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New Insights into Cascaded Geometric Flight Control: From Performance Guarantees to Practical Pitfalls

Brett T. Lopez

TL;DR

The paper develops a new stability proof for cascaded geometric control of aerial vehicles tracking time-varying trajectories by integrating a quaternion-based sliding-variable attitude controller with a linear position controller. It proves global/exponential convergence of the attitude and almost global exponential convergence of the position, while revealing how attitude errors couple into the outer loop and how model uncertainties affect the closed-loop; it also discusses robustness and practical pitfalls such as the need for acceleration and jerk feedback. The work highlights implications for robust planning and points toward new control strategies to address practical limitations, including integration with safe trajectory planning and handling higher-order dynamics. Overall, the approach provides a rigorous framework for provable-safe, high-performance trajectory tracking on $SE(3)$.

Abstract

We present a new stability proof for cascaded geometric control used by aerial vehicles tracking time-varying position trajectories. Our approach uses sliding variables and a recently proposed quaternion-based sliding controller to demonstrate that exponentially convergent position trajectory tracking is theoretically possible. Notably, our analysis reveals new aspects of the control strategy, including how tracking error in the attitude loop influences the position loop, how model uncertainties affect the closed-loop system, and the practical pitfalls of the control architecture.

New Insights into Cascaded Geometric Flight Control: From Performance Guarantees to Practical Pitfalls

TL;DR

The paper develops a new stability proof for cascaded geometric control of aerial vehicles tracking time-varying trajectories by integrating a quaternion-based sliding-variable attitude controller with a linear position controller. It proves global/exponential convergence of the attitude and almost global exponential convergence of the position, while revealing how attitude errors couple into the outer loop and how model uncertainties affect the closed-loop; it also discusses robustness and practical pitfalls such as the need for acceleration and jerk feedback. The work highlights implications for robust planning and points toward new control strategies to address practical limitations, including integration with safe trajectory planning and handling higher-order dynamics. Overall, the approach provides a rigorous framework for provable-safe, high-performance trajectory tracking on .

Abstract

We present a new stability proof for cascaded geometric control used by aerial vehicles tracking time-varying position trajectories. Our approach uses sliding variables and a recently proposed quaternion-based sliding controller to demonstrate that exponentially convergent position trajectory tracking is theoretically possible. Notably, our analysis reveals new aspects of the control strategy, including how tracking error in the attitude loop influences the position loop, how model uncertainties affect the closed-loop system, and the practical pitfalls of the control architecture.
Paper Structure (9 sections, 11 theorems, 39 equations, 1 figure)

This paper contains 9 sections, 11 theorems, 39 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Results
  4. Overview
  5. Globally Exponentially Convergent Attitude Control
  6. Exponentially Convergent Cascaded Geometric Control
  7. Theoretical Guarantees & Practical Pitfalls
  8. Concluding Remarks
  9. Appendix

Key Result

Proposition 1

Let the manifold ${\mathcal{S}} = \{({q}_e,\omega_e) \in \mathbb{S}^3 \times \mathbb{R}^3 \, | \, {s({q}_e,\omega_e)}=0\}$ be invariant. Then, for any trajectory initialized on ${\mathcal{S}}$, the vector part of $q_e$ globally exponentially converges to zero with rate $\lambda$.

Figures (1)

  • Figure 1: Cascaded geometric control architecture for aerial vehicles.

Theorems & Definitions (29)

  • Definition 1: pavlov2004convergent
  • Remark 1
  • Proposition 1
  • proof
  • Theorem 1
  • proof
  • Remark 2
  • Corollary 1
  • proof
  • Lemma 1
  • ...and 19 more