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Observability-Aware Control for Quadrotor Formation Flight with Range-only Measurement

H S Helson Go, Ching Lok Chong, Longhao Qian, Hugh H. -T. Liu

TL;DR

This work tackles range-only cooperative localization for quadrotor leader–follower formations in GNSS-denied environments by introducing an observability-aware control framework. It derives a Short-Term Local Observability Gramian (STLOG) via a Lie-derivative expansion and couples it with a receding-horizon Observability Predictive Controller (OPC) that maximizes the minimum STLOG eigenvalue to strengthen the worst-observed state direction. The authors prove weak local observability for the range-only CLS, analyze STLOG asymptotics with respect to the local observability index $r_*$, and demonstrate that choosing STLOG order $r=5$ maintains observability under OPC for quadrotor dynamics. Through Monte Carlo simulations and flight tests, the OPC yields markedly improved positioning accuracy and estimator robustness compared to baseline trajectories, validating the practical value of observability-aware control for GNSS-denied, range-only CLS in quadrotor teams.

Abstract

Cooperative Localization is a promising approach to achieving safe quadrotor formation flight through precise positioning via low-cost inter-drone sensors. This paper develops an observability-aware control principle tailored to quadrotor formation flight with range-only inter-drone measurements. The control principle is based on a novel approximation of the local observability Gramian (LOG), which we name the Short-Term Local Observability Gramian (STLOG). The validity of STLOG is established by proving its link to directional estimation precision in nonlinear systems. We propose the Observability Predictive Controller (OPC), a receding-horizon controller that generates optimal inputs to enhance information gain in weakly observable state directions by maximizing the minimum eigenvalue of the STLOG. This reduces the risk of estimator divergence due to the unbounded growth of uncertainty in weakly observed state components. Monte Carlo simulations and flight experiments are conducted with quadrotors in a GNSS-denied ferrying mission, showing that the OPC improves positioning confidence and estimator robustness.

Observability-Aware Control for Quadrotor Formation Flight with Range-only Measurement

TL;DR

This work tackles range-only cooperative localization for quadrotor leader–follower formations in GNSS-denied environments by introducing an observability-aware control framework. It derives a Short-Term Local Observability Gramian (STLOG) via a Lie-derivative expansion and couples it with a receding-horizon Observability Predictive Controller (OPC) that maximizes the minimum STLOG eigenvalue to strengthen the worst-observed state direction. The authors prove weak local observability for the range-only CLS, analyze STLOG asymptotics with respect to the local observability index , and demonstrate that choosing STLOG order maintains observability under OPC for quadrotor dynamics. Through Monte Carlo simulations and flight tests, the OPC yields markedly improved positioning accuracy and estimator robustness compared to baseline trajectories, validating the practical value of observability-aware control for GNSS-denied, range-only CLS in quadrotor teams.

Abstract

Cooperative Localization is a promising approach to achieving safe quadrotor formation flight through precise positioning via low-cost inter-drone sensors. This paper develops an observability-aware control principle tailored to quadrotor formation flight with range-only inter-drone measurements. The control principle is based on a novel approximation of the local observability Gramian (LOG), which we name the Short-Term Local Observability Gramian (STLOG). The validity of STLOG is established by proving its link to directional estimation precision in nonlinear systems. We propose the Observability Predictive Controller (OPC), a receding-horizon controller that generates optimal inputs to enhance information gain in weakly observable state directions by maximizing the minimum eigenvalue of the STLOG. This reduces the risk of estimator divergence due to the unbounded growth of uncertainty in weakly observed state components. Monte Carlo simulations and flight experiments are conducted with quadrotors in a GNSS-denied ferrying mission, showing that the OPC improves positioning confidence and estimator robustness.

Paper Structure

This paper contains 18 sections, 18 theorems, 75 equations, 9 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Mathematical Preliminaries
  4. The Quadrotor Relative Motion Model
  5. The Inter-drone Distance-only Observation Model
  6. The Follower Drone Localization Problem with Range-Only Measurements
  7. Observability Analysis with Range-Only Measurement
  8. The Measure of Observability via STLOG
  9. Observability-aware control
  10. OPC
  11. Satisfaction of local weak observability under OPC control
  12. Simulation and Experimental Validation
  13. Simulation
  14. Quadrotor Flight Experiments
  15. Conclusion
  16. ...and 3 more sections

Key Result

Proposition III.1

The range-only quadrotor CLS given by Eqs. eq:dynamicsModel and eq:observationModel is weakly locally observable, since its 3rd-order observability matrix may be expressed as: This matrix attains a rank of 10. Therefore, the system satisfies the observability rank condition.

Figures (9)

  • Figure 1: Example configurations of a CL-aided leader-follower quadrotor team.
  • Figure 2: Translation acceleration required by optimized commands for a first-order kinematic model
  • Figure 3: Visualizing initial state estimation by (our) observation process and (classical) discrete observations.
  • Figure 4: The overall flow chart of the system.
  • Figure 5: Simulated trajectories with squares/circles marking starting/end positions, respectively.
  • ...and 4 more figures

Theorems & Definitions (38)

  • Proposition III.1
  • proof
  • Proposition IV.1
  • proof
  • Definition IV.1: Band-limited white noise model with pink tail
  • Proposition IV.2
  • proof
  • Remark
  • Definition IV.2
  • Proposition V.1
  • ...and 28 more