WO2000034837A1

WO2000034837A1 - A method for automatic positioning of a vessel

Info

Publication number: WO2000034837A1
Application number: PCT/NO1999/000348
Authority: WO
Inventors: Thor I. Fossen; Jann Peter Strand
Original assignee: Abb Industri As
Priority date: 1998-11-19
Filing date: 1999-11-18
Publication date: 2000-06-15
Also published as: AU1417600A; GB0112088D0; NO985388L; GB2359149A; NO985388D0; NO308334B1

Abstract

The present invention relates to a method for automatic positioning of a vessel or a craft or the like, particularly for orienting the vessel energy-optimally in relation to external forces which influence the vessel, and with the object of devising an improved method which is independent of measurement of wind, wave and stream forces, and which is practically independent on type of vessel and thrust configuration. It is according to the invention proposed that the automatic positioning takes place by means of a steering system based on a virtual circle or sphere, the center of which is intended to have a certain position (p0 = (x0, y0)) in relation to the vessel. The resultant radius (Rref) of the circle or sphere represents the mean force (F) of the external forces which influence the vessel, and determines the angular position (γ), which the vessel should converge towards and coincide with for the most energy-optimal position.

Description

A METHOD FOR AUTOMATIC POSITIONING OF A VESSEL

Field of the invention

The present invention relates to a method for automatic positioning of a vessel or the like, particularly for orienting the vessel energy-optimally in relation to the external forces which influence the vessel.

More specifically, the invention relates to a method for energy-optimal positioning for under, fully and over actuated marine vessels, in which the vessel's orienting is optimal regarding non-measured wind, stream and wave interferences .

Field of application

The method is applicable for all marine vessels thereof, including submarines, freely floating vessels such as ships, speed-boats, platforms, buoys etc., as well as moored vessels. The concept can also be used for steering an aeroplane, for helicopters, missiles and other flying objects. The method teaches how a vessel is steered optimally regarding minimum energy consumption in 3 degrees of freedom: surge, sway, yaw, and alternatively 6 degrees of freedom: surge, sway, heave, roll , pitch and yaw by means of feedback from position, angles and velocities. Crafts in 3 degrees of freedom can be controlled by means of 2 thrusts (under actuated steering), 3 thrusts (fully actu- ated steering) and more than 3 thrusts (over actuated steering) . Corresponding methods can also be used for general movement in 6 degrees of freedom.

There are many objects of an energy-optimal positioning system. Possible applications are supply ships lying in a stand-by position at floating production platforms, aircraft carriers lying in the open sea for longer periods, floating airports which are rotated according to the weather situation, positioning of floating platforms, submarine vessels performing work etc. Common to all these applications is the fact that they can be performed by using less energy (fuel) than is possible by conventional methods for positioning control.

Prior art

In current systems for dynamic positioning (DP) of surface vessels in 3 degrees of freedom, the positioning and orientation is controlled in Cartesian co-ordinates, i.e. position, p = (x, y) , and course angle, ψ. For most of these systems desired course angle is chosen manually by an operator or chosen automatically based on measurements of wind direction, possibly measurements of stream and wave disturbances, if these are available.

A principle for automatic course control which does not use measurements of the environmental interferences is sug- gested by Pinkster (1986) . This principle controls the Cartesian position, p = (x, y) , of the ship by means of PID- based feedback, while the course angle is stabilized by means of a D-based feedback, i.e. feedback from course rate. In other words, the vessel is allowed to rotate freely until it turns towards the weather on a wea ther- optimal course angle, i.e. the angle that gives minimum energy. This principle assumes, however, that the vessel is equipped with bow thrusters located at a certain distance in front of the ship's point of gravity, as well as one or more actuators behind the vessel's point of gravity. This method is not valid for vessels, in which all thrusting means are located behind the point of gravity.

Pinkster's method also assumes that the vessel's rotation point (the point which is directed into the desired position of the DP system) is positioned in front of the point of gravity. However, the rotation point can be determined to reside on the side outside of the hull, as long as it is in front of the gravity point. The vessel's closed loop stability (stability when the vessel is steered by the DP system) increases, if the reference point is moved forward, while the vessel can become unstable when the reference point is sufficiently near or behind the point of gravity, which is a substantial limitation of the me hod.

Objects of the invention

A main object of the present invention is to device a new method for energy-optimal positioning of marine crafts, aeroplanes, helicopters and missiles, where the crafts' orientation (course angle for steering in 3 degrees of freedom or roll, pitch and course angle for steering in 6 degrees of freedom) is optimal regarding environmental loading and energy consumption.

Additional objects of the invention are to devise a method, by which the drawbacks and limitations of prior art methods are avoided.

Summary of the invention

These objects are achieved by a method according to the preamble, which, according to the invention, is characterised by the features which appear from the appended patent claims .

The main idea of the invention is thus to steer the vessel on a circular path, while the circle centre is concurrently moved on-line in such a way that the vessel's position is constant. In contrast to systems in which the position and course angle is controlled directly, this will result in the vessel turning towards a mean environmental force, which means that the course moment becomes zero (energy- optimal course angle) . The drawback of conventional methods for control of position is that it is impossible to turn the vessel towards mean environmental force, as this can not be measured directly. The resultant force as a consequence of wave drift forces, slowly variating wind forces and stream forces will be unknown in both direction and magnitude. A mathematical calculation of these force components will be too inaccurate for practical use, as this demands perfect knowledge of wind, wave and stream coefficients, which is impossible. Such computations are also dependent on type of vessel.

However, the proposed method can be realised for all types of vessels without prior knowledge of wind, wave and stream coefficients, and could in addition be realised without the use of sensors for measuring environmental forces. In other words :

• The method does not demand the measuring wind, stream and wave disturbances

• The method is not based on computations of wind, wave and stream forces, which in practice is difficult/impossible due to great uncertainty in the experimental and theoretical values of the force coeffi- cients. This means that the method is independent of type of vessel.

• The method works for under, fully and over actuated crafts with arbitrary thrust configuration (placement of thrusters, propels, rudders, steering planes, water- jet etc.), if the only requirement is that the vessel can be steered.

• The method has no limitation in regard to choice of ro- tation point, as its position can be placed on board or outside the hull Additional features and advantages of the present method will appear from the following description of the embodiments in reference to the appended drawings and the appended patent claims.

Brief description of the drawings

• Figur 1 includes sketches illustrating the present concept of weather-optimal steering of crafts based on energy-optimal stabilisation, corresponding to a pendulum in the gravity field

• Figure 2 is a block diagram of an example of a steering system according to the invention, feedback of veloc- ity, radius and course angle

• Figure 3 is a picture of a first supply ship, on which the present energy-optimal positioning method has been tested in a scale model

• Figure 4 shows a picture of a scale model of a second supply ship, on which the present method has been tested

• Figure 5 is a sketch showing an experimental set-up for weather-optimal positioning steering

• Figure 6 is a representation of a first test result, in which the model ship is moving on a circular path and converges towards a given angular position

• Figure 7 shows graphs of performance of the radius controller when the adjustment point is a certain radius, and the change of the course angle by moving the wind generator, respectively

• Figure 8 shows graphs for x and y positions as a function of time, respectively Figure 9 shows graphs for estimated surge, sway and yaw velocities, as a function of time, respectively

Figure 10 shows graphs for thruster force as a function of time

• Figure 11 shows a representation of a second test result with combined weather-optimal steering and trans- lation of the circular centre

• Figure 12 shows graphs for the effect of the radius controller for a constant set point, and changing the weather-optimal course angle due to movement of the wind generator, respectively

• Figure 13 shows graphs for x and y positions as function of time, respectively

• Figure 14 shows graphs for estimated surge, sway and yaw velocities as a function of time, respectively

• Figure 15 shows graphs of thruster force as a function of time

Description of embodiments

The present concept can be illustrated with a pendulum in the gravity field (vertical plane) , where the mass of the pendulum rotates around a rotation point until it reaches the stable point of equilibrium (the bottom point) , where the pendulum is hanging down. Since the system is exposed to a gravity force, the pendulum will never remain in the other point equilibrium (the top point) , as this is an un- stable point of equilibrium, see the left hand sketch on Figure 1. This is analogous to a vessel in the horisontal plane, where the vessel corresponds to the mass of the pendulum and the gravity force corresponds to the unknown environmental force (resulting force from slowly variating stream, wind and waves) , see the sketch at the left hand side of Figure 1.

If the vessel's steering system forces the vessel to point the bow inwards towards the circle centre (possibly a con- stant offset angle) corresponding to the rotation point of the pendulum, simultaneously as the vessel is limited to moving around the circle with constant radius, the position of the vessel will converge towards the stable point of equilibrium, cf. the pendulum. In this point, the bow points towards the resulting environmental force, such that the vessel is not subjected to a medium turning moment due to the environment (minimum energy configuration) . The rotation point of the circle is moving continuously, so that the vessel obtains the desired position p = (x, y) , simultaneously as it keeps its optimal orientation.

The closed loop steering system with circle movement kinematics is illustrated in Figure 2.

The method is based on the vessel's dynamics and kinematics is represented in polar co-ordinated for steering in 3 degrees of freedom and spherical co-ordinates for steering in 6 degrees of freedom. Conventional systems are based on steering systems, were the dynamics and kinematics are represented by means of Cartesian co-ordinates. The controlled variables controlled can be illustrated by means of the following examples, see Figure 2:

• Controlling surge, sway and yaw (3 degrees of freedom) by means of 2 thrusts (under actuated) : Control variables : Circle radius, R, and course angle, ψ. The sys- tern' s damping tangentially on the circle radius is given by the vessel's dynamics.

• Con trolling surge , sway and ya w (3 degrees of freedom) by means of 3 or more thrus ts (fully or over a ctua ted) : control variables: Circle radius, R, course angle, ψ, and tangential velocity, V_τ. This makes for extra damping in the system tangentially on the circle radius

• Controlling surge, sway, heave, roll , pitch and yaw (6 degrees of freedom) : Control variables : Spherical radius, R, roll angle, φ, pitch angle, θ, course angle, ψ, and possibly tangential velocity, V_τ.

For 3 degrees of freedom, the vessel will move in a circle towards the optimal point of equilibrium (minimum energy) , if there are designed 3 control loops, for example by proportional integral derivative (PID) type, i.e.:

Radius controller (PID-type) with reference, Rd = constant :

• Course controller (PID-type) with reference ψd = γ + π

• Tangential velocity controller (D-controller) with ref- erence V_TD = 0

Stabilisation/steering of the vessel can also be realised by using other methods from the control theory, for instance :

Feedback linearization

• Backstepping (recursive Lyapunov analysis)

• Linear and non-linear optimal control

• Polar positioning methods • Model based predictive control

A technical report describing a control system based on backstepping can be found i reference 1. The mathematical analysis shows the system being global uniform asymptotic stable (GUAS) , which guarantees that all state variables converges to real (optimal) value in finite time (global convergence) .

The control system described, herein, has been implemented and tested on a model vessel, CyberShip I, at the Institute for technical kybernetics, NTNU, Trondheim, Norway. The tests confirm the theoretical analysis and thus sup- port the basis of the patent application. The tests and laboratory set-up is described in the following, while the theoretical analysis is planned being published in a scientific article (Fossen and Strand, 1998), see reference 1.

The energy-optimal positioning system has been tested on a scale model of a supply ship, see Figure 3.

Description of the laboratory

The tests was conducted in the laboratory of navigation and vessel steering at the Institute of technical kybernetics, NTNU in spring 1998. The laboratory consist of two model ships, CyberShip I and CyberShip II and an model pool. CyberShip I is shown on Figure 4.

The size of the model pool is 6 x 10 metres with a water depth of 0.3 m. Stream forces are generated by using a water pump ejecting water to three jets by the end of the pool. A wave generator is mounted on the opposite side.

This consists of a data controlled vane. The vane can move with different frequencies, which is necessary in order to generate regular waves. Wind forces are generated by using a fan with jet. This can be moved into the desired posi- tion, for instance in front of a ship lying on DP. The experimental set-up is shown in Figure 5. CyberShip I is a scale model 1:70 of a real supply ship. The mass of the model is 17.6 kg, while the length is 1.19 m.

By assuming constant Froude number during the tests, i.e.:

V F„ = , = constan t

Where V is the velocity of the ship, L the length and g the gravity acceleration, we will get the following formulas of scale (Bis scaling) :

Position LJ L_m

Velocity L L_m

Velocity of angle L_m l L Acceleration 1

Angular acceleration L IL

Force ^{m m}

Moment (m m_m)(L L_m)

Where m is the mass and the indexes m and s represent the model and the ship. For a supply ship with length, L = 76 metres (Northern Clipper) , the following velocity scale appears from the tests:

V_ ^« 8.37P.

Two experiments were conducted:

1. Weather-optimal steering, where the ship was allowed to move in a circular path with a radius of 2.0 m. The course angle were stabilised at 85 degrees, which was the course angle of the wind force. Notice that even though the course angle starts at 130 degrees and moves towards 70 degrees, the ship keeps constant radius 2.0 m during the whole test.

2. In the other test, the circle centre was translated on- line, such that the position of the ship did not change. The desired position was chosen as (x, y) = (4.0, 4.0), while the desired radius was chosen as 2.0 m. This corresponds to classical DP, apart from the ship is allowed to rotate around the rotation point until the energy- optimal course angle is reached. At the start of the test, the course angle was 90 degrees. After a while, the ship rotated into 120 degrees, which is the weather- optimal course angle. This is done without influencing the ships (x, y) position.

Figures 6-10 visualise the first of the experiments, and this can be summarised as:

Experiment 1: Constant radius (the ship is moving along a circular path)

Figure 6: Circular movement of the model ship until the course angle and position converges into the point of equilibrium given by R = 2.0 m and ψ = 70 degrees.

Figure 7: The upper Figure shows the effect of the radius controller when the set point is 2.0 m. The lower Figure shows how the course angle changes into 70 degrees when the wind generator is relocated.

Figure 8: The x and y positions as a function of time (seconds)

Figure 9: Velocities as a function of time (seconds)

Figure 10: Thruster force (Azimuth thrusters) as a function of time (seconds) Figure 11-15 visualises the other experiments, and this can be summarised as:

Experiment 2: Constant radius and position (the ship is rotating around a constant point)

Figure 11: Combined weather-optimal steering and translation of the circle centre. Notice that the ship keeps its position (4, 4) even though the circle centre is moving along the dotted line. However, the optimal course angle varies as a function of the environmental forces.

Figure 12: The upper Figure shows the effect of the radius controller for a constant set point equal to 2 m, while the lower Figure shows how the weather-optimal course angle is changing from 90 into 120 degrees. This is due to the wind generator being relocated during the test.

Figure 13: The x and y positions as a function of time (seconds)

Figure 14: Velocities as a function of time (seconds)

Figure 15: Thruster force (Azimuth thrusters) as a function of time (seconds)

References :

1. Fossen, T.I. and J.P. Strand (1998). A Weather-optimal Positioning System for Ships, to be submitted to the IEEE Transactions on Control Systems Technology.

2. Pinkster, J.A. and U. Nienhuis (1986). Dynamic Position- ing of Large Tankers at Sea. Proceedings of the Offshore Technology Conference (OTC'86), Houston, TX, pp. 459- 477.

Claims

P a t e n t c l a i m s

1. Method for automatic positioning of a vessel or a craft or the like, particularly for energy-optimal orienta- tion of the vessel in relation to the external forces which influence the vessel, c h a r a c t e r i z e d i n that the automatic positioning is done by means of a steering system based on a virtual circle or sphere, the centre of which is intended to be in a certain position (p₀ = (x₀, y₀) ) in relation to the vessel, and if resultant radius (R_ref) , which represents the mean force (F) of the external forces which influence the vessel, determines the angular position (ψ) towards which the vessel shall converge and coincide with for most energy-optimal position.

2. Method as claimed in claim 1, c h a r a c t e r i z e d i n that by change of magnitude and direction of the mean force (F) , the centre of the cir- cle (p₀ = (x₀, y₀) ) will be moved correspondingly, such that the vessel obtains desired position (p = (x, y) ) while the vessel converges to a new energy-optimal orientation corresponding to the new direction of the resultant radius

3. Method as claimed in claim 1, c h a r a c t e r i z e d i n that the centre of the circle or sphere can be placed on board or outside the vessel.

4. Method as claimed in any of the preceding claims, c h a r a c t e r i z e d i n that the vessel ' s dynamics and kinematics are represented in polar co-ordinates for steering in three degrees of freedom, and spherical co-ordinates for steering in six degrees of freedom.

5. Method as claimed in any of the preceding claims, c h a r a c t e r i z e d i n that for steering in three degrees of freedom comprising a surge, sway and yaw, by means of two thrusts (under actuated) , the circle radius (R) and course angle (Ψ) are used as control variables, wherein the system's damping tangentially on the circle radius is given by the vessel's dynamics.

6. Method as claimed in any of the claims 1-5, c h a r a c t e r i z e d i n that for steering in three degrees of freedom comprising surge, sway and yaw, by means of three or more thrusts (fully or over actuated) , the circle radius (R) , course angle (Ψ) and tangential velocity (V_τ) are used as controlling variables, whereas this giving conditional damping in the system tangentially on the circle radius.

7. Method as claimed in any of the claims 1-4, c h a r a c t e r i z e d i n for steering in six de- grees of freedom comprising surge, sway, heave, roll, pitch and yaw, the sphere radius (R) , roll angle (φ) , pitch angle (θ) , course angle (Ψ) , and possibly tangential velocity (V_τ) .

8. Method as claimed in any of the claims 4-6, c h a r a c t e r i z e d i n for steering in three degrees of freedom, three controlling loops are utilized, which satisfy:

• radius controller (PID-type) with reference, R_d = constant

• course controller (PID-type) with reference, Ψ_d = γ + φ

• tangential velocity controller (D-controller) with reference, D_τd = 0 which means that the vessel is moving in a circle towards the optimal point of equilibrium (minimum energy) .

9. Method as claimed in any of the preceding claims, c h a r a c t e r i z e d i n that it includes:

• feedback linearization

• backstepping

• linear and non-linear optimal control • polar placement methods

• model-based predictive control