Method for determining a sail path of at least one vessel of a fleet of vessels, corresponding device, computer program product and non-transitory computer-readable carrier medium

A method comprising:

• determining a sail path of a fleet comprising at least two vessels on a map representative of a marine geographic area, to perform a turn between a start point and an end point, each vessel having a turn radius, which turn radius defines the smallest circle the vessel is able to sail, the start point, respectively the end point, being associated with a start curvilinear geometric form and an end curvilinear geometric form, said start and end curvilinear geometric forms comprising a combination of at least a circle and/or an ellipse which each has a predefined radius of curvature larger than or equal to said turn radius, the sail path being curvilinear and composed of arc segments and straight segments and comprising at least one segment of arc of the start curvilinear geometric form and at least one segment of arc of the end curvilinear geometric form, wherein determining the sail path comprises acts of:
• detecting, in the map, at least one obstacle likely to interfere with said fleet of vessels
• and for said fleet of vessels:
• encompassing, for each vessels, said at least one detected obstacle into a curvilinear geometric form consisting of an intermediate circle or ellipse or of a combination of intermediate circle(s) and/or ellipse(s) each having a radius of curvature, at every point of the circumference of said intermediate curvilinear geometric form, that is greater or equal to said turn radius of each vessel,
• determining the sail paths of the fleet vessels by minimizing, under a set of predefined constraints, a sum of individual cost functions, each individual cost function being associated with a distinct vessel of the fleet, and comprising:
• a first term representative of the length of arc segments making up the sail path to be determined, taking into account the start and end curvilinear geometric forms and the intermediate curvilinear geometric form into which is encompassed said at least one detected obstacle,
• a second term representative of the length of straight segments making up the sail path to be determined, taking into account the start and end curvilinear geometric forms and the intermediate curvilinear geometric form into which is encompassed said at least one detected obstacle.

A non-transitory computer-readable medium storing a computer program product comprising program code instructions for implementing a method, when said instructions are executed on a computer or a processor of a vessel of a fleet of at least one vessel, the method comprising:

• determining by the computer or processor a sail path of the vessel on a map representative of a marine geographic area, to perform a turn between a start point and an end point, each vessel having a turn radius, which turn radius defines the smallest circle the vessel is able to sail, the start point, respectively the end point, being associated with a start curvilinear geometric form and an end curvilinear geometric form, respectively, said start and end curvilinear geometric forms comprising a combination of at least a circle and/or an ellipse which each has a predefined radius of curvature larger than or equal to said turn radius, the sail path being curvilinear and composed of arc segments and straight segments and comprising at least one segment of arc of the start curvilinear geometric form and at least one segment of arc of the end curvilinear geometric form,
• wherein determining a sail path comprises acts of:
• receiving the map by the computer or processor:
• detecting, in the map, at least one obstacle likely to interfere with said at least one vessel:
• and for a given vessel:
• encompassing said at least one detected obstacle into an intermediate curvilinear geometric form consisting of a circle or ellipse or of a combination of circle(s) and/or ellipse(s) each having a radius of curvature, at every point of the circumference of said intermediate curvilinear geometric form, that is greater or equal to said turn radius of said given vessel,
• determining a sail path of said at least one vessel by minimizing, under a set of predefined constraints, an individual cost function comprising:
• a first term representative of the length of arc segments making up the sail path to be determined, taking into account the start and end curvilinear geometric forms and the intermediate curvilinear geometric form into which is encompassed said at least one detected obstacle.
• a second term representative of the length of straight segments making up the sail path to be determined, taking into account the start and end curvilinear geometric forms and the intermediate curvilinear geometric form into which is encompassed said at least one detected obstacle.

A device for determining a sail path of at least one vessel on a map representative of a marine geographic area, to perform a turn between a start point and an end point, each vessel having a turn radius, which turn radius defines the smallest circle the vessel is able to sail, the start point, respectively the end point, being associated with a start curvilinear geometric form and an end curvilinear geometric form, respectively, said start and end curvilinear geometric forms comprising a combination of at least a circle and/or an ellipse which each has a predefined radius of curvature larger than or equal to said turn radius, the sail path being curvilinear and composed of arc segments and straight segments and comprising at least one segment of arc of the start curvilinear geometric form and at least one segment of arc of the end curvilinear geometric form, wherein the device comprises:

• means for detecting, in the map, at least one obstacle likely to interfere with said at least one vessel;
• and for a given vessel:
• means for encompassing said at least one detected obstacle into an intermediate curvilinear geometric form consisting of a circle or ellipse or of a combination of circle(s) and/or ellipse(s) each having a radius of curvature, at every point of the circumference of said intermediate curvilinear geometric form, that is greater or equal to said turn radius of said given vessel,
• means for determining a sail path of said at least one vessel by minimizing, under a set of predefined constraints, an individual cost function comprising:
• a first term representative of the length of arc segments making up the sail path to be determined, taking into account the start and end curvilinear geometric forms and the intermediate curvilinear geometric form into which is encompassed said at least one detected obstacle,
• a second term representative of the length of straight segments making up the sail path to be determined, taking into account the start and end curvilinear geometric forms and the intermediate curvilinear geometric form into which is encompassed said at least one detected obstacle.

A device for determining a sail path of a fleet comprising at least two vessels on a map representative of a marine geographic area, to perform a turn between a start point and an end point, each vessel having a turn radius, which turn radius defines the smallest circle the vessel is able to sail, the start point, respectively the end point, being associated with a start curvilinear geometric form and an end curvilinear form, respectively, said start and end curvilinear geometric forms comprising a combination of at least a circle and/or an ellipse which each has a predefined radius of curvature larger than or equal to said turn radius, the sail path being curvilinear and composed of arc segments and straight segments and comprising at least one segment of arc of the start curvilinear geometric form and at least one segment of arc of the end curvilinear geometric form, wherein the device comprises:

• means for detecting, in the map, at least one obstacle likely to interfere with said fleet of vessels
• and for said fleet of vessels:
• means for encompassing, for each vessels, said at least one detected obstacle into a curvilinear geometric form consisting of an intermediate circle or ellipse or of a combination of intermediate circle(s) and/or ellipse(s) each having a radius of curvature, at every point of the circumference of said intermediate curvilinear geometric form, that is greater or equal to said turn radius of each vessel,
• means for determining the sail paths of the fleet vessels by minimizing, under a set of predefined constraints, a sum of individual cost functions, each individual cost function being associated with a distinct vessel of the fleet, and comprising:
• a first term representative of the length of arc segments making up the sail path to be determined, taking into account the start and end curvilinear geometric forms and the intermediate curvilinear geometric form into which is encompassed said at least one detected obstacle,
• a second term representative of the length of straight segments making up the sail path to be determined, taking into account the start and end curvilinear geometric forms and the intermediate curvilinear geometric form into which is encompassed said at least one detected obstacle.