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Station-keeping control of an unmanned surface vehicle exposed to current and wind disturbances

Edoardo I. Sarda, Huajin Qu, Ivan R. Bertaska, Karl D. von Ellenrieder

arXiv:1702.04941v1eess.SYcs.ROcs.SY

TL;DR

Wind and current can disrupt USV station-keeping, which supports tasks requiring steady position and heading. This paper tests nonlinear feedback controllers with and without wind feedforward in on-water trials. Sliding mode performs best overall, while feedforward benefits PD and backstepping under transverse mean wind; turbulent length scales support using one anemometer on this USV.

  • Problem

    Wind and current disturbances make it difficult for USVs to maintain position and heading, which are needed for tasks such as underwater localization and AUV recovery.

    Source: §I · pp. 1–2

  • Method

    The authors test nonlinear PD, backstepping, and sliding mode station-keeping controllers with and without wind feedforward in on-water experiments.

    Source: §I · p. 2, §VIII · p. 40

  • Results

    Sliding mode performs best overall; wind feedforward does not significantly improve it but substantially improves PD and backstepping when mean wind is perpendicular to the USV’s longitudinal axis.

    Source: A. Station-keeping Trials at Location… · p. 35, §VIII · p. 40

  • Takeaways & Limitations

    Turbulent wind length scales were much larger than the USV, supporting the conclusion that a single anemometer is sufficient for wind feedforward control.

    Source: §VIII · p. 41

Abstract

from arXiv · show

Field trials of a 4 meter long, 180 kilogram, unmanned surface vehicle (USV) have been conducted to evaluate the performance of station-keeping heading and position controllers in an outdoor marine environment disturbed by wind and current. The USV has a twin hull configuration and a custom-designed propulsion system, which consists of two azimuthing thrusters, one for each hull. Nonlinear proportional derivative, backstepping and sliding mode feedback controllers were tested in winds of about 4-5 knots, with and without wind feedforward control. The controllers were tested when the longitudinal axis of the USV was aligned with the mean wind direction and when the longitudinal axis was perpendicular to the mean wind direction. It was found that the sliding mode controller performed best overall and that the addition of wind feedforward control did not significantly improve its effectiveness. However, wind feedforward control did substantially improve the performance of the proportional derivative and backstepping controllers when the mean wind direction was perpendicular to the longitudinal axis of the USV. An analysis of the length scales present in the power spectrum of the turbulent speed fluctuations in the wind suggests that a single anemometer is sufficient to characterize the speed and direction of the wind acting on the USV.

I. INTRODUCTION

Station-keeping lets USVs hold position and heading for tasks such as underwater localization and AUV recovery, but wind and current can impede that control. The paper develops and tests nonlinear feedback controllers, with and without wind feedforward, for a small twin-hulled USV.

I. INTRODUCTION

  • Holding position and heading can support underwater object localization and simplify AUV recovery by making the USV a fixed docking platform.Acoustic localization may require a fixed position for up to one minute, while camera-based localization depends on a steady heading.Source: §I · pp. 1–2
  • Wind is a major station-keeping disturbance for lightweight USVs with relatively large windage areas, while rapidly changing disturbances can be addressed with feedforward control.The introduction contrasts wind’s rapid variation with slowly varying currents, which robust feedback laws can attenuate.Source: §I · p. 2
  • The introduction identifies uncertain current effects as a source of difficulty in reaching and maintaining the desired state.It presents robust nonlinear control and wind feedforward as approaches to correcting control effort.Source: §I · p. 2
  • The paper designs and tests nonlinear PD, backstepping, and sliding mode station-keeping controllers, both with and without wind feedforward.On-water tests evaluate heading and position station-keeping.Source: §I · p. 2

II. LITERATURE REVIEW

Prior USV station-keeping studies often used simulation or small-scale tests, focused on underactuated vehicles, and did not address heading together with position. This work uses extensive on-water trials to examine robust feedback combined with wind feedforward.

II. LITERATURE REVIEW

  • Prior USV station-keeping work often focused on underactuated vehicles and position alone, rather than simultaneous position and orientation control.The review also notes that validation of USV control laws has often been limited to simulation or small-scale experiments rather than full-scale sea trials.Source: §II · p. 3
  • Wind feedforward for USVs remained relatively unexplored, with challenges including representative wind measurements, force coefficients, sensor placement, and validating wind models for small vehicles.The review notes that wind can vary across a vessel and that models are largely based on large vessels and floating objects.Source: §II · p. 4
  • This work extends prior studies to small USVs by combining robust control and wind feedforward for heading and position station-keeping, evaluated through extensive on-water trials.Source: §II · p. 4

III. THE WAM-V USV16

The WAM-V USV16 is a twin-hulled vessel equipped with a custom propulsion system that enables control across surge, sway, and yaw. Its onboard sensing and wind instrumentation support navigation and wind-feedforward control.

III. THE WAM-V USV16

  • The WAM-V USV16 is a 4.9 m twin-hull pontoon vessel with inflatable pontoons, a payload tray, supporting arches, and a suspension system.Its structure is designed to mitigate payload-tray heave, pitch, and roll in waves.Source: A. Overview · p. 4
  • Two thrusters and two linear actuators provide pivoting thrust that lets the vessel generate surge, sway, and yaw forces independently.The four actuators serve three degrees of freedom, making the propulsion configuration overactuated.Source: B. Propulsion System · pp. 5–6, Figure 2 · p. 6, Figure 3 · p. 7
  • The GNC system uses an IMU/GPS and digital compass to estimate position and monitor heading, with sensor data logged at 4 Hz.The GPS can provide up to 1 m latitude and longitude accuracy, depending on cloud cover and satellite availability.Source: C. Guidance, Navigation, and Control… · p. 7
  • A 1 Hz ultrasonic anemometer measures apparent wind, and its single-point reading is treated as representative of wind across the small vessel.It is mounted at the elevated aft end of the payload tray to reduce wind blockage and structural interference.Source: C. Guidance, Navigation, and Control… · pp. 7–8

IV. SYSTEM IDENTIFICATION

The WAM-V USV16’s three-degree-of-freedom maneuvering model was developed from sea-trial system-characterization tests and refined by manually tuning hydrodynamic coefficients against experimental state outputs. The model assumes planar motion and port/starboard symmetry, with surge drag characterized by a quadratic fit.

System characterization

  • Bollard-pull, acceleration, circle, and zig-zag sea trials characterized the USV16 in a low-disturbance lake environment, with thruster angles held at zero.The bollard-pull test averaged five load-scale readings for each motor command; the zig-zag test was used to evaluate the model against simulation.Source: A. System Characterization · pp. 8, 11

Surge drag

  • A quadratic fit of surge speed and drag estimates the linear and nonlinear surge drag coefficients, assuming propeller thrust has no speed dependence.The paper states this assumption does not affect station-keeping experiments because forward speed typically remains small.Source: Figure 4 · p. 9, Figure 5 · p. 10

System characterization

  • The hydrodynamic coefficients were entered into the three-degree-of-freedom equations of motion and manually tuned until simulated and sea-trial state outputs matched under the same open-loop inputs.The authors describe the resulting model as sufficiently accurate for control-system design.Source: §IV · p. 8, A. System Characterization · p. 11

Coefficient estimation

  • Hydrodynamic coefficients were estimated over approximately 0.7–1.5 m/s, although the target application is station-keeping under wind perturbations.The authors note that environmental disturbances and uneven forcing make low-speed open-loop system-identification maneuvers difficult to manage.Source: A. System Characterization · p. 13

Dynamic model

  • The three-degree-of-freedom model represents surge, sway, and yaw, assuming planar motion, low speeds, mild sea states, and port/starboard symmetry.The model places its body-fixed origin at the center of gravity and sets x_G and y_G to zero.Source: B. Equations of Motion · p. 13

Hull drag model

  • The model’s port and starboard surge-drag terms use the experimental polynomial fit, with transformed velocities accounting for each pontoon’s offset from the center of gravity.The unequal hull drag forces also contribute a yaw moment.Source: B. Equations of Motion · p. 15

V. STATION-KEEPING CONTROL

This section develops station-keeping feedback and wind-feedforward controllers for USV16. It describes the controllers’ formulation and how anemometer data are used to estimate wind disturbance and provide a compensating input.

A. Proportional Derivative (PD) Control

  • The full PID controller could not reach steady state in field trials: weak sway control authority caused lateral errors and difficult actuator commands, so the researchers used PD instead.Anti-windup techniques did not sufficiently mitigate the problem.Source: A. Proportional Derivative (PD) Control · p. 17

B. Backstepping Control

  • A MIMO backstepping controller was designed to address model mismatch and environmental disturbances after PD performance diverged from simulation.Its Lyapunov-exponent gain matrix was selected with unmodeled resonance, hardware delays, and sampling rate in mind.Source: B. Backstepping Control · pp. 17–18

C. Sliding Mode Control

  • Sliding mode control was designed to resist slowly varying disturbances and unmodeled dynamics, using an integral term to reduce persistent errors over extended station-keeping.The integral term prioritizes robustness and stability over faster settling; saturation scaling also serves as anti-windup when the control output saturates.Source: C. Sliding Mode Control · pp. 19–20

D. Wind Feedforward Control

  • The wind-feedforward model estimates wind forces and moment from apparent wind speed and angle of attack, with coefficients manually tuned to cx = 0.50, cy = 0.50, cz = 0.33.The coefficients were initially set to cx = 0.70, cy = 0.80, cz = 0.10.Source: D. Wind Feedforward Control · pp. 22–23
  • About 90% of turbulent wind kinetic energy occurred below 0.03 Hz; the resulting 78 m length scale supported using one wind measurement to characterize conditions across the much shorter USV16.The estimate used an average wind speed of 2.43 m/s.Source: D. Wind Feedforward Control · pp. 22–23, Figure 17 · p. 24

V. STATION-KEEPING CONTROL

  • The wind model assumes zero vehicle velocity during steady-state station-keeping, equating apparent and true wind speed and direction; feedforward warrants caution because it may destabilize or degrade feedback.Wind forces and moment can be derived from true or apparent wind speed and direction.Source: D. Wind Feedforward Control · pp. 24–25
  • Wind feedforward uses filtered apparent-wind speed and direction to estimate disturbance, then subtracts it from the state-feedback controller output.Anemometer data are smoothed with a 20-sample moving average; the combined wind and state estimate yields a more accurate required control output.Source: D. Wind Feedforward Control · pp. 25–26, Figure 19 · p. 25
  • Three feedforward variants were derived: PD, backstepping, and sliding-mode station-keeping controllers, each paired with a wind model.The variants follow their corresponding feedback controllers; the wind input is designed to oppose wind forces and moments on the vehicle.Source: D. Wind Feedforward Control · pp. 25–26, Figure 20 · p. 26

VI. CONTROL ALLOCATION

The section formulates actuator allocation as a weighted optimization mapping controller forces to actuator forces and azimuth commands. A Lagrangian solution and actuator-limit handling make the scheme computationally efficient for the USV’s embedded processor.

VI. CONTROL ALLOCATION

  • The extended force representation maps controller output τ to surge and sway forces across four actuators: two linear actuators and two thrusters.The USV16 propulsion system uses two linear actuators and two thrusters.Source: A. Extended Force Representation · p. 27
  • The weighted cost minimizes actuator force while constraining the difference between desired and attainable control forces.The weight matrix can favor the more efficient actuators.Source: B. Lagrangian Multiplier Solution · p. 27
  • For identical port/starboard actuators, the weight matrix can be identity, making the inverse transformation the Moore-Penrose pseudoinverse.Source: B. Lagrangian Multiplier Solution · p. 28
  • Once actuator force components are found, a four-quadrant arctan gives azimuth angles and the force components give thrust magnitudes.Source: B. Lagrangian Multiplier Solution · p. 28
  • With azimuth travel limited to ±45°, allocation logic zeroes or reverses thrust for unreachable angles, while low-pass filters temper actuator response.The filters account for thruster and actuator dynamics that are not precisely modeled in the allocation scheme.Source: Figure 21 · p. 28, Figure 22 · p. 28, B. Lagrangian Multiplier Solution · p. 29

VII. STATION-KEEPING EXPERIMENTS

Sea trials compared three station-keeping controllers, with and without wind feedforward, at two sites with different disturbance exposure. Sliding mode performed best overall; feedforward benefits depended on controller and conditions.

VII. STATION-KEEPING EXPERIMENTS

  • In 700-second station-keeping trials, Location 1 and Location 2 were selected for minimum and maximum local disturbances, with headings chosen to create the friendliest and harshest scenarios, respectively.Trials took place in calm sections of the U.S. Intracoastal Waterway; no open-ocean tests were performed, and the vehicle lacked a sensor to measure water currents.Source: §VII · pp. 29, 30, 32
  • At Location 1, PD held position error at or below GPS accuracy through heading oscillations, while wind feedforward increased heading oscillations without affecting position error.Heading error fluctuated between -20° and +20°; position error was below 1 meter most of the time.Source: A. Station-keeping Trials at Location… · p. 33, Figure 25 · p. 33
  • At Location 1, backstepping maintained a small (~1 m) position error while reducing heading error variation; wind feedforward made no relevant performance difference.Unlike PD, position holding did not depend on high, steady heading oscillations.Source: A. Station-keeping Trials at Location… · p. 34, Figure 26 · p. 34
  • At Location 2, PD had larger heading and position errors than at Location 1, and wind feedforward did not improve station-keeping.As at Location 1, heading oscillations enabled position holding.Source: A. Station-keeping Trials at Location… · p. 37, Figure 28 · p. 37
  • At Location 2, backstepping’s position error increased dramatically without feedforward, including a 3 m steady-state error; feedforward substantially improved performance.With feedforward, the vehicle corrected position error despite heading-error peaks.Source: A. Station-keeping Trials at Location… · p. 38, Figure 29 · p. 38
  • At both locations, sliding mode outperformed PD and backstepping; at Location 2, position and heading errors increased slowly and returned to zero.Wind feedforward further minimized errors at Location 2, but did not improve sliding mode at Location 1.Source: A. Station-keeping Trials at Location… · pp. 35, 39, Figure 27 · p. 35, Figure 30 · p. 39

VIII. SUMMARY AND CONCLUDING REMARKS

The paper reports sea trials of three feedback controllers, alone and with wind feedforward, for USV station-keeping. Sliding mode performed best overall, while feedforward substantially helped PD and backstepping under transverse wind disturbance.

VIII. SUMMARY AND CONCLUDING REMARKS

  • Sliding mode performed best overall, while wind feedforward did not significantly improve it; feedforward substantially improved PD and backstepping under perpendicular mean wind.For disturbances aligned with the vehicle’s longitudinal axis, feedforward did not significantly improve station-keeping controllers.Source: §VIII · p. 40
  • Two azimuthing thrusters were sufficient for the tested twin-hull USV to station-keep heading and position simultaneously under similar environmental conditions.The approach was developed for operation with two transom-mounted thrusters.Source: §VIII · p. 40
  • PD or backstepping feedback alone did not provide sufficient control effort to maintain heading and position simultaneously.The conclusions identify a compromise between heading and position station-keeping.Source: §VIII · p. 41
  • Within the tested setting, choosing an appropriate controller, such as sliding mode, can minimize errors associated with the heading–position compromise.The conclusion also identifies gain or parameter tuning as relevant.Source: §VIII · p. 41
  • The dominant turbulent wind length scales were much larger than the USV, supporting the conclusion that one anemometer is sufficient for wind feedforward control.The conclusion is based on representative wind data.Source: §VIII · p. 41
  • For nonlinear PD or backstepping, wind feedforward worked better against transverse than longitudinal disturbances; direction-weighting the feedforward term may be beneficial.The direction-weighting strategy is suggested, not reported as a tested result.Source: §VIII · p. 41
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