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Trajectory Tracking Control Design for Autonomous Helicopters with Guaranteed Error Bounds

Philipp Schitz, Johann C. Dauer, Paolo Mercorelli

Abstract

This paper presents a systematic framework for computing formally guaranteed trajectory tracking error bounds for autonomous helicopters based on Robust Positive Invariant (RPI) sets. The approach focuses on establishing a closed-loop translational error dynamics which is cast into polytopic linear parameter-varying form with bounded additive and state-dependent disturbances. Ellipsoidal RPI sets are computed, yielding explicit position error bounds suitable as certified buffer zones in upper-level trajectory planning. Three controller architectures are compared with respect to the conservatism of their error bounds and tracking performance. Simulation results on a nonlinear helicopter model demonstrate that all architectures respect the derived bounds, while highlighting trade-offs between dynamical fidelity and conservatism in invariant set computation.

Trajectory Tracking Control Design for Autonomous Helicopters with Guaranteed Error Bounds

Abstract

This paper presents a systematic framework for computing formally guaranteed trajectory tracking error bounds for autonomous helicopters based on Robust Positive Invariant (RPI) sets. The approach focuses on establishing a closed-loop translational error dynamics which is cast into polytopic linear parameter-varying form with bounded additive and state-dependent disturbances. Ellipsoidal RPI sets are computed, yielding explicit position error bounds suitable as certified buffer zones in upper-level trajectory planning. Three controller architectures are compared with respect to the conservatism of their error bounds and tracking performance. Simulation results on a nonlinear helicopter model demonstrate that all architectures respect the derived bounds, while highlighting trade-offs between dynamical fidelity and conservatism in invariant set computation.
Paper Structure (25 sections, 52 equations, 5 figures, 1 table)

This paper contains 25 sections, 52 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Contribution and structure of the paper
  3. Notation
  4. Problem statement and preliminaries
  5. Control oriented helicopter model
  6. Control-oriented model simplification
  7. Input transformation and disturbance bounding
  8. Attitude-induced disturbance
  9. Drag-induced disturbance
  10. Reference model inversion
  11. Control
  12. Drag compensation using flatness-based feedforward
  13. Feedback control
  14. Disturbance observer
  15. C-G: Geodetic gains and reference model
  16. ...and 10 more sections

Figures (5)

  • Figure 1: Generalized overview of the proposed outer loop controller architecture.
  • Figure 2: Projections of RPI sets onto the on the position-velocity subspace for the three considered feedback controllers.
  • Figure 3: Position trajectories of the considered maneuver in the $x$-$y$-plane for the C-GH controller with snapshots of the helicopter heading, position and the associated projection of the RPI ellipsoid onto the horizontal position subspace.
  • Figure 4: Projection of RPI sets onto the $x$-$y$ position subspace with heading-fixed error trajectories for all three feedback architectures.
  • Figure 5: Trajectories of horizontal velocities in the heading frame (top row), disturbances in the heading frame (middle row), tilt angle error (bottom left), and yaw error (bottom right).

Theorems & Definitions (2)

  • Definition 1: Robust Positive Invariance
  • Definition 2: Ellipsoidal Set