Robust Helicopter Ship Deck Landing With Guaranteed Timing Using Shrinking-Horizon Model Predictive Control
Authors: Philipp Schitz, Paolo Mercorelli, Johann C. Dauer
Organizations: Institute of Flight Systems, German Aerospace Center (DLR), 38108 Braunschweig, Germany · Institute for Production Technology and Systems, Leuphana University of Lueneburg, 21335 Lueneburg, Germany
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.
Figures & tables
Fig. 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 .
Fig. 2: Visual representation of the used set operations where dots mark the coordinate origin of the respective sets. The top row shows set addition S1⊕S2 , the middle row set erosion S1⊖S2 , and the bottom row an affine transformation AS1+b .
Fig. 3: Constraint set 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 [ 14 ] .
Fig. 4: Terminal sets for NTD=50 . Left: Projections of touchdown constraint set FTD , the starting set XˉTD encoding a successful touchdown, and the resulting terminal set XˉT . Right: Projections of XˉT for different slices in dˉx .
Man.
∣Δϕ∣
∣Δθ∣
∣Δph∣
∣Δvh∣
∣Δvz∣
T
a)
0.6∘
0.2∘
0.06 m
0.04 m/s
0.95 m/s
10.30 s
b)
0.7∘
0.6∘
0.15 m
0.33 m/s
0.91 m/s
10.44 s
c)
0.6∘
1.1∘
0.14 m
0.54 m/s
0.98 m/s
10.54 s
max
4∘
6∘
0.60 m
0.60 m/s
1.15 m/s
10.90 s
TABLE I: Ship-relative attitude Δϕ , Δθ , horizontal position and velocity Δph and Δvh , and vertical velocity Δvz at touchdown, as well as maneuver time T .
Fig. 5: Ship and helicopter trajectories for the considered maneuvers.
Fig. 6: Pitch angles θ (left) and roll angles ϕ (right) trajectories during the landing maneuvers with true and commanded values to the attitude controller marked by solid and dashed lines, respectively.
Fig. 7: Longitudinal (left) and lateral (right) disturbance trajectories during the landing maneuvers. The boundaries of disturbance set D=dˉ+Dv are marked by dashed lines.
Fig. 8: Error trajectories in the longitudinal (left) and vertical (right) axis.
Aerial robotics studies the design, perception, control, and coordination of flying robots for navigation, inspection, transport, and physical interaction.
Autonomous Vehicles Laboratory, Department of Aerospace Engineering, Toronto Metropolitan University, Toronto, Canada · University of Toronto Institute for Aerospace Studies, University of Toronto, Toronto, Canada