Patent Publication Number: US-2021161066-A1

Title: System and method for operating an autonomous robotic working machine within a travelling containment zone

Description:
This application claims the benefit of both U.S. Provisional Application No. 62/599,938, filed 18 Dec. 2017, and U.S. Provisional Application No. 62/588,680, filed 20 Nov. 2017, both of which are hereby incorporated by reference in their respective entireties. 
     The present disclosure relates to autonomous robotic working machines including vehicles such as lawn mowers and, more particularly, to methods and systems for controlling operation of such machines on a property or other work region. 
    
    
     BACKGROUND 
     Lawn and garden machines are known for performing a variety of tasks. For instance, powered lawn mowers are used by both homeowners and professionals alike to maintain grass areas within a property or yard. 
     Robotic lawn mowers that autonomously perform the grass cutting function are also known. Robotic lawn mowers are typically battery-powered and are often limited to cutting only a portion of the property before requiring re-charging, which typically requires the mower to return to a charging base station. 
     Robotic lawnmowers also generally cut grass in a random travel pattern within a fixed property boundary, wherein the boundary is defined by a continuous boundary marker, e.g., an energized wire laying on or buried beneath the lawn at the property boundary. Such boundary wires may also extend into the interior of the yard to demarcate obstacles (e.g., trees, flower beds, etc.) or other exclusion zones. The mower may then move randomly within the areas delineated by the boundary wire. 
     While effective, the random pattern of the mower combined with the variability of the boundary (i.e., shape of property lines, shape and size of obstacles, etc.) can create problems. For example, the mower may sometimes mow the same areas longer than needed, while missing areas not yet mowed. This occurs when the layout of the yard (e.g., the boundaries and excluded areas/obstacles), combined with the random pattern motion of the mower, leads to increased difficultly accessing certain areas (e.g., those areas of the yard having narrow entry passages). If the mower is unable to access these areas, such areas may be missed, reducing the perceived quality of cut. Conversely, when the mower is able to reach these areas, it may get unduly “hung-up,” potentially extending the time it takes to complete the mowing task before requiring recharging. 
     SUMMARY 
     Embodiments described herein may provide a method of operating an autonomous working vehicle within a predefined work region, the method comprising: defining, with a controller associated with the working vehicle, a travelling containment zone that lies at least partially within the work region, the travelling containment zone defining a zone area that is less that an area of the work region; autonomously operating the working vehicle within the travelling containment zone; constraining a position of the working vehicle to be within the travelling containment zone; and moving the travelling containment zone across the work region while the working vehicle operates within the travelling containment zone. 
     In another embodiment, a method of operating an autonomous working vehicle within a predefined work region is provided, the method comprising: defining, with a controller associated with the working vehicle, a travelling containment zone that lies at least partially within the work region, the travelling containment zone defining a zone area that is less that an area of the work region; autonomously transporting the working vehicle from a location beyond the travelling containment zone to a location within the travelling containment zone; autonomously operating an implement attached to the working vehicle within the travelling containment zone; and moving the travelling containment zone across the work region while the working vehicle operates within the travelling containment zone. 
     In yet another embodiment, a mowing system is provided that includes an autonomously operating mower adapted to cut grass growing in a work region as the mower travels about the work region. The mower includes: a chassis supported upon a grass surface by ground support members, wherein one or more of the ground support members comprises a drive member; a grass cutting element attached to the chassis; a motor adapted to power the cutting element and the drive member; and a controller adapted to control the cutting element and a speed and direction of the drive member. The controller is further adapted to: identify a travelling containment zone at least partially within the work region, the travelling containment zone comprising a zone area that is less than an area of the work region; and constrain operation of the mower to be within both the travelling containment zone and the work region as the travelling containment zone travels across the work region. 
     In yet another embodiment, a method of operating an autonomous working vehicle within a predefined work region is provided, wherein the method includes defining, with a controller associated with the working vehicle, a travelling containment zone that lies at least partially within the work region, wherein the work region bounds a first plurality of grid cells and the travelling containment zone bounds a lesser second plurality of grid cells. The method further includes: autonomously operating the working vehicle within the travelling containment zone; constraining a position of the working vehicle to be within the travelling containment zone; moving the travelling containment zone across the work region while the working vehicle operates within the travelling containment zone; and deciding, with the controller, a direction in which to advance the travelling containment zone. 
     In still another embodiment, a method of operating an autonomous working vehicle within a predefined work region is provided. The method may include one or more of: defining, with an electronic controller associated with the working vehicle, a travelling containment zone that lies at least partially within the work region, the travelling containment zone defining a zone area that is less that an area of the work region; autonomously operating the working vehicle within the travelling containment zone; constraining a position of the working vehicle to be within the travelling containment zone; and moving the travelling containment zone across the work region while the working vehicle operates within the travelling containment zone. One or more aspects may be additionally included, in any combination, to produce yet additional embodiments. For example, the working vehicle may be configured as a lawn mower. In another aspect, the work region may comprise a grass surface of a property. In another aspect, a shape of the travelling containment zone may be varied as the travelling containment zone moves across the work region. In still another aspect, the method may further comprise moving the working vehicle in a random manner within the travelling containment zone. In yet another aspect, the method includes controlling a steering angle and a ground speed of the working vehicle with the controller. In yet another aspect, the method further includes maintaining an initial position of the travelling containment zone for a period of time before moving the travelling containment zone across the work region. In still yet another aspect, the method includes estimating, with the controller, a time at which operation of the working vehicle over the entire work region will be complete. In still another aspect, the method includes either: maintaining the zone area of the travelling containment zone constant as the travelling containment zone moves across the work region; or varying the zone area of the travelling containment zone as the travelling containment zone moves across the work region. In yet another aspect, the method includes either: maintaining a speed of the working vehicle while operating the working vehicle within the travelling containment zone; or varying a speed of the working vehicle while operating the working vehicle within the travelling containment zone. In yet another aspect, moving the travelling containment zone comprises moving the travelling containment zone at either: a constant rate or a variable rate. 
     In another embodiment, a mowing system is provided comprising an autonomously operating mower adapted to cut grass within a work region as the mower travels about the work region. In one aspect, the system may comprise one or more of: a chassis supported upon a grass surface by ground support members, wherein one or more of the ground support members comprises a drive member; a grass cutting element carried by the chassis; one or more motors adapted to power the cutting element and the drive member; and an electronic controller adapted to control operation of the cutting element and a speed and direction of the mower. The controller is adapted to: identify a travelling containment zone at least partially within the work region, the travelling containment zone comprising a zone area that is less than an area of the work region; and constrain operation of the mower to be within both the travelling containment zone and the work region as the travelling containment zone travels across the work region. One or more aspects may be additionally included, in any combination, to produce yet additional embodiments. For example, in one aspect, the controller may maintain an initial position of the travelling containment zone for a period of time before moving the travelling containment zone across the work region. In another aspect, the mower further comprises a positioning system adapted to estimate a position of the mower within the work region, wherein the positioning system is operatively connected to the controller. In yet another aspect, the system further comprises a base station located in or near the work region. 
     In still yet another embodiment, a method of operating an autonomous working vehicle within a predefined work region is provided. In one aspect, the method may comprise one or more of: defining, with an electronic controller associated with the working vehicle, a travelling containment zone that lies at least partially within the work region, wherein the work region bounds a first plurality of grid cells and the travelling containment zone bounds a lesser second plurality of grid cells; autonomously operating the working vehicle within the travelling containment zone; constraining a position of the working vehicle to be within the travelling containment zone; deciding, with the controller, a direction in which to advance a leading edge of the travelling containment zone; and moving the travelling containment zone across the work region while the working vehicle operates within the travelling containment zone. One or more aspects may be additionally included, in any combination, to produce yet additional embodiments. For example, in one aspect, deciding the direction to advance the travelling containment zone comprises scoring two or more grid cells, the two or more grid cells being externally adjacent to a boundary of the travelling containment zone. In another aspect, the scoring the two or more grid cells comprises evaluating a wavefront grid value of each cell of the two or more grid cells. In another aspect, scoring the two or more grid cells comprises comparing a distance from each cell of the two or more grid cells to a centroid of the travelling containment zone. In yet another aspect, the method further includes detecting bifurcation of the leading edge into at least a first segment and a second segment upon contact of the leading edge with an exclusion zone contained within the work area. In still another aspect, the method further comprises replacing the leading edge with either the first segment or the second segment. In still yet another aspect, moving the travelling containment zone comprises advancing a trailing edge of the travelling containment zone, while in another aspect, moving the travelling containment zone comprises adding grid cells from the first plurality of grid cells to the travelling containment zone. In yet another aspect, moving the travelling containment zone comprises removing grid cells from the travelling containment zone. 
     The above summary is not intended to describe each embodiment or every implementation. Rather, a more complete understanding of illustrative embodiments will become apparent and appreciated by reference to the following Detailed Description of Exemplary Embodiments and claims in view of the accompanying figures of the drawing. 
    
    
     
       BRIEF DESCRIPTION OF THE VIEWS OF THE DRAWING 
       Exemplary embodiments will be further described with reference to the figures of the drawing, wherein: 
         FIG. 1A  illustrates an exemplary property defining work regions, exclusion zones, and transit zones in accordance with embodiments of the present disclosure; 
         FIG. 1B  is a diagrammatic view of an autonomous working vehicle, e.g., robotic lawn mower, in accordance with embodiments of the present disclosure; 
         FIG. 2  illustrates an exemplary method of operating the mower within a travelling containment zone of a work region; 
         FIGS. 3A-3K  illustrate an exemplary method of operating a mower in another, more complex, work region, wherein:  FIG. 3A  illustrate an initial travelling containment zone at a time t=t 1 ;  FIG. 3B  illustrates the travelling containment zone at a time t=t 2 ;  FIG. 3C  illustrates the travelling containment zone at a time t=t 3 ;  FIG. 3D  illustrates the travelling containment zone at a time t=t 4 ;  FIG. 3E  illustrates the travelling containment zone at a time t=t 5 , wherein the travelling containment zone is shown moving around an exclusion zone to prevent bisecting the travelling containment zone;  FIG. 3F  illustrates the travelling containment zone at a time t=t 6 ;  FIG. 3G  illustrates the travelling containment zone at a time t=t 7 ;  FIG. 3H  illustrates the travelling containment zone at a time t=t 8 ;  FIG. 3I  illustrates the travelling containment zone at a time t=t 9 ;  FIG. 3J  illustrates the travelling containment zone at a time t=t 10 ; and  FIG. 3K  illustrates the travelling containment zone at a time t=t 11 ; 
         FIG. 4  illustrates a map of yet another exemplary work region defined by a boundary and containing multiple exclusion zones, the work region laid over an x-y grid, the grid defining a plurality of grid cells; 
         FIG. 5  is a visual depiction of an exemplary wavefront grid of the work region map of  FIG. 4 ; 
         FIGS. 6A-6H  illustrate an exemplary computer-simulated method of operating a mower within the work region shown in the map of  FIG. 4 , wherein:  FIG. 6A  illustrates a travelling containment zone at time t=t 1 ;  FIG. 6B  illustrates the travelling containment zone at time t=t 2 , illustrating a leading edge of the travelling containment zone as it encounters an exclusion zone;  FIG. 6C  illustrates the travelling containment zone at time t=t 3 ;  FIG. 6D  illustrates travelling containment zone at time t=t 4 ;  FIG. 6E  illustrates the travelling containment zone at time t=t 5 ;  FIG. 6F  illustrates the travelling containment zone at time t=t 6  after the mower finished in the area shown in  FIG. 6E  and has relocated to a new starting area; and  FIG. 6G  illustrates the travelling containment zone at time t=t 7  after the mower has again relocated to a new starting area; and  FIG. 6H  is an enlarged view of the travelling containment zone of  FIG. 6B ; and 
         FIG. 7  illustrates an exemplary process that assists in preventing bifurcation or “splitting” of the travelling containment zone. 
     
    
    
     The figures are rendered primarily for clarity and, as a result, are not necessarily drawn to scale. Moreover, various structure/components, including but not limited to fasteners, electrical components (wiring, cables, etc.), and the like, may be shown diagrammatically or removed from some or all of the views to better illustrate aspects of the depicted embodiments, or where inclusion of such structure/components is not necessary to an understanding of the various exemplary embodiments described herein. The lack of illustration/description of such structure/components in a particular figure is, however, not to be interpreted as limiting the scope of the various embodiments in any way. 
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     In the following detailed description of illustrative embodiments, reference is made to the accompanying figures of the drawing which form a part hereof. It is to be understood that other embodiments, which may not be described and/or illustrated herein, are certainly contemplated. 
     All headings provided herein are for the convenience of the reader and should not be used to limit the meaning of any text that follows the heading, unless so specified. Moreover, unless otherwise indicated, all numbers expressing quantities, and all terms expressing direction/orientation (e.g., vertical, horizontal, parallel, perpendicular, etc.) in the specification and claims are to be understood as being modified in all instances by the term “about.” Further, the term “and/or” (if used) means one or all of the listed elements or a combination of any two or more of the listed elements. Still further, “i.e.” may be used herein as an abbreviation for id est, and means “that is,” while “e.g.,” may be used as an abbreviation for exempli gratia, and means “for example.” 
     Embodiments of the present disclosure provide autonomous robotic working vehicles and methods of operating the same within a predefined work region to achieve improved vehicle coverage (e.g., with an implement associated with the vehicle) of the work region during operation. For example, the vehicle may be an autonomous robotic mower adapted to cut grass, using an associated cutting member, on a working surface located within a work region (e.g., a turf (grass) surface of a residential or commercial property) as the mower travels across the work region. By implementing methods like those described and illustrated herein, such a mower may be able to achieve more efficient cutting coverage than may otherwise be provided with known random-travel coverage methods. 
     As used herein, “property” is defined as a geographic region (such as a yard) circumscribed by a fixed boundary within which the vehicle may perform work (e.g., mow grass). For example,  FIG. 1A  illustrates an exemplary property or yard  50  defined by a boundary  59 . “Work region” (see areas labeled as “ 51 ” in  FIG. 1A ) is used herein to refer to those areas contained (or mostly contained) within the property boundary  59  within which the vehicle will perform work. For example, work regions could be defined by grass surfaces of the property or yard  50  upon which an autonomous lawn mower will operate. As further shown in  FIG. 1A , a property may contain one or more work regions  51  including, for example, a front yard area and a back yard area, or two yard areas separated by a sidewalk or driveway  52 . “Exclusion zone” is defined herein as an area contained within a work region in which the vehicle is not intended to operate (e.g., not intended to mow grass). Examples of exclusion zones include landscaped areas and gardens such as areas  53  shown in  FIG. 1A , pools, buildings, driveways (see, e.g., driveway  52 ), and other yard features. “Transit zones” (see transit zones  55  in  FIG. 1A ) may be used herein to refer to paths the vehicle may take when travelling between different work regions of the property. Typically, the vehicle will not perform work when moving through a transit zone. 
     While described herein as a robotic mower, such a configuration is exemplary only as systems and methods described herein also have application to other autonomously operated machines/vehicles including, for example, commercial mowing products, other ground working vehicles (e.g., debris blowers/vacuums, aerators, material spreaders, snow throwers), as well as indoor working vehicles such as vacuums and floor scrubbers/cleaners. 
     It is noted that the terms “comprises” and variations thereof do not have a limiting meaning where these terms appear in the accompanying description and claims. Further, “a,” “an,” “the,” “at least one,” and “one or more” are used interchangeably herein. Moreover, relative terms such as “left,” “right,” “front,” “fore,” “forward,” “rear,” “aft,” “rearward,” “top,” “bottom,” “side,” “upper,” “lower,” “above,” “below,” “horizontal,” “vertical,” and the like may be used herein and, if so, are from the perspective shown in the particular figure, or while the vehicle  100  is in an operating configuration (e.g., while the vehicle  100  is positioned such that wheels  106  and  108  rest upon a generally horizontal ground surface  103  as shown in  FIG. 1B ). These terms are used only to simplify the description, however, and not to limit the interpretation of any embodiment described. 
       FIG. 1B  illustrates an autonomously operating working vehicle (e.g., a robotic lawn mower  100 ) of a lawn mowing system, the mower constructed in accordance with exemplary embodiments of the present disclosure (for simplicity of description, the mower  100  is illustrated schematically). As shown in this view, the mower  100  may include a frame or chassis  102  that carries and/or encloses various components of the mower as described below. The mower may further include ground support members, e.g., one or more rear wheels  106  and one or more front wheels  108 , that support the chassis  102  upon a ground (grass) surface  103 . 
     One or more of the ground support members may include a drive member. For example. one or both of the rear wheels  106  may be driven (e.g., by one or more electric wheel motors  104 ) to propel the mower  100  over the ground surface  103 . In some embodiments, the front wheels  108  may freely caster relative to the chassis  102  (e.g., about vertical axes). In such a configuration, mower direction may be controlled via differential rotation of the two rear wheels  106  in a manner similar to a conventional zero-turn-radius (ZTR) riding mower. That is to say, a separate wheel motor  104  may be provided for each of a left and right rear wheel  106  so that speed and direction of each rear wheel may be independently controlled. In addition or alternatively, the front wheels  108  could be actively steerable (e.g., using one or more steer motors  105 ) to assist with control of mower  100  direction, and/or could be driven (i.e., to provide a front-wheel or all-wheel-drive mower). 
     A grass cutting element (e.g., blade  110 ) may be carried by the chassis. For example, the cutting element may be coupled to a cutting motor  112  that is itself attached to the chassis  102 . When the motors  112  and  104  are energized, the mower  100  may be propelled over the ground surface  103  such that vegetation (e.g., grass) over which the mower passes is cut by the blade  110 . While illustrated herein using only a single blade  110 /motor  112 , mowers incorporating multiple blades, powered by single or multiple motors, are contemplated within the scope of this disclosure. Moreover, while described herein in the context of one or more conventional “blades,” other cutting elements including, for example, nylon string or line elements, knives, cutting reels, etc., are certainly possible without departing from the scope of this disclosure. Still further, embodiments combining various cutting elements, e.g., a rotary blade with an edge-mounted string trimmer, are also contemplated. 
     The exemplary mower  100  may further include a power source, which in one embodiment, is a battery  114  having a lithium-based chemistry (e.g., lithium-ion). Other embodiments may utilize batteries of other chemistries, or other power source technologies (e.g., solar power, fuel cell, internal combustion engines) altogether, without departing from the scope of this disclosure. It is further noted that, while shown as using independent blade and wheel motors, such a configuration is exemplary only as embodiments wherein blade and wheel power is provided by a single prime mover are also contemplated. 
     The mower  100  may further include one or more sensors to provide location data. For instance, some embodiments may include a positioning system (e.g., global positioning system (GPS) receiver  116  and/or other position system that may provide similar data) adapted to estimate a position of the mower  100  within a work region and provide such information to a controller  120  (described below). For example, one or more of the wheels  106 ,  108  (e.g., both rear wheels  106 ) may include encoders  118  that provide wheel rotation/speed information that may be used to estimate mower position (e.g., based upon an initial start position) within a given work region. Other sensors (e.g., infrared, radio detection and ranging (radar), light detection and ranging (lidar), etc.) now known or later developed may also be incorporated into the mower  100 . The mower  100  may further include a sensor  115  adapted to detect a boundary wire when the latter is used to define a boundary of the work region. 
     The mower  100  may also include a controller  120  adapted to monitor and control various mower functions. The exemplary controller  120  may include a processor  122  that receives various inputs and executes one or more computer programs or applications stored in memory  124 . The memory  124  may include computer-readable instructions or applications that, when executed, e.g., by the processor  122 , cause the controller  120  to perform various calculations and/or issue commands. That is to say, the processor  122  and memory  124  may together define a computing apparatus operable to process input data and generate the desired output to one or more components/devices. For example, the controller may be operatively connected to the positioning system such that the processor  122  may receive various input data including positional data from the GPS receiver  116  and/or encoders  118 , and generate speed and steering angle commands to the drive wheel motor(s)  104  to cause the drive wheels  106  to rotate (at the same or different speeds and in the same or different directions). In other words, the controller  120  may control the steering angle and ground speed (the speed and direction) of the mower  100 , as well as operation of the cutting blade  110  (including blade actuation/de-actuation and blade rotation speed). 
     In view of the above, it will be readily apparent that the functionality of the controller  120  may be implemented in any manner known to one skilled in the art. For instance, the memory  124  may include any volatile, non-volatile, magnetic, optical, and/or electrical media, such as a random-access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), electrically-erasable programmable ROM (EEPROM), flash memory, and/or any other digital media. While shown as both being incorporated into the controller  120 , the memory  124  and the processor  122  could be contained in separate modules. 
     The processor  122  may include any one or more of a microprocessor, a controller, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA), and/or equivalent discrete or integrated logic circuitry. In some embodiments, the processor  122  may include multiple components, such as any combination of one or more microprocessors, one or more controllers, one or more DSPs, one or more ASICs, and/or one or more FPGAs, as well as other discrete or integrated logic circuitry. The functions attributed to the controller  120 /processor  122  herein may be embodied as software, firmware, hardware, or any combination thereof. 
     In  FIG. 1B , schematic connections are generally shown between the controller  120  and the battery  114 , wheel motor(s)  104 , blade motor  112 , optional boundary wire sensor  115 , wireless radio  117  (which may communicate with, for example, a remote computer such as a mobile phone  119 ), and GPS receiver  116 . This interconnection is exemplary only as the various subsystems of the mower  100  could be connected in most any manner, e.g., directly to one another, wirelessly, via a bus architecture (e.g., controller area network (CAN) bus), or any other connection configuration that permits data and/or power to pass between the various components of the mower. 
     Exemplary methods of using the mower  100  will now be described, initially with reference to  FIG. 2 . This figure illustrates a generic rectangular work region  200  (e.g., residential yard) in which the mower  100  may operate. For purposes of describing operation of the exemplary mower, it is assumed that a peripheral boundary  250  of the work region  200  (as well as any exclusion zones (if present) contained within the work region (see, e.g.,  FIG. 3A )) is known to the mower  100 . For instance, the boundary  250  of the work region (and any exclusion zone) may be marked by an energized boundary wire detectable by a sensor (see sensor  115  in  FIG. 1B ) provided on the mower during a training phase. In addition or alternatively, the boundary  250  may be detectable or known via other techniques without departing from the scope of the disclosure. For instance, the mower  100  may detect machine-visible markings located on the property, or it may map and store boundary information during a training phase of the mower. 
     In  FIG. 2 , the boundary  250  of the yard encloses, and defines, the work region  200 . As stated above, the exemplary work region  200  is generally rectangular in shape and lacks any exclusion zones (e.g., flower beds, trees, etc.). However, such a shape is exemplary only as embodiments of the present disclosure may find application to work regions (e.g., yards) of most any size and shape and having any number of exclusion zones (see, e.g., work region  300  shown in  FIGS. 3A-3K ). 
     The hatched portion of  FIG. 2  illustrates what will be referred to herein as a travelling containment zone  202  (see exemplary zones  202   t   1  and  202   t   2 ). The travelling containment zone  202  represents a dynamically changing (e.g., travelling, expanding, contracting, or otherwise moving) subarea of the work region  200  (i.e., the travelling containment zone lies at least partially within the work region and defines a zone area that is less than an area of the work region). A position of the mower  100  may, at any time during operation, be constrained to being within both the travelling containment zone  202  and the work region as the travelling containment zone travels across the work region for reasons that are further described below. In accordance with embodiments of the present disclosure, at least some portions of the travelling containment zone  202  may be delineated by a virtual boundary electronically defined and recognized with the controller  120 , i.e., some (or all) portions of the travelling containment zone  202  may not be delineated by any physical demarcation or sensor-detected border. It is further noted that, while illustrated as rectangular, the travelling containment zone  202  may vary in shape as the travelling containment zone moves across the work region. 
     Unlike the generally fixed work region  200  though, the travelling containment zone  202  may be designed to move or travel across the work region  200  (while the mower autonomously operates within the travelling containment zone) so that all of the working surface (grass surface) of the work region  200  is eventually enveloped within the travelling containment zone. For example, when mower operation is initiated, the controller  120  (see  FIG. 1B ) may (e.g., based on control algorithms, the known shape of the work region, and previous cutting history, etc.) define or otherwise identify an initial travelling containment zone  202   t   1  as shown in  FIG. 2 . Once again, to identify the travelling containment zone  202 , the controller  120  may utilize not only the physical boundary  250  of the work region  200  (e.g., that boundary defined by a boundary wire), but also one or more virtual boundaries  252  (e.g., one or more boundaries ultimately extending between physical boundaries of the work area) created by the controller  120 . In some embodiments, the travelling containment zone  202  will, although moving, remain a singular enclosed region (e.g.,  202   t   1 ,  202   t   2 ) during the entire mowing operation. 
     The travelling containment zone  202  is able to provide generally even coverage of the entire work region  200 . However, such “even” coverage may not always be optimal. For instance, it is not uncommon for the grass growth rate of some areas of the work region  200  to be different than others. As a result, the controller  120  may maintain historical information regarding the cutting load on the mower at most any given position within the work region  300 . “Cutting load,” as used herein, refers to the work required by the mower to cut grass. The cutting load may thus be a function of both: power drawn by/supplied to the cutting motor  112  (see  FIG. 1B ); and the propulsion or ground speed of the mower (which is proportional to power drawn by/supplied to the wheel motor(s)  104 ). Accordingly, if the controller  120  detects that the cutting load is higher than a predetermined limit, it may slow the speed at which the travelling containment zone  202  moves to ensure that the mower  100  has adequate opportunity to cut the grass within the travelling containment zone  202 . Conversely, the controller  120  may increase the rate of movement of the travelling containment zone  202  when cutting load is lower than a predetermined limit. In addition to, or instead of, changing the speed of travelling containment zone  202  movement, the travel speed of the mower  100  could also be increased or decreased. That is, the controller may maintain a speed of the mower  100  while autonomously operating the mower within the travelling containment zone (which may move at a constant or variable rate of speed), or alternatively vary a speed of the mower while operating the mower within the travelling containment zone. 
     In some embodiments, the mower  100  may move autonomously and in a random manner within the travelling containment zone  202  during operation. Because the travelling containment zone  202  is, by definition, a geographic subset of the work region  200 , the travelling containment zone (at any given time) is likely less complex (e.g., has fewer (or no) narrow passages or “bottlenecks” that may cause the mower to get hung-up) and more geographically uniform (e.g., have consistent turf quality) than the work region as a whole. Moreover, the travelling containment zone is also likely to have fewer obstacles than a larger area (i.e., fewer obstacles than contained within the entire work region  200 ). As a result, the mower  100  is more likely (during random movement) to evenly cover all areas of the travelling containment zone  202  (and thus eventually evenly cover the entire work region  200 ) than if the randomly-moving mower was only limited to the larger physical boundary of the work region  200 . 
     To ensure the entire work region  200  is covered (cut) by the mower  100 , the travelling containment zone  202  may move or travel across the work region, e.g., from left to right in  FIG. 2 , as the mowing operation progresses. Moving of the travelling containment zone may occur at either a constant rate or a variable rate. As the travelling containment zone  202  moves within the work region  200  depicted in  FIG. 2 , area is both added to the zone  202  (e.g., by advancement of the virtual leading edge  252 L of the virtual boundary  252 ) and subtracted from the zone  202  (by advancement of the trailing edge  252 T of the virtual boundary  252 ). For example, at some time after mower operation begins, the travelling containment zone  202  will have moved from the initial travelling containment zone (depicted as travelling containment zone  202   t   1  in  FIG. 2 ) to a new position (depicted as travelling containment zone  202   t   2 ). In the illustrated embodiment, the area of  202   t   1  and  202   t   2  may remain constant (i.e., the controller may maintain a zone area of the travelling containment zone constant as the travelling containment zone moves across the work region). However, in other embodiments, the area of the travelling containment zone  202  may change (i.e., the controller may vary the zone area of the travelling containment zone as the travelling containment zone moves across the work region). Note that the suffixes “t 1 , t 2 , etc.” in relation to the containment zone  202  are used only to indicate a different point in time of mower operation. That is to say, the travelling containment zones  202  represented in  FIG. 2  illustrate the cutting area at separate instantaneous points in time. 
     In reality, the area added to and removed from the travelling containment zone  202  via advancement of the leading and trailing edges  252 L,  252 T may, at least in some embodiments, be set at a rate (constant or variable) selected to ensure adequate cutting of all portions of the travelling containment zone. While dynamic movement of the travelling containment zone  202  may allow efficient coverage of the entire work region  200 , it is contemplated that the controller  120  may, occasionally, slow or stop movement of the travelling containment zone for a given period of time. For example, it may be advantageous to maintain an initial position of the travelling containment zone  202   t   1  for a period of time before the travelling containment zone travels across the work region to ensure that the mower  100  has adequate opportunity to cover the portions of the lawn adjacent the work region boundary (the left-most boundary  250  in  FIG. 2 ). Whether to maintain the position of the travelling containment zone  200  fixed, and how long it remains fixed, may be determined by the controller  120  based upon, e.g., the size of the travelling containment zone, the size and speed of the mower  100 , cutting load, and statistical and/or historical coverage information for the mower  100  that may be retained in the memory  124  (see  FIG. 1B ). 
     In other embodiments, the initial travelling containment zone  202   t   1  may, instead of being held stationary, actually start with its trailing edge  252 T outside (e.g., to the left in  FIG. 2 ) of the physical boundary  250  of the property (i.e., the travelling containment zone may extend beyond the work region). Although the trailing edge  252 T is located beyond the boundary  250 , the mower  100  may still be restricted from travelling beyond the work region  200 , i.e., the mower may remain within the work region at all times during mowing. As a result, as the travelling containment zone  202  travels during mower operation, the leftmost boundary of the property (e.g., along a boundary  250 ) will remain in the travelling containment zone for some period of time, i.e., until the trailing edge  252 T of the containment zone  202  moves through (to the right of) the yard boundary  250 . To practically implement this functionality, the controller  120  could set the initial travelling containment zone equal to a small area, then move the leading edge  252 L until the area of the travelling containment zone is equal or “filled” to the desired area, at which point the trailing edge  252 T is introduced and starts advancing in relation to the leading edge  252 L to ensure the desired area remains constant. This process is illustrated in more detail below (see, e.g.,  FIGS. 6A-6G ). 
     As mower  100  operation continues, the travelling containment zone  202  may reach the last portions of the work region as shown by work region  202   tn  in  FIG. 2 . Again, the controller  120  may maintain the position of the travelling containment zone  202   tn  for a fixed period of time to ensure portions (the right-most boundary  250 ) of this containment zone are adequately covered, or it may continue to move the containment zone to the right, effectively shrinking or “emptying” the area of the travelling containment zone as the trailing edge  252 T of the travelling containment zone approaches the right-most boundary  250  of the work region  200 . Of course, the controller  120  may prevent the travelling containment zone from becoming so small that mower operation is compromised, e.g., the travelling containment zone may avoid contracting beyond a minimum size that would interfere with the mower&#39;s ability to move. 
     By controlling the mower  100  as described above, the mower is, at any given time, limited to operating within a subarea (i.e., a travelling containment zone  202 ) of the overall work region  200 . Given the mower&#39;s random travel pattern, it is thus more likely that the mower will cover the entire work region evenly (e.g., avoid leaving uncut sections of lawn) than a mower that is not so restricted. Further, by containing the mower  100  to a smaller travelling containment zone, it is more likely that isolated areas of the lawn (e.g., narrow turf passages between exclusion zones; described with reference to  FIGS. 3A-3K  below) will be adequately covered, while also minimizing the chance that the mower may get hung-up or trapped for an extended period within such isolated areas. 
     The actual movement of the travelling containment zone  202  may occur in increments defined by the controller  120 . For example, once the work region  200  is mapped by the mower (e.g., during a teaching phase), the controller  120  may overlay a virtual grid on the work region (see, e.g., exemplary grid cells or elements  251  in  FIG. 2 ) as further described below. The grid element size may be small, effectively allowing the travelling containment zone  202  to be defined with high resolution boundaries (at the expense of increased computational loading of the controller  120 ). Alternatively, if the grid element size is large, the travelling containment zone  202  may move in relatively larger, discrete steps resulting in the travelling containment zone  202  having lower resolution (e.g., “courser”) boundaries. In practice, the grid element size is selected to be at least as small as the physical footprint of the mower  100 , thereby ensuring that all areas of the work region  200  in which the mower can fit will eventually be covered by the travelling containment zone. To adequately provide coverage along various (e.g., curved) boundaries (see boundary  350  in  FIG. 3A ) of the work region and exclusion zones (see zones  354  and  355  described below), however, the grid cell size may be set even smaller than the mower footprint. Moreover, while shown as 4-sided elements, other grid cells may be of any polygonal shape (e.g., any shape having three or more sides (e.g., triangular, pentagonal, hexagonal, octagonal, etc.-shaped elements)) without departing from the scope of this disclosure. 
     The speed at which the travelling containment zone moves, however, may be independent of, and unaffected by, grid size. Rather, at least in some embodiments, movement of the travelling containment zone may be defined by the following equation: 
       Δ A=B*t   (Equation 1)
 
     wherein: 
     ΔA=area added to, and subtracted from, the travelling containment zone, e.g., meter (m 2 ); 
     B=rate at which area is covered by the mower in unit-area per unit-time, e.g., m 2 /second; and 
     t=time interval, e.g., seconds (sec). 
     Accordingly, the area added to and removed from the travelling containment zone may be independent of actual containment zone size. Rather, the area (e.g., grid cells) added/removed (ΔA) is dependent on parameter B. The nominal or initial value of B may be directly dependent upon the average speed and cutting width of the mower  100 . For instance, a given robotic mower  100  may cover ground area at some unit-area-per-time rate referred to herein as Bo. During normal operation, the controller  120  may set B=Bo. However, when the controller  120  determines that more or less cutting is desired, the parameter B may be adjusted. For example, B may be increased or decreased by an incremental value ΔB (i.e., B=Bo+ΔB). Finally, the time interval t may be dependent upon both ΔA and B. 
     As an example, ΔA may be set equal to one (or a multiple thereof) grid cell  251  as shown in  FIG. 2  (e.g., ΔA may be equal to 8 grid cells  251  such that 8 cells are simultaneously added to and substracted from the travelling containment zone  202 ). The parameter t is thus the time interval at which grid cells  251  are added and removed from the travelling containment zone (it may thus be constructive to view ΔA and B as dependent variables and t as independent in Equation 1 above). 
     In addition to potentially improving coverage efficiency, a dynamically travelling containment zone  202  may also allow the controller  120  to better predict time-to-completion of the mowing operation. That is, by knowing the rate of movement of the travelling containment zone and the size and shape of the yard (which may be known from initial training of the mower and/or historical mowing information), the controller may be able to accurately estimate the time at which the mower will complete mowing of the entire property (e.g., estimate the time at which operation of the mower over the entire work region (over the working surface of the work region) will be complete). This estimate may improve over time as the controller  120  learns how to optimize travelling containment zone movement. Such estimated information may be provided to a homeowner or operator via any number of methods. For example, the mower may include a display that provides, among other data, a time-to-completion estimate. In other embodiments, the mower may include a wireless radio (e.g., IEEE 802.11 “Wi-Fi” radio  117  shown in  FIG. 1B ) that may communicate over a local area or wide area network with a mobile device (e.g., cellular phone  119 ). In the case of the latter, the mower may provide the time-to-completion estimate via an application running on the mobile device, or via periodic notifications (e.g., text messages) provided to the mobile device. 
     While  FIG. 2  illustrates a basic methodology in accordance with embodiments of the present disclosure, most properties present a more complicated geometry than the rectangular shape shown in  FIG. 2 .  FIGS. 3A-3K  illustrate operation of the mower  100  in accordance with embodiments of the present disclosure over such an exemplary property. 
       FIG. 3A  illustrate a property or work region  300  having an irregular boundary  350  detectable and/or known by the mower  100 . The work region  300  may further include exclusion zones  354 ,  355  that may also be identified by the controller  120  (see  FIG. 1B ) as boundaries (which boundaries could again be physical (e.g., a wire) or virtual (e.g., an electronic map of the work region  300  known, or otherwise determined, by the controller). Unlike the work region  200  shown in  FIG. 2 , the work region  300  of  FIG. 3A  presents a more complicated shape that requires the controller  120  of the mower  100  (see  FIG. 1B ) to make correspondingly more sophisticated decisions as to how to cover the work region. For purposes of describing  FIGS. 3A-3K , the instantaneous or current travelling containment zone  302  (see initial zone  302   t   1 ) is represented by hatched lines, the portions of the work region that have been covered by the mower are represented by the double-hatched lines, and the uncut portions of the work region are shown unmarked. 
     As shown in  FIG. 3A , the controller  120  may select an initial travelling containment zone  302   t   1  (various containment zones illustrated in  FIGS. 3A-3K  may be referred to generically as “ 302 ”) and control the mower&#39;s drive wheels until the mower  100  is located at some position within the zone  302   t   1 . That is to say, if the mower  100  is not within the travelling containment zone selected by the controller, the mower may be autonomously transported (under control of the controller) from a location beyond the travelling containment zone to a location within the desired containment zone before autonomous mowing begins. For example, the controller  120  may chart a path from its current position to a position somewhere within the travelling containment zone, such path being within the work region  300  and outside of any exclusion zones (e.g., zones  354 ,  355 ). Once the path is identified, the controller  120  may control the drive wheels  106  (see  FIG. 1B ) to transport the mower to the desired position. 
     The initial travelling containment zone may be selected based on any number of factors including, for example, proximity of the mower  100  to the zone  302   t   1  at the time mower operation begins, and how long it has been since the zone  302   t   1  was last mowed. In some embodiments, the controller  120  may utilize a wavefront grid (further described below), wherein the controller calculates a linear distance from each grid cell to a base position (which may be the location of the mower&#39;s base station (see, e.g.,  220  in  FIG. 2 )). Such distances may be calculated based on a path that obeys all boundaries (work region and exclusion zones). The initial travelling containment zone may then be determined to be a zone containing cells farthest from the base position, i.e., the location identified by the greatest value in the wavefront grid. 
     Once positioned within the travelling containment zone  302   t   1 , the mower  100  may activate its cutting motor  112  (see  FIG. 1B ) and begin cutting grass as the mower moves randomly within the confines of the travelling containment zone  302   t   1 . As described above, the travelling containment zones  302   t   1  may be fixed for some period of time to ensure the physical boundary of the work region (the left-most edge of the work region boundary  350  in  FIG. 3A ) is adequately covered. Alternatively, the travelling containment zone could grow or “fill” outwardly (e.g., toward the right) from an initial location at or near the physical boundary  350  of the work region until the containment zone reaches the desired size, at which time a trailing edge of the containment zone would also advance. In either scenario, virtual boundary  352  (e.g., leading edge  352 L thereof) may begin to travel (e.g., to the right in  FIG. 3A ) as time progresses. As shown in  FIG. 3B , as the leading edge  352 L advances, a trailing edge  352 T of the virtual boundary  352  may ultimately follow. 
     In some embodiments, the “leading edge” is thus a set of grid cells that have been iteratively scored by the controller and added to the travelling containment zone (although not all grid cells along the leading edge are populated, thus avoiding expansion of the travelling containment zone into unintended open areas). Scoring may be performed based upon the wavefront grid values described elsewhere herein. In this way, the controller  120  may better identify direction of movement of the travelling containment zone, and ensure adequate coverage of the containment zone boundaries. Of course, other aspects may also be taken into consideration when populating leading edge grid cells (e.g., maintaining shape quality of the travelling containment zone). 
     In some embodiments, the boundaries of the travelling containment zone  302  may behave somewhat like a virtual, continuous rope that can “morph” to accommodate most any boundary shape. As a result, the travelling containment zone  302  may accommodate the irregular shaped left boundary of the work region  300  shown in  FIG. 3A , and then, once the trailing edge  352 T has moved beyond (e.g., to the right of) the left-most work region boundary, the trailing edge  352 T may assume another (e.g., linear) shape as shown by the travelling containment zone  302   t   2  in  FIG. 3B . While shown as transitioning to a linear trailing edge  352 T to allow efficient mower operation, such a transition is only exemplary as most any shape of travelling containment zone is possible without departing from the scope of this disclosure. In fact, when scoring algorithms like those described herein are utilized to advance the travelling containment zone, the leading edge (and trailing edges) of the travelling containment zone (as well as other edges of the containment zone) may likely have non-linear shapes as illustrated in, for example, the simulations shown in  FIGS. 6A-6G . 
     Again, while the travelling containment zone  302  is illustrated as a distinct zone at any given time in  FIGS. 3A-3K  (as well as in  FIGS. 6A-6G ), such depiction is exemplary as the travelling containment zone may move generally continuously (e.g., via small discrete steps) or periodically (e.g., via larger discrete steps) across the work region  300  during mower operation. Thus, the travelling containment zones illustrated in the figures are intended to illustrate only the size and shape of the travelling containment zones at different arbitrary (but discrete) points in time. 
     In  FIG. 3C , the leading edge  352 L of the travelling containment zone  302  (zone  302   t   3 ) is shown immediately prior to encountering the first exclusion zone  354 . Once zone  354  is encountered by the leading edge  352 L, the controller  120  decides which segment of the leading edge, i.e., the upper segment  353 - 1  above the exclusion zone  354 , or the lower segment  353 - 2  below the exclusion zone  354 , (in alternate cases, three or more potential leading edges could exist) will become the effective new leading edge  352 L. Stated alternatively, the controller  120  may decide at this time whether to move the travelling containment zone to either side of (e.g., along the top or the bottom of) the exclusion zone  354  by selecting either the upper segment  353 - 1  or the lower segment  353 - 2  as the “new” leading edge  352 L. As shown in  FIG. 3D , the controller  120  decides to select segment  353 - 2  as the new leading edge and thus the travelling containment zone  302  slides or morphs along a lower side of the exclusion zone  354  as illustrated by travelling containment zone  302   t   4 . By utilizing algorithms that ensure the boundary of the travelling containment zone remains continuous, the active cutting area may move along the lower boundary of the exclusion zone  354  (and avoid being bisected by the exclusion zone) while the controller  120  logs that an area  356  above the exclusion zone  354  remains uncut. 
     In some embodiments, when the leading edge  352 L “splits” (e.g., as shown herein upon encountering the exclusion zone  354 ), the two potential leading edges (e.g., segments  353 - 1  and  353 - 2 ) may be scored against one another by the controller  120  to assist the controller in selecting one of the potential segments to become the new leading edge (e.g., using the wavefront grid values, most desirable zone shapes, most efficient mowing patterns, etc.). Once the most optimal leading edge segment is selected, the controller  120  may then populate grid cells along that selected segment/leading edge path. This process continues until the leading edge  352 L again encounters a boundary. Such boundary encounters include: encountering another boundary that causes the leading edge to again split into two or more segments (see, e.g., encounter with exclusion zone  355  in  FIG. 3F ); and encountering a dead-end either by hitting a boundary of the work region (see, e.g., encounter with boundary  350  as shown in  FIG. 3K ); or by hitting the boundary of a previously cut portion of the work region (see, e.g., encounter with previously mowed section as shown in  FIG. 3J ). In the case of the exclusion zone encounter, the potential leading edges are evaluated as indicated above and operation continues as described. However, when a dead-end is encountered, the trailing edge(s)  352 T may move toward the leading edge  352 L until the area of the travelling containment zone is effectively zero (in practice, the zone may stay of a sufficient size to avoid constraining movement of the mower). If areas of the work region still remain uncut, the controller  120  may then move the mower  100  to these uncut areas in a manner similar to that described above with regard to moving the mower to the initial travelling containment zone. An example of the latter occurring is shown in  FIGS. 3J and 3K  and described below. 
     In practice, the controller  120  may also need to apply algorithms that generally prevent the travelling containment zone from becoming too restrictive for effective mower navigation. For example, as the travelling containment zone progresses (e.g., from the zone  302   t   4  shown in  FIG. 3D  toward the zone  302   t   5  shown in  FIG. 3E ), the controller  120  encounters various decision points, such as reaching the exclusion zone  354 . Upon reaching the exclusion zone  354 , the travelling containment zone  302  may, as described above, slide down along the lower side of the exclusion zone as shown in  FIGS. 3D and 3E . However, while the travelling containment zone continues to move, the controller  120  must also apply some constraints on the shape of the zone. For instance, the controller  120  may prevent the trailing edge  352 T of  FIG. 3E  from moving so far to the right that the area indicated by reference numeral  357  becomes too narrow, making mower navigation in the area  357  problematic. Rather, the controller  120  may, as shown in  FIG. 3E , limit the minimum width of the area  357  and instead begin drawing an upper trailing edge  352 Tu downwardly as the travelling containment zone  302   t   5  expands toward the right. In this way, the travelling containment zone  302  may add area (by moving the leading edge  352 L as indicated in  FIG. 3E ) while subtracting equivalent area (by sliding the upper trailing edge  352 Tu downwardly), all while maintaining a position of the left trailing edge  352 T to minimize mower navigation issues. 
     As the travelling containment zone  352  continues to travel across the work region  300 , the leading edge  352 L of the virtual boundary may reach the second exclusion zone  355  as indicated in  FIG. 3F . When this occurs, the controller  120  may again determine—based upon grid cell scoring (or random selection)—to pursue a course (e.g., a segment) above the exclusion zone  355  (e.g., in zone  358  between zones  354  and  355 ), or a route that first takes the mower  100  below the exclusion zone  355  (e.g., between the zone  355  and the work region boundary), the latter being illustrated by travelling containment zone  302   t   6  in  FIG. 3F . 
     Once the travelling containment zone travels past the exclusion zone  355 , the travelling containment zone may expand both toward the right-most boundary  350  (in  FIG. 3G ) of the work region  300 , as well as upwardly as represented by the travelling containment zone  302   t   7  and virtual boundary leading edge  352 L. As the travelling containment zone  302  moves above the exclusion zone  355 , it may expand into the previously uncut zone  358  (between the two exclusion zones  354 ,  355 ) as represented by the travelling containment zone  302   t   8  in  FIG. 3H . 
     As the travelling containment zone  302  continues to move (e.g., upwardly in  FIG. 3I ) it again encounters the exclusion zone  354  and may begin to wrap around the right and top side of the exclusion zone to cover the previously uncut area  356  as represented by travelling containment zone  302   t   9  in  FIG. 3I . Once the virtual leading edge  352 L encounters the boundary  350  as shown in  FIG. 3I , the controller  120 , knowing that two isolated areas ( 356  and  359 ) of the work region  300  remain to be cut, decides whether to move left (e.g., into area  356 ) or right (e.g., into area  359 ). In the embodiment illustrated in  FIG. 3J , the controller  120  has decided to move the mower  100  left and mow the area  356  as indicated by the travelling containment zone  302   t   10 . 
     Once the mower  100  completes mowing of the area  356 , the controller  120  may recognize that area  359  remains uncut and may command the mower to proceed to that area. Once within that area, the mower  100  may re-activate the cutting unit and continue to mow the final uncut area represented by travelling containment zone  302   t   11  as shown in  FIG. 3K . 
     As indicated in  FIGS. 3A-3K , the controller  120  may make decisions as to how the travelling containment zone travels to ensure adequate coverage of the work region  300  in an efficient manner. As the mower  100  completes multiple mowing sessions, the controller  120  may also learn which decisions resulted in the most efficient operation. For example, the controller  120  may determine that it would be more efficient to first transition the travelling containment zone above the exclusion zone  354  (rather than below the exclusion zone as shown in  FIG. 3D ). Once the controller has gathered data for both paths, it may be able to accurately determine which path results in the most efficient operation and pursue that path in the future. Such decisions may be required at various points during the mowing process (e.g., when the exclusion zone  355  (see  FIG. 3F ) or a dead-end (see  FIG. 3J ) is encountered). After comparing historical data from previous mowing sessions, the controller  120  may achieve a travelling containment zone travel path that seeks to optimize mower efficiency as well as permits an accurate estimation of job time-to-completion. While the controller  120  may learn and provide the most efficient cutting path for most any work region  300 , algorithms may also be provided that permit the mower to pursue alternative paths during different mowing sessions where such alternative paths may be beneficial (e.g., to prevent undesirable effects such as lawn “burn-in” when some boundaries of the travelling containment zone are repeatedly in the same location). Such alternative paths could be provided by storing multiple wavefront grids (i.e., emanating from different base cells on the work area) such that the mower may begin mowing operation at different initial locations and correspondingly make potentially different decisions upon encountering the various boundaries and exclusion zones. 
       FIGS. 4, 5, and 6A-6H  illustrate computer-simulated mowing coverage of another work area  400  in accordance with embodiments of the present disclosure. As with the work area  300 , the work area  400  may be circumscribed by a boundary  450  and includes various exclusion zones  454 - 1 ,  454 - 2 , and  454 - 3  (collectively “ 454 ”) contained therein. Data defining the boundary/exclusion zones may be stored in memory  124 , e.g., after a training process, or otherwise known by the controller  120 . Values shown on the axes in these figures represent units of length (e.g., meters). 
     As shown in  FIG. 4 , an x-y grid may be superimposed over the work area  400  with an initial position (e.g., origin at coordinate 0,0) at work area vertex  451 . The initial position may be a location of the system base station  220  used to house and re-charge the mower when not in use, the base station typically being located in or near the work region. While the grid is generally illustrated as two-dimensional in  FIG. 4 , it is certainly adaptable to work areas having elevational variation without departing from the scope of this disclosure. 
     Initial wavefront grid values may be calculated (e.g., with the controller  120 ), propagating from this initial position. For general information regarding wavefront grids, see, e.g., E. Galceran, M. Carreras,  A Survey on Coverage Path Planning for Robotics , Robotics and Autonomous Systems 61 (2013) 1258-1276. 
     An exemplary wavefront grid  500  for the work area  400  is visually represented in  FIG. 5 . In this figure, a distance (measured along a path that avoids all exclusion zones) from the initial cell to any other cell within the work area  400  is represented by the vertical or z-axis. As further shown in this view, the wavefront grid  500  also accounts for both the boundary  450  of the work area  400 , as well as the exclusion zones  454 . Again, while a single wavefront grid  500  is illustrated herein, mowers and systems in accordance with embodiments of the present disclosure may map and store multiple wavefront grids, e.g., emanating from different initial cells. 
     With the data from this map, the controller  120  may compute the shortest travel distance from the base cell (i.e., cell from which the wavefront grid propagates, which is located at coordinates 0,0 in the example of  FIG. 5 ) to any other cell on the grid (e.g., within the work area  400 ), considering all boundaries (including boundaries of the work area and the exclusion zones). Accordingly, the controller  120  may identify efficient mower routes (e.g., to return to base station, to travel to new, uncut portion of the work area, etc.) as needed during operation. For instance, if the mower  100  were to require re-charging when at the location shown in  FIG. 4 , the controller  120  could determine, based upon the wavefront grid, that route  370  is shorter than route  372  and select the former travel path to return to the base station  220 . 
     With the wavefront grid values computed and stored in memory  124 , the controller  120  may command the mower to first move, e.g., from the initial cell (proximate base station  220 ) to the cell farthest from this initial position (i.e., the cell having the highest wavefront grid value) and commence mowing. In the exemplary workspace  400 , the mower  100  would thus move to, and commence mowing at, the cells nearest vertex  460  of the boundary  450  as shown in  FIG. 6A . 
     The controller  120  may establish an initial travelling containment zone  402   t   1  (containment zones are darkly hatched in  FIGS. 6A-6G , while cut portions are double-hatched and unmowed areas are unhatched) and grow that zone outwardly from vertex  460 . In order to determine the expansion directions of the travelling containment zone  402 , the controller  120  may perform a scanning function wherein it analyzes and records (e.g., continuously or periodically) data regarding each of the grid cells externally adjacent to a virtual perimeter of the travelling containment zone  402 . For example, initially the travelling containment zone  402  may expand in multiple directions (e.g., generally radially) as shown in  FIG. 6A . However, as shown in  FIG. 6B , the leading edge of the expanding travelling containment zone  402  may eventually contact a side of the exclusion zone  454 - 1  and split as indicated by the segments  452 L- 1  and  452 L- 2  of the zone  402   t   2  (as used herein, the term “segment” is used to identify a virtual boundary that is delimited by a containment boundary (e.g., boundary  450 ) and/or an exclusion zone (e.g., exclusion zone  454 - 1 )). In this example simulation, the controller  120  may, upon contact of the leading edge with an exclusion zone, detect impending bifurcation of the leading edge into first and second segments  452 L- 1  and  452 L- 2 . That is to say, once the advancing virtual perimeter of the travelling containment zone  402  contacts the exclusion zone  454 - 1 , the controller  120 , in order to avoid bifurcating the travelling containment zone  402 /leading edge  452 , performs a decision-making function, wherein it decides a direction in which to advance the leading edge of the travelling containment zone. In the illustrated example, the controller may decide to either: expand the travelling containment zone above the exclusion zone  454 - 1  (pursue mower movement by replacing the leading edge with the first segment  452 L- 1 ); or expand the travelling containment zone downwardly along the side of the exclusion zone  454 - 1  (pursue mower movement by replacing the leading edge with the second segment  452 L- 2 ). 
     To make this decision, the controller  120  may identify grid cells that are adjacent each of these segments but not within the travelling containment zone  402   t   2  (or that were not previously visited by the travelling containment zone). These adjacent grid cells are then scored based upon mean values previously calculated in the wavefront grid (in some embodiments, other parameters of the cells may also be scored). Information concerning each segment score (as well as other information such as identifiers for the boundaries spanned by each segment (e.g., the border  450  may have one boundary ID, and each exclusion zone  454  may have its own unique boundary ID), and geographic location of the segment) may then be passed to a decision-making algorithm executed by the controller  120 . 
     In the example work area  400  shown in the simulation of  FIG. 6B , the wavefront grid values are higher along segment  452 L- 2  (see, e.g.,  FIG. 5 ). As a result, the controller  120  may direct the travelling containment zone  402  to move forward with the segment  452 L- 2  becoming the new leading edge of the travelling containment zone. 
     Once the decision is made regarding which segment will be pursued, the controller  120  may execute a population function, wherein it adds cells to the travelling containment zone (e.g., immediately forward of the new leading edge), and, optionally, a depopulation function, wherein it removes cells (e.g., by advancing the trailing edge of the travelling containment zone). In this way, the travelling containment zone may move across the work region while the mower operates therein. 
     The travelling containment zone  402  may continue to travel downwardly (e.g., with leading edge  452 L- 2  in  FIG. 6B ), populating cells forward of the leading edge and ultimately depopulating cells along the trailing edge (away from the segment  452 L- 1  shown in  FIG. 6B ). This process continues when the leading edge  452 L- 2  reaches the lower vertex  461  of the exclusion zone  454 - 1  (see  FIG. 6C ). At this point, the leading edge of the travelling containment zone  402  can continue to move both downwardly (between the right-hand boundary  450  and the containment zone  454 - 2 ), as well as move to the left between the containment zones  454 - 1  and  454 - 2 . 
     However, once the leading edge of the travelling containment zone contacts the upper right vertex  462  of the exclusion zone  454 - 2  in  FIG. 6C , the leading edge again splits into two segments  452 L- 3  and  452 L- 4 . To again avoid bifurcation of the travelling containment zone/leading edge, the controller  120  may receive cell scores from the scanning algorithm regarding the grid cells externally adjacent each of these segments based at least in part upon the cell values in the wavefront grid, and provide those scores to the decision-making algorithm. As evident in  FIG. 5 , the cells along the segment  452 L- 3  have a higher wavefront grid value than the cells along the segment  452 L- 4 . As a result and as shown in  FIG. 6C , the decision-making algorithm thus decides to move the travelling containment zone  402  ( 402   t   3 ) downwardly by advancing the segment  452 L- 3  as the new leading edge. At some point, the segment  452 L- 4  may then become a trailing edge following the travelling containment zone downwardly, depopulating cells in the process. 
     This process of scanning and making decisions that prevent bifurcation of the travelling containment zone/leading edge may continue throughout the work area  400 . Typically, the decision-making algorithm will pursue population of cells that score higher, (i.e., those having a higher wavefront grid value). However, scoring may also consider other parameters as further described below. 
     As shown in  FIG. 6D , the travelling containment zone  402  ( 402   t   4 ) may travel down and beneath the exclusion zone  454 - 2  and then, based on leading edge scoring, travel up the left side of the exclusion zone  454 - 2 . As the controller  120  tracks those cells already visited, the travelling containment zone may ultimately cover the uncut area between the exclusion zones  454 - 1  and  454 - 2  (abutting the segment  452 L- 4  in  FIG. 6C ). 
     As shown in  FIG. 6E , the travelling containment zone  402  ( 402   t   5 ) may eventually dead-end (i.e., at the segment  452 L- 1  also shown in  FIG. 6B ). When this occurs, the travelling containment zone  402  may collapse to a minimally navigable size to ensure adequate coverage of the dead-end area. Once covered, the mower  100  may disable its cutting blades (e.g., de-energize the motor  112  ( FIG. 1B )) and then travel to a portion of the work area  400  that is yet to be cut. This uncut area again may be determined by evaluating the wavefront grid values of the remaining uncut cells of the work area  400  and determining which cells have the highest scores. In the simulation shown in  FIGS. 6A-6G  (see  FIG. 5 ), the controller  120  may thus command the mower  100  to move to the portion of the work area  400  in and around the cells adjacent the vertex  463  as shown in  FIG. 6F . The cutting blades may then again engage, and the temporary cutting zone  402  ( 402   t   6 ) may grow/move to cover the portion of the work area in the upper left quadrant of  FIG. 6F . 
     The travelling containment zone  402  (e.g., zone  402   t   6  in  FIG. 6F ) may then advance until it dead-ends against the previously cut portion of the work zone  400 . At this point, the mower  100  may again disable its cutting blades and travel to another portion of the work area  400  that is yet to be cut. Again, determination of the next starting point may be selected based upon the remaining cells having the highest wavefront grid value, e.g., the portion of the work area in and around the cells near vertex  464  in  FIG. 6G . The travelling containment zone  402  ( 402   t   7 ) may then expand and travel to cover the remaining uncut portions of the work area  400 , e.g., those portions above, to the left of, and below the exclusion zone  454 - 3  in  FIG. 6G . Once the entire work area  400  has been covered by the mower  100 , the mower may de-energize its blade(s) and return to the base station  220  for re-charging. 
     The “dead-end” situation illustrated in  FIG. 6E  is not the result of encountering a physical boundary (i.e., encountering the boundary  450  or an exclusion zone  454 ), but rather the result of the leading edge segmentation algorithm implemented in the illustrated embodiments. That is, the dead-end encountered in  FIG. 6E  is really a “virtual” dead-end created by the previously established segment  452 L- 1  (see  FIG. 6B ). Examples of hard dead-end scenarios that occur independent of work area segmentation are shown in, for example, encountering the boundary  350  in  FIG. 3K , and encountering the right-most boundary  250  in  FIG. 2 . 
     While not illustrated, methods and systems in accordance with embodiments of this disclosure may avoid at least some of these virtual dead-ends. For example, in the situation illustrated in  FIG. 6E , the controller could alternatively recognize that the previous segment  452 L- 1  will ultimately result in a dead-end. It could then evaluate other segments of the travelling containment zone (e.g., the left-most edge  452 L- 5  in  FIG. 6E ) to determine a travel path that could avoid such a dead-end result. For instance, instead of collapsing into the dead-end in  FIG. 6E , the travelling containment zone  402   t   5  could instead, at or before the time represented in  FIG. 6E , begin travelling to the left using the leading edge  452 L- 5 . In this scenario, the static segment  452 L- 1  would eventually begin travelling to the left as well, forming the trailing edge of the travelling containment zone. The travelling containment zone could then continue to advance toward the left-most boundary  450  in the upper left quadrant of the work area  400 , where it would then dead-end against the physical boundary  450 . 
     As evident from the description above regarding  FIGS. 6A-6G , travelling containment zone systems and methods in accordance with embodiments of the present disclosure may involve at least four processing functions: scanning (scoring externally adjacent cells); decision-making (deciding where to direct the travelling containment zone); populating cells (adding cells along the leading edge of the travelling containment zone); and depopulating cells (i.e., removing cells along the trailing edge of the travelling containment zone). As used herein, “externally adjacent” refers, at any given time, to cells that are outside of the travelling containment zone, but are located adjacent to a boundary of the containment zone. 
       FIG. 6H  is an enlarged portion of the zone  402   t   2  shown in  FIG. 6B . The cells illustrated in this view are enlarged for clarity. As stated above, actual grid cell size may be smaller than that illustrated (e.g., to provide a higher resolution grid). The work region itself may bound a first plurality of grid cells (only some of these cells (peripheral or externally adjacent to the edges  452 L- 1  and  452 L- 2 ) are illustrated in this figure), while the travelling containment zone bounds a lesser, second plurality of grid cells (the second plurality being a subset of the first plurality of grid cells). 
     At the particular point in time represented in  FIG. 6H , the first processing function (scanning) may score two or more cells, wherein one of the two or more cells is selected from the cells  453  externally adjacent to the edge  452 L- 1 ; and another of the two or more cells is selected from the cells  455  externally adjacent to the edge  452 L- 2 . Such scoring may again be based on parameter(s) including, for example: evaluating or comparing wavefront grid values of each of these two or more grid cells; and comparing a distance from each cell of these two or more grid cells to a centroid  457  of the travelling containment zone. Based upon this analysis, the controller may execute the second (decision-making) function and select one of these edges to form the new leading edge of the travelling containment zone. The controller may then populate cells (e.g., add cells  455  (e.g., from the first plurality of grid cells) to the travelling containment zone) along the new leading edge  452 L- 2  (third function) and depopulate cells (e.g., remove cells  459  from the travelling containment zone) along what will now be the trailing edge of the travelling containment zone (fourth function). 
       FIG. 7  is a flow chart illustrating a decision-making process  700  of the travelling containment zone (e.g., executed by the controller  120 ) in accordance with embodiments of the present disclosure. As described above, scoring values of relevant cells in the grid by the scanning function would be known before entry into this algorithm. 
     The process is entered at  701 . At  702 , it is determined, based upon the scanning function described elsewhere herein, whether the travelling containment zone is dead-ended. If the answer is yes, the process proceeds to  704 , wherein no further cells are populated, after which the process exits at  706 . 
     If the travelling containment zone is not dead-ended at  702 , the process may next determine whether there is a previously selected leading edge of the travelling containment zone at  708 . If the answer is no, the process may select the highest scoring segment in which to establish the leading edge of the travelling containment zone at  710  after which the process proceeds to  716 . At  716 , the process evaluates whether the leading edge is dead-ended. If the answer is yes, the process declares a dead-end at  718  and returns to  702 . If, however, the leading edge is not determined to be dead-ended at  716 , the process proceeds to populate the leading edge at  720 , after which the process ends. 
     If, on the other hand, the answer is yes at  708 , the process may next determine if the leading edge has bifurcated or split at  712 . If the answer at  712  is no, the process may process directly to  716 . If, however, the answer at  712  is yes, the process may first select the highest scoring segment from the split at  714  before proceeding to  716 . 
     The populator function/algorithm may only be active during times that the travelling containment zone is travelling (both leading edge and trailing edge are moving) or filling (a stage where the travelling containment zone is initially growing to the desired size as shown, for example, in  FIGS. 6A and 6B ). 
     In some embodiments, the “score” of a relevant cell as determined by the scanning function may be an aggregate score that depends on different factors. For example, one sub-score value may be based upon the wavefront grid value as described above, while a secondary sub-score value may be based upon, for example, a distance of the particular cell from a centroid or other geometric feature of the current travelling containment zone. These sub-scores may then be summed (ensuring that units or weights of the respective sub-scores are consistent) to yield the total cell score used in the decision-making algorithm. Moreover, while the entire leading edge may be scored by the scanning function, the controller  120  may only populate (e.g., add cells to the travelling containment zone) a portion, for example, the top 20%-50%, (30% in one embodiment), of the cells along the leading edge. 
     Like the populator function, the depopulator is only active during certain times, i.e., when the travelling containment zone is travelling (both leading and trailing edges are moving) or emptying (a stage where the travelling containment zone is contracting such as at a dead-end as indicated in  FIG. 6E ). In some embodiments, the depopulator function may simply analyze the entire border of the travelling containment zone and remove a portion of the “oldest” cells therein, e.g., the oldest 40%-60%. However, in other embodiments, the depopulator function could also evaluate individual “segments” in a manner similar to the populator function in an effort to more efficiently remove cells from the travelling containment zone. 
     Moreover, as with the populator function, the depopulator function could utilize a scoring algorithm (e.g., evaluated during the scanning function/phase) to calculate various cell sub-scores. For example, in addition to cell “age” within the travelling containment zone, the scoring algorithm could sub-score each cell on a distance of the cell from the centroid or other geometric feature of the current travelling containment zone. Once again, the sub-scores may be added to obtain an overall cell score for depopulation. 
     The concept of depopulation is an iterative process that seeks to remove a target number of cells equivalent to those added by the populator function when the travelling containment zone is moving, and remove an arbitrary target number of cells when the travelling containment zone is emptying (when the travelling containment zone is filling, the depopulator function may be inactive until the zone reaches the desired size, and which point the depopulator may actively remove cells). 
     While described herein in the context of a single mowing session, the mower  100  may be unable to complete mowing of the entire work region in a single session without exhausting its battery. Accordingly, the controller  120  may log positional data at all times and store such data regarding which areas were mowed and what time they were mowed. As a result, the mower may suspend cutting when the battery needs recharging, and then subsequently resume cutting (after charging) in the same area where cutting was previously suspended. 
     As shown in  FIGS. 2, 4, and 6A , the mower system may also include the base station  220  that may be located in or near the work region. The base station may house the mower  100  between mowing sessions and permit the mower battery to recharge. In some embodiments, some aspects of the mower controller could be incorporated into the base station. For example, the base station  220  may, in addition or alternatively, incorporate the controller  120 . In this instance, the base station  220  may be able to wirelessly and bidirectionally communicate with the mower (e.g., via Wi-Fi) to receive data from, and provide data to, the mower. 
     The complete disclosures of the patent documents and other various publications cited herein are incorporated by reference in their entirety as if each were individually incorporated. In the event that any inconsistency exists between the disclosure of the present application and the disclosure(s) of any document incorporated herein by reference, the disclosure of the present application shall govern. 
     Illustrative embodiments are described and reference has been made to possible variations of the same. These and other variations, combinations, and modifications will be apparent to those skilled in the art, and it should be understood that the claims are not limited to the illustrative embodiments set forth herein.