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Hyperion -- A fast, versatile symbolic Gaussian Belief Propagation framework for Continuous-Time SLAM

David Hug, Ignacio Alzugaray, Margarita Chli

TL;DR

This work addresses the computational and centralization limitations of continuous-time SLAM by introducing Hyperion, a fast, symbolic Gaussian Belief Propagation framework for distributed, continuous-time SLAM. It combines continuous-time motion modeling with Lie-group-aware GBP, aided by automated symbolic factor generation (SymForce) for spline-based costs, and supports synchronous and dropout update strategies. The approach yields strong convergence and competitive accuracy relative to centralized NLLS while enabling scalable, multi-agent, asynchronous state estimation, with substantial speedups for spline evaluation and a practical open-source implementation. Empirical results on absolute MoCap-like and localization scenarios demonstrate robustness to noise and dropout and highlight the potential for real-time performance on moderately sized problems, albeit with areas for improvement in fully distributed, real-world SLAM loops.

Abstract

Continuous-Time Simultaneous Localization And Mapping (CTSLAM) has become a promising approach for fusing asynchronous and multi-modal sensor suites. Unlike discrete-time SLAM, which estimates poses discretely, CTSLAM uses continuous-time motion parametrizations, facilitating the integration of a variety of sensors such as rolling-shutter cameras, event cameras and Inertial Measurement Units (IMUs). However, CTSLAM approaches remain computationally demanding and are conventionally posed as centralized Non-Linear Least Squares (NLLS) optimizations. Targeting these limitations, we not only present the fastest SymForce-based [Martiros et al., RSS 2022] B- and Z-Spline implementations achieving speedups between 2.43x and 110.31x over Sommer et al. [CVPR 2020] but also implement a novel continuous-time Gaussian Belief Propagation (GBP) framework, coined Hyperion, which targets decentralized probabilistic inference across agents. We demonstrate the efficacy of our method in motion tracking and localization settings, complemented by empirical ablation studies.

Hyperion -- A fast, versatile symbolic Gaussian Belief Propagation framework for Continuous-Time SLAM

TL;DR

This work addresses the computational and centralization limitations of continuous-time SLAM by introducing Hyperion, a fast, symbolic Gaussian Belief Propagation framework for distributed, continuous-time SLAM. It combines continuous-time motion modeling with Lie-group-aware GBP, aided by automated symbolic factor generation (SymForce) for spline-based costs, and supports synchronous and dropout update strategies. The approach yields strong convergence and competitive accuracy relative to centralized NLLS while enabling scalable, multi-agent, asynchronous state estimation, with substantial speedups for spline evaluation and a practical open-source implementation. Empirical results on absolute MoCap-like and localization scenarios demonstrate robustness to noise and dropout and highlight the potential for real-time performance on moderately sized problems, albeit with areas for improvement in fully distributed, real-world SLAM loops.

Abstract

Continuous-Time Simultaneous Localization And Mapping (CTSLAM) has become a promising approach for fusing asynchronous and multi-modal sensor suites. Unlike discrete-time SLAM, which estimates poses discretely, CTSLAM uses continuous-time motion parametrizations, facilitating the integration of a variety of sensors such as rolling-shutter cameras, event cameras and Inertial Measurement Units (IMUs). However, CTSLAM approaches remain computationally demanding and are conventionally posed as centralized Non-Linear Least Squares (NLLS) optimizations. Targeting these limitations, we not only present the fastest SymForce-based [Martiros et al., RSS 2022] B- and Z-Spline implementations achieving speedups between 2.43x and 110.31x over Sommer et al. [CVPR 2020] but also implement a novel continuous-time Gaussian Belief Propagation (GBP) framework, coined Hyperion, which targets decentralized probabilistic inference across agents. We demonstrate the efficacy of our method in motion tracking and localization settings, complemented by empirical ablation studies.
Paper Structure (25 sections, 24 equations, 7 figures, 1 table)

This paper contains 25 sections, 24 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Preliminaries
  5. Continuous-Time Motion
  6. Continuous-Time Optimization
  7. GBP
  8. Node Updates:
  9. Node-to-factor Messages:
  10. Factor Updates:
  11. Factor-to-Node Messages:
  12. Robust Residuals and Energies:
  13. Non-Gaussian Nodes:
  14. Sensor Models
  15. Absolute Sensor Model
  16. ...and 10 more sections

Figures (7)

  • Figure 1: Both the proposed continuous-time GBP solver (in magenta) and the conventional NLLS solver Agarwal:etal:Ceres (in white) converge to identical solutions close to the ground truth (in green) even under poor initialization ($\pm 1.00$ m/rad) and substantial pose measurement noise ($\pm 0.05$ m/rad).
  • Figure 2: For every (valid) instance in time $t$, a collection of adjacent bases (in orange) gives rise to an individual segment (in green) of a cubic B-Spline. An interpolated pose at query time $t$ is then obtained from the (cumulative) blending of these bases.
  • Figure 3: \ref{['fig:eccv2024:factor_graphs']} Qualitative illustration of the factor graphs resulting from a continuous-time motion parametrization. Notably, even one of the simplest factor archetypes, which purely relies on the motion-parameterizing nodes as well as some landmarks, introduces a considerable amount of loops in the continuous-time realm. This can be attributed to the fact that poses $\boldsymbol{T}_{{w}{b}}(t)$ depend on multiple bases for any given time $t$. \ref{['fig:eccv2024:message_passing']} Visualization of the message passing algorithm between nodes and factors in a graph $\mathcal{G}$.
  • Figure 4: \ref{['fig:eccv2024:absolute_dropout']} Graph energy vs. number of iterations conditioned on the dropout probability in the absolute setup (batch). \ref{['tab:eccv2024:timings']} Performance comparison between our symbolically, auto-generated and optimized B-Spline implementation and the recursively-defined, hand-crafted implementation used by Sommer et al.Sommer:etal:CVPR2020 on an M3 Max @4.05GHz.
  • Figure 5: ChArUco Garrido:etal:PR2014 setup with overlapping motion estimates \ref{['fig:eccv2024:charuco_estimate']} from https://github.com/VIS4ROB-lab/hyperion and Ceres Agarwal:etal:Ceres in magenta and white, respectively. Illustration of the corresponding convergence \ref{['fig:eccv2024:charuco_energy']} and the relative errors between the two converged estimates \ref{['fig:eccv2024:charuco_error']}.
  • ...and 2 more figures