Patent Publication Number: US-10308039-B2

Title: System for printing images on a surface and method thereof

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation-in-part application of and claims priority to pending U.S. application Ser. No. 15/244,967 filed on Aug. 23, 2016, and entitled AUTOMATED SYSTEM AND METHOD FOR PRINTING IMAGES ON A SURFACE, which is a divisional application of and claims priority to U.S. application Ser. No. 14/726,387 filed on May 29, 2015, now U.S. Pat. No. 9,452,616 issued on Sep. 27, 2016, and entitled SYSTEM AND METHOD FOR PRINTING AN IMAGE ON A SURFACE, the entire contents of each one of the above-referenced applications being expressly incorporated by reference herein. 
    
    
     FIELD 
     The present disclosure relates generally to coating application systems and, more particularly, to an automated system and method of printing images on a surface using a robotic 
     BACKGROUND 
     The painting of an aircraft is a relatively challenging and time-consuming process due to the wide range of dimensions, the unique geometry, and the large amount of surface area on an aircraft. For example, the wings protruding from the fuselage can interfere with the painting process. The height of the vertical tail above the horizontal tail can present challenges in accessing the exterior surfaces of the vertical tail. Adding to the time required to paint an aircraft are complex paint schemes that may be associated with an aircraft livery. In this regard, the standard livery of an airline may include images or designs with complex geometric shapes and color combinations and may include the name and logo of the airline which may be applied to different locations of the aircraft such as the fuselage, the vertical tail, and the engine nacelles. 
     Conventional methods of painting an aircraft require multiple steps of masking, painting, and demasking. For applying an aircraft livery with multiple colors, it may be necessary to perform the steps of masking, painting, and demasking for each color in the livery and which may add to the overall amount of time required to paint the aircraft. In addition, the aircraft livery must be applied in a precise manner to avoid gaps that may otherwise expose a typically-white undercoat which may detract from the overall appearance of the aircraft. Furthermore, the process of applying paint to the aircraft surfaces must be carried out with a high level of control to ensure an acceptable level of coating thickness to meet performance (e.g., weight) requirements. 
     As can be seen, there exists a need in the art for a system and method for painting an aircraft including applying complex and/or multi-colored images in a precise, cost-effective, and timely manner. 
     SUMMARY 
     The above-noted needs associated with aircraft painting are specifically addressed and alleviated by the present disclosure which provides a system for printing an image on a surface using a robot having at least one arm. A printhead may be mounted to the arm and may be movable by the arm over a surface along a rastering path while printing an image slice on the surface. The image slice may have opposing side edges. The printhead may be configured to print the image slice with an image gradient band along at least one of opposing side edges wherein an image intensity within the image gradient band decreases from an inner portion of the image gradient band toward the side edge. 
     Also disclosed is a system for printing an image comprising a robot having at least one arm and a printhead mounted to the arm. The printhead may be movable by the arm over a surface along a rastering path while printing a new image slice on the surface. The system may include a reference line printing mechanism configured to print a reference line on the surface when printing the new image slice. The system may include a reference line sensor configured to sense the reference line of an existing image slice and transmit a signal (e.g., a path-following-error signal) to the robot causing the arm to adjust the printhead such that a side edge of the new image slice is aligned with the side edge of the existing image slice. 
     In addition, disclosed is a method of printing an image on a surface. The method may include positioning an arm of a robot adjacent to a surface. The arm may have a printhead mounted to the arm. The method may further include moving, using the arm, the printhead over the surface along a rastering path while printing an image slice on the surface. In addition, the method may include printing an image gradient band along at least one side edge of the image slice when printing the image slice. The image gradient band may have an image intensity that decreases along a direction toward the side edge. 
     A further method of printing an image on a surface may include printing, using a printhead mounted to an arm of a robot, a new image slice on the surface while moving the printhead over the surface along a rastering path. The method may additionally include printing a reference line on the surface when printing the new image slice. The method may also include sensing, using a reference line sensor, the reference line of an existing image slice while printing the new image slice. Furthermore, the method may include adjusting the lateral position of the new image slice based on a sensed position of the reference line in a manner aligning a side edge of the new image slice with the side edge of the existing image slice. 
     In a further example, the system for printing the image includes a robot, a printhead, a laser device, and a reference line sensor. The robot has at least one arm. The printhead is mounted to the arm and is movable by the arm over a surface along a rastering path while printing a new image slice over the surface. The laser device is configured to etch, during printing of the new image slice, a reference line into either the new image slice or, more preferably, into the basecoat at a location adjacent to the new image slice. The reference line sensor is configured to sense the reference line of an existing image slice and transmit to the robot a signal (e.g., a path-following-error signal) representing the magnitude of the error in the position of the printhead relative to the reference line. The system may include a position servo loop for continuously adjusting the printhead in a manner such that a side edge of the new image slice is maintained in alignment with the side edge of the existing image slice. 
     In another example, the system includes a high-bandwidth actuator coupling an inkjet printhead to an end of the arm of the robot. The inkjet printhead is movable by the arm over a surface along a rastering path while printing a new image slice over the surface. The laser device is configured to etch, during printing of the new image slice, a reference line into either the new image slice or into a basecoat at a location adjacent to the new image slice. The system further includes a camera configured to sense the reference line of an existing image slice and transmit a signal (e.g., a path-following-error signal) to the robot resulting in a correction command to the high-bandwidth actuator to adjust the inkjet printhead in a manner such that the side edge of the new image slice is maintained in alignment with the side edge of the existing image slice. 
     Also disclosed is a method of printing an image on a surface. The method includes printing, using a printhead mounted to an arm of a robot, a new image slice on the surface while moving the printhead over the surface along a rastering path. The method additionally includes etching, using a laser device, a reference line into either the new image slice or into a basecoat while printing the new image slice. The method further includes sensing, using a reference line sensor, the reference line of an existing image slice while printing the new image slice. Additionally, the method includes adjusting, using a controller, the printhead based on a sensed position of the reference line in a manner maintaining alignment of a side edge of the new image slice with the side edge of the existing image slice. 
     The features, functions and advantages that have been discussed can be achieved independently in various embodiments of the present disclosure or may be combined in yet other embodiments, further details of which can be seen with reference to the following description and drawings below. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other features of the present disclosure will become more apparent upon reference to the drawings wherein like numbers refer to like parts throughout and wherein: 
         FIG. 1  is a block diagram of an example of an image forming system; 
         FIG. 2  is perspective view of an aircraft surrounded by a plurality of gantries supporting one or more image forming systems for printing one or more images on the aircraft; 
         FIG. 3  is a perspective view of the aircraft showing one of the gantries positioned adjacent to a vertical tail and supporting an image forming system for printing an image on the vertical tail; 
         FIG. 4  is an end view of the aircraft showing image forming systems positioned on opposite sides of the aircraft; 
         FIG. 5  is a perspective view of a robot taken along line  5  of  FIG. 4  and illustrating the robot mounted to a crossbeam of a gantry and having a printhead mounted on an arm of the robot; 
         FIG. 6  is a side view of the image forming system taken along line  6  of  FIG. 4  and illustrating the printhead printing an image on the vertical tail; 
         FIG. 7  is a plan view of an example of a printhead being moved along a rastering path to form an image slice having an image gradient band overlapping the image gradient band of an adjacent image slice; 
         FIG. 8  is a sectional view of a printhead taken along line  8  of  FIG. 7  and illustrating overlapping image gradient bands of the image slices printed by the printhead; 
         FIG. 9  is a magnified view of a portion of a printhead taken along line  9  of  FIG. 8  and showing progressively increasing droplet spacings as may be ejected by active nozzles to form an image gradient band; 
         FIG. 10  is a magnified view of a portion of a printhead showing progressively decreasing droplet sizes as may be ejected by the nozzles to form an image gradient band; 
         FIG. 11  is a diagrammatic sectional view of adjacent image slices with overlapping image gradient bands; 
         FIG. 12  is a plan view of the adjacent image slices of  FIG. 11  showing the overlapping image gradient bands; 
         FIG. 13  is an example of a printhead printing a reference line while printing a new image slice; 
         FIG. 14  is a sectional view taken along line  14  of  FIG. 13  and illustrating a printhead including a reference line printing mechanism and one or more reference line sensors for sensing the reference line of an existing image slice; 
         FIG. 15  is a magnified view taken long line  15  of  FIG. 14  and showing one of the nozzles of the printhead printing the reference line while the remaining nozzles of the printhead print the image slice; 
         FIG. 16  is a magnified view of an example of a printhead having a reference line sensor for sensing the reference line of an existing image slice; 
         FIG. 17  is a side view of an example of a robot having one or more high-bandwidth actuators coupling the printhead to an arm of the robot; 
         FIG. 18  is a side view of an example of a plurality of high-bandwidth actuators coupling a printhead to an arm of a robot; 
         FIG. 19  is a side view of the printhead after repositioning by the high-bandwidth actuators into alignment with the reference line and reorientation of the printhead face parallel to the surface; 
         FIG. 20  is a perspective view of an example of a delta robot having a plurality of high-bandwidth actuators coupling the printhead to an arm of a robot; 
         FIG. 21  is a flowchart having one or more operations included in method of printing an image on a surface wherein the parallel image slices each have one or more image gradient bands along the side edges of the image slices; 
         FIG. 22  is a flowchart having one or more operations included in a method of printing an image on a surface wherein the image slices have a reference line for aligning a new image slice with an existing image slice; 
         FIG. 23  is a further example of an image forming system in which the printhead includes one or more laser devices for etching a reference line into a basecoat or into a new image slice while printing each new image slice; 
         FIG. 24  is a plan view of the example of  FIG. 23  and illustrating the printhead printing a new image slice while tracking a reference line previously etched into the existing image slice by the laser device and while etching a reference line into the new image slice; 
         FIG. 25  is a sectional view taken along line  25  of  FIG. 24  and illustrating the printhead having one or more position sensors, one or more laser devices, and one or more reference line sensors for sensing the reference line etched by the laser device; 
         FIG. 26  is a magnified view taken along line  26  of  FIG. 25  and showing one of the reference line sensors configured as a camera for detecting variations in specular reflectivity of the surface of the new image slice during illumination of the reference line and surrounding area by a light source coupled to the printhead; 
         FIG. 27  is a magnified view taken along line  27  of  FIG. 25  and showing an example of a laser device for etching a reference line into a new image slice during printing of the new image slice by the printhead; 
         FIG. 28  is a plan view of an example of a printhead in which the laser device is configured to etch the reference line into a basecoat covering the surface onto which the new image slice is printed; 
         FIG. 29  is a sectional view taken along line  29  of  FIG. 28  and illustrating a laser device etching the reference line into the basecoat at a location immediately adjacent to a side edge of the new image slice; 
         FIG. 30  is a magnified view of a portion of a new image slice showing the reference line etched as a series of line segments forming an encoding pattern representing information regarding the image being printed; and 
         FIG. 31  is a flowchart of operations included in a method of printing an image on a surface using a printhead having a laser device for etching a reference line into either the new image slice or into a basecoat. 
     
    
    
     DETAILED DESCRIPTION 
     Referring now to the drawings wherein the showings are for purposes of illustrating various embodiments of the present disclosure, shown in  FIG. 1  is a block diagram of an example of an image forming system  200  as may be implemented for robotically (e.g., automatically or semi-automatically) printing an image  400  (e.g.,  FIGS. 2, 3, 6, 23 ) on a surface  102 . The system  200  includes a robot  202  (a robotic mechanism) and/or at least one arm (e.g., a first and second arm  210 ,  212 ). The printhead  300  may be mounted on an arm (e.g., the second arm  212 ). In some examples, the system  200  may include one or more high-bandwidth actuators  250  (e.g.,  FIGS. 17-20 ) coupling the printhead  300  to the end  214  ( FIG. 5 ) of the arm. As described below, such high-bandwidth actuators  250  may provide precise and rapid control over the position and orientation of the printhead  300  during printing of an image slice  404 . 
     The printhead  300  may be configured as an inkjet printhead having a plurality of nozzles  308  (e.g.,  FIGS. 8-10, 14-15, 25-27, and 29 ) or orifices for ejecting droplets  330  ( FIGS. 9-10 ) of ink, paint, or other fluids or colorants onto a surface  102  to form an image  400 . The inkjet printhead  300  may be configured as a thermal inkjet printer, a piezoelectric printer, or a continuous printer. However, the printhead  300  may be provided in other configurations such as a dot matrix printer or other printer configurations capable of printing an image  400  on a surface  102 . 
     The image forming system  200  prints image slices  404  on a surface  102  along a series of parallel rastering paths  350  (e.g.,  FIGS. 7, 13, 24, 28 ). The parallel image slices  404  may collectively form an image  400 . In one example, the printhead  300  may print an image slice  404  in overlapping relation to an adjacent image slice  404 . In this regard, the printhead  300  may be configured to print an image slice  404  with an image gradient band  418  along at least one side edge  416  ( FIG. 6 ) of the image slice  404 . The image gradient band  418  of one image slice  404  may overlap the image gradient band  418  of an adjacent image slice  404 . The image intensity within an image gradient band  418  may decrease along the direction transverse to the direction of the rastering path  350 . By overlapping the image gradient bands  418  of adjacent image slices  404 , gaps in the image  400  may be prevented. In the present disclosure, the image intensity within overlapping image gradient bands  418  may result in a substantially uniform image gradient across the width of an image  400  such that the overlaps may be visually imperceptible. In one example, the image intensity within the overlapping image gradient bands  418  may be substantially equivalent to the image intensity within an inner portion  414  of each image slice  404 . 
     In another example of the image forming system  200 , the printhead  300  may include a reference line printing mechanism  320  that may print (e.g.,  FIGS. 13-16 ) or etch (e.g.,  FIGS. 23-30 ) a reference line  322  during the printing of an image slice  404 . For example, a reference line  322  may be printed ( FIGS. 13-16 ) or etched ( FIGS. 23-30 ) along a side edge  416  of an image slice  404 . The printhead  300  may include a reference line sensor  326  configured to detect and/or sense the reference line  322  of an existing image slice  408  and transmit a path-following-error signal to the robot  202  causing the robot arm ( FIG. 5 ) and/or high-bandwidth actuators  250  (see  FIGS. 17-20 ) to correct or adjust the printhead  300  (e.g., in real time) such that the side edge  416  of the new image slice  406  is maintained in alignment with the side edge  416  of the existing image slice  408  during the printing of the new image slice  406 . In this manner, the reference line  322  may allow the printhead  300  to precisely follow the rastering path  350  of a previously-printed image slice  404  such that the side edges  416  of the new and existing image slices  406 ,  408  ( FIG. 7 ) are aligned in non-gapping and/or non-overlapping relation to one another, and thereby avoiding gaps between adjacent image slices  404  which may otherwise detract from the quality of the image  400 . 
       FIG. 2  is perspective view of an aircraft  100  and a gantry system which may be implemented for supporting one or more image forming systems  200  as disclosed herein. The aircraft  100  may have a fuselage  104  having a nose  106  at a forward end and an empennage  108  at an aft end of the fuselage  104 . The top of the fuselage  104  may be described as the crown, and the bottom of the fuselage  104  may be described as the keel. The aircraft  100  may include a pair of wings  114  extending outwardly from the fuselage  104 . One or more propulsion units may be mounted to the aircraft  100  such as to the wings  114 . The empennage  108  may include a horizontal tail  110  and a vertical tail  112 . 
     In  FIG. 2 , the gantry system may be housed within a hangar  120  and may include a plurality of gantries  124  positioned on one or more sides on the aircraft  100 . Each one of the gantries  124  may include a pair of vertical towers  126  that may be movable via a motorized base  128  along a floor track system  130  that may be coupled to or integrated into a floor  122 . Each gantry  124  may include a crossbeam  132  extending between the towers  126 . The crossbeam  132  of each gantry  124  may include a personnel platform  134 . In addition, the crossbeam  132  may support at least one robot  202  that may be movable along the crossbeam  132 . Advantageously, the gantry system may provide a means for positioning the robot  202  such that the printhead  300  has access to the crown, the keel, and other exterior surfaces  102  of the aircraft  100  including the sides of the fuselage  104 , the vertical tail  112 , the propulsion units, and other surfaces  102 . 
     Although the system  200  and method of the present disclosure is described in the context of printing images on an aircraft  100 , the system  200  and method may be implemented for printing images on any type of surface, with out limitation. In this regard, the surface  102  may be a surface of a motor vehicle including a tractor-trailer, a building, a banner, or any other type of movable or non-movable structure, object, article, or material having a surface to be printed. The surface may be planar, simply curved, and/or complexly curved. 
       FIG. 3  shows a gantry  124  positioned adjacent to the vertical tail  112 . A robot  202  mounted to the crossbeam may support an image forming system  200  for printing an image  400  on the vertical tail  112 . In  FIG. 3 , the image  400  is shown as a flag which may be printed on the vertical tail  112  such as by using ink from an inkjet printhead  300 . In  FIG. 23 , the image is shown as a model designation printed on a vertical tail  112  using an inkjet printhead  300 . However, the printhead  300  may be configured to apply images using other fluids including, but not limited to paint, pigment, and/or other colorants and/or fluids. In addition, the image forming system  200  disclosed herein is not limited to forming graphic images. 
     In the present disclosure, the term “image” includes any type of coating that may be applied to a surface  102  ( FIG. 2 ). An image may have a geometric design, any number of color(s) including a single color, and/or may be applied in any type of coating composition(s). In one example, the image  400  may include a graphic design, a logo, lettering, numbers, symbols, and/or any other types of indicia. In this regard, an image  400  may include an aircraft livery  402  which may comprise a geometric design or pattern that may be applied to the exterior surfaces  102  of an aircraft  100 , as described above. The image  400  may include a reproduction of a photograph. Even further, an image  400  may be a monotone coating of paint, ink, or other colorant or fluid, and is not limited to a graphic design, logo, or lettering or other indicia. 
       FIG. 4  is an end view of an aircraft  100  showing image forming systems  200  positioned on opposite sides of the aircraft  100 . Each image forming system  200  may include a robot  202  having one or more arms and a printhead  300  coupled to a terminal end  214  ( FIG. 4 ) of the arm of the robot  202 . One of the image forming systems  200  is shown printing an image  400  (e.g., a flag) on a vertical tail  112 . The other image forming system  200  is shown printing an image  400  such as the geometric design of an aircraft livery  402  (e.g., see  FIG. 2 ) on a side of fuselage  104 . 
     Although the robot  202  of the image forming system  200  is described as being mounted on a gantry  124  supported on a crossbeam  132  suspended between a pair of towers  126  ( FIGS. 1-5 ), the robot  202  may be supported in any manner, without limitation. For example, the robot  202  may be suspended from an overhead gantry  124  (not shown). Alternatively, the robot  202  may be mounted on another type of movable platform. Even further, the robot  202  may be non-movably or fixedly supported on a shop floor (not shown) or other permanent feature. 
       FIG. 5  is a perspective view of a robot  202  mounted to a crossbeam  132  of a gantry  124  and having a printhead  300  mounted on an arm of the robot  202 . The robot  202  may be movable along guide rails  206  extending along a lengthwise direction of the crossbeam  132 . In the example shown, the robot  202  may include a robot base  204 , a first arm  210 , and a second arm  212 , with the printhead  300  mounted on the end  214  of the second arm  212 . The robot base  204  may allow for rotation of the robot base  204  about a first axis  216  relative to the crossbeam  132 . The first arm  210  may be rotatable about a second axis  218  defined by a joint coupling the first arm  210  to the robot base  204 . The second arm  212  may be rotatable about a third axis  220  defined by a joint coupling the second arm  212  to the first arm  210 . In addition, the second arm  212  may be swivelable about a fourth axis  222  extending along a length of the second arm  212 . The length of the second arm  212  may be extendable and retractable to define a fifth axis  224  of movement. 
     In  FIGS. 4 and 5  the printhead  300  is shown being rotatable about a sixth axis  226  defined by a joint coupling the printhead  300  to the second arm  212 . The robot base  204  may include a robot drive system (not shown) for propelling the robot base  204  along the length of the crossbeam  132  and defining a seventh axis  228  of movement of the robot  202 . The robot  202  may include a controller  208  for controlling the operation of the base  204 , the arms, and/or the printhead  300 . Although shown as having a first arm  210  and a second arm  212 , the robot  202  may include any number of arms and joints for movement about or along any number of axes to allow the printhead  300  to reach any one of a variety of different locations and orientation relative to a surface  102 . In some examples, the robot  202  may be devoid of a base  204  and/or the robot may comprise a single arm to which the printhead  300  may be directly or indirectly coupled. 
       FIG. 6  is a side view of the image forming system  200  printing an image  400  on the vertical tail  112 . The first arm  210  and second arm  212  may be movable relative to the base  204  of the robot  202  to position the printhead  300 . The printhead  300  is movable by the arms over the surface  102  along one or more rastering paths  350  to print an image slice  404  on the surface  102 . In any one of the image printing systems  200  disclosed herein, the printhead  300  may be moved along parallel rastering paths  350  to form parallel images slices  404  that collectively define the image  400 . The robot  202  may be configured to maintain the orientation of the printhead face  304  parallel to the local position on the surface  102  as the printhead  300  is moved over the surface  102 . 
       FIG. 7  shows an example of a printhead  300  being moved along a rastering path  350  to form an image slice  404 . Each one of the rastering paths  350  is shown as being straight when viewed from above along a direction normal to the surface  102 . However, in any one of the image printing systems  200  disclosed herein, the printhead  300  may be moved along a rastering path  350  that is curved or a combination of curved and straight. The printhead  300  may sequentially print a plurality of parallel image slices  404  side-by-side to collectively form an image  400  on the surface  102 . 
       FIG. 8  is a sectional view of a printhead  300  printing image slices  404  on a surface  102 . The printhead width  302  may be oriented parallel to a transverse direction  354  ( FIG. 13 ) to the rastering path  350 . The printhead  300  may include a plurality of nozzles  308  or orifices distributed between opposing widthwise ends  306  of the printhead  300 . For example, an inkjet printhead may include thousands of orifices. The printhead  300  may eject droplets  330  ( FIG. 10 ) of ink, paint, or other fluids from the orifices to form a coating having a coating thickness  336  on the surface  102 . 
     Each image slice  404  ( FIG. 8 ) may have opposing side edges  416  defining a bandwidth  410  of the image slice  404 . The printhead  300  may be configured to print an image slice  404  with an image gradient band  418  along at least one of the side edges  416 . In the example shown, an image slice  404  may contain an inner portion  414  bounded on opposite sides by an image gradient band  418 . An image gradient band  418  may be described as a band within which the intensity of the color of the image slice  404  changes (e.g., decreases) along a transverse direction  354  relative to the direction of the rastering path  350  from an inner boundary  420  of the image gradient band  418  to the side edge  416 . For example, the inner portion  414  of the image slice  404  may be black in color. Within the image gradient band, the color may gradually change from black at the inner boundary  420  (e.g., a relatively high intensity) to white (e.g., a relatively low intensity) at the side edge  416  of the image slice  404 . An image gradient band  418  of an image slice  404  may be wider than the inner portion  414  of the image slice  404 . For example, an image gradient band  418  may be no more than 30% the bandwidth  410  of the image slice  404 . 
     In the example of  FIGS. 8-12 , the printhead  300  may be moved along the rastering paths  350  such that the image gradient bands  418  of the image slices  404  overlap. Advantageously, the overlapping rastering paths  350  allow for gaps and overlaps representing deviations from the nominal spacing between adjacent image slices  404  resulting in a reduced likelihood that such deviations from the nominal image slice spacing are visually perceptible. In this regard, the image gradient bands  418  on the side edges  416  of the adjacent image slices  404 , when superimposed, result in imperceptible image edges even with imperfect tracking by the robot  202  along the rastering paths  350 . In this manner, the image gradient bands  418  allow for printing of complex, intricate, and multi-colored images in multiple, single-pass image slices  404  on large-scale surfaces  102  using large-scale rastering devices such as the robot  202  shown in  FIGS. 1-5 . 
       FIG. 9  is a magnified view of a printhead  300  showing one example for forming an image gradient band  418 . As indicated above, the decrease in the intensity of the image gradient band  418  may be achieved by reducing or tapering the coating thickness  336  along a transverse direction  354  ( FIG. 13 ) from the inner boundary  420  of the image gradient band  418  to the side edge  416  of the image slice  404 . The droplet spacing  332  may be uniform within the inner portion  414  of the image slice  404 . In  FIG. 9 , the coating thickness  336  within the image gradient band  418  may be tapered by progressively increasing the droplet spacing  332  between the droplets  330  ejected by the nozzles  308 . In this regard, some of the nozzles  308  (e.g., orifices) of the printhead  300  in the area wherein the image gradient band  418  is to be printed may be electronically deactivated and may be referred to as inactive nozzles  312 , and only active nozzles  310  within the image gradient band  418  may eject droplets  330  to form the image gradient band  418 . In other examples, the printhead  300  may be provided with progressively larger gaps between nozzles  308  for the area wherein the image gradient band  418  is to be printed. 
       FIG. 10  is a magnified view showing another example of a printhead  300  forming an image gradient band  418  by maintaining the nozzles  308  as active nozzles  310  producing a uniform droplet spacing, and progressively decreasing the droplet size  334  in the area where the image gradient band  418  is to be formed. In still further examples, an image gradient band  418  may be formed by a combination of controlling the droplet spacing  332  and controlling the droplet size  334 . However, other techniques may be implemented for forming image gradient bands  418  and are not limited to the examples shown in the figures and described above. The printhead  300  may be configured to form the image gradient band  418  with an image gradient that is linearly decreasing. Alternatively, the image gradient within the image gradient band  418  may be non-linear. 
       FIG. 11  is a diagrammatic sectional view of adjacent image slices  404  with overlapping image gradient bands  418 . Shown is the coating thickness  336  ( FIG. 10 ) in the image gradient band  418  and in the inner portion  414  of each image slice  404 .  FIG. 12  is a plan view of the image slices  404  of  FIG. 11  showing the overlapping image gradient bands  418  and the parallel rastering paths  350  of the image slices  404 . In the system  200  as shown, the arm ( FIG. 7 ) may move the printhead  300  to print a new image slice  406  in parallel relation to an existing image slice  408  (e.g., a previously-printed image slice  404 ) in a manner such that an image gradient band  418  of the new image slice  406  ( FIG. 8 ) overlaps an image gradient band  418  of the existing image slice  408 . In this regard, the side edge  416  of each image slice  404  may be aligned with an inner boundary  420  of an overlapping or overlapped image gradient band  418 . However, in an example not shown, the printhead  300  may print image slices  404  in a manner to form a gap between the side edge  416  of an image gradient band  418  of a new image slice  406  and an existing image slice  408 . As indicated above, the printhead  300  may print the image gradient band  418  of the new image slice  406  and the existing image slice  408  such that the overlap has an image intensity equivalent to the image intensity of the inner portion  414  of the new image slice  406  and/or the existing image slice  408 . 
     In a still further example not shown, the printhead  300  ( FIG. 10 ) may form an image gradient end on at least one of opposing ends of an image slice  404 . An image gradient end may have an image intensity that may decrease toward an end edge (not shown) of the image slice  404 . Such an image gradient end may provide a means for blending (e.g., feathering) the image slice  404  with the color and design of the existing color and design of the surface  102  area surrounding the newly-applied image  400 . For example, the system may apply a newly-applied image  400  to a portion of a surface that may have undergone reworking such as the removal and/or replacement of a portion of a composite skin panel (not shown) and/or underlying structure. The image gradient ends of the newly-applied image slices  404  may provide a means for blending into the surrounding surface  102 . The image gradient end may also facilitate the blending on a new image slice  406  with the image gradient end of another image  400  located at an end of a rastering path  350  of the new image slice  406 . 
     Referring to  FIG. 13 , shown is an example of a printhead  300  mounted on an end  214  of a robot arm and being movable by the arm over a surface  102  along a rastering path  350  while printing a new image slice  406  adjacent to an existing image slice  408 . The printhead  300  includes a reference line printing mechanism  320  configured to print a reference line  322  when printing the new image slice  406 . The reference line  322  provides a means for the printhead  300  to precisely track the rastering path  350  of an existing image slice  408 . The printhead  300  includes at least one reference line sensor  326  such as an image detection system for sensing the reference line  322  and providing path error feedback to the controller  208  ( FIG. 14 ) to allow the robot  202  to generate path correction inputs to the printhead  300  such that the side edge  416  of the new image slice  406  is maintained in alignment with the side edge  416  of the existing image slice  408 . 
       FIG. 14  shows an example of a printhead  300  printing an image slice  404  adjacent to an existing image slice  408 . The existing image slice  408  may include a reference line  322  along one of the side edges  416 . The printhead  300  may have one or more reference line sensors  326  mounted on each one of the widthwise ends  306  of the printhead  300 . One or more of the reference line sensors  326  may be configured to sense the reference line  322  of an existing image slice  408 . In addition, the printhead  300  may include one or more position sensors  314  for monitoring the position and/or orientation of the printhead  300  relative to the surface  102 . In some examples, the reference line sensors  326  may be configured as position sensors  314  to sense the position and/or orientation of the printhead  300  in addition to sensing the reference line  322 . 
     The position sensors  314  at one or both of the widthwise ends  306  of the printhead  300  may measure a normal spacing  338  of the printhead  300  from the surface  102  along a direction locally normal to the surface  102 . Feedback provided by the position sensors  314  to the controller  208  may allow the controller  208  to adjust the arm position such that the face of the printhead  300  is maintained at a desired normal spacing  338  from the surface  102  such that the droplet may be accurately placed on the surface  102 . In further examples, the controller  208  may use continuous or semi-continuous feedback from the position sensors  314  to rotate the printhead  300  as necessary along a roll direction  358  such that the face of the printhead  300  is maintained parallel to the surface  102  as the printhead  300  is moved over the surface  102  which may have a changing and/or curved contour. 
       FIG. 15  shows an example of a printhead  300  wherein the reference line printing mechanism  320  comprises one or more dedicated nozzles  308  configured to print the reference line  322  on at least one of opposing side edges  416  of a new image slice  406 . The remaining nozzles  308  of the printhead  300  may be configured to print the image slice  404 . In other examples not shown, the reference line printing mechanism  320  may comprise a dedicated line-printing device that may be mounted on the printhead  300  and configured to print a reference line  322  while the nozzles  308  of the printhead  300  print the image slice  404 . 
     The printhead  300  may print the reference line  322  to be visible within a certain spectrum such as the visible spectrum and/or the infrared spectrum. In some examples, the reference line  322  may have a thickness that prevents detection by the human eye beyond a certain distance (e.g., more than 10 feet) from the surface  102 . In other examples, the reference line  322  may be printed as a series of spaced dots (e.g., every 0.01 inch) which may be visually imperceptible beyond a certain distance to avoid detracting from the quality of the image. In still other examples, the color of the reference line  322  may be imperceptible relative to the local color of the image  400 , or the reference line  322  may be invisible in normal ambient lighting conditions (e.g., shop light or sunlight) and may be fluorescent under a fluorescent light that may be emitted by the reference line sensor  326 . Even further, the reference line  322  may be invisible within the visible spectrum, or the reference line  322  may initially be visible under ambient light and may fade over time under ambient conditions such as due to exposure to ultraviolet radiation. 
     In still further examples, the reference line  322  may be printed with at least one encoding pattern  324  (e.g., see  FIG. 13 ) along at least a portion of the reference line  322 . The encoding pattern  324  may comprise a system of line segments  323  separated by gaps  321 . The encoding pattern  324  may represent information about the image slice  404 . For example, the encoding pattern  324  may represent information regarding the distance from the current location (e.g., the location where the encoding pattern  324  is currently detected) of the printhead  300  relative to an end  412  of the image slice  404 . Such information may be included in the signal (e.g., the path-following-error signal) transmitted to the controller  208  to allow the controller  208  to control the operation of the printhead  300 . For example, the encoding pattern  324  may signal the controller  208  to synchronize or align a new image slice  406  being printed with the existing image slice  408 , or to signal to the controller  208  to halt the ejection of droplets  330  in correspondence with the end of the existing image slice  408 . 
       FIG. 16  is a magnified view of an example of a printhead  300  having a reference line sensor  326  for sensing a reference line  322  of an image slice  404 . The reference line sensor  326  may transmit to the controller  208  ( FIG. 14 ) a path-following-error signal representing the lateral spacing  340  between the reference line  322  and an indexing feature. The indexing feature may be the centerline of the reference line sensor  326 , a hardpoint on the printhead  300  such as the nozzle  308  at an extreme end of the printhead  300 , or some other indexing feature. As the printhead  300  is moved along a rastering path  350 , the reference line sensor  326  may sense and transmit (e.g., continuously, in real-time) the path-following-error signal to the controller  208  representing the lateral spacing  340 . Based on the signal, the controller  208  may cause the lateral position of the printhead  300  to be adjusted (e.g., by the arm) such that the side edge  416  of the new image slice  406  is maintained in alignment with the side edge  416  of an existing image slice  408 . 
     The reference line sensor  326  may be configured as an optical sensor of a vision system. In  FIG. 16 , the optical sensor may emit an optical beam  328  (e.g., an infrared beam) for detecting the reference line  322 . The optical sensor may generate a signal (e.g., a path-following-error signal) representing the lateral location where the optical beam  328  strikes the reference line  322 . The signal may be transmitted to the robot  202  controller  208  on demand, at preprogrammed time intervals, continuously, or in other modes. In one example, the reference line sensor  326  may provide real-time alignment feedback to the robot  202  controller  208  for manipulating or adjusting the printhead  300  such that the side edges  416  of the new image slice  406  and existing image slice  408  are aligned. For example, the robot  202  may adjust the lateral position of the printhead  300  such that the side edges  416  of the new image slice  406  and the existing image slice  408  are aligned in non-gapped and/or non-overlapping relation as a new image slice  406  is being printed. 
     In other examples, instead of adjusting the lateral position of the printhead  300 , the robot controller  208  may maintain the lateral position of the printhead  300  during movement along the rastering path  350 , and the controller  208  may electronically control or shift the nozzles  308  on the printhead  300  that are actively ejecting droplets  330 . In this regard, a printhead  300  may have additional (e.g., unused) nozzles  308  located at one or both of the widthwise ends  306  of the printhead  300 . Upon the controller  208  determining that a new image slice  406  is misaligned with an existing image slice  408 , the controller  208  may activate one or more of the unused nozzles  308  at one of the widthwise ends  306 , and deactivate an equal number of nozzles  308  at an opposite widthwise end  306  of the printhead  300  to maintain the same image slice width of the new image slice  406  while effectively shifting the lateral position of the new image slice  406  without laterally moving the printhead  300 . In this regard, an image slice  404  may be electronically offset in real-time or near real-time such that the side edge  416  of the new image slice  406  is maintained in non-gapping and/or non-overlapping relation with the side edge  416  of an existing image slice  408 . In this manner, the reference line  322  advantageously provides a means for the printhead  300  to precisely maintain a nominal distance of a new image slice  406  relative to the rastering path  350  of an existing or previous-applied image slice  404 , and thereby avoid gap between the image slices  404 . 
       FIG. 17  is a side view of an example of a robot  202  having high-bandwidth actuators  250  coupling the printhead  300  to an arm of the robot  202  and showing the printhead  300  printing an image  400  (e.g., an aircraft livery  402 ) on a surface  102  of a fuselage  104 . As indicated above, a relatively large robot  202  may be required for printing large surfaces  102 . Such a large-scale robot  202  may have a relatively high mass and relatively low stiffness which may result in an inherently large tolerance band of movement at the end  214  of the arm (e.g., the last axis of the robot) on which the printhead  300  may be mounted. In attempts to compensate for such inherently large tolerances, a large-scale robot  202  may require extensive computer programming (e.g., CNC or computer-numerical-control programming) which may add to production cost and schedule. Advantageously, by printing image slices  404  with the above-described image gradient bands  418  ( FIGS. 7-12 ) and/or reference lines  322  ( FIGS. 13-16 and 24-31 ), the robot-mounted printhead  300  of the present disclosure may print a high-quality image  400  on a surface  102  without the occurrence of gaps between adjacent image slices  404  that would otherwise detract from the overall quality of the image. 
     In  FIG. 17 , one or more high-bandwidth actuators  250  may be mounted in series with the one or more arms of the robot  202 . Such high-bandwidth actuators  250  may couple a printhead  300  (e.g.,  FIGS. 18, 19, 25 and 29 ) to the last axis or arm of the robot  202  and provide a relatively small tolerance band for adjusting the orientation and/or position of the printhead  300  relative to the surface  102  during movement of the printhead  300  along a rastering path  350  such that a new image slice  406  may be accurately aligned with an existing image slice  408 . The high-bandwidth actuators  250  may be described as high-bandwidth in the sense that the high-bandwidth actuators  250  may have small mass and inherently high stiffness which may result in increased precision and rapid response time in positioning and orienting a printhead  300  relative to the large mass, low stiffness, and corresponding slow response time of a large-scale robot  202 . Further in this regard, the high-bandwidth actuators  250  may rapidly respond to commands from the robot controller  208  based on path-following-error signals provided in real-time by the reference line sensor  326 . 
     Referring still to  FIG. 17 , the system  200  may include one or more high-bandwidth actuators  250  which may be configured to adjust the position of the printhead  300  along at least one of the following directions: (1) a transverse direction  354  of translation of the printhead  300  parallel to the surface  102  and perpendicular to the rastering path  350 , (2) a normal direction  356  of translation of the printhead  300  locally normal to the surface  102 , and (3) a roll direction  358  of rotation of the printhead  300  about an axis parallel to the rastering path  350 . In addition, one or more high-bandwidth actuators  250  may be configured to adjust the position of the printhead  300  along other directions including, but not limited to, a parallel direction  352  of translation which may be described as parallel to the primary direction of movement of the printhead  300  along the rastering path  350  during the printing of an image slice  404 . 
       FIG. 18  shows an example of three (3) high-bandwidth actuators  250  coupling a printhead  300  to an arm of a robot  202  ( FIG. 17 ). In an example, the high-bandwidth actuators  250  include a first actuator  250   a , a second actuator  250   b , and a third actuator  250   c  which may be generally aligned in an in-plane tripod configuration enabling adjustment of the printhead  300  along the transverse direction  354 , the normal direction  356 , and the roll direction  358  as described above. The first, second, and third actuators  250   a ,  250   b ,  250   c  may each have an upper end  268  and a lower end  270 . The upper ends  268  of the first, second, and third actuators  250   a ,  250   b ,  250   c  may be pivotably coupled to the end of the arm of the robot and may have parallel pivot axes. The lower ends  270  of the first, second, and third actuators  250   a ,  250   b ,  250   c  may be pivotably coupled to the printhead  300  and may also have parallel pivot axes. As shown in  FIG. 18 , the upper ends  268  of the first  250   a  and third actuator  250   c  are spaced apart from one another at the pivotable attachment to the end  214  of the arm, and the lower ends  270  of the first  250   a  and third actuator  250   c  are spaced apart from one another at the pivotable attachment to the printhead  300 . In this regard, the first actuator  250   a  and the third actuator  250   c  may be oriented generally parallel to one another. However, the first actuator  250   a  and the third actuator  250   c  may be oriented non-parallel relation to one another without detracting from the movement capability of the printhead  300  along the transverse direction  354 , the normal direction  356 , and the roll direction  358 . 
     In  FIG. 18 , the upper end  268  of the second actuator  250   b  may be located adjacent to the upper end  268  of the first actuator  250   a . The lower end  270  of the second actuator  250   b  may be located adjacent to the lower end  270  of the third actuator  250   c  such that the second actuator  250   b  extends diagonally between the upper end  268  of the first actuator  250   a  and the lower end  270  of the third actuator  250   c . In operation, the first, second, and third actuators  250   a ,  250   b ,  250   c  may be extended and retracted by different amounts to adjust the printhead  300  along the transverse direction  354 , the normal direction  356 , and the roll direction  358 . In any one of the examples disclosed herein, one or more of the high-bandwidth actuators  250  may be configured as pneumatic cylinders or in other high-bandwidth actuator configurations including, but not limited to, hydraulic cylinders, electromechanical actuators, or other actuator configurations. In  FIG. 18 , the printhead face  304  is oriented non-parallel to the surface  102  and laterally offset relative to the reference line  322 . 
       FIG. 19  is a side view of the printhead  300  after being repositioned by the high-bandwidth actuators  250  (e.g., the first, second, and third actuators  250   a ,  250   b ,  250   c ) into alignment with the reference line  322  and reorientation of the printhead face  304  into parallel relation with the surface  102 . In this regard, the controller  208  ( FIG. 14 ) may command the translation and re-orientation of the printhead  300  based on continuous input signals that may be received in real-time from the position sensors  314  and/or reference line sensors  326  tracking the reference line  322  during printing of a new image slice  406 . For example, the high-bandwidth actuators  250  may translate the printhead  300  along the transverse direction  354  and the normal direction  356  and may rotate the printhead  300  along the roll direction  358  to orient the printhead face  304  parallel the local surface  102  while aligning the side edge  416  of a new image slice  406  with the side edge  416  of an existing image slice  408 . 
       FIG. 20  is a further example of high-bandwidth actuators  250  configured as a delta robot  252  and mounted in series with the robot arm and coupling the printhead  300  to the end  214  ( FIG. 19 ) of the robot arm ( FIG. 17 ). In  FIG. 20 , the delta robot  252  may include an actuator base  254  which may be attached to the end  214  of a robot arm (e.g., a second arm  212 ). Three (3) actuator upper arms  256  may be pivotably coupled to the actuator base  254  and may have co-planar pivot axes oriented at 60 degrees relative to one another. Each actuator upper arm  256  may be coupled by a hinge joint  260  to a pair of actuator lower arms  258 . Each pair of actuator lower arms  258  may be configured as a parallelogram four-bar-mechanism. Each one of three (3) pairs of lower arms  258  may be pivotably coupled to an actuator platform  262  through six (6) hinge joints wherein each hinge joint is capable of rotation about a single axis. The three (3) parallelogram four-bar-mechanisms of the three (3) actuator lower arms  258  limit movement of the actuator platform  262  to translation (e.g., movement in the x-y direction) and extension (e.g., movement in the z-direction), and prevent rotation of the actuator platform  262 . In this regard, the actuator platform  262  is maintained in parallel relation with the actuator base  254  regardless of the direction of translation and/or extension of the actuator platform  262 . In an example not shown, the delta robot  252  may be provided with spherical joints (not shown) and upper and lower arms (not shown) arranged in a manner that maintains the actuator platform  262  in parallel relation to the actuator base  254  during translation and/or extension of the actuator platform  262 . 
     In  FIG. 20 , the translation capability of the actuator platform  262  provides for translation of the printhead  300  along the above-described transverse direction  354  (e.g., the y-direction) and normal direction  356  (e.g., the z-direction) relative to the surface  102  being printed. The high-bandwidth actuator  250  arrangement of  FIG. 20  may provide rotational capability of the printhead  300  along the roll direction  358  by means of one or more roll actuators  264  for pivoting the printhead  300  about one or more attachment links  266 . The upper ends of the attachment links  266  may be fixedly coupled to the actuator platform  262 . The lower ends of the attachment links  266  may be pivotably coupled to the printhead  300 . The high-bandwidth actuator  250  arrangement of  FIG. 20  may represent a low mass, high stiffness actuator system providing increased precision and improved response time for adjusting the position of the printhead  300  according to a path-following-error that may be resolved using the reference line sensor  326  tracking the reference line  322  of an existing image slice  408 . As indicated above, the high-bandwidth actuators  250  may adjust the position and/or orientation of the printhead  300  with a precision that may be unobtainable with the robot  202  acting alone. 
       FIG. 21  is a flowchart of one or more operations that may be included in method  500  of printing an image  400  on a surface  102 . The method may be implemented using the system  200  described above. Step  502  of the method  500  may include positioning an arm of a robot  202  adjacent to a surface  102 . As indicated above, a printhead  300  may be mounted on an end  214  of the arm. In some examples, the printhead  300  may be an inkjet printhead  300  having an array of nozzles  308  or orifices for ejecting droplets  330  of ink, paint, or other fluids or colorants. 
     Step  504  of the method  500  may include moving, using the arm, the printhead  300  over the surface  102  along a rastering path  350  while the printhead  300  prints an image slice  404  on the surface  102 , as shown in  FIG. 7 . The printhead  300  may be moved by the arm along the rastering path  350  to print a new image slice  406  in parallel relation to an existing image slice  408 . 
     Step  506  of the method  500  may include printing an image gradient band  418  along at least one side edge  416  of an image slice  404  when printing the image slice  404  on the surface  102 , as shown in  FIG. 8 . As described above, the image gradient band  418  may have an image intensity that decreases along a transverse direction  354  (e.g., relative to the rastering path  350 ) toward a side edge  416  of the image slice  404 . In some examples, the image gradient of the image gradient band  418  may be linear (e.g., a linear decrease in the image density) along the transverse direction  354 . In other examples, the image gradient of an image gradient band  418  may be non-linear. 
     As shown in  FIG. 8 , a printhead  300  may print a new image slice  406  such that the image gradient band  418  of the new image slice  406  overlaps the image gradient band  418  of an existing image slice  408 . For example, the side edge  416  of the new image slice  406  may be aligned with an inner boundary  420  of an overlapping or overlapped image gradient band, as mentioned above. The method may include printing, using the printhead  300 , the image gradient band  418  of the new image slice  406  and the existing image slice  408  such that the overlapping image gradient bands  418  have a collective image intensity that is equivalent to the image intensity of the inner portion  414  of the new image slice  406  and/or the existing image slice  408   
     As shown in  FIG. 9  and mentioned above, an image gradient band  418  may be generated by ejecting droplets  330  from the printhead  300  nozzles  308  with progressively larger droplet spacings  332  along a direction toward the side edge  416  of the image slice  404  as compared to a uniform droplet spacing  332  for the nozzles  308  that print the inner portion  414  of the image slice  404 . As shown in  FIG. 10 , an image gradient band  418  may also be generated by ejecting progressively smaller droplet sizes  334  along a direction toward the side edge  416 . The method may optionally include forming a new image slice  406  with an image gradient end (not shown) on at least one of opposing ends of the new image slice  406  as a means to blend or feather the image slice  404  into an area bordering the new image slice  406 . 
       FIG. 22  is a flowchart of one more operations that may be included in a further method  600  of printing an image  400  on a surface  102 . Step  602  of the method  600  may include printing, using a printhead  300  mounted on an arm of a robot  202 , a new image slice  406  on the surface  102  while moving the printhead  300  over the surface  102  along a rastering path  350 . Step  604  of the method  600  may include printing a reference line  322  on the surface  102  when printing the new image slice  406 , as shown in  FIG. 13  and described above. The printhead  300  may include a reference line printing mechanism  320  configured to print the reference line  322  on the surface  102  when printing the new image slice  406 . In some examples, the reference line printing mechanism  320  may comprise at least one nozzle  308  of the printhead  300  which may eject ink or paint that is a different color that the ink or paint ejected by adjacent nozzles  308 . In other examples, the reference line printing mechanism  320  may comprise a dedicated reference line printer (not shown). 
     The printhead  300  may print a reference line  322  on at least one of opposing side edges  416  of a new image slice  406  when printing the new image slice  406 . The step of printing the reference line  322  may include printing the reference line  322  with at least one encoding pattern  324  along at least a portion of the reference line  322 . The encoding pattern  324  may comprise a series of line segments separated by gaps. The encoding pattern  324  may alternatively or additionally comprise localized changes in the color of the reference line  322 , or a combination of both line segments, gaps, color changes, and other variations in the reference line for encoding information. The encoding pattern  324  may represent information regarding the image slice  404  such as the distance to the end  412  of the image slice  404  or other information about the image  400 . The information may be transmitted to the controller  208  which may adjust one or more printing operations based on the information contained in the encoding pattern  324 . 
     Step  606  of the method  600  may include sensing, using a reference line sensor  326  included with the printhead  300 , the reference line  322  of an existing image slice  408  while printing the new image slice  406 . As indicated above, a reference line sensor  326  may sense the reference line  322  of an existing image slice  408  and transmit a signal (e.g., a path-following-error signal) to the robot  202  and/or controller  208  causing the arm to adjust the printhead  300  such that the side edge  416  of the new image slice  406  is aligned with and/or is maintained in non-gapping and non-overlapping relation with the side edge  416  of the existing image slice  408 . 
     Step  608  of the method  600  may include adjusting the lateral position of the new image slice  406  based on a sensed position of the reference line  322  to align a side edge  416  of the new image slice  406  with the side edge  416  of the existing image slice  408 . In one example, the method may include detecting a misalignment of the side edge  416  of a new image slice  406  with the side edge  416  of an existing image slice  408  and providing real-time alignment feedback to the robot  202  and/or controller  208  for manipulating or adjusting the lateral position of the printhead  300  such that the side edge  416  of the new image slice  406  is aligned with the side edge  416  of the existing image slice  408 . In this regard, the step of adjusting the lateral position of the new image slice  406  may include transmitting a signal from the reference line sensor  326  (e.g., an optical sensor) to the robot  202  and/or controller  208 . The robot  202  and/or controller  208  may determine a correction input for the robot based on the misalignment of the printhead  300 . 
     The method may include adjusting the position of the printhead  300  such that the side edge  416  of the new image slice  406  is maintained in non-gapped and non-overlapping relation with the side edge  416  of the existing image slice  408 . In this regard, the lateral position of the printhead  300  may be physically adjusted to align the side edge  416  of the new image slice  406  with the side edge  416  of the existing image slice  408 . Alternatively, the method may include electronically shifting the nozzles  308  that are actively ejecting droplets  330  to align the side edge  416  of the new image slice  406  with the side edge  416  of the existing image slice  408 , as mentioned above. 
     The adjustment of the position and/or orientation of the printhead  300  may be facilitated using one or more high-bandwidth actuators  250  coupling the printhead  300  to an end  214  of an arm of the robot  202 , as described above and illustrated in  FIGS. 17-20 . The high-bandwidth actuators  250  may adjust an orientation and/or position of the printhead  300  relative to the surface  102  during movement of the printhead  300  along the rastering path  350 . The reference line sensor  326  may sense the reference line  322  and transmit a signal to the robot  202  for determining an adjustment to the lateral position of the printhead  300 . The robot  202  and/or controller  208  may command the high-bandwidth actuators  250  to adjust the position of the printhead  300  such that the side edge  416  of the new image slice  406  is maintained in non-gapped relation with the side edge  416  of the existing image slice  408 . 
     The method may include adjusting the printhead  300  by translating the printhead  300  along a transverse direction  354  parallel to the surface  102  and perpendicular to the rastering path  350 , translating the printhead  300  along a normal direction  356  that is normal to the surface  102 , and/or rotating the printhead  300  along a roll direction  358  about an axis parallel to the rastering path  350 . Advantageously, the high-bandwidth actuators  250  may provide increased precision and rapid response time in adjusting the position and/or orientation of the printhead  300 . 
     Referring now to  FIGS. 23-31 , disclosed are examples of an image forming system  200  ( FIGS. 23-29 ) and method  700  ( FIG. 31 ) that uses one or more laser devices  342  (e.g.,  FIGS. 24-25 ) for etching a reference line  322  during the printing of a new image slice  406 . As described in greater detail below, in one example of the image forming system  200  shown in  FIGS. 24-27 , as the printhead  300  prints a new image slice  406 , the laser device  342  etches a reference line  322  into the new image slice  406 . In an alternative and preferred example of the image forming system  200  shown in  FIGS. 28-30 , the laser device  342  etches the reference line  322  into a basecoat  103  that may be previously applied to the surface  102 . The laser device  342  may etch the reference line  322  into the basecoat  103  at a location immediately adjacent to a side edge  416  of the new image slice  406  as shown in  FIG. 29 . 
     The printhead  300  of the image forming system  200  includes at least one reference line sensor  326  configured to detect and/or sense the reference line  322  of an existing image slice  408 . The reference line sensor  326  is configured to transmit a path-following-error signal to the robot  202  to correct or adjust the printhead  300  in a manner such that the side edge  416  of the new image slice  406  is maintained in alignment with the side edge  416  of an existing image slice  408  during the printing of the new image slice  406 . 
     Referring to  FIG. 23 , shown is an example of the image forming system  200  printing an image  400  on a vertical tail  112  of an aircraft  100 . As described above, the printhead  300  may be coupled to an arm (e.g., a second arm  212 ) of a robot  202  which may have a base  128  ( FIGS. 4-5 ) that may be supported on a gantry  124  as shown in  FIGS. 2-5 . Alternatively, the base (not shown) of the robot  202  may be mounted on another type of movable platform (not shown), or the base of the robot  202  may be non-movably supported on or fixed to a shop floor (not shown). As described in greater detail below, the use of a laser device  342  for etching a reference line  322  provides a means for increasing the precision with which the printhead  300  can be controlled during the printing of an image  400  on a surface  102 . Advantageously, the increased precision of control of the printhead  300  allows for increased accuracy in maintaining new image slices  406  in alignment with existing image slices  408 , resulting in an overall improvement in the quality and appearance of the completed image  400 . 
     In  FIG. 23 , the arm of the robot  202  is configured to move the printhead  300  over the surface  102  along parallel rastering paths  350  ( FIG. 24 ) for printing a plurality of image slices  404  in parallel, side-by-side relation to each other to collectively form the image  400  being printed. As described in greater detail below, the laser device  342  emits a laser beam  344  configured to vaporize or ablate an upper surface of a new image slice  406  (e.g.,  FIGS. 24-27 ) or basecoat  103  (e.g.,  FIGS. 28-30 ) and thereby form a reference line  322 . Advantageously, the vaporization or ablation of the upper surface of the new image slice  406  or basecoat  103  is performed without burning and/or without significantly altering the color of the new image slice  406  or basecoat  103 . The reference line  322  may be described as a small groove that penetrates only the upper surface of the new image slice  406  or basecoat  103 , and may be formed at a relatively shallow line depth ( FIG. 26 ) and relatively narrow line width ( FIG. 26 ). Due to the ablation of the upper surface of the new image slice  406  or basecoat  103 , the reference line  322  has a reduced level of gloss, shine, or reflectivity relative to the level of gloss, shine, or reflectivity of the surrounding area adjacent to the reference line  322 , allowing the reference line  322  to be sensed by one or more reference line sensors  326 . 
     In  FIG. 23 , each one of the reference lines  322  may extend across an entire length of the image  400  which, in the example shown, comprises a series of numbers “777”. The printhead  300  is configured to follow the reference line  322  of an existing image slice  408  while printing a new image slice  406  and simultaneously etching a new reference line  322  along each rastering path  350  for the printhead  300  to follow during the printing of a subsequent image slice (not shown). As mentioned above, the printhead  300  is controlled in a manner to start and stop the ejection of droplets  330  (e.g.,  FIGS. 26-27 ) of ink at the appropriate points along each rastering path  350  in longitudinal (i.e., parallel to the rastering path  350 ) correspondence with the image details (not shown) and/or color variations (not shown) in the existing image slice  408 . In  FIG. 23 , the printhead  300  may be controlled in a manner to start and stop the ejection of droplets  330  in longitudinal correspondence with the outline of the numbers being printed. 
     Although an image slice  404  may start and stop at multiple locations along the length of the image slice  404 , the reference lines  322  may extend continuously across the length of each image slice  404 . As mentioned above, the reference lines  322  penetrate only the upper surface of an image slice  404  or a basecoat  103 . After all image slices  404  have been printed and the image  400  is complete, a layer of clearcoat (not shown) may be applied over the surface  102  including over the completed image  400 . The clearcoat may cover any exposed reference lines  322 , resulting in the reference lines  322  having the same level of reflectivity as the surrounding area such that the reference lines  322  become visually imperceptible. 
     Referring to  FIG. 24 , shown is an example of a printhead  300  printing a new image slice  406  while tracking a reference line  322  previously etched into the existing image slice  408  and while the laser device  342  etches a reference line  322  into the new image slice  406 . As described above, the printhead  300  is movable by the arm of the robot  202  along each rastering path  350  for printing a new image slice  406 . Each new image slice  406  is printed either directly onto the surface  102  uncoated (not shown), or onto a basecoat  103  covering the surface  102 . The system  200  includes at least one laser device  342  and at least one reference line sensor  326 . As described above, the reference line sensor  326  senses the reference line  322  of an existing image slice  408  and transmits a signal (e.g., a path-following-error signal) to the robot  202  causing the printhead  300  to be adjusted in a manner such that a side edge  416  of the new image slice  406  is aligned with the side edge  416  of an existing image slice  408 . In the example shown, the printhead  300  includes a laser device  342  and a reference line sensor  326  at each one of the four (4) corners of the printhead  300 . The laser devices  342  and the reference line sensors  326  may be coupled to the printhead  300  or integrated into the printhead  300 , and move in unison with the printhead  300 . For example, one or more laser devices  342  and one or more reference line sensors  326  may be coupled to opposite widthwise ends  306  of the printhead  300 . 
     Referring to  FIGS. 24-25 , the system  200  may be configured such that a single one of the laser devices  342  is activated to etch a reference line  322  when the printhead  300  is moved along a rastering path  350 . Likewise, a single one of the reference line sensors  326  may be actively sensing the reference line  322  of an existing image slice  408  when the printhead  300  is moving along a rastering path  350 . For a printhead  300  having multiple laser devices  342  and multiple reference line sensors  326 , the selection of a laser device  342  for etching a new reference line  322 , and the selection of a reference line sensor  326  for sensing an existing reference line  322  is dependent at least in part upon the movement direction of the printhead  300 . For example, in  FIG. 24  in which the existing image slice  408  is located above the new image slice  406  being printed, the printhead  300  is moving from left to right such that only the laser device  342  located in the lower left-hand corner of the printhead  300  is actively etching a reference line  322  into the new image slice  406  while the remaining laser devices  342  are inactive. Also in  FIG. 24 , only the reference line sensor  326  in the upper right-hand corner of the printhead  300  may be actively sensing the reference line  322  associated with the existing new image slice  406 , while the remaining reference line sensors  326  are inactive. 
     However, in another example not shown in which the printhead  300  is moving along a direction from right to left while printing a new image slice  406 , only the laser device  342  in the lower right-hand corner of the printhead  300  may be actively etching a reference line  322  while the remaining laser devices  342  are inactive. In such example, only the reference line sensor  326  in the upper left-hand corner of the printhead  300  may be actively sensing the reference line  322  associated with the new image slice  406  while the remaining reference line sensors  326  are inactive. In some examples, the system  200  may be configured such that two or more reference line sensors  326  are actively sensing a reference line  322  to provide a level of redundancy or to improve the accuracy with which a reference line  322  is sensed by averaging the sensed lateral spacing (e.g.,  FIG. 26 ) measurements generated by each reference line sensor  326 . 
     In  FIG. 26 , shown is an example of a portion of a printhead  300  having a reference line sensor  326  and a position sensor  314  coupled to the printhead  300 . As described above, the reference line sensor  326  may sense the reference line  322  etched in the existing image slice  408 , and may transmit to a controller  208  of the robot  202  a path-following-error signal representing the lateral spacing  340  between the reference line  322  and an indexing feature. For example, as shown in  FIG. 16 , the reference line sensor  326  may be an optical sensor configured to emit an optical beam  328  (e.g., an infrared beam) and determine a lateral spacing  340  between an indexing feature and the lateral location where the optical beam  328  strikes the reference line  322 . In the example, shown, the indexing feature may be the centerline of the reference line sensor  326 . 
     During printing of a new image slice  406 , the reference line sensor  326  may continuously or periodically sense the reference line  322  and transmit to the controller  208  the signal representing the lateral spacing  340 . The controller  208  may process the signal and may adjust the lateral position of the printhead  300  to cause the side edge  416  of the new image slice  406  to be maintained in alignment with the side edge  416  of the existing image slice  408 . In this regard, the robot  202  may adjust the lateral position of the printhead  300  along a transverse direction  354  in a manner such that the side edge  416  of the new image slice  406  is maintained in non-gapped and non-overlapping relation with the side edge  416  of the existing image slice  408 . In some examples, the signal represents the magnitude of the error in the position (i.e., lateral position error) of the printhead relative to the reference line  322 . The system  200  may include a position servo loop (not shown) for continuously correcting for the lateral position of the printhead  300  by minimizing the lateral distance between the current printhead location relative to a nominal printhead location (e.g., for non-gapped and non-overlapping image slices), causing the printhead  300  to be adjusted in a manner such that a side edge  416  of the new image slice  406  is maintained in alignment with the side edge  416  of the existing image slice  408 . 
     In other examples, instead of adjusting the lateral position of the printhead  300 , the controller  208  of the robot  202  may electronically shift or offset the nozzles  308  on the printhead  300  that are actively ejecting droplets  330 . For example, as shown in  FIG. 25 , a printhead  300  may include additional nozzles  308  that are located at one or both of the widthwise ends  306  of the printhead  300 . If the controller  208  determines that a new image slice  406  may become misaligned with an existing image slice  408  during printing of a new image slice  406 , the controller  208  may activate one or more inactive nozzles (not shown) at one of the widthwise ends  306 , and may deactivate an equal number of active nozzles (not shown) at an opposite widthwise end  306  of the printhead  300  as a means to shift the lateral position of the new image slice  406  without physically moving the printhead  300 , and such that the new image slice  406  is maintained in non-gapped and non-overlapping relation with the side edge  416  of the existing image slice  408 . In still further embodiments, the robot  202  may be configured to perform a combination of physically adjusting the lateral position of the printhead  300 , and electronically shifting the nozzles  308  that actively eject droplets  330 . 
     In  FIG. 26 , the optical sensor may be provided as a camera  327  such as color camera  327  or a monochrome camera. The camera  327  may be configured to visually acquire the reference line  322  and detect misalignment of the side edge  416  of the new image slice  406  with the side edge  416  of the existing image slice  408 . In this regard, the camera  327  may be configured to continuously or periodically image the reference line  322  and surrounding area during the printing of a new image slice  406 . The camera  327  may have a relatively high image resolution capability allowing the camera  327  to accurately sense the reference line  322  in a variety of lighting conditions. For example, the camera  327  may have an image resolution capability of greater than 1 megapixel, although image resolution capabilities of less than 1 megapixel are contemplated. The system  200  may further include a light source  329  that may be mounted to the printhead  300 . The light source  329  may be oriented at a non-perpendicular angle relative to the basecoat  103  or new image slice  406  into which the reference line  322  is etched such that light emitted by the light source  329  may reflect off of the reference line  322  and surrounding area and may be received by the camera  327 . The light source  329  may be configured to continuously illuminate the reference line  322  and surrounding area. 
     The camera  327  may be oriented to receive the light emitted by the light source  329  and reflected off of the reference line  322  and the surrounding area. The camera  327  may sense the lateral location of the reference line  322  based on variations in specular reflectivity of the surface into which the reference line  322  is etched. The camera  327  may periodically or continuously generate a signal representative of the lateral location of the reference line  322 . The signal may be transmitted to the controller  208  of the robot  202  to provide real-time alignment feedback to allow the controller  208  to adjust the printhead  300  in a manner such that the side edge  416  of the new image slice  406  is maintained in alignment with the side edge  416  of the existing image slice  408 . As mentioned above, the adjustment of the printhead  300  may include physically moving the printhead  300  during the printing of a new image slice  406  and/or the adjustment of the printhead  300  may include electronically offsetting or shifting nozzles  308  that actively eject droplets  330  of ink during the printing of a new image slice  406 . 
     Referring to  FIG. 27 , shown is an example of a laser device  342  etching a reference line  322  into a new image slice  406  during the printing of the new image slice  406  by the printhead  300 . As mentioned above, the laser device  342  is configured to etch the reference line  322  into the new image slice  406  (or into the basecoat  103 — FIG. 29 ) at a relatively shallow depth. For example, the reference line  322  may be etched at a line depth  348  of less than approximately 0.005 inch and, more preferably, at a line depth  348  of less than approximately 0.001 inch although the reference line  322  may be etched at a line depth  348  of greater than 0.001 inch. In addition, the reference line  322  may be etched at a relatively narrow line width  346  such as a line width  346  in the range of approximately 0.002-0.010 inch, although line widths  346  larger than 0.010 inch are contemplated. The relatively small line depth  348  and line width  346  of the reference line  322  may result in the reference line  322  being visually imperceptible after the image  400  is coated with clearcoat (not shown). 
     In some examples, the laser device  342  may be provided as a Class 4 industrial laser capable of emitting a laser beam  344  in the range of approximately 1-5 watts in the visible spectrum. However, the laser device  342  may be provided as a Class 3 (or lower class) laser device  342  and may be configured to emit a laser beam  344  in the visible spectrum or in other spectrums such as in the infrared spectrum. As mentioned above, the laser device  342  may be configured to ablate the reference line  322  into the upper surface of a new image slice  406  or a basecoat  103  without burning or altering the local color of the new image slice  406  or basecoat  103 . The required optical intensity of the laser beam  344  for ablating the surface to the extent required to form the reference line  322  may be dependent upon several factors including, but not limited to, the chemical composition of the new image slice  406  or basecoat  103 , the printhead velocity, the focus requirements for etching the reference line  322  at the desired line depth  348  and line width  346 , and other factors. The laser device  342  may be configured such that the laser beam  344  is focused when the printhead  300  is maintained at a desired normal spacing  338  ( FIGS. 26-27 ) from the surface  102  for optimal printing. The laser device  342  may include laser optics (not shown) that cause the laser beam  344  to become unfocused at distances greater than the normal spacing  338 . 
     Referring to  FIGS. 26-27 , the system  200  may include one or more position sensors  314  coupled to the printhead  300  and configured to measure the normal spacing  338  between the printhead  300  and the basecoat  103  and/or new image slice  406  or existing image slice  408 . For example, the printhead  300  may include at least three positions sensors  314  (e.g., four position sensors  314  arranged in a rectangular pattern) provided as line lasers and configured to measure the normal spacing  338  at different locations on the printhead  300 . The robot  202  may adjust the orientation of the printhead  300  based on the normal spacing  338  sensed by the position sensors  314  at each location as a means to maintain the printhead  300  locally parallel to the surface  102  during printing of the new image slice  406 . In this manner, the nozzles  308  may be maintained approximately at a nominal distance from the surface  102  during the printing of each new image slice  406 . 
     As indicated above, the normal spacing  338  is measured along a direction locally normal to the surface  102 . As described above, the robot  202  may be configured to adjust the position of the printhead  300  based on the normal spacing  338  measured by the position sensor  314  in a manner maintaining the normal spacing  338  at a constant value. As mentioned above, the robot  202  may be configured to command the robot  202  arm and/or a high-bandwidth actuator  250  (e.g.,  FIGS. 17-20 ) to adjust the location and/or orientation of the printhead  300  relative to the local surface as a means to maintain the printhead  300  within a predetermined value of the normal spacing  338  for optimal printing of image slices  404 . For example, the robot  202  may be configured to adjust the orientation of the printhead  300  to maintain the normal spacing  338  to within 0.010 inch of a predetermined value of the normal spacing  338 . In examples where the position sensor  314  at one widthwise end  306  ( FIG. 26 ) of the printhead  300  measures the normal spacing  338  relative to an image slice  404 , and the position sensor  314  at the opposite widthwise end  306  ( FIG. 27 ) of the printhead  300  measures the normal spacing  338  relative to the basecoat  103 , the robot  202  (e.g., the controller  208 ) may adjust one of the normal spacing  338  measurements to compensate for the thickness of the image slice  404  in a manner such that the face of the printhead  300  is maintained in parallel relation to the surface  102  over which the new image slice  406  is being printed. 
     Referring to  FIGS. 28-30 , shown is an example of a printhead  300  of which the laser device  342  is configured to etch the reference line  322  into a basecoat  103  covering the surface  102  onto which the new image slice  406  is printed. The printhead  300  shown in  FIG. 28  may be similar to the printhead  300  of  FIG. 23 , with the exception that the laser device  342  in  FIG. 28  is configured, positioned, and/or oriented to etch the reference line  322  into the basecoat  103  at a location immediately adjacent to (e.g., within 1.0 inch) the side edge  416 , as shown in  FIG. 29 . The reference line  322  is etched at a location that will be in the field of view of the reference line sensor  326  (e.g., a camera  327 ) during printing of a new image slice  406 . In some examples, the laser device  342  may be movably mounted to the printhead  300  in a manner allowing one to capability to select whether the reference line  322  will be etched into the new image slice  406  (e.g.,  FIGS. 24-27 ) or into the basecoat  103  (e.g.,  FIGS. 28-31 ). The reference line sensor  326  may have a field of view capable of capturing the reference line  322  regardless of whether the reference line  322  is etched into the new image slice  406  on one side of the side edge  416  of the new image slice  406 , or into the basecoat  103  on an opposite side of the side edge  416  of the new image slice  406 . 
       FIG. 29  shows a laser device  342  etching a reference line  322  into a basecoat  103  and further illustrates a camera  327  for sensing the location of the reference line  322  based upon variations in specular reflectivity of light emitted by the light source  329  and reflecting off of the reference line  322  prior to the reference line  322  of the existing image slice  408  being printed over by the new image slice  406 . As mentioned above, during the sensing of the reference line  322 , the camera  327  may continuously generate and transmit a path-following-error signal to the robot  202  resulting in the adjustment of the printhead  300  such that the side edge  416  of the new image slice  406  is maintained in alignment with the side edge  416  of the existing image slice  408  during the printing of the new image slice  406 . For example, the camera  327  may transmit the signal to the robot  202  resulting in a correction command to the high-bandwidth actuator  250  to adjust the printhead  300  in a manner such that the side edge  416  of the new image slice  406  is maintained in alignment with the side edge  416  of the existing image slice  408 . In addition, position sensors  314  at one or more locations around the printhead  300  may continuously measure the normal space (e.g., normal distance) between the printhead  300  and the surface  102 . The controller  208  may continuously receive from the position sensors  314  signals representing the normal spacing  338  measurements, and may adjust the orientation of the printhead  300  as required to maintain the printhead face  304  locally parallel to the surface  102  during printing of the new image slice  406 . 
     In  FIGS. 28 and 30 , the laser device  342  may be configured to etch the reference line  322  with an encoding pattern  324  comprising a series of line segments  323  forming a dashed line. The line segments  323  may be of uniform length and uniform spacing separated by gaps. The laser device  342  may have a relatively short response time with pulsewidths in the millisecond range or less and allowing for the etching of correspondingly short line segments  323  that make up the reference line  322 . The reference line sensor  326  (e.g., camera  327 ) may have a field of view of (e.g., less than 1 inch) that allows the camera  327  to view upcoming line segments  323  of the reference line  322 . The reference line sensor  326  may continuously sense the line segments  323  and may continuously transmit a representative signal (e.g., a path-following-error signal) to the robot  202 . 
     The controller  208  may determine the printhead velocity during the printing of the new image slice  406  based on the rate at which the line segments  323  are sensed by the reference line sensor  326 , and may adjust the printhead velocity such that the printhead  300  is maintained at substantially the same (e.g., within 10 percent and, more preferably, within 1 percent) printhead velocity during printing of the new existing image slice  408  as the printhead velocity recorded during the printing of the existing image slice  408 . For example, during the printing of the existing image slice  408 , the laser device  342  may have etched a line segment  323  every 10 millisecond with a 5 millisecond (ms) gap between each line segment. If, during printing of the new image slice  406 , the reference line sensor  326  senses a line segment  323  of the existing image slice  408  every 9 ms, then the controller  208  of the robot  202  may reduce the printhead velocity until the reference line sensors  326  sense a spacing of 10 ms between line segments  323 . The printhead velocity may be adjusted via the above-described high-bandwidth actuator  250  (e.g.,  FIGS. 17-20 ) optionally coupling the printhead  300  to the arm of the robot  202 . If the required adjustment of the printhead  300  approaches the limits of the range of motion of the high-bandwidth actuator  250 , then further adjustment of the printhead velocity may be facilitated by adjusting the movement of the robot base  128  along the crossbeam  132  ( FIGS. 4-5 ) and/or by adjusting the movement of the arm of the robot  202 . 
     Adjustment of the printhead velocity may maintain longitudinal correspondence of the new image slice  406  with the existing image slice  408 . For example, as described above with regard to printing the numbers “777” that make up the image  400  of  FIG. 23 , the printhead velocity may be controlled in a manner such that the constant-rate ejection of droplets  330  (e.g.,  FIGS. 26-27 ) during printing of each new image slice  406  is started and stopped at the corresponding or same locations as during the printing of the existing image slice  408 . Adjustment of the printhead velocity may also provide a means to maintain longitudinal matching of the droplet density and image details of the new image slice  406  with the droplet density and image details of the existing image slice  408 . As mentioned above, such image details may include changes in color during the printing of an image slice  404 . By maintaining longitudinal correspondence of image slices  404  by continuously tracking the encoding pattern  324  (e.g.,  FIGS. 28 and 30 ) of the reference line  322 , and by maintaining lateral alignment of image slices  404  by continuously tracking and correcting for the lateral spacing  340  (e.g., FIG.  26 ) between the reference line  322  and an indexing feature (e.g., the centerline of the camera  327 ), the visual quality of the completed image  400  may be significantly improved. 
     Referring to  FIG. 30 , shown is an example of a reference line  322  in which one or more of the line segments  323  is etched with an individual encoding pattern  324  comprising a series of dash segments  325 . The combined end-to-end length of the dash segments  325  may be equivalent to the length of a single line segment  323 , and may provide a means to signal to the controller  208  that a start or a stop (e.g.,  FIG. 23 ) within the new image slice  406  is approaching. By encoding one or more of the line segments  323  as a plurality of dash segments  325 , the controller  208  may more precisely control the printhead  300  to stop or start the constant-rate ejection of droplets  330  to match the starts and stops of a given segment of the existing image slice  408 . 
     As an alternative to ejecting droplets  330  at a constant rate, the controller  208  of the robot  202  may operate the printhead  300  in a manner in which the ejection rate of droplets  330  is modulated in correspondence with the line segments  323  of the existing image slice  408  during the printing of a new image slice  406 . For example, the printhead  300  may be operated in a manner to start ejecting droplets  330  at the start of each line segment  323  sensed by the reference line sensor  326 . The time period within which the printhead  300  ejects droplets  330  is adjusted such that a predetermined number of droplets  330  are ejected within the time period between the start of each line segment  323  and the end of the gap  321  following the same line segment  323 . The time period between the sensing of the start of each line segment  323  to the end of the gap  321  following the same line segment  323  is used as the amount of time allotted for the ejection of the predetermined number of droplets  330  for the next line segment  323  and gap  321 . The modulation process adjusts the amount of time between the predetermined number of droplets  330  based on the amount of time between the dashes  321 , thereby providing a uniform density of droplets  330  (along a lengthwise direction of the new image slice  406 ) independent of the velocity of the printhead  300 . 
       FIG. 31  is a flowchart of operations in a method  700  for printing an image  400  on a surface  102  using a printhead  300  having a laser device  342  for etching a reference line  322 . Step  702  of the method  700  comprises printing, using a printhead  300  mounted to an arm of a robot  202 , a new image slice  406  on the surface  102  while moving the printhead  300  over the surface  102  along a rastering path  350 . As mentioned above, the printhead  300  may be an inkjet printhead  300  having one or more rows of nozzles  308  for ejecting droplets  330  of ink, paint, or other colorants onto a surface  102 . Alternatively, the printhead  300  may be configured as a dot matrix printer or other printer configuration capable of printing an image  400  on a surface  102 . 
     Step  704  of the method  700  comprises etching, using a laser device  342 , a reference line  322  into either the new image slice  406  as shown in  FIGS. 24-27 , or into a basecoat  103  over which the new image slice  406  is printed as shown in  FIGS. 28-30 . As mentioned above, reference line  322  may be etched into the new image slice  406  or into the basecoat  103  at a location immediately adjacent to the side edge  416  of the new image slice  406 . In some examples, the laser device  342  may be pivotably or translatably mounted to the printhead  300  to allow a user to re-orient the laser device  342  in order to change whether the reference line  322  is etched into the new image slice  406  or alternatively is etched into the basecoat  103 . The step  704  of etching the reference line  322  may include etching the reference line  322  into the new image slice  406  or into the basecoat  103  at a line depth  348  of less than approximately 0.005 inch. More preferably, the reference line  322  may be etched at a line depth  348  of less than approximately 0.001 inch. In addition, the reference line  322  may be etched at a line width  346  in the range of approximately 0.002-0.010 inch. By etching the reference line  322  at a relatively small line depth  348  and relatively small line width  346 , the reference line  322  may be visually imperceptible after being covered by a layer of clearcoat (not shown). 
     Step  706  of the method  700  comprises sensing, using a reference line sensor  326 , the reference line  322  of an existing image slice  408  while printing the new image slice  406 . In some examples, the step  706  of sensing the reference line  322  may comprise emitting, using an optical sensor, an optical beam  328  toward the reference line  322  as shown in  FIG. 16 . The method may further include generating, using the optical sensor, a signal representing a lateral location where the optical beam  328  strikes the reference line  322 . The method may additionally include transmitting the signal to the controller  208  of the robot  202  to allow the controller  208  to adjust the printhead  300  in a manner maintaining alignment of the side edge  416  of the new image slice  406  with the side edge  416  of the existing image slice  408 . 
     In a further example shown in  FIG. 26 , the step  706  of sensing the reference line  322  may comprise illuminating, using a light source  329 , the reference line  322  and a surrounding area during printing of a new image slice  406 . As mentioned above, the light source  329  may be coupled to the printhead  300  and may be oriented in a manner such that the emitted light is reflected off of the surface into which the reference line  322  is etched. The light source  329  may continuously illuminate the reference line  322  and the surrounding area during printing of the new image slice  406 . The method may additionally include receiving, at a camera  327  (e.g., a monochrome camera  327 ), the light emitted by the light source  329  and reflected off of the reference line  322  and the surrounding area. The method may additionally include determining, using the camera  327 , the lateral location of the reference line  322  based on variations in specular reflectivity of the light emitted by the light source  329 . The camera  327  may generate a signal representative of the lateral location of the reference line  322  relative to an indexing feature such as a vertical centerline of the camera  327 , and may transmit the signal to the controller  208  of the robot  202  to allow the controller  208  to adjust the printhead  300  in a manner maintaining alignment of the new image slice  406  with the existing image slice  408 , as described below. 
     Step  708  of the method  700  comprises adjusting, using the controller  208 , the printhead  300  based on a sensed position of the reference line  322  in a manner maintaining alignment of a side edge  416  of the new image slice  406  with the side edge  416  of the existing image slice  408 . For example, the step  708  of adjusting the printhead  300  may comprise physically adjusting the lateral position of the printhead  300  such that the side edge  416  of the new image slice  406  image slice  404  is maintained in non-gapped and non-overlapping relation with the side edge  416  of the existing image slice  408 . As an alternative to physically adjusting the lateral position of the printhead  300 , the step  708  of adjusting the printhead  300  may comprise electronically offsetting or shifting nozzles  308  or groups of nozzles  308  actively ejecting droplets  330  in a manner such that the side edge  416  of the new image slice  406  is maintained in non-gapped and non-overlapping relation with the side edge  416  of the existing image slice  408 . In a still further example, the method may include a combination of adjusting the lateral position of the printhead  300 , and electronically shifting nozzles  308  actively ejecting droplets  330 . 
     In some examples, the step  708  of adjusting the printhead  300  may include adjusting the position of the printhead  300  using at least one high-bandwidth actuator  250  coupling the printhead  300  to an end  214  of the second arm  212 , as shown in  FIGS. 17-20 . The adjustment of the printhead  300  using the high-bandwidth actuator  250  may include translating the printhead  300  along a lateral or transverse direction  354  ( FIG. 25 ) parallel to the surface  102  and perpendicular to the rastering path  350 , translating the printhead  300  along a normal direction  356  ( FIG. 25 ) normal to the surface  102 , and/or rotating the printhead  300  along a roll direction  358  ( FIG. 25 ) about an axis parallel to the rastering path  350 .  FIG. 18  shows an example of a high-bandwidth actuator  250  comprised of a first actuator  250   a , a second actuator  250   b , and a third actuator  250   c  arranged in an in-plane tripod configuration. As described above, the lower end of the second actuator  250   b  may be located adjacent to the lower end of the third actuator  250   c  such that the second actuator  250   b  extends diagonally between the upper end of the first actuator  250   a  and the lower end of the third actuator  250   c . The arrangement of the first actuator  250   a , second actuator  250   b , and third actuator  250   c  enables the adjustment of the printhead  300  along the transverse direction  354 , the normal direction  356 , and the roll direction  358 . 
     Referring briefly to  FIGS. 28 and 30 , shown is an example of the system  200  in which the reference line  322  is etched with an encoding pattern  324  comprising a series of line segments  323  forming a dashed line. The line segments  323  may be of uniform length and uniform spacing and may be separated by gaps of uniform length. The reference line sensor  326  may sense the line segments  323  and transmit to the robot  202  a signal representative of the sensed line segments  323 . The method may include determining, using the controller  208  of the robot  202 , the printhead velocity during the printing of a new image slice  406 . The determination of the printhead velocity may be based on the rate at which the line segments  323  are sensed by the reference line sensor  326  during printing of the new image slice  406  while ejecting droplets  330  at a constant rate. The method may further include adjusting, using the robot  202 , the printhead velocity such that the printhead  300  is maintained at substantially the same (e.g., within 1 percent) printhead velocity as during the printing of the existing image slice  408 . As mentioned above, the controller  208  may record the printhead velocity during printing of the existing image slice  408  for comparison to the printhead velocity during the printing of the new image slice  406 . 
     The adjustment of the printhead velocity may be performed using a high-bandwidth actuator  250  ( FIGS. 17-20 ). If approaching the limits of the range of motion of the high-bandwidth actuator  250 , the adjustment of the printhead velocity may be performed by adjusting the movement of the robot  202  base  128  along the crossbeam  132  (e.g.,  FIGS. 4-5 ) and/or by adjusting the movement of an arm of the robot  202 . As mentioned above, matching the printhead velocity during printing of the new image slice  406  with the printhead velocity during printing of the existing image slice  408  provides a means to maintain longitudinal correspondence of the droplet density and image details of the new image slice  406  with the droplet density and image details of the existing image slice  408 . Referring briefly to  FIG. 30 , the method may include etching one or more of the line segments  323  as a series of dash segments  325  as a means to signal to the controller  208  that an end of at least a portion of the image slice  404  is approaching, allowing the controller  208  to operate the printhead  300  to stop or start the ejection of droplets  330  at the appropriate time to substantially match (e.g., within 0.010 inch) the existing image slice  408 . 
     As an alternative to adjusting the printhead velocity for a printhead  300  with constant-rate ejection of droplets  330 , the method may include operating the printhead  300  in a manner in which the ejection rate of droplets  330  is modulated during printing of the new image slice  406 . In this regard, as mentioned above, the ejection of droplets  330  is started in correspondence with the start of each one of the line segments  323  of the existing image slice  408 , and is spaced in time such that eject a predetermined number of droplets  330  are ejected by the end of the gap  321  following the same line segment  323 . 
     Referring briefly to  FIGS. 26-27 , the method may include periodically or continuously measuring, using at least one position sensor  314  coupled to the printhead  300 , the normal spacing  338  between the printhead face  304  and the surface  102  along a direction locally normal to the surface  102 . The method may additionally include periodically or continuously adjusting, during printing of the new image slice  406 , the position of the printhead  300  based on the normal spacing  338  measured by the position sensor  314  in a manner to maintain the normal spacing  338  at a constant value. The adjustment of the position of the printhead  300  may include adjusting the lateral location of the printhead  300  and/or adjusting the orientation about the printhead  300  relative to the surface  102  locally. In some examples, the printhead  300  may be adjusted in a manner to maintain the printhead face  304  within approximately 0.010 inch of a predetermined value of the normal spacing  338  as a means to provide consistency of droplet application onto the surface  102  across the width of the printhead  300 . In addition, maintaining the normal spacing  338  at a constant value during printing of a new image slice  406  may improve the longitudinal matching of the image details (not shown) of the new image slice  406  with the image details of the existing image slice  408 , and may improve the accuracy with which the side edge  416  of the new image slice  406  is maintained in non-gapped and non-overlapping relation with the side edge  416  of the existing image slice  408 . 
     The method may additionally include measuring, using at least three positions sensors  314 , the normal spacing  338  at different locations on the printhead  300 . For example, four position sensors  314  may be arranged in a rectangular pattern around the printhead  300 . The method may include adjusting the orientation of the printhead  300  based on the normal spacing  338  sensed by the position sensors  314 . The orientation of the printhead  300  may be adjusted in a manner maintaining the printhead  300  locally parallel to the surface  102  upon which the new image slice  406  is being printed. Maintaining the printhead  300  locally parallel to the surface  102  may maintain all of the nozzles  308  across the printhead width  302  at approximately same spacing from the surface  102 , which may improve the consistency with which the droplets  330  are deposited onto the surface  102  to thereby improve the image  400  quality. 
     Additional modifications and improvements of the present disclosure may be apparent to those of ordinary skill in the art. Thus, the particular combination of parts described and illustrated herein is intended to represent only certain embodiments of the present disclosure and is not intended to serve as limitations of alternative embodiments or devices within the spirit and scope of the disclosure.