{-1/2}$

The inverse problem is solved by nonlinear least squares using Levenberg–Marquardt optimization, minimizing residuals between observed and predicted star-pair separations. For a modest configuration (20 stars, 1″ angular distance accuracy), position and velocity can be determined to within 3 au and 2 km/s, respectively. The accuracy improves linearly with $\sigma_\theta$, the angular measurement precision.

2. Algorithmic Trajectory Planning and Astrogator Toolkits

Modern astrogator systems for interplanetary trajectory design implement automated strategies to solve NP-hard mixed combinatorial-continuous planning problems, such as Multiple Gravity-Assist (MGA) trajectories. An algorithm inspired by Ant Colony Optimization (ACO) systematically explores the combinatorial tree of planetary sequences, DSM flags, resonance counts, and other discrete parameters (Ceriotti et al., 2011).

The underlying trajectory model decomposes mission profiles into:

• Planar conic arcs (deep-space legs)
• Instantaneous events: launch, DSM per leg, swing-bys, and final capture

The algorithm encodes each potential transfer as a vector $s\in\mathbb{N}^{2np}$, where $\mathbf{v}$0 is the number of legs. Ants construct solutions by sampling planetary encounters and transfer types, maintaining pheromone tables updated in proportion to the objective cost and feasibility of archived trajectories. The evaluation kernel includes phasing equations, swing-by geometry, and constraints on pericenter, DSM magnitude, and time of flight.

Performance benchmarks (e.g., optimal transfers among Galilean moons, Cassini-style V-E-J-S tours) show high feasibility rates and solution qualities comparable to full 3D optimizers, with the 2D ACO-MGA delivering viable first guesses for subsequent post-processing.

3. Autonomous State Estimation and Passive Astrogators

Autonomous passive astrogators implement on-board navigational state estimation from only line-of-sight (LOS) range measurements to nearby celestial bodies. The system architecture by Vance, Thangavelautham, and Asphaug (Vance et al., 2019) employs an Extended Kalman Filter (EKF) to estimate a high-dimensional joint state encompassing the spacecraft and multiple tracked asteroids — notably, without requiring a priori knowledge of any body's initial ephemeris.

The recursive EKF operates over a 27-dimensional state vector that stacks positions, velocities, and accelerations for the observer and two asteroids. At each measurement update, normalized LOS vectors serve as observations, with process noise set to negligible levels and measurement noise modeled according to the tracker’s angular pointing precision (e.g., 10 μrad).

Simulation results demonstrate that, even with initial errors of order $\mathbf{v}$1 km in position and $\mathbf{v}$2 km/s in velocity, the estimator converges within tens of kilometers and meters per second after weeks to months of hourly LOS updates, especially when tracking more than one asteroid.

4. Star-Based Measurement Models and Kalman Navigation

In the outer solar system, star-based navigation for heliocentric trajectory estimation generalizes the parallax and aberration approach to extreme distances, with all computations referenced to the ICRS/Sun-centered frame (Franzese, 6 Mar 2026). The measurement model incorporates:

• Proper motion correction: $\mathbf{v}$3
• Delta-light-time: negligible shift $\mathbf{v}$4 for 250 AU
• First-order parallax/aberration: combined as

$\mathbf{v}$5

with $\mathbf{v}$6 the orthogonal projector.

Both batch least-squares solutions (simultaneous measurements, closed-form $\mathbf{v}$7) and sequential EKFs (propagating a 6D state, incorporating process and measurement updates with appropriate Jacobians) are supported.

Monte Carlo studies of representative deep-space trajectories show position errors $\mathbf{v}$81 au and velocity errors %%%%19$$\mathbf{n}_i = (\mathbf{s}_i-\mathbf{r})/\|\mathbf{s}_i-\mathbf{r}\|$$20$\mathbf{v}$021%%%% au/day at 250 au, for weekly star sightings given centroiding noise of 6″. Increased observation frequency improves estimation bounds further.

5. Astrogator for Code Verification in LLM-Augmented Development

A recent extension of the astrogator paradigm is its application to formal verification of LLM-generated code for configuration management, notably for the Ansible language (Councilman et al., 17 Jul 2025). Here, astrogator denotes a system architecture combining:

• A natural-language–to–formal query pipeline: mapping ambiguous prompts to a highly structured "Formal Query Language" (FQL) with English-like syntax but formally defined semantics.
• Semantics via a state-based imperative calculus: representing both the FQL and Ansible programs as state transformers over an abstract system state.
• Symbolic interpreter and verification engine: executing both queries and candidate playbooks to collect path-wise pairs of initial and final states under corresponding constraints.
• Path-unification and coverage testing: for every path in the query, some program path must match (i.e., $i$2).

Empirical evaluation over 21 Ansible automation tasks found that Astrogator verified 83% of truly correct LLM-generated programs and rejected 92% of incorrect programs, with median verification times on the order of 50 ms per play. The FQL step addresses potential semantic ambiguity by requiring explicit user confirmation before code generation and checking.

6. Implementation Considerations and Performance Scaling

Astrogator methods for deep-space and software applications share an emphasis on iterative forward modeling, uncertainty-aware estimation, path- or solution-archive management, and computational efficiency compatible with on-board or interactive use.

Key performance considerations for astrogation in navigation contexts include:

• Memory and computation: With 20–100 stars, loop unrolling, and fixed-point/hardware support, angular-based solvers run in ≪1 s with minimal memory footprint ($i$310 kB).
• Error scaling: In parallax navigation, the achievable state uncertainty scales linearly with angular measurement error and inversely with the number of calibration sources (stars/asteroids), up to geometric or catalog limits.
• Toolkit integration: Automated MGA planners encapsulate trajectory propagation, combinatorial scheduler (ACO), and high-level API for solution enumeration, with batch outputs suitable for follow-on 3D optimization.

7. Applications, Limitations, and Prospects

Astrogator architectures and algorithms are integral to the autonomy required by next-generation uncrewed explorations in the solar system and beyond, swarm coordination for asteroid belt surveys, and robust, user-verifiable automation of mission-critical code. Limitations primarily arise from sensor precision, catalog ephemerides, and coverage gaps in environment modeling (e.g., shell modules in Ansible, planetary light-bending in star-based navigation).

A plausible implication is that as LLM and navigation sensor technologies advance, astrogator frameworks provide a canonical path for combining human guidance, automated search/planning, and correctness assurance in environments where communication, situational knowledge, or direct supervision are fundamentally constrained.