Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Robust Helicopter Ship Deck Landing With Guaranteed Timing Using Shrinking-Horizon Model Predictive Control

Philipp Schitz, Paolo Mercorelli, Johann C. Dauer

Abstract

We present a runtime efficient algorithm for autonomous helicopter landings on moving ship decks based on Shrinking-Horizon Model Predictive Control (SHMPC). First, a suitable planning model capturing the relevant aspects of the full nonlinear helicopter dynamics is derived. Next, we use the SHMPC together with a touchdown controller stage to ensure a pre-specified maneuver time and an associated landing time window despite the presence of disturbances. A high disturbance rejection performance is achieved by designing an ancillary controller with disturbance feedback. Thus, given a target position and time, a safe landing with suitable terminal conditions is be guaranteed if the initial optimization problem is feasible. The efficacy of our approach is shown in simulation where all maneuvers achieve a high landing precision in strong winds while satisfying timing and operational constraints with maximum computation times in the millisecond range.

Robust Helicopter Ship Deck Landing With Guaranteed Timing Using Shrinking-Horizon Model Predictive Control

Abstract

We present a runtime efficient algorithm for autonomous helicopter landings on moving ship decks based on Shrinking-Horizon Model Predictive Control (SHMPC). First, a suitable planning model capturing the relevant aspects of the full nonlinear helicopter dynamics is derived. Next, we use the SHMPC together with a touchdown controller stage to ensure a pre-specified maneuver time and an associated landing time window despite the presence of disturbances. A high disturbance rejection performance is achieved by designing an ancillary controller with disturbance feedback. Thus, given a target position and time, a safe landing with suitable terminal conditions is be guaranteed if the initial optimization problem is feasible. The efficacy of our approach is shown in simulation where all maneuvers achieve a high landing precision in strong winds while satisfying timing and operational constraints with maximum computation times in the millisecond range.
Paper Structure (15 sections, 1 theorem, 31 equations, 4 figures)

This paper contains 15 sections, 1 theorem, 31 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Notation
  3. Problem Description and Preliminaries
  4. Robust Shrinking-Horizon MPC with Move Blocking
  5. Control-Oriented Helicopter Modeling
  6. Model simplification
  7. Disturbance modeling
  8. State-space dynamics
  9. SHMPC Design
  10. Disturbance-observer-based ancillary controller
  11. RPI set design
  12. Constraints
  13. Terminal set
  14. Landing Algorithm
  15. Simulation

Key Result

Proposition 1

Let $\mathcal{Z}$ be a RPI set for system eq:system. If $x_0 \in z_0 \oplus \mathcal{Z}$ and then $x_{k} \in z_{k} \oplus \mathcal{Z}$ for all $d_k \in \mathcal{D}$ and $k \in \mathbb{N}$.

Figures (4)

  • Figure 1: Common ship deck landing approaches for helicopters. Maneuver $a)$ is called straight-in, $b)$ a diagonal and $c)$ a lateral approach. The wind velocity vector is denoted by $w$.
  • Figure 2: Visual representation of the used set operations where dots mark the coordinate origin of the respective sets. The top row shows set addition $\mathcal{S}_1 \oplus \mathcal{S}_2$, the middle row set erosion $\mathcal{S}_1 \ominus \mathcal{S}_2$, and the bottom row an affine transformation $A \mathcal{S}_1 + b$.
  • Figure 3: Constraint set $\mathcal{F}$. Left: Attitude constraint and maximum accelerations for which geometric features intersect the ground. Right: Linear VRS constraint and exemplary nonlinear boundary computed based on johnsonVortex2005.
  • Figure 4: Terminal sets for $N_{TD} = 50$. Left: Projections of touchdown constraint set $\mathcal{F}_{TD}$, the starting set $\bar{\mathcal{X}}_{TD}$ encoding a successful touchdown, and the resulting terminal set $\bar{\mathcal{X}}_T$. Right: Projections of $\bar{\mathcal{X}}_T$ for different slices in $\bar{d}_x$.

Theorems & Definitions (6)

  • Definition 1: Robust Positive Invariance
  • Proposition 1: Proposition 1 in mayneRobustModelPredictive2005
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4