Method and arrangement for determining a position and/or an alignment of a movable object of an arrangement of objects

An arrangement for determining a position of a movable object of an arrangement of objects, the arrangement comprising:

• at least one capture structure arrangeable at the movable object or at an object that is not moved along with the movable object;
• a capturing device configured to optically capture the at least one capture structure and to thereby obtain capture information;
• the at least one capture structure having a profile of an optical property that varies along a surface of the at least one capture structure;
• the optical property being expressible by a corresponding numerical value in accordance with a specified mapping, at least at each location along a surface direction of the at least one capture structure, and said optical property being varied such that the profile of the optical property that varies along the surface corresponds to a progression of numerical values with a plurality of local maxima and a plurality of local minima on an ordered scale of the numerical values, which is interpretable as a first mathematical function of the location;
• the optical property varying along the surface such that:
• the plurality of local maxima or all of the local maxima are values of a second mathematical function of the location along the surface direction, which has an absolute maximum corresponding to a maximum value of the optical property or an absolute minimum corresponding to a minimum value of the optical property within a local region with at least three local maxima of the first mathematical function of the location, and/or
• the plurality of local minima or all of the local minima are values of a third mathematical function of the location along the surface direction, which has the absolute maximum corresponding to the maximum value of the optical property or the absolute minimum corresponding to the minimum value of the optical property within the local region with at least three local minima of the first mathematical function of the location;
• an evaluation device, wherein the evaluation device or the capturing device is configured to assign to the optical property captured by the capture information corresponding numerical values in accordance with the specified mapping such that a progression of the numerical values has the plurality of local maxima and the plurality of local minima and corresponds to the first mathematical function of the location;
• and
• the evaluation device being configured to determine the position of the movable object in respect of the surface direction by performing a frequency analysis of the progression of the numerical values of the second mathematical function of the location and/or the third mathematical function of the location.

A capture structure for determining a position of a movable object of an arrangement of objects by virtue of the capture structure being connected either to the movable object or to a capturing device that is not moved along with the movable object, the capture structure being captured and corresponding capture information in respect of the position of the movable object being evaluated, the capture structure comprising:

• a profile of an optical property that varies along a surface of the capture structure;
• the optical property being expressible by a corresponding numerical value in accordance with a specified mapping, at least at each location along a surface direction of the capture structure, and the optical property being varied such that the profile of the optical property that varies along the surface corresponds to a progression of numerical values with a plurality of local maxima and a plurality of local minima on an ordered scale of the numerical values, which is interpretable as a first mathematical function of the location;
• the optical property varying along the surface such that:
• the plurality of local maxima or all of the local maxima are values of a second mathematical function of the location along the surface direction, which has an absolute maximum at a unique location corresponding to a maximum value of the optical property or an absolute minimum at the unique location corresponding to a minimum value of the optical property within a local region with at least three local maxima of the first mathematical function of the location, and/or
• the plurality of local minima or all of the local minima are values of a third mathematical function of the location along the surface direction, which has the absolute maximum at a first unique location corresponding to the maximum value of the optical property or the absolute minimum at a second unique location corresponding to the minimum value of the optical property within the local region with at least three local minima of the first mathematical function of the location.

A method for producing a capture structure which serves to determine a position of a movable object of an arrangement of objects by virtue of the capture structure being connected either to the movable object or to a capturing device that is not moved along with the movable object, the capture structure being captured and corresponding capture information in respect of the position of the movable object being evaluated, the capture structure being configured such that (i) the capture structure has a profile of an optical property that varies along a surface of the capture structure, and (ii) the optical property is expressible by a corresponding numerical value in accordance with a specified mapping, at least at each location along a surface direction of the capture structure, and the optical property is varied such that the profile of the optical property that varies along the surface corresponds to a progression of numerical values with a plurality of local maxima and a plurality of local minima on an ordered scale of the numerical values, which is interpretable as a first mathematical function of the location, the optical property varies along the surface such that (iii) the plurality of local maxima or all of the local maxima are values of a second mathematical function of the location along the surface direction, which has an absolute maximum corresponding to a maximum value of the optical property or an absolute minimum corresponding to a minimum value of the optical property within a local region with at least three local maxima of the first mathematical function of the location, and/or (iv) the plurality of local minima or all of the local minima are values of a third mathematical function of the location along the surface direction, which has the absolute maximum corresponding to the maximum value of the optical property or the absolute minimum corresponding to the minimum value of the optical property within the local region with at least three local minima of the first mathematical function of the location, the method comprising:

• producing the capture structure by at least one of:
• digital printing methods,
• methods of partial material removal of surface material, and
• methods in which material is applied to the surface or generated by displaying the capture structure on a display or projecting the capture structure on the surface.

A method for producing an arrangement which serves to determine a position and/or alignment of a movable object of an arrangement of objects, the method comprising:

• equipping the arrangement with at least one capture structure, the at least one capture structure serving to be arranged at the movable object or at an object that is not moved along with the movable object;
• equipping the arrangement with a capturing device for capturing the at least one capture structure or for capturing at least one of the capture structures;
• the capturing device being configured to optically capture the at least one capture structure and to thereby obtain capture information;
• the at least one capture structure having a profile of an optical property that varies along a surface of the at least one capture structure;
• the optical property being expressible by a corresponding numerical value in accordance with a specified mapping, at least at each location along a surface direction of the at least one capture structure, and the optical property being varied such that the profile of the optical property that varies along the surface corresponds to a progression of numerical values with a plurality of local maxima and a plurality of local minima on an ordered scale of the numerical values, which is interpretable as a first mathematical function of the location;
• the optical property varying along the surface such that:
• the plurality of local maxima or all of the local maxima are values of a second mathematical function of the location along the surface direction, which has an absolute maximum corresponding to a maximum value of the optical property or an absolute minimum corresponding to a minimum value of the optical property within a local region with at least three local maxima of the first mathematical function of the location, and/or
• the plurality of local minima or all of the local minima are values of a third mathematical function of the location along the surface direction, which has the absolute maximum corresponding to the maximum value of the optical property or the absolute minimum corresponding to the minimum value of the optical property within the local region with at least three local minima of the first mathematical function of the location;
• equipping the arrangement with an evaluation device, the evaluation device or the capturing device being configured to assign to the optical property captured by the capture information corresponding numerical values in accordance with the specified mapping such that a progression of the numerical values has the plurality of local maxima and the plurality of local minima and corresponds to the first mathematical function of the location;
• and
• configuring the evaluation device to determine the position of the movable object in respect of the surface direction by performing a frequency analysis of the progression of the numerical values of the second mathematical function of the location and/or the third mathematical function of the location.