the present invention is directed to maximizing the amount of cargo in a limited three - dimensional space . referring to fig5 a and 5 b , the illustrated embodiment utilizes a modified “ slide - puzzle ” principle to maximize storage capacity , while facilitating easy access to cargo in an expedited manner . under the “ slide puzzle ” principle , a storage area is divided into a storage matrix 1 , wherein every cell module 100 comprises a moving carrier and cargo disposed thereon , except for one or two empty cell modules . by using all but one or two cell modules , the storage space may stow more cargo than previously was possible with conventional rack and aisle operations . further resulting from the one or two empty spaces , the system devises a carrier movement scheme through the use of a computer controlled indexing algorithm based on the “ slide puzzle ” principle . in this carrier movement scheme , a payload carrier in the back corner of a storage area may be moved to the front of the storage area matrix through the coordinated movement of one or more carriers . for more details on the “ slide puzzle ” principle , u . s . pat . no . 6 , 842 , 665 , and u . s . patent application ser . no . 11 / 552 , 845 are incorporated by reference herein , in its entirety . the system components of the present invention will utilize a modified form of the “ slide puzzle ” principle , wherein some of the cell modules may only facilitate uni - directional movement of the carriers . referring to fig1 , the storage matrix 1 comprises a plurality of stationary cell modules arranged in a matrix . the storage matrix 1 may constitute any three dimensional storage location , warehouse , or facility suitable for stowing containers or palletized loads . in an exemplary embodiment , the storage matrix 1 is a hold of a ship , configured to stow cargo , e . g . weapon payloads . the storage matrix embodiment of fig1 is a 5 × 5 matrix ; however , various other matrix sizes and dimensions are contemplated herein . “ payload ”, as used herein , refers to cargo and supplies , especially cargo such as military pallets comprising bombs , missiles , grenades , and combinations thereof . each cell module , whether an outer row cell module 10 or an inner cell module 20 , is a permanent structure embedded in or securely mounted to the floor of a storage matrix 1 . in the embodiments of fig1 - 3 , the cell modules define a substantially flat rectangular plate structure , but other shapes and dimensions are also possible . although the cell modules are permanent structures , it is contemplated that they may be removed from the floor , for example , if it is necessary to detach the modules from the floor for repair or replacement . in accordance with the embodiment of fig1 , the storage matrix 1 comprises two types of cell modules : outer row cell modules 10 and inner row cell modules 20 . the outer row cell modules 10 comprises motors 12 , 14 arranged along both planar axes of the storage matrix 1 , e . g . the x and y axes as shown in fig1 . by having motors disposed along both planar axes , the outer row cell modules 10 are operable to move the carrier bi - directionally within the storage matrix 1 . in contrast , the inner cell modules 20 comprise at least one motor 22 disposed along one of the planar axes , for example , the y axis as shown in fig1 . by having motors disposed along only one planar axis , the inner row cell modules 20 are operable to move carriers uni - directionally within the storage matrix 1 . in an exemplary embodiment , the motors of the inner row cell modules 20 and the outer row cell modules 10 may comprise linear synchronous motors , for example , short drive linear synchronous motors , long drive linear synchronous motors , or combinations thereof . in a further embodiment , the motors may comprise iron - core linear synchronous motors , for example , and not by way of limitation , the ic55 - 250 direct drive linear synchronous motor assembly manufactured by kollmorgen . referring to fig6 a and 6 b , the storage matrix 1 also comprises a plurality of carriers 30 configured to couple with a cell module in the storage area matrix 1 . like the cell modules 10 , 20 , the carriers 30 define a substantially flat rectangular plate structure . referring to fig6 b , the carriers 30 comprise at least one magnet 32 , 34 disposed on an underside of the carrier 32 . the carriers may comprise various sizes as desired by the user , or as dictated by the storage area in which the carriers are incorporated . the magnets 32 , 34 are configured to engage the motors of the inner row cell modules 10 or outer row cell modules 20 to secure the carriers 30 to the respective module when the carriers 30 are at a stationary position . the magnets 32 , 34 comprise various materials suitable to magnetically couple to a motor , for example , lanthanides , metals , transition metals , metalloids , and combinations thereof . the magnetic coupling stabilizes the carrier and attached payloads thereon under dynamic loads , including environmental loads such as those due to ship motion in high sea states via magnetic attraction between the permanent magnets on the underside of the moving carrier and the stationary iron - core linear electric motors or the ferrous metal plates . in an embodiment , the magnets 32 , 34 may comprise neodymium , iron , and boron . suitable magnets may include the mc250 neodymium - iron - boron permanent magnet way produced by kollmorgen , and which may be used with the icc - 250 iron core linear synchronous motors of the cell modules 10 , 20 . as shown in the embodiment of fig6 b , the carriers 30 may comprise at least one long drive ( x axis ) magnet 32 that engages the x axis linear motor 14 of the outer row cell module 10 , and may also comprise at least one short drive ( y axis ) magnet 34 that engages a y axis linear motor 12 of the outer row cell module 10 or a y axis linear motor 22 of the inner row cell module 20 . when coupling the carriers 30 to the outer row cell modules 10 , arranging the short drive magnets 34 and long drive magnets 32 on the four sides of the carrier 32 ensures that the carriers 30 are firmly secured in multiple directions . this is especially beneficial when the carriers are inside a storage area 1 of a ship that pitches and yaws unpredictably at sea . when coupling the carriers to the inner cell modules 20 , the inner row cell modules 20 may not provide a sufficient down - force to stabilize a payload disposed thereon , because the inner row cell modules 20 only comprise motors along one planar axis . consequently , the inner row cell modules 20 may comprise a metal plate 24 , for example a ferrous metal plate , as shown in fig1 - 3 . the metal plate 24 is capable of providing a downward force to stabilize a payload disposed on a carrier 30 by magnetically coupling to the magnets of the carrier 30 , for example , the long drive magnet 32 of the carrier . the metal plate 24 may comprise various metal materials known to one of ordinary skill in the art . for example , and not by way of limitation , the metal plate may comprise steel , iron , or combinations thereof . in one exemplary embodiment , the metal plate 24 may be arranged parallel to and between a pair of motors 22 . in addition to securing the carriers 20 , the motors of the inner row cell module 20 and the outer row cell module 10 are also configured to transfer a carrier from one cell module to another cell module . as stated above , due to the placement of the motors , the outer row cell modules 10 may move the carriers 30 bi - directionally , whereas the inner row cell modules 10 may move the carriers 30 uni - directionally . when a carrier 30 is present on an outer row cell module 10 , the linear synchronous motors 12 , 14 deliver a thrust force in the x and y direction , which decouples the carrier magnets 34 , 32 from the motors 12 , 14 , respectively , and moved the carrier in either planar axis to an adjacent inner or outer row cell module . when a carrier 30 is present on an inner row cell module 20 , the linear synchronous motors 22 delivers a thrust force in only one planar axis , e . g . the y axis , which decouples the carrier magnets 34 from the motors 22 , and move the carrier in only one planar axis , e . g . in the y direction to an adjacent inner or outer row cell module . this uni - directional movement of the inner row cell modules 20 modifies the movement sequence , which is modeled after the sliding puzzle principle . fig5 a and 5 b provide an example of the movement sequence ( steps 1 - 20 ) in which carriers move from an unloading / loading area 50 to another location in the storage matrix 1 . in contrast to the zigzag path of the sliding puzzle principle , the carriers 30 may move in a rectangular circulation pattern through the storage matrix as shown in fig5 a and 5 b . by limiting the movement flexibility of many of the cell modules , the carrier movement scheme may require more movement steps ; however , the minimal increase in steps is offset by the reduced costs in reducing the amount of linear motors in the system . in addition to the costs of purchasing and installing linear synchronous motors on all sides of the cell modules , the energy costs required to produce the motor thrust force in both the x and y directions is also significant . consequently , eliminating motors , e . g . x axis motors , on the inner row cell modules 20 may greatly reduce system costs . to reduce friction as a carrier 30 slides from one cell module to another and thereby further reduce the required amount of thrust , the outer row cell modules 10 and the inner row cell modules 20 may both comprise friction - reducing surfaces . the friction reducing surfaces may comprise any suitable material operable to minimize sliding friction as a carrier or another vehicle moves over the cell modules 10 or 20 . in one exemplary embodiment , the friction reducing surfaces may comprise a fluoropolymer material , such as pfa or ptfe . in another exemplary embodiment , the friction reducing surfaces may comprise rulon ®. alternatively , the bearings may also comprise ball transfer units or air bearings . as shown in fig3 , the outer row cell module 10 may comprise plenums 16 or openings . to produce a substantially frictionless air bearing surface on the top surface of the outer row cell module 10 , air is delivered through these plenums 16 , for example , via air bearing nozzles ( not shown ) and air supply lines ( not shown ) contained within the outer row cell module 10 . referring to the embodiment of fig3 , the inner row cell modules 20 comprise roller bearings 26 , which are generally lightweight and non - powered , resulting in reduced system weight and cost . in a further embodiment , the roller bearings 26 are arranged perpendicular to and between a pair of motors 22 . referring to the embodiment of fig6 a , the carrier 30 may comprise at least one engagement mechanism 36 disposed on a top side of the carrier 30 for coupling with a payload interface 40 . the engagement mechanism 36 may comprise any suitable component for coupling with one or more payload interfaces 40 at various locations along the carrier surface 30 . for more details on the payload interfaces as shown in fig4 and other components of the storage and retrieval system , please review u . s . pat . no 6 , 842 , 665 , and u . s . patent application ser . no . 11 / 552 , 845 , which are incorporated by reference herein , in its entirety . it is noted that terms like “ specifically ,” “ preferably ,” “ generally ”, “ commonly ,” and “ typically ” are not utilized herein to limit the scope of the claimed invention or to imply that certain features are critical , essential , or even important to the structure or function of the claimed invention . rather , these terms are merely intended to highlight alternative or additional features that may or may not be utilized in a particular embodiment of the present invention . it is also noted that terms like “ substantially ” and “ about ” are utilized herein to represent the inherent degree of uncertainty that may be attributed to any quantitative comparison , value , measurement , or other representation . having described the invention in detail and by reference to specific embodiments thereof , it will be apparent that modifications and variations are possible without departing from the scope of the invention defined in the appended claims . more specifically , although some aspects of the present invention are identified herein as preferred or particularly advantageous , it is contemplated that the present invention is not necessarily limited to these preferred aspects of the invention .