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Consistent Distributed Cooperative Localization: A Coordinate Transformation Approach

Chungeng Tian, Ning Hao, Fenghua He, Haodi Yao

TL;DR

A consistent distributed cooperative localization algorithm conducting state estimation in a transformed coordinate using a linear time-varying coordinated transformation to render the propagation Jacobian independent of the state and make it suitable for a distributed manner.

Abstract

This paper addresses the consistency issue of multi-robot distributed cooperative localization. We introduce a consistent distributed cooperative localization algorithm conducting state estimation in a transformed coordinate. The core idea involves a linear time-varying coordinated transformation to render the propagation Jacobian independent of the state and make it suitable for a distributed manner. This transformation is seamlessly integrated into a server-based distributed cooperative localization framework, in which each robot estimates its own state while the server maintains the cross-correlations. The transformation ensures the correct observability property of the entire framework. Moreover, the algorithm accommodates various types of robot-to-robot relative measurements, broadening its applicability. Through simulations and real-world dataset experiments, the proposed algorithm has demonstrated better performance in terms of both consistency and accuracy compared to existing algorithms.

Consistent Distributed Cooperative Localization: A Coordinate Transformation Approach

TL;DR

A consistent distributed cooperative localization algorithm conducting state estimation in a transformed coordinate using a linear time-varying coordinated transformation to render the propagation Jacobian independent of the state and make it suitable for a distributed manner.

Abstract

This paper addresses the consistency issue of multi-robot distributed cooperative localization. We introduce a consistent distributed cooperative localization algorithm conducting state estimation in a transformed coordinate. The core idea involves a linear time-varying coordinated transformation to render the propagation Jacobian independent of the state and make it suitable for a distributed manner. This transformation is seamlessly integrated into a server-based distributed cooperative localization framework, in which each robot estimates its own state while the server maintains the cross-correlations. The transformation ensures the correct observability property of the entire framework. Moreover, the algorithm accommodates various types of robot-to-robot relative measurements, broadening its applicability. Through simulations and real-world dataset experiments, the proposed algorithm has demonstrated better performance in terms of both consistency and accuracy compared to existing algorithms.
Paper Structure (20 sections, 37 equations, 7 figures, 3 tables, 1 algorithm)

This paper contains 20 sections, 37 equations, 7 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem description
  3. Motion Model
  4. Measurement Model
  5. Linearized Error State Model
  6. Observability
  7. Coordinate Transformation Based DCL
  8. Transformed Linearized Error State System
  9. Transformed Server-based DCL
  10. Propagation in the transformed system
  11. Update in the transformed system
  12. Observability Property
  13. Monte Carlo Simulations
  14. Setup
  15. Metrics
  16. ...and 5 more sections

Figures (7)

  • Figure 1: Transformed server-based DCL framework. The covariance matrices corresponding to the transformed error states propagate and update in the transformed coordinates.
  • Figure 2: Simulated trajectories of 9, 16, 25, and 36 robots. The unit is meter. The robots move in a circle with a radius of four meters. The period of one circle of motion varies from 20 to 40 seconds.
  • Figure 3: Orientation and position RMSE with $N=16$ in 100 Monte Carlo runs with different sensor range limits.
  • Figure 4: Average RMSE and NEES of 100 Monte Carlo simulations over time with $N=16$ and sensor range limited to 15 m.
  • Figure 5: Orientation and position RMSE of $N$ robots in 100 Monte Carlo runs with sensor range limited to 10 m.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Remark 1
  • Remark 2