CN116400708A - Ship track tracking method based on event triggering and hybrid logic dynamic model - Google Patents
Ship track tracking method based on event triggering and hybrid logic dynamic model Download PDFInfo
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Abstract
The invention discloses a ship track tracking method based on event triggering and hybrid logic dynamic model, which comprises the following steps: dividing rudder angles into gears, and constructing a dynamic model of the rotating speed of a ship propeller and the motion of the ship under different rudder angle gears by combining a ship MMG model; constructing definition of an event included angle, namely defining the event included angle as an included angle between the ship speed direction and the target track point direction, and setting an included angle threshold as an event triggering mechanism; constructing a hybrid logic dynamic model according to a ship MMG model, a dynamic model of ship propeller rotating speed and ship motion and an event triggering mechanism; and taking the hybrid logic dynamic model as a prediction model to track and control the ship track. The invention can reduce unnecessary resource loss of ship control and improve control instantaneity on the premise of ensuring track control precision.
Description
Technical Field
The invention belongs to the technical field of ship navigation control, and particularly relates to a ship track tracking method based on event triggering and hybrid logic dynamic model.
Background
With the intelligent continuous lifting of ships, the research of ship motion control gradually becomes a hot spot, and the ship track tracking control is also widely focused as an important ship motion control mode, and with the development of diversification and complexity of water tasks, the requirements on the ship track tracking control are also higher and higher.
At present, control methods such as PID control, model predictive control, self-adaptive control and sliding mode control are proposed for ship track tracking control research, in order to eliminate the influence of external interference, a controller usually needs to frequently operate a propeller and a steering engine to ensure stable tracking of a target track, but in actual sailing driving, frequent operation is usually avoided to reduce unnecessary energy consumption and mechanical abrasion, in addition, in the track control process, the propeller and the steering engine have coupling action, and meanwhile, continuous change can increase the difficulty of track control and reduce the real-time performance of control.
At present, many methods are proposed for the field of ship track tracking control, research and development are carried out in open water areas, in the open water areas, interference such as ocean currents, sea waves and wind and changes of navigational speed and loading can have certain influence on ship navigation tracks, which means that ship drivers need to frequently operate propellers and rudders and have complex relations, so that the current research mostly takes force and moment as control inputs without considering the control process of the propellers, but a propeller rotating speed control system is a hybrid system formed by combining discrete systems and continuous systems, and large inertia of the propeller speed control process in actual navigation is ignored. Thus, the existing design method mainly has the following two defects: the model relationship in the control system is complex, which makes real-time calculation difficult and solving of the model difficult. Under the condition that the control system has uncertain models and external marine environment interference, the controller executing mechanism needs to perform frequent actions, and the service life of the executing mechanism is shortened.
Disclosure of Invention
The invention aims to provide a ship track tracking method based on an event triggering and hybrid logic dynamic model, which can reduce unnecessary resource loss of ship control and improve control instantaneity on the premise of ensuring track control accuracy.
In order to solve the technical problems, the technical scheme of the invention is as follows: the method for tracking the ship track based on the event triggering and the confounding logic dynamic model comprises the following steps:
s1, dividing rudder angles into gears, and constructing a kinetic model of ship propeller rotation speed and ship motion under different rudder angle gears by combining a ship MMG model;
s2, constructing definition of an event included angle, and setting an included angle threshold as an event trigger mechanism; the event included angle is an included angle between the ship speed direction and the target track point direction;
s3, constructing a hybrid logic dynamic model according to a ship MMG model, a dynamic model of ship propeller rotating speed and ship motion, an event included angle and an event trigger mechanism of the event included angle;
s4, taking the hybrid logic dynamic model as a prediction model to track and control the ship track.
The gear division of the rudder angle in S1 is specifically as follows:
according to actual navigation requirements, setting rudder angle gear g, wherein g epsilon {1,2,3,4}, and representing the gear g after coding by using logic variables as follows:
g(k)＝1+ξ 1 (k)+2ξ 2 (k)
wherein xi 1 (k),ξ 2 (k) Is a logic variable and ζ 1 (k)，ξ 2 (k) E {0,1}, each gear corresponds to a fixed rudder angle value.
The construction method of the kinetic model of the ship propeller rotating speed and the ship motion in the S1 comprises the following steps: based on a ship MMG model, combining divided rudder angle gears, using rudder angle values of different gears as model parameters, converting the ship MMG model into a dynamic model which takes the rotating speed of a propeller as single input and takes the track and the gesture of the ship as output, and obtaining the rotating speed of the propeller of the ship and the motion of the ship as follows:
wherein u, v and r respectively represent the longitudinal speed, the transverse speed and the heading angular speed of the ship, psi,
Respectively representing the bow direction and the roll angle, x and y respectively representing the transverse position and the longitudinal position of the ship, and delta and n respectively representing the rudder angle and the rotating speed of the ship propeller; u, L the ship's speed and length; x, Y, K, N the applied external force and moment: x represents the motion force of the ship body in the transverse direction, and comprises a plurality of factors such as turbulent flow resistance, wind resistance, frictional resistance and the like; y represents the motion force of the ship body in the longitudinal direction, and comprises a plurality of factors such as buoyancy, gravity, propulsion force and the like; k represents the motion moment of the ship body in the steering direction, and comprises various rudder force factors such as a side thruster, a control surface, a propeller and the like; n represents the motion moment of the ship body in the roll direction, and comprises factors such as a side thruster, a control surface, a propeller, earth attraction and the like; detm=m 22 ·m 33 ·m 44 -m 32 ·m 44 -m 42 ·m 33 ，m 11 ＝(m+m x )，m 22 ＝(m+m y )，m 32 ＝-m y ·I y ，m 42 ＝m y ·α y ，m 33 ＝(I x +J x )，m 44 ＝(I z +J z )；
m 11 、m 22 、m 33 、m 44 、m 32 、m 42 These coefficients represent the mass and moment of inertia of the rigid body in three dimensions: m is m 11 Representing the sum of the mass of the rigid body itself and the additional mass on the x-axis; m is m 22 Representing the sum of the mass of the rigid body itself and the additional mass on the y-axis; m is m 33 Representing inertia of a rigid body about the x-axisMoment, representing a measure of resistance to rotational movement of the rigid body about the axis; m is m 44 Representing the moment of inertia of the rigid body about the z-axis, which is a measure of the resistance of the rigid body to rotational movement about that axis, including the moment of inertia itself about that axis and the additional moment of inertia in the z-axis; m is m 32 Is the product of the additional mass on the y-axis and the distance of the mass from the centroid along the y-axis; m is m 42 Representing the product of the additional mass on the y-axis and the distance of the mass from the centroid along the z-axis.
The event triggering mechanism in S2 specifically comprises: setting the threshold value of the included angle to be 10 DEG, and when the time t epsilon t k ，t k+1 ) When the event trigger mechanism algorithm is expressed as:
τ(t k )＝(CB) -1 {-CF(γ(t k )，η q (t k ))}
wherein C is the weight matrix of the triggering condition,
γ(t k ) To the angle error value of the trigger time, t k For event trigger time, ++>
For the desired trajectory, when |γ (t k ) When the I is more than 10, the triggering condition is reached.
The hybrid logic dynamic model in S3 is specifically:
x(m+1)＝Ax(m)+B 1 u(m)+B 2 δ(m)+B 3 z(m)
y(m)＝Cx(m)+D 1 u(m)+D 2 δ(m)+D 3 z(m)
E 2 δ(m)+E 3 z(m)≤E 4 x(m)+E 1 u(m)+E 5
wherein A, B, C, D is matrix parameter, A is state transition matrix, describing system state evolution with time, B 1 、B 2 、B 3 All are input transition matrices, C is an output transition matrix describing the state of mapping the state to the output, D 1 、D 2 、D 3 Respectively represent the control input, disturbance input and the influence moment of the measurement input on the outputAn array; the rudder angle gear is used as discrete input, the rotating speed of the propeller is continuous input, in the following steps
Representing the system state, i.e. the ship motion state, y comprises a continuous output and a discrete output,/for>
Vector values for output; />
For controlled input, including successive instructions u c (m) and dyadic instruction u b (m); delta is an auxiliary binary variable,>
z is a continuous auxiliary variable, ">
x(m)＝[ζ(m),V c (m),n(m),F R (m),S r (m)] M M is the moment, ζ is the distance deviation between the actual position of the ship and the corresponding point of the expected track, V c Is the ship speed, n is the rotating speed of the propeller, F R Is a rudder angle instruction; s is S r For steering event-triggered mode, S when the angle is smaller than the event angle r An event is not triggered when the included angle is 0, the ship normally sails, and the ship is triggered when the included angle is larger than the set threshold value, at the moment S r 1.
And S4, introducing the hybrid logic dynamic model into the MPC controller as a prediction model, designing the MPC controller, and carrying out tracking control on the ship track.
The design mode of the MPC controller in S4 is as follows:
wherein N is the predicted step length in the controller, N C For controlling step length, and N is greater than or equal to N C 。
The method for tracking and controlling the ship track in the S4 is to solve quadratic optimization performance indexes, and is expressed as follows:
wherein u is the control quantity including rudder angle command F R The rotating speed instruction n, Q is an output weight matrix, and R is an input weight matrix;
solving the quadratic optimization performance index to obtain an optimal solution sequence of the ship control instruction at each moment, and taking the first element of the optimal control sequence as the control input at the current moment.
There is also provided a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps of the method as claimed in any one of the preceding claims when the computer program is executed.
A computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the method according to any of the preceding claims.
Compared with the prior art, the invention has the beneficial effects that:
the invention can reduce unnecessary resource loss of ship control and improve control instantaneity on the premise of ensuring track control precision; the control frequency of the rudder angle actuator is reduced, and the real-time performance of control calculation is improved; the model relation inside the control system is simplified, the real-time calculation is facilitated, and the model solving is simplified; the controller executing mechanism does not need to perform frequent actions, and the service life of the executing mechanism is prolonged.
Drawings
FIG. 1 is a system frame diagram of an embodiment of the present invention;
FIG. 2 is a schematic view of a navigation track coordinate system of a ship according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a dynamic flow of a hybrid logic dynamic model in an embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The technical scheme adopted by the invention is as follows: a ship track tracking control method based on event triggering and confounding logic dynamic model comprises the following steps:
s1, dividing rudder angles into gear positions, and constructing a dynamic model between the rotating speed of the ship propeller and the ship motion under different rudder angle gear positions by combining an MMG model (split mathematical model).
S2, defining an event included angle (an included angle between the ship speed direction and the target track point direction) and setting an included angle threshold as an event trigger mechanism.
S3, constructing a continuous/discrete relation model of tracking error, rudder angle gear and propeller rotating speed by combining a rudder angle gear switching trigger mechanism and a ship dynamics model under all gears, and converting the model into a hybrid logic dynamic model.
S4, taking the hybrid logic dynamic model as a prediction model, and designing the MPC controller to realize ship track tracking control.
According to the method, the rudder angle division of the S1 is specifically as follows:
according to actual navigation needs, rudder angle gears are set, ship operation gears are distinguished, the rudder angle division rules are applied to both the left rudder and the right rudder of ship operation, wherein g epsilon {1,2,3,4} represents the currently operated gear (each value of gear g has a corresponding rudder angle). The gear after encoding with logical variables can be expressed as:
g(k)＝1+ξ 1 (k)+2ξ 2 (k)
wherein xi 1 (k),ξ 2 (k) Is a logic variable and ζ 1 (k)，ξ 2 (k) E {0,1}. According to specific division, each gear corresponds to a fixed rudder angle value.
Based on an MMG model, combining divided rudder angle gears, and converting the MMG model into a ship dynamics model taking the rotating speed of a propeller as a single input and taking the track and the gesture of a ship as output by taking rudder angle values of different gears as model parameters:
for parameters in the ship dynamics model, wherein u, v and r respectively represent the longitudinal speed, the transverse speed and the heading angular speed of the ship, psi,
Respectively representing the bow direction and the roll angle, x and y respectively representing the transverse position and the longitudinal position of the ship, and delta and n respectively representing the rudder angle and the rotating speed of the ship propeller; u, L the ship's speed and length; x, Y, K, N the various external forces and moments to which the ship is subjected: x represents the motion force of the ship body in the transverse direction, and comprises a plurality of influencing factors such as turbulent flow resistance, wind resistance, frictional resistance and the like; y represents the motion force of the ship body in the longitudinal direction, and the motion force comprises a plurality of influencing factors such as buoyancy, gravity, propulsion force and the like; k represents the motion moment of the ship body in the steering direction, and comprises various rudder force influencing factors such as a side thruster, a control surface, a propeller and the like; n represents the motion moment of the ship body in the roll direction, and comprises various rudder force influencing factors such as a side thruster, a control surface, a propeller and the like, and factors such as earth attraction and the like; detm=m 22 ·m 33 ·m 44 -m 32 ·m 44 -m 42 ·m 33 ，m 11 ＝(m+m x )，m 22 ＝(m+m y )，m 32 ＝-m y ·I y ，m 42 ＝m y ·α y ，m 33 ＝(I x +J x )，m 44 ＝(I z +J z )；
m 11 、m 22 、m 33 、m 44 、m 32 、m 42 These coefficients represent the mass and moment of inertia of the rigid body in three dimensions: m is m 11 Representing the sum of the mass of the rigid body itself and the additional mass on the x-axis; m is m 22 Representing the sum of the mass of the rigid body itself and the additional mass on the y-axis; m is m 33 Representing the moment of inertia of the rigid body about the x-axis, representing a measure of the resistance to rotational movement of the rigid body about the axis; m is m 44 Representing the moment of inertia of the rigid body about the z-axis, which is a measure of the resistance of the rigid body to rotational movement about that axis, including the moment of inertia itself about that axis and the additional moment of inertia in the z-axis; m is m 32 Is the product of the additional mass on the y-axis and the distance of the mass from the centroid along the y-axis; m is m 42 Representing the product of the additional mass on the y-axis and the distance of the mass from the centroid along the z-axis. Therefore, the parameter values corresponding to different rudder angles are different, and different rudder angle gears also correspond to different ship dynamics models.
According to the method, the S2 event triggering mechanism specifically comprises the following steps:
for ship track tracking control, an included angle between the speed direction and a connecting line between the speed direction and a position of the ship and an expected track point is defined as an event included angle for triggering rudder angle gear control, and an included angle threshold value is set to be 10 degrees, wherein in fig. 2, a solid line is an actual track of the ship, and a dotted line is an expected track of the ship.
When t is E [ t ] k ，t k+1 ) When the event trigger control law is designed as follows:
τ(t k )＝(CB) -1 {-CF(γ(t k )，η q (t k ))}
wherein c is the weight matrix of the triggering condition,
γ(t k ) To the angle error value of the trigger time, t k Indicating event trigger time, ++>
Represents the desired trajectory when |gamma (t k ) When the I is more than 10, the triggering condition is reached.
According to the method, the S3 hybrid logic dynamic model specifically comprises the following steps:
x(m+1)＝Ax(m)+B 1 u(m)+B 2 δ(m)+B 3 z(m)
y(m)＝Cx(m)+D 1 u(m)+D 2 δ(m)+D 3 z(m)
E 2 δ(m)+E 3 z(m)≤E 4 x(m)+E 1 u(m)+E 5
wherein A, B, C, D is matrix parameter, A is state transition matrix, describing system state evolution with time, B 1 、B 2 、B 3 All are input transition matrices, C is an output transition matrix describing the state of mapping the state to the output, D 1 、D 2 、D 3 Respectively representing the influence matrix of control input, disturbance input and measurement input on output; the rudder angle gear is used as discrete input, the rotating speed of the propeller is continuous input, in the following steps
Representing the system state, i.e. the ship motion state, y comprises a continuous output and a discrete output,/for>
Vector values for output; />
For controlled input, including successive instructions u c (m) and dyadic instruction u b (m); delta is an auxiliary binary variable,>
z is a continuous auxiliary variable, ">
x(m)＝ζ(m),V c (m),n(m),F R (m),S r (m)] M M is the moment, ζ is the distance deviation between the actual position of the ship and the corresponding point of the expected track, V c Is the ship speed, n is the rotating speed of the propeller, F R Is a rudder angle instruction; s is S r For steering event-triggered mode, S when the angle is smaller than the event angle r An event is not triggered when the included angle is 0, the ship normally sails, and the ship is triggered when the included angle is larger than the set threshold value, at the moment S r 1.
According to the above method, the MPC controller of S4 specifically includes:
wherein, the predicted step length in the controller is N, and the control step length is N C And N is greater than or equal to N C 。
The MPC control of the S4 specifically comprises solving of quadratic optimization performance indexes:
wherein ζ is the distance deviation between the actual position of the ship and the corresponding point of the expected track, u is the control quantity including rudder angle command F R And a rotational speed command n, S r And if the trigger is not the trigger of the gear switching, the trigger is 0, the trigger is 1, Q is an output weight matrix, and R is an input weight matrix.
According to the method, the ship can obtain the optimal solution sequence of the ship control instruction at each moment by solving the quadratic optimization performance index, and the first element of the optimal control sequence is used as the control input at the current moment, so that the ship track tracking control can be realized.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (10)
1. The method for tracking the ship track based on the event triggering and hybrid logic dynamic model is characterized by comprising the following steps of:
s1, dividing rudder angles into gears, and constructing a kinetic model of ship propeller rotation speed and ship motion under different rudder angle gears by combining a ship MMG model;
s2, constructing definition of an event included angle, and setting an included angle threshold as an event trigger mechanism; the event included angle is an included angle between the ship speed direction and the target track point direction;
s3, constructing a hybrid logic dynamic model according to a ship MMG model, a dynamic model of ship propeller rotating speed and ship motion, an event included angle and an event trigger mechanism of the event included angle;
s4, taking the hybrid logic dynamic model as a prediction model to track and control the ship track.
2. The method for tracking the ship track based on the event triggering and confounding logic dynamic model according to claim 1, wherein the gear division of the rudder angle in S1 is specifically as follows:
according to actual navigation requirements, setting rudder angle gear g, wherein g epsilon {1,2,3,4}, and representing the gear g after coding by using logic variables as follows:
g(k)＝1+ξ 1 (k)+2ξ 2 (k)
wherein xi 1 (k)，ξ 2 (k) Is a logic variable and ζ 1 (k)，ξ 2 (k) E {0,1}, each gear corresponds to a fixed rudder angle value.
3. The method for tracking the ship track based on the event triggering and confounding logic dynamic model according to claim 1, wherein the method for constructing the dynamic model of the ship propeller rotating speed and the ship motion in the S1 is as follows: based on a ship MMG model, combining divided rudder angle gears, using rudder angle values of different gears as model parameters, converting the ship MMG model into a dynamic model which takes the rotating speed of a propeller as single input and takes the track and the gesture of the ship as output, and obtaining the rotating speed of the propeller of the ship and the motion of the ship as follows:
wherein u, v and r respectively represent the longitudinal speed, the transverse speed and the heading angular speed of the ship, psi,
Respectively representing the bow direction and the roll angle, x and y respectively representing the transverse position and the longitudinal position of the ship, and delta and n respectively representing the rudder angle and the rotating speed of the ship propeller; u, L the ship's speed and length; x, Y, K, N the applied external force and moment are as follows: x represents the motion force of the ship body in the transverse direction, including turbulence resistance, wind resistance and friction resistance; y represents the motion force of the ship body in the longitudinal direction, including buoyancy, gravity and propelling force; k represents the motion moment of the ship body in the steering direction, and comprises rudder force born by a side thruster, a control surface and a propeller; n represents the motion moment of the ship body in the roll direction, and comprises rudder force and earth attraction of a side thruster, a control surface and a propeller; detm=m 22 ·m 33 ·m 44 -m 32 2 ·m 44 -m 42 2 ，m 33 ，m 11 ＝(m+m x )，m 22 ＝(m+m y )，m 32 ＝-m y ·I y ，m 42 ＝m y ·α y ，m 33 ＝(I x +J x )，m4 4 ＝(I z +J z )；m 11 、m 22 、m 33 、m 44 、m 32 、m 42 Representing the mass and moment of inertia of a rigid body in three-dimensional space, specifically: m is m 11 Representing the sum of the mass of the rigid body itself and the additional mass on the x-axis; m is m 22 Representing the sum of the mass of the rigid body itself and the additional mass on the y-axis; m is m 33 Representing the moment of inertia of the rigid body about the x-axis, representing a measure of the resistance to rotational movement of the rigid body about the axis; m is m 44 Representing the moment of inertia of the rigid body about the z-axis as a measure of the resistance of the rigid body to rotational movement about the axis, including the moment of inertia itself about the axis and additional moment of inertia in the z-axis; m is m 32 For attachment on the y-axisAdding the product of the mass and the distance of the mass from the centroid along the y-axis; m is m 42 Representing the product of the additional mass on the y-axis and the distance of the mass from the centroid along the z-axis.
4. The method for tracking the ship track based on the event triggering and confounding logic dynamic model according to claim 1, wherein the event triggering mechanism in S2 specifically comprises: setting the threshold value of the included angle to be 10 DEG, and when the time t epsilon t k ，t k+1 ) When the event trigger mechanism algorithm is expressed as:
τ(t k )＝(CB) -1 {-CF(γ(t k )，η q (t k ))}
wherein C is the weight matrix of the triggering condition,
γ(t k ) To the angle error value of the trigger time, t k For event trigger time, ++>
For the desired trajectory, when |γ (t k ) When the I is more than 10, the triggering condition is reached.
5. The method for tracking a ship track based on an event trigger and hybrid logic dynamic model according to claim 1, wherein the hybrid logic dynamic model in S3 specifically comprises:
x(m+1)＝Ax(m)+B 1 u(m)+B 2 δ(m)+B 3 z(m)
y(m)＝Cx(m)+D 1 u(m)+D 2 δ(m)+D 3 z(m)
E 2 δ(m)+E 3 z(m)≤E 4 x(m)+E 1 u(m)+E 5
wherein A, B, C, D is a matrix parameter, A is a state transition matrix, and describes the evolution condition of the system state along with time; b (B) 1 、B 2 、B 3 Are input transfer matrices; c is an output transition matrix, describing the state mapping to the output; d (D) 1 、D 2 、D 3 Respectively representing the influence matrix of control input, disturbance input and measurement input on output; the rudder angle gear is used as discrete input, the rotating speed of the propeller is continuous input,
representing the system state, i.e. the ship motion state, y comprises a continuous output and a discrete output,/for>
Vector values for output; />
For controlled input, including successive instructions u c (m) and dyadic instruction u b (m); delta is an auxiliary binary variable,>
z is a continuous auxiliary variable, ">
x(m)＝[ζ(m)，V c (m)，n(m)，F R (m)，S r (m)] M M is the moment, ζ is the distance deviation between the actual position of the ship and the corresponding point of the expected track, V c Is the ship speed, n is the rotating speed of the propeller, F R Is a rudder angle instruction; s is S r For steering event-triggered mode, S when the angle is smaller than the event angle r When the ship is 0, the ship does not trigger an event, and the ship normally sails; when the included angle is larger than the set threshold, the trigger event is the S r 1.
6. The method for tracking a ship track based on an event trigger and a hybrid logic dynamic model according to claim 5, wherein the hybrid logic dynamic model is imported as a prediction model into an MPC controller and the MPC controller is designed to perform tracking control on the ship track in S4.
7. The method for tracking a ship track based on an event triggering and confounding logic dynamic model according to claim 6, wherein the design manner of the MPC controller in S4 is as follows:
wherein N is the predicted step length in the controller, N C For controlling step length, and N is greater than or equal to N C 。
8. The method for tracking a ship track based on an event triggering and confounding logic dynamic model according to claim 7, wherein the method for tracking and controlling the ship track in S4 is to solve a quadratic optimization performance index, which is expressed as:
wherein u is the control quantity including rudder angle command F R The rotating speed instruction n, Q is an output weight matrix, and R is an input weight matrix;
solving the quadratic optimization performance index to obtain an optimal solution sequence of the ship control instruction at each moment, and taking the first element of the optimal control sequence as the control input at the current moment.
9. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the method according to any of claims 1-8 when the computer program is executed.
10. A computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the method according to any of claims 1-8.
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