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Robust Global Position and Heading Tracking on SE(3) via Saturated Hybrid Feedback

Luís Martins, Carlos Cardeira, Paulo Oliveira

Abstract

This letter presents a novel control solution to the robust global position and heading tracking problem for underactuated vehicles, equipped with single-axis thrust and full torque actuation, operating under strict, user-defined actuation limits. The architecture features a saturated position tracking controller augmented with two first-order filters. This formulation ensures the boundedness of the first and second derivatives, yielding less conservative bounds and systematically generating bounded attitude references whose limits are easily tuned via design parameters. To track these dynamic references, the inner loop comprises a saturated, modified Rodrigues parameter (MRP)-based controller paired with a hybrid dynamic path-lifting mechanism. This approach allows the attitude tracking law to be designed on a covering space of the configuration manifold. By leveraging a stability equivalence framework, the methodology establishes that the resulting interconnected system achieves robust global asymptotic and semi-global exponential tracking on SE(3), while complying with user-defined input saturation bounds. Numerical simulations validate the proposed solution.

Robust Global Position and Heading Tracking on SE(3) via Saturated Hybrid Feedback

Abstract

This letter presents a novel control solution to the robust global position and heading tracking problem for underactuated vehicles, equipped with single-axis thrust and full torque actuation, operating under strict, user-defined actuation limits. The architecture features a saturated position tracking controller augmented with two first-order filters. This formulation ensures the boundedness of the first and second derivatives, yielding less conservative bounds and systematically generating bounded attitude references whose limits are easily tuned via design parameters. To track these dynamic references, the inner loop comprises a saturated, modified Rodrigues parameter (MRP)-based controller paired with a hybrid dynamic path-lifting mechanism. This approach allows the attitude tracking law to be designed on a covering space of the configuration manifold. By leveraging a stability equivalence framework, the methodology establishes that the resulting interconnected system achieves robust global asymptotic and semi-global exponential tracking on SE(3), while complying with user-defined input saturation bounds. Numerical simulations validate the proposed solution.
Paper Structure (11 sections, 5 theorems, 132 equations, 3 figures, 1 table)

This paper contains 11 sections, 5 theorems, 132 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Motivation and Literature Review
  3. Contributions
  4. Organization
  5. Notation and Preliminaries
  6. Problem Statement
  7. Filtered Saturated Position Tracking
  8. Saturated Global Trajectory Tracking
  9. Simulation Results
  10. Conclusion
  11. Hybrid Dynamic Path-lifting Algorithm

Key Result

Theorem 1

Suppose the conditions of assump:ReferenceTrajectory hold for all $t \geq 0$. Then, the origin $\mathbf{\Tilde{x}_p} = \boldsymbol{0}$ of the tracking dynamics eq:PositionTrackingDynamics is globally asymptotically stable and semi-globally exponentially stable. Furthermore, along any solution $\math

Figures (3)

  • Figure 1: Simplified structural comparison of the control loops. (a) The real system inherently embeds the finite-bandwidth filter dynamics within the feedback loop. (b) The global diffeomorphism maps the system to the transformed coordinates, algebraically masking the filter states.
  • Figure 2: Position and attitude responses in simulation.
  • Figure 3: Actuation and saturation functions in simulation.

Theorems & Definitions (13)

  • Definition 1
  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • Remark 1
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • ...and 3 more