Abstract

This paper presents an adaptive control strategy to optimize the sailing maneuvers of an AC75 foiling sailboat competing in America's Cup. Foiling yachts have nonlinear, high-dimensional, and unstable dynamics due to several articulations for fast motions and maneuverability. Achieving aggressive and optimal maneuvers requires taking these complex dynamics into account instead of analytical optimizations using reduced-order models. We compared extremum-seeking and Jacobian learning (JL) control approaches on a full-order model to achieve optimal maneuvers and used JL to optimize articulations. The controllers were integrated with a high-fidelity sailboat simulator for safe and efficient maneuver optimization. The optimal solutions were subject to physical/actuator constraints and those enforced to ensure the feasibility of the maneuvers by humans (sailors). The close-hauled and tacking maneuvers were optimized to achieve maximum velocity made good (VMG) and minimum loss of VMG, respectively. The optimal maneuvers boast a marginal VMG loss of less than 1.5%, which enables exploiting areas of good wind conditions in the racing environment.

References

1.
Rodriguez
,
R.
,
Wang
,
Y.
,
Ozanne
,
J.
,
Sumer
,
D.
,
Filev
,
D.
, and
Soudbakhsh
,
D.
,
2022
, “
Adaptive Takeoff Maneuver Optimization of a Sailing Boat for America's Cup
,”
J. Sailing Technol.
,
7
(
01
), pp.
88
103
. 1010.5957/jst/2022.7.4.88
2.
Bencatel
,
R.
,
Keerthivarman
,
S.
,
Kolmanovsky
,
I.
, and
Girard
,
A. R.
,
2021
, “
Full State Feedback Foiling Control for America's Cup Catamarans
,”
IEEE Trans. Control Syst. Technol.
,
29
(
1
), pp.
1
17
.10.1109/TCST.2019.2955059
3.
Horel
,
B.
,
2019
, “
System-Based Modelling of a Foiling Catamaran
,”
Ocean Eng.
,
171
, pp.
108
119
.10.1016/j.oceaneng.2018.10.046
4.
Le Bars
,
F.
, and
Jaulin
,
L.
,
2013
, “
An Experimental Validation of a Robust Controller With the Vaimos Autonomous Sailboat
,”
Robotic Sailing 2012
,
Springer
,
Berlin/Heidelberg
, pp.
73
84
.
5.
Sun
,
Q.
,
Qiao
,
Z.
,
Strömbeck
,
C.
,
Qu
,
Y.
,
Liu
,
H.
, and
Qian
,
H.
,
2018
, “
Tacking Control of an Autonomous Sailboat Based on Force Polar Diagram
,” 13th World Congress on Intelligent Control and Automation (
WCICA'13
), Changsha, China, July 4–8, pp.
467
473
. 10.1109/WCICA.2018.8630752
6.
Corno
,
M.
,
Formentin
,
S.
, and
Savaresi
,
S.
,
2016
, “
Data-Driven Online Speed Optimization in Autonomous Sailboats
,”
IEEE Trans. Intell. Transp. Syst
.,
17
(
3
), pp.
762
771
.10.1109/TITS.2015.2483022
7.
Xiao
,
L.
,
Alves
,
J. C.
,
Cruz
,
N. A.
, and
Jouffroy
,
J.
,
2012
, “
Online Speed Optimization for Sailing Yachts Using Extremum Seeking
,” 2012
Oceans
, Hampton Roads, VA, Oct. 14–19, pp.
1
6
. 10.1109/OCEANS.2012.6404876
8.
Deng
,
Y.
,
Zhang
,
X.
, and
Zhang
,
G.
,
2020
, “
Line-of-Sight-Based Guidance and Adaptive Neural Path-Following Control for Sailboats
,”
IEEE J. Ocean. Eng
.,
45
(
4
), pp.
1177
1189
.10.1109/JOE.2019.2923502
9.
Ren
,
J.
, and
Yang
,
Y.
,
2004
, “
Fuzzy Gain Scheduling Attitude Control for Hydrofoil Catamaran
,” Proceedings of the 2004 American Control Conference (
ACC'04
), Vol.
2
, Boston, MA, June 30–July 2, pp.
1103
1108
. 10.23919/ACC.2004.1386719
10.
Furrer
,
F.
, and
Siegwart
,
R.
,
2010
,
Developing a Simulation Model of a Catamaran Using the Concept of Hydrofoils
,
ETH Zurich
, Zürich, Switzerland.
11.
Xiao
,
L.
, and
Jouffroy
,
J.
,
2014
, “
Modeling and Nonlinear Heading Control of Sailing Yachts
,”
IEEE J. Ocean. Eng.
,
39
(
2
), pp.
256
268
.10.1109/JOE.2013.2247276
12.
Abrougui
,
H.
,
Dallagi
,
H.
, and
Nejim
,
S.
,
2019
, “
Autopilot Design for an Autonomous Sailboat Based on Sliding Mode Control
,”
Autom. Control Comput. Sci.
,
53
(
5
), pp.
393
407
.10.3103/S0146411619050031
13.
Rodriguez Nunez
,
R.
, and
Soudbakhsh
,
D.
,
2019
, “
Modeling and Predictive Control of an Unmanned Underwater Vehicle
,”
ASME
Paper No. DSCC2019-9154. 10.1115/DSCC2019-9154
14.
Wille
,
K. L.
,
Hassani
,
V.
, and
Sprenger
,
F.
,
2016
, “
Modeling and Course Control of Sailboats
,”
IFAC-PapersOnLine
,
49
(
23
), pp.
532
539
.10.1016/j.ifacol.2016.10.490
15.
AlaviMehr
,
J.
,
Lavroff
,
J.
,
Davis
,
M. R.
,
Holloway
,
D. S.
, and
Thomas
,
G. A.
,
2017
, “
An Experimental Investigation of Ride Control Algorithms for High-Speed Catamarans Part 1: Reduction of Ship Motions
,”
J. Ship Res.
,
61
(
1
), pp.
35
49
.10.5957/JOSR.61.1.160041
16.
Alves
,
J. C.
, and
Cruz
,
N. A.
,
2015
, “
Ais-Enabled Collision Avoidance Strategies for Autonomous Sailboats
,” World Robotic Sailing championship and International Robotic Sailing Conference (
WRSC'15
), Mariehamn, Åland Islands, Sept. 1–4, pp.
77
87
. https://link.springer.com/chapter/10.1007/978-3-319-23335-2_6
17.
Stelzer
,
R.
,
Proll
,
T.
, and
John
,
R. I.
,
2007
, “
Fuzzy Logic Control System for Autonomous Sailboats
,” IEEE International Fuzzy Systems Conference (
Fuzz-IEEE'07
), London, UK, July 23–26, pp.
1
6
. 10.1109/FUZZY.2007.4295347
18.
dos Santos
,
D. H.
, and
Goncalves
,
L. M. G.
,
2019
, “
A Gain-Scheduling Control Strategy and Short-Term Path Optimization With Genetic Algorithm for Autonomous Navigation of a Sailboat Robot
,”
Int. J. Adv. Robot. Syst.
,
16
(
1
), pp.
1
15
.10.1177/1729881418821830
19.
Silva Junior
,
A. G. D.
,
Santos
,
D. H. D.
,
Negreiros
,
A. P. F. D.
,
Silva
,
J. M. V. B. D S.
, and
Gonçalves
,
L. M. G.
,
2020
, “
High-Level Path Planning for an Autonomous Sailboat Robot Using q-Learning
,”
Sensors (Basel)
,
20
(
6
), p.
1550
.10.3390/s20061550
20.
Skjetne
,
R.
,
Fossen
,
T.
, and
Kokotović
,
P. V.
,
2004
, “
Robust Output Maneuvering for a Class of Nonlinear Systems
,”
Automatica
,
40
(
3
), pp.
373
383
.10.1016/j.automatica.2003.10.010
21.
Rodriguez
,
R.
,
2021
, “
Optimal Control of the ac75 Sailboat for the America's Cup Race
,” Master's thesis,
Temple University Libraries
, Philadelphia, PA.
22.
Heppel
,
P.
,
2015
, “
Fligh Dynamics of Sailing Foilers
,”
Proceedings of the e 5th High Performance Yacht Design Conference, HPYD'15
, Mar. 10–12, Auckland, NZ, pp.
180
189
.
23.
Bousquet
,
G. D.
,
Triantafyllou
,
M. S.
, and
Slotine
,
J.-J. E.
,
2017
, “
Control of a Flexible, Surface-Piercing Hydrofoil for High-Speed, Small-Scale Applications
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS'17
, Vancouver, BC, Canada, Sept. 24–28, pp.
4203
4208
.
24.
Plumet
,
F.
,
Pêtrès
,
C.
,
Romero-Ramirez
,
M.
,
Gas
,
B.
, and
Ieng
,
S.
,
2015
, “
Toward an Autonomous Sailing Boat
,”
IEEE J. Ocean. Eng.
,
40
(
2
), pp.
397
407
.10.1109/JOE.2014.2321714
25.
Alves
,
J. C.
, and
Cruz
,
N. A.
,
2008
, “
Fast-an Autonomous Sailing Platform for Oceanographic Missions
,”
OCEANS
Conference, Quebec City, QC, Canada, Sept. 15–18, pp.
1
7
. 10.1109/OCEANS.2008.5152114
26.
Masuyama
,
Y.
, and
Fukasawa
,
T.
,
2011
, “
Tacking Simulation of Sailing Yachts With New Model of Aerodynamic Force Variation During Tacking Maneuver
,”
J. Sailboat Technol.
,
2
(
01
), pp.
1
34
.
27.
Bai
,
J.
, and
Kim
,
Y.
,
2010
, “
Control of the Vertical Motion of a Hydrofoil Vessel
,”
Ships Offshore Struct.
,
5
(
3
), pp.
189
198
.10.1080/17445300903354224
28.
Zheng
,
L.
,
Liu
,
Z.
,
Li
,
G.
,
Yuan
,
S.
, and
Yang
,
S.
,
2021
, “
Experimental and Numerical Investigation on Control Strategies for Heave and Pitch Motion Reduction of a Catamaran
,”
Proc. Inst. Mech. Eng. M
,
235
(
2
), pp.
311
326
.10.1177/1475090221993650
29.
Najafi
,
A.
,
Nowruzi
,
H.
, and
Ghassemi
,
H.
,
2018
, “
Performance Prediction of Hydrofoil-Supported Catamarans Using Experiment and Anns
,”
Appl. Ocean Res.
,
75
, pp.
66
84
.10.1016/j.apor.2018.02.017
30.
Sclavounos
,
P.
, and
Borgen
,
H.
,
2004
, “
Seakeeping Analysis of a High-Speed Monohull With a Motion-Control Bow Hydrofoil
,”
J. Ship Res.
,
48
(
02
), pp.
77
117
.10.5957/jsr.2004.48.2.77
31.
Angelou
,
M.
, and
Spyrou
,
K. J.
,
2017
, “
A New Mathematical Model for Investigating Course Stability and Maneuvering Motions of Sailing Yachts
,”
J. Sail. Technol.
,
2
(
01
), pp.
1
42
.
32.
Ye
,
Z.
,
Zhang
,
D.
,
Cheng
,
J.
, and
Wu
,
Z.-G.
,
2022
, “
Event-Triggering and Quantized Sliding Mode Control of Umv Systems Under Dos Attack
,”
IEEE Trans. Veh. Technol.
,
71
(
8
), pp.
8199
8211
.10.1109/TVT.2022.3175726
33.
Filev
,
D. P.
,
Bharitkar
,
S.
, and
Tsai
,
M.-F.
,
1999
, “
Nonlinear Control of Static Systems With Unsupervised Learning of the Initial Conditions
,” 18th International Conference of the North American Fuzzy Information Processing Society
(NAFIPS)
NAFIPS'1999, New York, June 10–12, pp.
169
173
. 10.1109/NAFIPS.1999.781676
34.
D'Amato
,
A.
,
Wang
,
Y.
,
Filev
,
D.
, and
Remes
,
E.
,
2017
, “
On the Tradeoffs Between Static and Dynamic Adaptive Optimization for an Automotive Application
,”
SAE Int. J. Commer. Veh.
,
10
(
1
), pp.
346
352
.10.4271/2017-01-0605
35.
Krstić
,
M.
, and
Wang
,
H.-H.
,
2000
, “
Stability of Extremum Seeking Feedback for General Nonlinear Dynamic Systems
,”
Automatica
,
36
(
4
), pp.
595
601
.10.1016/S0005-1098(99)00183-1
36.
Choi
,
J.-Y.
,
Krstic
,
M.
,
Ariyur
,
K. B.
, and
Lee
,
J. S.
,
2002
, “
Extremum Seeking Control for Discrete-Time Systems
,”
IEEE Trans. Autom. Control
,
47
(
2
), pp.
318
323
.10.1109/9.983370
37.
Gupta
,
R.
,
Kolmanovsky
,
I. V.
,
Wang
,
Y.
, and
Filev
,
D. P.
,
2012
, “
Onboard Learning-Based Fuel Consumption Optimization in Series Hybrid Electric Vehicles
,”
American Control Conference
, Montréal, Canada, QC, June 27–29, pp.
1308
1313
. 10.1109/ACC.2012.6314797
38.
American Magic
,
2020
, “New York Yacht Club American Magic,” America's Cup Website, accessed Jan. 5, 2021, https://americanmagic.americascup.com
39.
Filev
,
D.
,
Larsson
,
T.
, and
Ma
,
L.
,
2000
, “
Intelligent Control for Automotive Manufacturing-Rule Based Guided Adaptation
,” 2000
IEEE
International Conference on Industrial Electronics, Control and Instrumentation, IECON'00, Nagoya, Japan, Oct. 22–28, pp.
283
288
. 10.1109/IECON.2000.973164
40.
Larsson
,
T.
,
Ma
,
L.
, and
Filev
,
D.
,
2000
, “
Adaptive Control of a Static Multiple Input Multiple Output System
,”
Proceedings of the American Control Conference, ACC'00
, Vol.
4
, Chicago, IL, June 28–30, pp.
2573
2577
. 10.1109/ACC.2000.878672
41.
Gilbert
,
E.
, and
Kolmanovsky
,
I.
,
2002
, “
Nonlinear Tracking Control in the Presence of State and Control Constraints: A Generalized Reference Governor
,”
Automatica
,
38
(
12
), pp.
2063
2073
.10.1016/S0005-1098(02)00135-8
42.
Garone
,
E.
,
Di Cairano
,
S.
, and
Kolmanovsky
,
I.
,
2017
, “
Reference and Command Governors for Systems With Constraints: A Survey on Theory and Applications
,”
Automatica
,
75
, pp.
306
328
.10.1016/j.automatica.2016.08.013
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