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Who Went Where When on the Lunar Surface: Forensic Trajectory Analysis to Identify Byzantine Rovers

Lachlan Holden, Feras Dayoub, Melissa de Zwart, David Harvey, Tat-Jun Chin

arXiv:2610.02694v1cs.ROcs.MA

TL;DR

Verifying operational constraints for co-located planetary rovers requires post-hoc trajectory reconstruction from sparse data, even when some agents may provide misleading measurements. This paper estimates rover credibility before reconstructing trajectories, and reports that its method identifies Byzantine rovers and improves trajectory estimates over robust pose-graph baselines.

  • Problem

    Post-hoc trajectory reconstruction from sparse telemetry is needed to assess rover compliance with operational constraints, while existing methods do not address coherent adversarial measurement sources in this setting.

    Source: §I · p. 1, C. Byzantine Robotics · p. 2

  • Method

    The method scores candidate credible rover subsets using relative-detection consistency, then estimates trajectories using measurements attributed to credible rovers.

    Source: §I · p. 1, §III · p. 2

  • Results

    Across synthetic and planetary-analogue trajectories, the method identifies non-credible rovers and improves reconstruction, while conventional robust pose graph optimisation can be misled by Byzantine agents.

    Source: §I · p. 1, §V · p. 8

  • Takeaways & Limitations

    For co-located rover operations, post-hoc trajectory reconstruction provides a way to assess compliance with constraints such as Lunar Safety Zones.

    Source: §I · p. 1

    Evaluation with real odometry, localisation, and relative-detection front-ends, broader Byzantine behaviours, and further platform validation remain future work.

    Source: §V · p. 8

Abstract

from arXiv · show

Future planetary surface missions are likely to involve multiple independently operated rovers sharing the same deployment region, raising the need to verify compliance with operational constraints such as Lunar Safety Zones. Because continuous in-situ observability is rarely available, such verification requires post-hoc reconstruction of rover trajectories from sparse telemetry, including odometry, pose priors, and relative inter-rover detections. We introduce the problem of forensic trajectory analysis for non-cooperative planetary rovers in the presence of Byzantine agents: rovers that provide miscalibrated or deliberately falsified measurements to support an incorrect trajectory. We show that standard outlier-robust pose graph optimisation methods are vulnerable in this setting, because Byzantine rovers can generate measurements that are internally consistent and numerous enough to make truthful incriminating measurements appear as outliers. To address this, we propose an attribution-aware trajectory estimation method that reasons over rover credibility rather than individual measurement validity. The method evaluates candidate credible rover subsets by comparing the statistical consistency of their internal and boundary relative detections against provided priors, and then estimates trajectories using only measurements attributed to credible agents. Across synthetic simulations and real planetary-analogue trajectory data, the proposed method identifies Byzantine rovers and produces significantly more accurate trajectory estimates than existing robust pose graph optimisation baselines.

I. INTRODUCTION

As multiple stakeholders operate rovers near one another, verifying constraints such as Lunar Safety Zones requires reconstructing trajectories from sparse data despite limited situational awareness. This paper frames that task as forensic trajectory analysis and distinguishes it from cooperative localisation and measurement-level outlier rejection.

I. INTRODUCTION

  • Co-located missions make it important to verify rover compliance with Lunar Safety Zones using post-hoc trajectories reconstructed from low-fidelity data.Relevant data include odometry, map-localisation estimates, and relative detections from infrequent images.Source: §I · p. 1
  • The paper formulates forensic trajectory analysis as post-hoc state estimation for non-cooperative rovers with Byzantine measurement sources.Such sources may provide poorly calibrated or deliberately misleading data.Source: §I · p. 1
  • The proposed method infers rover credibility by scoring candidate subsets with internal consistency and boundary inconsistency of relative detections.Source: §I · p. 1
  • The work demonstrates that conventional robust pose graph optimisation can be misled by Byzantine agents, while its method identifies non-credible rovers and improves reconstruction.Source: §I · p. 1

II. RELATED WORK

  • Unlike cooperative multi-robot localisation and mapping, forensic trajectory analysis treats independently operated rovers as potentially non-credible sources of evidence.The paper situates the problem at the intersection of multi-robot localisation, robust pose graph optimisation, and Byzantine-resilient robotics.Source: §II · p. 1, A. Multi-Robot Localisation · p. 2

B. Robust Pose Graph Optimisation

Robust PGO addresses measurement outliers, while Byzantine robotics has largely been studied in settings distinct from post-hoc pose-graph reconstruction. This paper treats rover credibility, rather than individual measurement validity, as central to forensic trajectory analysis.

B. Robust Pose Graph Optimisation

  • Robust PGO methods such as PCM and GNC handle loop-closure outliers but are insufficient for identifying and rejecting actively misleading Byzantine information.PCM uses pairwise-consistent measurements; GNC uses robust cost functions with an iterative solver.Source: B. Robust Pose Graph Optimisation · p. 2

C. Byzantine Robotics

  • Prior Byzantine-robotics work includes multiagent consensus, distributed learning, and online localization, whereas this work focuses on post-hoc reconstruction with attributed measurements.The paper distinguishes its approach through collaborative Byzantine groups, statistical identification criteria, and explicit measurement attribution and rover identification.Source: C. Byzantine Robotics · p. 2

III. METHOD

  • The method estimates putative trajectories from pose priors, scores candidate credible sets using internal and boundary consistency, selects a set, then optimizes using its attributed measurements and weak smoothness constraints.The paper reports that this two-step credibility-then-state-estimation structure performed more reliably than joint optimization in preliminary experiments.Source: §III · p. 2, A. Problem Definition · p. 3

A. Problem Definition

  • Forensic trajectory analysis estimates rover trajectories from priors and relative detections while identifying credible sources; the formulation assumes at least one and no more than half the rovers are non-credible.The inputs include pose priors, which may be absolute or relative, and relative detections that can provide bearing, range and bearing, or full pose.Source: A. Problem Definition · pp. 2–3

B. Identifying Byzantine Rovers

Candidate credible-rover sets are evaluated by comparing their internal and boundary relative detections with trajectories estimated from pose priors. The selected set determines which measurements inform final trajectory optimization, with smoothness constraints supplementing the retained observations.

B. Identifying Byzantine Rovers

  • Candidate sets are scored using internal detections between members and boundary detections crossing membership, comparing both against putative trajectories from pose priors.The method seeks high internal consistency and low boundary consistency.Source: B. Identifying Byzantine Rovers · p. 3
  • Residuals account for detection and pose uncertainty, so measurements less aligned with putative trajectories are penalized less when pose-prior uncertainty is higher.The expected residual distribution is used to calculate p-values for internal and boundary measurements under the assumption that all rovers are credible.Source: B. Identifying Byzantine Rovers · p. 4
  • The credibility score compares log probabilities for internal and boundary residuals, and the estimated credible set is the candidate set with the highest score.The intended set has relatively unsurprising internal measurements and surprising measurements across its boundary.Source: B. Identifying Byzantine Rovers · p. 4
  • Final pose-graph optimization trusts measurements attributed to the selected credible set and adds weak smoothness constraints to address underconstrained trajectories.The paper then estimates all rover trajectories using Levenberg-Marquardt optimization.Source: B. Identifying Byzantine Rovers · p. 4

C. Contrasting Against Robust Methods

Robust PGO methods rely on truthful inliers outnumbering internally consistent outliers, an assumption Byzantine rovers can violate with coherent data. The section contrasts this measurement-level outlier rejection with attribution-aware reasoning about rover credibility.

C. Contrasting Against Robust Methods

IV. EXPERIMENTS

The experiments compare the method with robust PGO baselines on simulated and real planetary-analogue trajectory data.

IV. EXPERIMENTS

  • The evaluation uses both simulated and real planetary-analogue trajectory data.Source: §IV · p. 5
  • GNC and PCM serve as robust PGO comparison methods.Source: §IV · p. 5
  • The experiments test whether robust PGO methods designed for false-positive loop closures remain tenable in the Byzantine case.Source: §IV · p. 5

A. Simulation Definition

The simulation evaluates groups of five rovers in a 2D environment across five initial positions.

A. Simulation Definition

1) Motion Model:

The simulation models each rover with white noise on acceleration and selects parameters to produce relatively smooth, rover-like trajectories.

1) Motion Model:

2) Trajectory Priors:

The experiments use two Gaussian-perturbed trajectory-prior modes: relative priors between timesteps with an initial world-frame pose prior, and independently perturbed absolute pose priors.

2) Trajectory Priors:

  • Relative priors perturb each true inter-timestep pose with forward, left, and orientation noise, and use a noisy pose prior at t=0 to ground odometry in the world frame.The respective standard deviations are 0.3 m, 0.2 m, and 2°; the initial prior uses 2 m in x and y and 5° in orientation.Source: 2) Trajectory Priors · p. 5
  • Absolute priors independently perturb the true absolute pose at every timestep with 1 m x/y and 5° orientation noise.The authors describe the Gaussian-perturbed prior setup as idealized, intended to demonstrate the method independently of front-end performance.Source: 2) Trajectory Priors · p. 5
  • Smoothness constraints use a 1 m forward-motion threshold, with forward, lateral, and turn noise parameters of 0.5 m, 0.25 m, and 5°.The stated parameters are δ_forward = 1 m, σ_forward = 0.5 m, σ_left = 0.25 m, and σ_turn = 5°.Source: 2) Trajectory Priors · p. 5

3) Relative Detections:

Relative detections are intermittent and field-of-view limited; the experiments also vary purported Byzantine trajectories and consider collaboration between two Byzantine agents.

3) Relative Detections:

  • Each rover produces relative observations every five timesteps and observes other rovers only within forward and backward fields of view.The relative-detection noise model uses 3 m range and 5° bearing and orientation standard deviations.Source: 3) Relative Detections · p. 5

4) Byzantine Behaviour:

  • Measurements from a Byzantine rover are generated from its purported trajectory, while credible rovers continue to observe its true state.The study considers one or two Byzantine agents among five rovers.Source: 4) Byzantine Behaviour · p. 5
  • The experiments include transformed purported paths with distance scaling and translation or rotation offsets, plus a late turn that diverges only in the second half.For two Byzantine agents, the authors assume collaboration: their mutual detections match differences between their purported trajectories and are internally consistent.Source: 4) Byzantine Behaviour · p. 5

B. Simulation Experiments

In simulation, the proposed method is compared with GNC and PCM across single- and two-Byzantine cases. It localizes Byzantine rovers more effectively than robust PGO methods, including when the Byzantine agents collaborate.

B. Simulation Experiments

  • The simulation comparisons use GNC and PCM, with five runs per parameter configuration and detection degrees of freedom selected according to each method’s requirements.B or RB detections are used to evaluate the proposed method and GNC; PCM is evaluated with RBO measurements.Source: B. Simulation Experiments · p. 5

1) One Byzantine Rover:

  • For one Byzantine rover, the proposed method alone provides comparable localization for Byzantine rovers across tested cases, with 83.3% and 90.8% recall versus less than 10% for robust PGO methods.The cases vary prior type, field of view, and Byzantine behavior; all methods localize credible rovers relatively accurately.Source: 1) One Byzantine Rover · pp. 5–6, Table I · p. 6, Figure 2 · p. 6
  • In the qualitative single-rover comparison, GNC follows the purported path, PCM fails to produce a meaningful estimate, and the proposed method tracks the true trajectory.The comparison is for one simulation run.Source: Figure 4 · p. 6, 1) One Byzantine Rover · p. 6

2) Two Byzantine Rovers:

  • With two collaborative Byzantine rovers, the same overall trend holds; bearing-only recall is 64.6%, compared with approximately 5% for robust PGO methods.The reported trend is consistent across experimental conditions.Source: 2) Two Byzantine Rovers · pp. 6–7, Figure 5 · p. 7

3) Simulated Occlusions:

The method maintains relatively consistent recall and precision through 80% relative-measurement dropout. In planetary-analogue data, it identifies rover B as Byzantine and clearly reconstructs its Safety Zone intrusion; the paper notes future validation needs.

3) Simulated Occlusions:

  • Recall and precision remain relatively consistent through 80% dropout, while bearing-only measurements perform worse than range-bearing measurements.Table II reports recall and precision by method, detection model, and dropout rate.Source: 3) Simulated Occlusions · p. 7, Table II · p. 7

C. Planetary Analogue Experiments

V. CONCLUSIONS

  • Experiments validate the method's accuracy across synthetic and real planetary-analogue trajectories, while traditional robust PGO is unsuitable with Byzantine agents..Source: §V · p. 8
  • Future work includes testing real odometry, localisation, and relative-detection front-ends, broader Byzantine behaviours, and additional platform validation.Source: §V · p. 8
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