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Decentralized State Estimation: An Approach using Pseudomeasurements and Preintegration

Charles Champagne Cossette, Mohammed Ayman Shalaby, David Saussié, James Richard Forbes

TL;DR

The paper tackles decentralized state estimation for multi-robot teams by introducing pseudomeasurements that encode generic nonlinear relationships between robot states, enabling cross-robot fusion without full centralization. It advances a preintegration-based, communication-efficient odometry sharing mechanism that preserves statistical independence and supports Lie-group state definitions, complemented by a mean-assisted autoencoder to aggressively compress transmitted covariance information. Covariance Intersection is used to maintain consistency in the presence of unknown cross-correlations, and an observability test that factors in the communication topology is derived. The framework is validated on toy, ground, and quadcopter experiments, achieving performance close to centralized estimators at substantially reduced communication rates (e.g., around 53 kB/s per robot in the quadcopter case) and providing a flexible, scalable approach for real-world collaborative robotics.

Abstract

This paper addresses the problem of decentralized, collaborative state estimation in robotic teams. In particular, this paper considers problems where individual robots estimate similar physical quantities, such as each other's position relative to themselves. The use of pseudomeasurements is introduced as a means of modelling such relationships between robots' state estimates, and is shown to be a tractable way to approach the decentralized state estimation problem. Moreover, this formulation easily leads to a general-purpose observability test that simultaneously accounts for measurements that robots collect from their own sensors, as well as the communication structure within the team. Finally, input preintegration is proposed as a communication-efficient way of sharing odometry information between robots, and the entire theory is appropriate for both vector-space and Lie-group state definitions. To overcome the need for communicating preintegrated-covariance information, a deep autoencoder is proposed that reconstructs the covariance information from the inputs, hence further reducing the communication requirements. The proposed framework is evaluated on three different simulated problems, and one experiment involving three quadcopters.

Decentralized State Estimation: An Approach using Pseudomeasurements and Preintegration

TL;DR

The paper tackles decentralized state estimation for multi-robot teams by introducing pseudomeasurements that encode generic nonlinear relationships between robot states, enabling cross-robot fusion without full centralization. It advances a preintegration-based, communication-efficient odometry sharing mechanism that preserves statistical independence and supports Lie-group state definitions, complemented by a mean-assisted autoencoder to aggressively compress transmitted covariance information. Covariance Intersection is used to maintain consistency in the presence of unknown cross-correlations, and an observability test that factors in the communication topology is derived. The framework is validated on toy, ground, and quadcopter experiments, achieving performance close to centralized estimators at substantially reduced communication rates (e.g., around 53 kB/s per robot in the quadcopter case) and providing a flexible, scalable approach for real-world collaborative robotics.

Abstract

This paper addresses the problem of decentralized, collaborative state estimation in robotic teams. In particular, this paper considers problems where individual robots estimate similar physical quantities, such as each other's position relative to themselves. The use of pseudomeasurements is introduced as a means of modelling such relationships between robots' state estimates, and is shown to be a tractable way to approach the decentralized state estimation problem. Moreover, this formulation easily leads to a general-purpose observability test that simultaneously accounts for measurements that robots collect from their own sensors, as well as the communication structure within the team. Finally, input preintegration is proposed as a communication-efficient way of sharing odometry information between robots, and the entire theory is appropriate for both vector-space and Lie-group state definitions. To overcome the need for communicating preintegrated-covariance information, a deep autoencoder is proposed that reconstructs the covariance information from the inputs, hence further reducing the communication requirements. The proposed framework is evaluated on three different simulated problems, and one experiment involving three quadcopters.
Paper Structure (25 sections, 1 theorem, 84 equations, 15 figures, 1 table, 2 algorithms)

This paper contains 25 sections, 1 theorem, 84 equations, 15 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Work
  4. Preliminaries
  5. Lie groups
  6. $\oplus$ and $\ominus$ operators.
  7. Gaussian distributions on Lie groups.
  8. Derivatives on Lie groups.
  9. Composite groups.
  10. Maximum A Posteriori
  11. Covariance Intersection
  12. A Toy Problem
  13. Solution via MAP
  14. General Problem
  15. An Observability Test
  16. ...and 10 more sections

Key Result

Lemma 1

The inequality which applies in the positive definite sense, holds for all $w \in (0,1)$, where ${\boldsymbol{\Sigma}}_{xx}, {\boldsymbol{\Sigma}}_{yy},$ and the right-hand-side of eq:ci_consistency are positive definite.

Figures (15)

  • Figure 1: Three examples of decentralized estimation problems within the scope of this paper. Left: A toy problem with 1D robots, each estimating both of their positions. Middle: A problem with an incomplete communication graph. Robots observe landmarks, have range measurements to each other, and estimate their own and neighbor absolute poses. Right: A more complicated experimentally-tested problem, where robots equipped with ultra-wideband radios estimate both their own absolute pose and relative poses of neighbors, in addition to IMU biases.
  • Figure 2: Estimation convergence for a single trial of the two-robot toy problem with ${\boldsymbol{\Psi}} = 10 \cdot \mbf{1}$. Due to pseudomeasurements, the robot states successfully converge to a common value.
  • Figure 3: Results of 100 Monte Carlo trials for a four-robot version of the toy problem. The top two plots consist of a NEES plot, which is a measure of consistency. The bottom plot is the RMSE of the state. The proposed solution, which performs CI, remains statistically consistent and has reasonably low error in many cases.
  • Figure 4: Concept diagram of mean-assisted autoencoder.
  • Figure 5: Mean percentage reconstruction error throughout training for various encoding sizes including no encoding. A single encoding number is sufficient to achieve less than 1% reconstruction error on average.
  • ...and 10 more figures

Theorems & Definitions (4)

  • Lemma 1: Consistency of Covariance Intersection
  • Example 1: Linear preintegration
  • Example 2: Wheel odometry preintegration on $SE(2)$
  • Example 3: IMU preintegration