Abstract:
A method of mowing an area with an autonomous mowing robot comprises storing, in non-transient memory of the robot, a set of geospatially referenced perimeter data corresponding to positions of the mowing robot as the mowing robot is guided about a perimeter of an area to be mowed, removing from the set of perimeter data one or more data points thereby creating a redacted data set and controlling the mowing robot to autonomously mow an area bounded by a boundary corresponding to the redacted data set, including altering direction of the mowing robot at or near a position corresponding to data in the redacted data set so as to redirect the robot back into the bounded area.

Description:
TECHNICAL FIELD 
       [0001]    This invention relates to an autonomous mobile robot for grass cutting. 
       BACKGROUND 
       [0002]    Autonomous robots that perform household functions such as floor cleaning and lawn cutting are now readily available consumer products. Commercially successful robots are not unnecessarily complex, and generally operate randomly within a confined area. In the case of floor cleaning, such robots are generally confined within (i) touched walls and other obstacles within the rooms of a dwelling, (ii) IR-detected staircases (cliffs) leading downward; and/or (iii) user-placed detectable barriers such as directed IR beams, physical barriers or magnetic tape. Walls provide much of the confinement perimeter. Other robots may try to map the dwelling using a complex system of sensors and/or active or passive beacons (e.g., sonar, RFID or bar code detection, or various kinds of machine vision). 
         [0003]    Some autonomous robotic lawn mowers use a continuous boundary marker (e.g., a boundary wire) for confining random motion robotic mowers. The boundary wire is intended to confine the robot within the lawn or other appropriate area, so as to avoid damaging non-grassy areas of the yard or intruding onto a neighboring property. The boundary marker is typically a continuous electrically conductive loop around the property to be mowed. Although the guide conductor can be drawn into the property in peninsulas to surround gardens or other off-limit areas, it remains a continuous loop, and is energized with an AC current detectable as a magnetic field at a distance of a few feet. The guide conductor loop must be supplied with power, usually from a wall socket. Within the bounded area, a mowing robot may “bounce” randomly as the robot nears the guide conductor, or may follow along the guide conductor. Some mowers also touch and bounce from physical barriers. 
       SUMMARY 
       [0004]    In some implementations of this disclosure, a method of mowing an area with an autonomous mowing robot, the method comprises storing, in non-transient memory of the robot, a set of geospatially referenced perimeter data corresponding to positions of the mowing robot as the mowing robot is guided about a perimeter of an area to be mowed, removing from the set of perimeter data one or more data points thereby creating a redacted data set, and controlling the mowing robot to autonomously mow an area bounded by a boundary corresponding to the redacted data set, including altering direction of the mowing robot at or near a position corresponding to data in the redacted data set so as to redirect the robot back into the bounded area. In some aspects, prior to storing the geospatially referenced data, determining locations of discrete markers along the perimeter of the area to be mowed. The geospatially referenced data are geospatially referenced as the mowing robot is guided about the perimeter in relation to the discrete markers. Prior to removing data points from the set of perimeter data, determining the reference point from a location of the mowing robot within the area to be mowed. The method comprises prompting an operator to position the mowing robot within the area to be mowed and to then initiate reference point determination. The boundary corresponding to the redacted data set is an interior boundary or an exterior boundary of the area to be mowed is determined from the location of the reference point with respect to the boundary. 
         [0005]    In other aspects of this disclosure, the method includes storing the geospatially referenced perimeter data comprises marking cells of a two-dimensional data array as corresponding to the positions of the mowing robot. Also possible is removing the one or more data points comprises altering entries in one or more marked cells to indicate that such cells do not correspond to perimeter locations. The data points to be removed are BOUNDARY cells that are not adjacent to both MOWABLE and NON-MOWABLE cells. Storing the set of perimeter data comprises determining whether the mowing robot is being guided in a forward or a backward direction, and pausing data storage while the mowing robot is being guided in the backward direction. Prior to controlling the robot to autonomously mow the area, determining whether the stored perimeter data represents a continuous path. The method can include adding data points to fill any path gaps of less than a predetermined width. Upon determining that the stored perimeter data represents a discontinuous path defining a gap of more than a predetermined width, signaling an operator to resume guidance of the mowing robot about the perimeter and storing additional perimeter data during resumed guidance. Prior to controlling the robot to autonomously mow the area, altering a portion of the stored perimeter data set corresponding to a perimeter path segment defining an interior angle less than 135 degrees, to define a smoothed boundary. The storage of the set of perimeter data is paused while the guided mowing robot remains stationary for less than a predetermined time interval, and resumes upon motion of the mowing robot. The storage of the set of perimeter data is concluded in response to the guided mowing robot remaining stationary for more than the predetermined time interval. Controlling the mowing robot to autonomously mow the area comprises determining whether the mowing robot is within a predetermined distance from the boundary, and in response to determining that the mowing robot is within the predetermined distance, slowing a mowing speed of the robot. The perimeter is an external perimeter circumscribing the area to be mowed. The perimeter is an internal boundary circumscribing an area surrounded by the area to be mowed. 
         [0006]    In other aspects of this disclosure, an autonomous mowing robot comprises a robot body carrying a grass cutter, a drive system including a motorized wheel supporting the robot body, a controller operably coupled to the motorized wheel for maneuvering the mowing robot to traverse a bounded lawn area while cutting grass. The controller is configured to: in a teaching mode, store in non-transient memory a set of geospatially referenced boundary data corresponding to positions of the mowing robot as the mowing robot is guided about a border of the lawn area, in the teaching mode, store reference data corresponding to a reference position within the lawn area, remove from the set of boundary data one or more data points corresponding to positions spatially closer to the reference position than another adjacent position represented by another data point of the set of boundary data, thereby creating a redacted boundary data set, and then, in an autonomous operating mode, control the mowing robot to autonomously mow an area bounded by a path corresponding to the redacted boundary data set, including altering direction of the mowing robot at or near a position corresponding to data in the redacted data set so as to redirect the robot back into the bounded area. 
         [0007]    Implementations can include an emitter/receiver carried on the robot body and configured to communicate with perimeter markers bounding the lawn area in the teaching mode. A removable handle securable to the robot body and graspable by an operator to manually guide the mowing robot about the border of the lawn area in the teaching mode. The robot is configured to detect if the handle is attached to the robot body. The controller is configured to initiate the teaching mode in response to detecting that the handle is attached. The handle comprises a kill switch in communication with the drive system, the kill switch configured to send a signal to turn off the mowing robot when the kill switch is not activated. 
         [0008]    The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims. 
     
    
     
       DESCRIPTION OF DRAWINGS 
         [0009]      FIG. 1A  is a schematic view of an autonomous mobile mowing robot placed on a lawn to be mowed, 
           [0010]      FIG. 1B  is a schematic view illustrating a human operator navigating the lawn&#39;s perimeter with an autonomous mobile mowing robot, 
           [0011]      FIG. 1C  is a schematic view illustrating an autonomous mobile mowing robot navigating a lawn autonomously, 
           [0012]      FIG. 2A  is a schematic top view image of a lawn with boundary markers, 
           [0013]      FIG. 2B  is a schematic top view image of a lawn with UWB beacons showing communication between each beacon, a dock, and the robot, 
           [0014]      FIG. 3  is a flow chart of a process for initializing and establishing the position of UWB beacons around a lawn, 
           [0015]      FIGS. 4A-F  are schematic drawings illustrating a UWB beacon based lawn mowing system initialization process, 
           [0016]      FIGS. 5A-5D  provide a schematic drawing illustrating a process for estimating the location of a sensor, 
           [0017]      FIG. 6A  is a schematic of a non-smooth path generated based on a path traversed by a human operator along the perimeter of a lawn and around an interior boundary inside the lawn, 
           [0018]      FIG. 6B  shows a schematic of a lawn with desired mowable and non-mowable zones, including a keep-out zone, 
           [0019]      FIG. 6C  is a schematic of a resulting mowable/non-mowable region determined by the robot for the lawn in  FIG. 6B , 
           [0020]      FIG. 6D  is an initial 2D grid map view indicating interior, boundary, and exterior cells in response to the human operator performing a push/pull action to determine the lawn perimeter, 
           [0021]      FIG. 6E  is the map of  FIG. 6D  after selection of only exterior edge boundary cells, 
           [0022]      FIG. 6F  is the map of  FIG. 6E  after smoothing with only exterior edge cells indicated as boundary, 
           [0023]      FIG. 7  is a flow chart of a method of determining a smoothed exterior boundary, 
           [0024]      FIG. 8  is a flow chart of a method of determining a smoothed interior boundary, 
           [0025]      FIG. 9A  is a schematic showing a “near boundary” or “caution” zone two feet from the boundary, 
           [0026]      FIG. 9B  is a flow chart of a process for speed/attitude adjustments performed by the robot while navigating the lawn, and 
           [0027]      FIG. 10  is a flow chart of an alternative method for determining a smoothed boundary. 
       
    
    
       [0028]    Like reference symbols in the various drawings indicate like elements. 
       DETAILED DESCRIPTION 
       [0029]    Referring to  FIGS. 1A-1C , an autonomous robot lawnmower  10  is configured to mow a lawn  20 . The autonomous robot lawnmower  10  moves about the lawn  20  and cuts grass  22  as it is traversing the lawn  20 . The robot lawnmower  10  includes a body  100 , a surface treater  200  secured to the body  100 , a drive system  400  including at least one motorized wheel  410 , and a sensor system  300  having at least one surface sensor  310  carried by the body  100  and responsive to at least one surface characteristic. The drive system  400  is carried by the body  100  and configured to maneuver the robot lawnmower  10  across lawn  20  while following at least one surface characteristic. In this example, surface treater  200  includes a reciprocating symmetrical grass cutter floating on a following wheel  410 . In some examples the wheel can be a continuous track, or tank tread. In other examples, surface treater  200  may comprise a rotary cutter, a spreader, or a gatherer. A grass comber  510  may also be carried by the body  100 . The robot body  100  supports a power source  106  (e.g., a battery) for powering any electrical components of the robot lawnmower  10 , including the drive system  400 . A wireless operator feedback unit  700  sends a signal to an emitter/receiver  151  on the robot lawnmower  10  that is in communication with a controller  150 . The drive system  400  is configured to follow the signal received from the operator feedback unit  700 . The robot lawnmower  10  may be docked at a base station or dock  12 . In some examples, the dock  12  includes a charging system for changing a battery  160  housed by the robot body  100 . 
         [0030]    An important step in the use of the robot lawnmower  10  is defining a perimeter  21  of the lawn  20  to be mowed. In some implementations, as a safety measure autonomous use of the robot lawnmower  10  can only be executed once a perimeter or boundary has been determined and stored in non-transitory memory of the robot lawnmower  10 . In some implementations, a human operator manually defines a perimeter  21  by pushing the robot  10  using a handle  116  attached to the robot body  100 , as shown in  FIG. 1B . Once the perimeter has been taught, the robot can navigate the lawn/area to be cut without further human intervention. 
         [0031]    Referring to  FIG. 1B , in a perimeter teaching mode, a human operator manually guides the robot lawnmower  10  to establish the perimeter  21  of the lawn  20 . Determining the perimeter  21  can include guiding the robot lawnmower  10  with a push bar or handle  116  attached to the body  100 . The push bar  116  may be detachable from or stowable on the robot body  100 . In some cases, the push bar  116  includes a switch, speed setting, or joystick to advance and steer the robot lawnmower  10 . In one instance, the push bar  116  includes one or more pressure or strain sensors, monitored by the robot lawnmower  10  to move or steer in a direction of pressure (e.g., two sensors monitoring left-right pressure or bar displacement to turn the robot lawnmower  10 ). In another instance, the push bar  116  includes a dead man or kill switch  117 A in communication with the drive system  400  to turn off the robot lawnmower  10 . The switch  117 A may be configured as a dead man switch to turn off the robot lawnmower  10  when an operator of the push bar  116  ceases to use, or no longer maintains contact with, the push bar  116 . The switch  117 A may be configured act as a kill switch when the push bar  116  is stowed, allowing a user to turn off the robot lawnmower  10 . The dead man or kill switch  117 A may include a capacitive sensor or a lever bar. In another instance, the push bar  116  includes a clutch  117 B to engage/disengage the drive system  400 . The robot lawnmower  10  may be capable of operating at a faster speed while manually operated by the push bar  116 . For example, the robot lawnmower  10  may operate at an autonomous speed of about 0.5 m/sec and a manual speed greeter than 0.5 m/sec (including a “turbo” speed actuatable to 120-150% of normal speed). In some examples, the push bar  116  may be foldable or detachable during the robot&#39;s autonomous lawn mowing. Alternatively, the push bar  116  can be configured as one of a pull bar, pull leash, rigid handle, or foldable handle. In some embodiments, the push bar  116  can be stowed on or in the robot body  100 . 
         [0032]    As noted above, prior to autonomously mowing the lawn, the robot lawnmower  10  completes a teaching phase. During the perimeter teaching phase, the human operator may pilot the robot lawnmower  10  in a manner that requires correction, thus putting the robot lawnmower  10  in an unteachable state. When the robot lawnmower  10  detects that it is in an unteachable state during a teach run, the robot lawnmower  10  alerts the operator (e.g., via operator feedback unit  700  such as a display on a mobile device or a display integrated in a handle  116 ) to change a direction or speed of the robot lawnmower  10  to enable the robot lawnmower  10  to continue to record the perimeter  21  and/or return to traveling on traversable terrain. For instance, the robot lawnmower  10  may enter the unteachable state when the operator pushes the robot lawnmower  10  into an area of the lawn  20  where the robot lawnmower  10  loses ability to determine its location, when the user is on a second teaching path that varies from a first teaching path, or when the user pushes the robot lawnmower  10  too fast or over terrain that is too bumpy or tilted. 
         [0033]    For example, the operator may try to push the robot lawnmower  10  between a divot and a rock, causing the robot lawnmower  10  to tilt at an excessive angle (e.g., over 30 degrees). Or the operator may attempt to teach the robot lawnmower  10  a path that goes through topography that the robot lawnmower  10  cannot traverse in the autonomous mode. In such cases, the robot lawnmower  10  alerts the operator (e.g., via the operator feedback unit  700 ) to select a different path. As previously described, the robot lawnmower  10  may alert the operator via the operator feedback unit  700  by a visual signal on a display, an audible signal through a speaker, and/or a tactile signal, such a vibration from a vibrational unit of the operator feedback unit  700 . 
         [0034]    If the operator is pushing the robot lawnmower  10  too fast or too slow during the teaching mode, thus placing the robot in the unteachable state, the robot lawnmower  10  prompts the user to either increase or decrease the speed of the robot lawnmower  10 . In some examples, operator feedback unit  700  includes a speed indicator that will light or flash (green, yellow, red light) when the robot lawnmower  10  is going at a speed greater or lower than a threshold speed. 
         [0035]    As will be discussed below in reference to  FIG. 2A , boundary markers  805  may be placed along the perimeter of the lawn  20  to aid localization of the robot lawnmower  10 . In some cases, boundary markers  805  send out a signal that the robot lawnmower interprets to determine its position relative to the boundary marker. In other examples, boundary markers  805  are passive. In either case, when the robot lawnmower  10  loses contact with the boundary markers  805 , the robot lawnmower  10  may alert the user to change paths to remain within the confinement of the boundary markers  805 . 
         [0036]    In some examples, the teaching routine requires the operator to traverse the perimeter  21  of the lawn  20  a second time (or more). Once the operator completes a first teaching run, completing a closed loop about the perimeter of the area to be mowed, the robot lawnmower  10  may alert the operator that a second run is needed. In one example, the operator hits a STOP button to affirmatively indicate completion of a teaching run around the perimeter  21  of the lawn  20 . In some examples, the robot lawnmower  10  allows the operator to either complete the second teaching run right after the first teaching run or wait until later. If the operator completes a second or subsequent teaching run and the robot lawnmower detects a variance between the two determined perimeters that is greater than a threshold variance, the robot lawnmower  10  alerts the user to the apparent discrepancy and prompts another teaching run to learn the perimeter  21  of the lawn  20 . 
         [0037]    When the perimeter-teaching process is complete, the user may dock the robot lawnmower  10  in its dock  12  (see  FIG. 1A ), allowing the robot lawnmower  10  to recharge before mowing. 
         [0038]    In some implementations, the robot lawnmower  10  includes a boundary detection system  800  that includes the emitter/receiver  151  disposed on the robot body  100  and passive boundary markers  805  ( FIG. 2A ). The types of passive boundary markers  805  may include: LIDAR scan match, passive LIDAR retro-reflectors (beacons) or both of those together. In some examples, the boundary markers  805  include: RADAR scan matching (blips), RADAR retro-reflectors or both. In implementations including boundary markers  805  placed along the perimeter  21  of the lawn  20 , the boundary markers  805  are individually identifiable by adjacent scan match data performed by the emitter/receiver  151  (see  FIG. 1B ). In scan matching, the robot lawnmower  10  can match scans taken at a given time while driving with scans stored in memory that are characteristic of each boundary marker  805 , and the robot lawnmower  10  is thus able to determine its position relative to each of the individually identifiable boundary markers  805 . In some implementations, the boundary markers  805  includes other individual identification means perceptible to the robot lawnmower  10 , such as a bar code or encoded signal to enable the robot lawnmower  10  to determine its relative position. 
         [0039]    As shown in  FIG. 2A , boundary markers  805  (e.g., beacons) are placed around the perimeter of the lawn  20  to constrain or influence behavior of the robot lawnmower  10 . In some implementations, the boundary markers  805  create a virtual wall that constrains the robot lawnmower  10  from going outside the marked boundary (i.e., perimeter  21 ). A user places the boundary markers  805  at desired positions along the perimeter  21 . To create the virtual wall, the boundary markers  805  are each within a line of sight of an adjacent boundary marker  805 . The boundary markers  805  may include a home marker that an operator can place in a position indicating a global origin (e.g., dock  12  or two boundary markers placed side by side). The operator distributes the boundary markers  805  as evenly as possible along the perimeter  21  of the lawn  20  to indicate the confinement area. Preferably each major corner of perimeter  21  is marked by a boundary marker  805 . 
         [0040]    Alternately, landmarks such as Ultra-wide Band (UWB) beacons can be placed in the environment, and the robot can use the landmarks to localize its position. These beacons can be placed inside the mowable area (e.g., beacon  810   b ), on the boundary (e.g., beacon  810   a ), or outside the boundary (e.g., beacon  810   c ). These beacons  810  ( FIG. 2B ) include UWB transceivers  811  that communicate with each other as well as with a UWB transceiver  11  located on the lawnmower robot  10 . Respective UWB transceivers are placed on the robot lawnmower  10  (e.g., the robot lawnmower  10  includes a receiver/emitter  151  communicating with each of the beacons  810   a - c ), each of the beacons  810   a - c , and optionally the dock  12 . Several beacons  810   a - c  are placed about a mowable area and are spaced apart from each other and from the dock  12 . As shown by the solid lines emanating from the robot lawnmower  10  in  FIG. 2B , the robot lawnmower  10  communicates with each of the beacons  810   a - c  and the dock  12 . Each beacon  810   a - c  communicates with each of the other beacons and the dock  12 . 
         [0041]    In general, ultra-wideband (also known as UWB, ultra-wide band and ultraband) is a radio technology which operates at a low energy level for short-range, high-bandwidth communications. Ultra-wideband transmits information spread over a large bandwidth (&gt;500 MHz). In some examples, UWB includes transmission from an antenna for which the emitted signal bandwidth exceeds the lesser of 500 MHz or 20% of the center frequency. The use of UWB beacons  810   a - c  (which include the UWB transceivers  811   a - c ) provides several advantages over other confinement/localization systems. In general, ultra-wideband characteristics are well-suited to short-distance applications. Use of ultra-wideband can be beneficial in autonomous lawn mowing because the signals can be transmitted past/through obstacles such as bushes or trees and provide precision localization of the lawn mowing robot  10  relative to the UWB beacons  810   a - c . UWB transceivers  811   a - c  emit an omnidirectional signal so the use of UWB signals can be more resistant to robot orientation than line-of-sight optical systems, such as vision-based or laser-based systems. Additionally, a UWB signal can pass through small obstacles such as trees and shrubs allowing placement of the UWB beacons in less visible locations about a mowable space (e.g., as shown by the transmission between beacon  810   b  and  810   c ). 
         [0042]    If UWB signals from UWB beacons  810   a - c  positioned about a yard are to be used to determine the autonomous lawn mowing robot&#39;s location within the yard, the location of the UWB beacons  810   a - c  needs to be established. In general, as described below in more detail in relation to  FIG. 3 , upon initial setup of a UWB system, an initialization process is performed. The process is based, in part, on a multidimensional scaling algorithm used to determine the location of the UWB beacons  810   a - c  relative to one another, which in turn can be used to establish the location of the robot  10  relative to the beacons. Thus, a home owner or other person installing the UWB beacons  810   a - c  is not required to place the UWB beacons  810   a - c  at particular locations because the system automatically determines the locations of the UWB beacons  810   a - c  upon initialization. This flexibility in positioning of the UWB beacons  810   a - c  is believed to provide the advantage of simplifying the installation and setup procedure for the autonomous lawn mowing robot system. Additionally, due to the omni-directional nature of the signal, the UWB beacons  810   a - c  can be lower to the ground than in certain line-of-sight based systems because the robot  10  does not need to align (e.g., in a line-of-sight arrangement) with the beacon in order for a signal to be received from the beacon. Upon subsequent use (e.g., prior to each time the autonomous lawn mowing robot mows the lawn), a calibration or confirmation process can be performed to confirm that the UWB beacons  810   a - c  are still in their expected, previously determined locations. 
         [0043]    Referring to  FIGS. 3 and 4A -F, a UWB beacon based lawn mowing system initialization process begins with a plurality of UWB beacons  862   a - e  that each include a UWB transceiver placed around a mowable space  870  ( FIG. 4A ). The UWB transceivers each have a unique identifier included in transmissions from the UWB transceiver to identify the source of the transmission. Additionally, the robot lawnmower  860  includes a UWB transceiver which allows the robot lawnmower  860  to communicate with the UWB transceivers in the UWB beacons  862   a - e . The UWB beacons  862   a - e  placed around a mowable space  870  are generally non-mobile and are intended to remain stationary once placed around the mowable space  870 . The UWB beacons can be positioned inside the mowable space  870 , outside the mowable space  870 , and/or on the border between the two. Additionally, due to the omnidirectional nature of the signals generated by the UWB transceivers in the UWB beacons  862   a - e , the robot can be placed inside or outside of the boundary at startup. 
         [0044]    The initialization process includes gathering/obtaining information about the distances between the UWB beacons positioned around the mowable space (step  850 ). More particularly, one UWB transceiver (e.g., the transceiver located on the robot  860  or on the dock) sends a request to each of the other UWB transceivers for information about the distance between itself and each of the other UWB transceivers. This information can include time-of-flight information or other data that can be used to determine distance. For example, in the examples shown in  FIGS. 4A-4D , upon receiving the request from the UWB transceiver on the robot  860 , the UWB transceiver in UWB beacon  862   a  sends a signal to the UWB transceivers in UWB beacons  862   b,    862   c,    862   d  and  862   e.  In response, the UWB transceiver in beacon  862   a  receives, from the UWB transceivers in UWB beacons  862   b,    862   c,    862   d  and  862   e,  time-of-flight information and the associated unique identifier for the UWB transceiver ( FIG. 4A ). Similarly, upon receiving the request from the UWB transceiver on the robot  860 , the UWB transceiver in beacon  862   b  sends a signal to the UWB transceivers in UWB beacons  862   a,    862   c,    862   d  and  862   e.  In response, the UWB transceiver in beacon  862   b  receives, from the UWB transceivers in UWB beacons  862   a,    862   c,    862   d  and  862   e,  time-of-flight information and the unique identifier for the associated UWB transceiver ( FIG. 4B ). Similar gathering of information occurs for beacons  862   c,    862   d,  and  862   e  ( FIG. 4C ). This information is sent from the individual UWB transceivers to the UWB transceiver that issued the request for information (e.g., the transceiver located on the robot  860  or on the dock). 
         [0045]    After receiving the information about the relative distances between the UWB transmitters in each of the UWB beacons, a processor in the robot lawnmower  10  (or a remotely located processor) uses a multi-dimensional scaling algorithm to determine the relative position (e.g., the x-y position relative to a global origin such as the dock position) of the UWB beacons ( 852 ,  FIG. 4D ). In general, multidimensional scaling (MDS) is a way of visualizing the level of similarity of individual cases of a dataset. It refers to a set of related ordination techniques used in information visualization, in particular to display the information contained in a distance matrix. An MDS algorithm aims to place each object in N-dimensional space such that the between-object distances are preserved as well as possible. Each object is then assigned coordinates in each of the N dimensions. The relative positions of the UWB beacons (e.g., beacons  862   a,    862   b,    862   c,    862   d  and  862   e ) determined using the MDS algorithm are stored in a memory. 
         [0046]    In some examples, the use of a multi-dimensional scaling (MDS) algorithm can generate a beacon map that is a mirror image of the actual beacon layout. If a mirror image of the actual beacon layout were used during navigation, this would result in the robot not turning in the intended direction when trying to face another point in space. To test for a mirror image layout, the autonomous lawn mowing robot  860  is moved in an orientation determination sequence (step  854 ). The system then determines whether the UWB beacon locations are mirrored (step  856 ) and if so, reassigns headings to the UWB beacon locations to correct the orientation (step  858 ). More particularly, after performing the initial beacon setup and localization, the robot stores its initial point and drives forward for a short distance (e.g., 15-30 cm) to a second point. This driving forward establishes a y-axis used to reassign beacon locations if the beacon map is determined to be a mirror image of the actual beacon layout. Then the robot turns roughly 90 degrees to the left and drives forward another short distance (e.g., 15-30 cm) as shown in path  872  in  FIG. 4E . The processor then computes the difference in bearing between the vector connecting the initial point to the second point and the vector connecting the second point to the third point. If the beacon locations are correct, this value will be close to 90 degrees. If the beacon locations are mirrored, the value will be close to minus 90 degrees, and the robot will reassign/reinterpret (e.g., flip) the beacon coordinates across the y-axis and thereby properly determine its pose. A similar procedure can be used with the robot turning to the right. 
         [0047]    After the UWB beacon locations are determined and stored, the system localizes the autonomous lawn mowing robot  860  by trilaterating based on received time-of-flight information (range) from each of the UWB transceivers ( FIG. 4F ). In general, trilateration is the process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres or triangles. In particular, the location of a sensor can be determined by measuring the range to at least three landmarks, drawing a circle of the corresponding radius around each landmark, and determining the point at which these range circles intersect. With perfect sensing, all of the circles would intersect at one point, and this location could be determined using a closed-form solution. However, all sensors have some noise, so these circles are unlikely to intersect at one point, and some means is necessary to estimate the sensor position based on multiple intersections between range circles. 
         [0048]    In one example, a least squares algorithm can be used to minimize the sum of squared error between the sensed ranges and the position estimate. 
         [0049]    In another example, as shown in  FIG. 5 , the robot&#39;s location can be determined using a technique referred to herein as minimum-distance intersection set trilateration (MIST). MIST is a technique for estimating the location of a sensor based on noisy range data from a set of fixed beacons at known locations. Like other trilateration techniques, MIST uses the intersections between circles corresponding to range readings to determine the location of the sensor. 
         [0050]    Using the MIST technique, the time-of-flight measurements are used to determine a circle of possible locations around each of the beacons where the radius of the circle is based on the distance between the UWB transceiver in the UWB beacon and the UWB transceiver in the robot. For every pair of range circles, there may be zero, one, or two intersection points. 
         [0051]    MIST works by examining all of the feasible sets of intersection points and selecting the set with the minimum total distance between points. A feasible set consists of a candidate point for each pair of range circles. There are three possible cases for each pair of circles. 
         [0052]    As shown in  FIG. 5A , in one case the circles do not intersect. In this case, the candidate point is set to the midpoint in the line connecting the closest points on the two range circles. 
         [0053]    As shown in  FIG. 5B , in another case the circles intersect at one point. In this case, the candidate point is set to the single intersection point. 
         [0054]    As shown in  FIGS. 5C and 5D , in another case the circles intersect at two points. In this case, the candidate point is set to one of the two intersection points. Since each pair of range circles may generate up to two candidate points, the computational complexity of this algorithm is exponential in the number of beacons. However, if the number of beacons is small, the algorithm remains computationally tractable. After selecting the feasible set of intersection points (e.g., 3 locations, 5 locations) with minimum total inter-point distance, MIST estimates the sensor position to be the centroid of the candidate points within this set. For example, as shown in  FIG. 5D , the small circles mark candidate points (e.g., the intersection locations for pairs of circles). The filled circles are the candidate points in the feasible set with the minimum total inter-point distance. The unfilled circles are the candidate points that are not in this set. The crosshairs mark the centroid of the points in the minimum distance intersection set and correspond to the estimated location of the sensor. 
         [0055]    In some examples, one or more of the UWB beacons may be in an isolated location and therefore it may be challenging to locate the UWB beacon relative to the other UWB beacons. For example, one beacon could be placed in a side-yard where the house prohibits communication with some of the other UWB beacons. As such, the initially determined location for the beacon may have a lower confidence since the location determination is based on communications between the isolated beacon and only a subset of the other beacons positioned about the yard. If a calculated confidence value is below a threshold confidence value, the system could request that the user move the mower (which itself includes a UWB transceiver) to a location where the mower can communicate with both the isolated beacon and a plurality of other beacons. The system can then use the UWB transceiver on the robot to help position the isolated UWB beacon (e.g., using a similar process to that described above). Once the isolated UWB beacon&#39;s revised location has been determined, the autonomous robot can be moved and the isolated beacon&#39;s location can be stored relative to the other beacons. 
         [0056]    Referring to  FIG. 6A , after setting up the UWB beacons the human operator will walk the robot around the lawn  20 . During this teaching mode, the human operator may experience difficulty manually navigating the robot lawnmower  10  around the perimeter  21  due to e.g., bumpy terrain or an obstacle blocking the path of the robot lawnmower  10 . In some cases, to avoid placing the robot lawnmower  10  in an unteachable state and/or to navigate the robot lawnmower  10  around challenging obstacles or sharp turns the user may generate non-smooth paths. For example, a user may perform jagged or staggered movements in order to navigate about the perimeter  21  during guidance of the robot lawnmower  10 . Thus, the initially established lawn outline (e.g., the actual teaching path  23  traversed by the robot) does not correspond in some location to the edge of mowable area. 
         [0057]    In order to establish the boundary of the mowable area, an algorithm will select the positions navigated by the robot lawnmower  10  during teaching mode. Once the rough lawn boundary is determined, the algorithm will perform edge selection and smoothing functions on the initial boundary data (or on a subset of the collected data). The edge selection function finds the outermost edge of the mowable area, maximizing the area to be mowed, and combined with the smoothing function results in a continuous boundary that the robot lawnmower  10  can navigate autonomously subsequent to the teaching mode. This process for determining and smoothing the boundary of the mowable space can be used with various beacon-based localization systems where distance is measured from the mobile asset (robot) to the beacons. Such technologies include but are not limited to time-of-flight (TOF), time distance of arrival (TDOA), or signal strength based systems. 
         [0058]    During the teaching mode a user will attempt to navigate the robot around perimeter  21  of the lawn  20 , illustrated by the solid boundary line, but in fact navigate along the actual teaching path  23  (illustrated by the dashed boundary line) which may be non-smooth, and can include irregularities. During the teaching mode the robot lawnmower  10  will determine and store its position at all times relative to the beacons  810 , via a data processing unit. This data processing unit may be the controller  150  mounted on the robot lawnmower (see  FIG. 1B ), or may be a separate data processing unit. The data processing unit generates a 2D grid or matrix  25  of cells to represent the lawn, and as the robot lawnmower  10  determines its position relative to the beacons  810 , the data processing unit determines and saves the coordinates of each cell containing the robot lawnmower  10  during its motion. Each cell in grid  25  can have one of three possible mowing-area values indicating whether the cell is understood to be outside the perimeter  21  or NONMOWABLE, inside the perimeter  21  or MOWABLE, or on the area perimeter  21  BOUNDARY. In  FIG. 6A , representative NONMOWABLE cells  25 A, MOWABLE cells  25 B, and BOUNDARY cells  25 C are illustrated. Each cell of the grid  25  can be assigned (x, y) coordinates based on a chosen origin or reference position (0, 0) cell. Each cell can represent a square area, with each cell having a pre-determined length and width (e.g., between 5-20 cm, between 8-12 cm, about 10 cm). For example, the grid  25  can be a grid of cells, each 10 cm×10 cm. The robot lawnmower  10  stores the (x, y) coordinates of each cell traversed by the robot lawnmower along the actual teaching path  23  travelled during the teaching mode. The robot lawnmower  10  can mark the actual teaching path  23  as a simple line tracing the path of the robot  10  through single cells as shown in  FIG. 6A . Alternatively the robot can mark all cells under the footprint of the robot as BOUNDARY cells  25 C. 
         [0059]    At the start of teaching, the values of all cells are initialized to NONMOWABLE. The operator presses the start button to start the teach process and then drives around the perimeter  21  of the mowing area. As the robot drives, the values of all cells along its actual teaching path  23  are set to BOUNDARY, the location of the cells being determined by the distance to the beacons  810 . After walking the perimeter, the operator presses a button to end the teaching process. Then, the operator positions the robot lawnmower  10  anywhere within the mowable area of lawn  20 , for example at position P, and presses a button, indicating to the robot lawnmower  10  that it is inside the perimeter. In response, the system performs a flood fill to set the values of all cells inside perimeter  21  defined by the BOUNDARY cells  25 C to mark them as MOWABLE cells  25 B corresponding to areas to be mowed. 
         [0060]    As shown in  FIGS. 6B and 6C , keep-out zones can also be trained using a method similar to that for teaching the boundary. For example, to create a keep-out zone around a tree, the user can move the robot to a point on the boundary of the tree; put the robot into teach mode; push the robot around the tree; and then take the robot out teach mode. All of the cells traversed by the robot will be marked as BOUNDARY cells (e.g., as indicated by thick line in  FIG. 6C ), and the area inside this closed boundary will remain NONMOWABLE (e.g., the solid area) and the area inside the perimeter of the lawn and outside of the closed boundary will remain MOWABLE (e.g., as indicated by the hatched area in  FIG. 6C ). 
         [0061]      FIG. 6E  shows a close-up of a portion of the perimeter  21  containing a portion of an actual teaching path  23  navigated by the human operator and lawnmower robot lawnmower  10  during the teaching mode. Actual teaching path  23  includes non-smooth characteristics, such as a jag  28 , resulting from where the human operator, for example, turned the robot lawnmower  10  and then partially retraced the path by pushing the robot lawnmower  10  backwards. NONMOWABLE cells  25 A, MOWABLE cells  25 B and BOUNDARY cells  25 C are shown in hatch, white, and grey, respectively. 
         [0062]      FIG. 6F  shows the grid map after performing an boundary smoothing function, in which the controller  150  has selected a subset of the initial BOUNDARY cell blocks by re-labeling any BOUNDARY cell that is not adjacent to both a MOWABLE and a NONMOWABLE cell as MOWABLE. 
         [0063]    In some additional examples, the system can re-label some of the previous BOUNDARY cells  25 C as MOWABLE cells  25 B, in order to determine the outermost edges of the path to be followed by the robot lawnmower  10  when it navigates the lawn  20  autonomously at a later time. In the edge-selection function, the controller  150  selects all the BOUNDARY cells  25 C and computes the distance between each BOUNDARY cell  25 C to the origin (0, 0) cell. For example, the origin call can be the interior position cell P shown in  FIG. 6A . The controller can calculate this distance given the known (x, y) coordinates determined for each BOUNDARY cell  25 C. 
         [0064]    The controller compares the distance of each BOUNDARY cell  25 C to select the BOUNDARY  25 C cells most distant from the origin P and determines a single-cell line of cells representing the outermost BOUNDARY cells  25 C. The controller  150  examines the mowing-area value of each cell adjacent to each cell labeled BOUNDARY. Any BOUNDARY cell  25 C that is in an adjacent position to more than one other BOUNDARY cell  25 C is then examined to determine which cell  25 C is furthest from the origin P and is thus the outermost limit to be mowed. To remove interior BOUNDARY cell  25 C data points from the set of perimeter data, for subsets of the perimeter data representing multiple spatially adjacent locations the controller  150  selects only those cells spatially farthest from the reference or origin point P. Thus, in a grouping of cells which are contiguous to each other, the controller selects only the outermost (e.g., farthest away) cells. In  FIG. 6F , interior cells which previously had a BOUNDARY-BOUNDARY border, have been relabeled as MOWABLE. 
         [0065]    In some additional examples, the system can identify a gap, or break in the contiguous BOUNDARY cells. The controller  150  can search for such discontinuities, by searching for BOUNDARY cells that are not adjacent to or corner to corner with any other BOUNDARY cell. The controller  150  can then select MOWABLE cells adjacent to the discontinuous BOUNDARY cells. In one implementation, the controller  150  can interpolate between the x, y values of the discontinuous BOUNDARY cells, and reassign all cells lying on the line between the discontinuous cells as BOUNDARY cells. In some implementations, the controller  150  can alter a portion of the stored perimeter data set corresponding to a perimeter path segment defining an interior angle less than 135 degrees, to define a smoothed boundary. For example, the interior angle can be less than 90 degrees, or less than 45 degrees. 
         [0066]    Referring again to  FIG. 6A , a similar process can be used to define an inside boundary  29  of an interior area enclosed within the lawn which is not to be mowed. In the illustrated example, inside boundary  29  circumscribes a pond. After tracing the actual teaching path  23 , the user navigates the robot lawnmower  10  along inside boundary  29  and then positions the robot lawnmower at a final position such as position P. This indicates that the lawnmower robot lawnmower  10  is located on MOWABLE area. The controller  150  then assigns the areas inside the inside boundary  29  as NOT MOWABLE, and outside actual teaching path  23 , which is also NOT MOWABLE. Referring to  FIG. 7 , a method  1000  for teaching a robot lawnmower  10  the perimeter of an area within the lawn allows the robot to autonomously mow the lawn  20  at a later time. The method begins when the robot lawnmower  10  enters boundary determination mode (step  1001 ). The robot lawnmower  10  first monitors if teach mode can be used by checking if the handle  116  is attached (step  1002 ). If the robot determines that the handle  116  is not attached, the robot will prompt the user to attach the handle  116  (by, e.g., beeping, or flashing a light on the operator feedback unit). Once the robot lawnmower has determined that handle  116  is attached, the emitter communicates with the beacons in a UWB calibration sequence (as described above with respect to  FIG. 2B ) (step  1008 ). The robot lawnmower then determines its initial location relative to the beacons and the dock, and initializes a virtual 2D grid of cells around its initial location, to represent lawn  20  (step  1010 ). For example, the robot lawnmower  10  may determine the distance to the farthest beacon  810 , and build a grid centered on the initial location, and extending on all sides by the distance to the farthest beacon. 
         [0067]    At this point, the robot lawnmower is ready to begin teachable mode motion by the operator. The robot lawnmower prompts the operator to push the robot lawnmower around the perimeter of the lawn (step  1012 ). As the robot lawnmower is pushed by the operator, the controller is in communication with the beacons and collects location data (step  1014 ). For example, the robot can collect time of flight data from each of the UWB beacons and use the data to determine the location (e.g., by triangulation). Each cell of the 2D grid corresponding to a detected position of the robot during this motion is set to a value marking the cell as a boundary cell (step  1016 ). The robot lawnmower continuously checks if it has received operator input indicating completion, or whether a length of non-mobile time greater than a stored threshold time has elapsed (step  1018 ). If not, the robot lawnmower continues collecting location data and marking the cells corresponding to those locations as boundary cells. 
         [0068]    Next, the operator may optionally define keep-out zones around any interior regions by pushing the mower around the internal boundary of these regions. Once at step  1018  the robot determines that the mapping of the perimeter is complete, the robot lawnmower prompts the operator to move the robot lawnmower  10  to a mowable, interior area of the lawn (i.e., the space to be mowed, step  1020 ), and then determines and saves the position of this initial interior position. The controller then identifies all boundary cells that are not adjacent to both mowable and non-mowable cells and relabels boundary cells that are adjacent to mowable or another boundary cell and not adjacent to non-mowable as mowable (step  1022 ) to calculate a final, smoothed boundary. Thus, in situations where multiple adjacent cells were identified initially as boundary, the system retains only the outermost cell as a boundary cell (e.g., the cell touching the non-mowable space) and relabels the other cells as mowable. For example, the re-labeling process selects the cells that are adjacent to only mowable cells and boundary cells and relabels those cells as mowable. The controller then uses a filling function to assign all locations inside the calculated smoothed boundary as inside/mowable area (step  1024 ). 
         [0069]    In another example, once the robot determines that the mapping of the perimeter is complete and determines and saves the position of this initial interior position, the controller then selects the outermost locations of the boundary cells in the map and performs the edge selection and smoothing operation on selected cells to calculate a final, smoothed boundary. The controller then uses a filling function to assign all locations inside the calculated smoothed boundary as inside/mowable area. 
         [0070]    Referring to  FIG. 8 , a method  2000  is shown for determining a boundary about an interior area not to be mowed (e.g., boundary  29  in  FIG. 6A ). The robot lawnmower  10  enters boundary determination mode (step  2001 ). The robot first checks if calculation of the outside perimeter boundary is complete (step  2002 ), and if not instructs the operator to complete the perimeter determination as described above (step  2004 ). The robot then determines whether all keep out zones (e.g., areas inside the defined perimeter of the lawn that should not be mowed such as flower beds, swing sets, ponds, etc.) have been defined (step  2003 ). The robot can determine whether all keep out zones have been defined by generating a prompt for a user to indicate whether the zones have been defined and receiving a response from the user indicative of their completion/non-completion. Is all keep out zones have been defined, the system proceeds to smoothing the boundaries of the keep out zones (step  2014 ). If all keep out zones have not been defined, the robot prompts the operator to push the robot lawnmower around the edge of any interior boundaries, if desired (step  2006 ). While the user pushes the robot lawnmower, the controller is in communication with, or otherwise monitors the location of, the beacons or boundary markers, and collects location data (step  2008 ). The value of each cell of the 2D grid corresponding to a location of the robot during this routine is set to BOUNDARY (step  2010 ). The robot continuously checks if it has received operator input indicating completion or whether a length of non-mobile time greater than a stored threshold time has elapsed (step  2012 ). If not, the robot lawnmower continues collecting location data and marking the cells of grid  25  corresponding to robot lawnmower&#39;s position as BOUNDARY cells. 
         [0071]    The robot lawnmower then prompts the operator to move to a mowable area of the lawn (step  2014 ) within the outside perimeter border and not inside any of the (optional) keep-out zones, and records the pose of the robot in the mowable space (step  2016 ). The system then uses a flood fill to set all cells within the boundary to NON-MOWABLE (e.g., all of the cells that are within the keep out zone) (step  2018 ). Finally, the system re-labels boundary cells for keep out perimeters that are adjacent to mowable and not adjacent to both mowable and non-mowable (keep out zone) to mowable (step  2020 ). 
         [0072]    In some additional examples, the system can perform the above-described smoothing operation on the entire grid map including both the interior boundaries of the keep out zones and the external perimeter in a single process. In such an example, the system uses a flood fill to fill all areas indicated by the robot pose in the mowable space. This flood fill sets all grid locations inside of the external perimeter of the lawn and outside of the defined keep out zones to MOWABLE. The system then performs a smoothing algorithm on both the perimeter of the lawn and the perimeters of the keep out zones. For example, the system can set all boundary cells that are not adjacent to both MOWABLE and NONMOWABLE to MOWABLE such that a boundary is generated where each boundary cell contacts both MOWABLE and NONMOWABLE space. 
         [0073]    Referring to  FIGS. 9A and 9B , after the robot lawnmower  10  has completed the teaching mode it is ready to navigate the lawn  20  autonomously. Control of the robot lawnmower  10  during autonomous operation includes allowing the robot lawnmower to traverse the lawn  20  within the area delineated by the determined boundaries. Operation of the drive system can include a slow-down mode initiated when the robot lawnmower  10  approaches a boundary, to help prevent the robot lawnmower  10  accidentally rolling past the boundary. Additionally, a slow-down mode can also be implemented when the robot lawnmower  10  approaches a boundary marker  805 . Referring to  FIG. 9A , to implement a slow-down safety mode of operation, the robot controller determines a “near boundary”  31  equidistant from and inside the previously determined final smoothed outer boundary  27 . Using the grid map and the final smoothed boundary  27 , the controller  150  selects cells close to the BOUNDARY cells. For example, the controller  150  can select all MOWABLE cells that are adjacent to a BOUNDARY cell, and re-label the selected cells which are close to and touching the boundary as being NEAR BOUNDARY cells. The controller can select all MOWABLE cells that are adjacent to a NEAR BOUNDARY cell, and re-label the newly selected sells as NEAR BOUNDARY. This process can be completed until all cells previously marked MOWABLE that are within a fixed distance of the boundary are relabeled NEAR BOUNDARY. For example, all MOWABLE cells that are within, 0.35 m (2 feet) of the boundary  27  can be labeled as being NEAR BOUNDARY cells, or part of a caution zone. The remaining interior cells are in the safe zone and remain labeled as MOWABLE cells. This grid cell labeling effectively defines the near boundary line  31 , equidistant at all or nearly all points from the actual outside boundary  27 . The near boundary line  31  can also be smoothed, as described above with respect to the actual boundary line. A similar method of creating a NEAR BOUNDARY or caution zone can be employed for interior boundaries as well. 
         [0074]    A method of autonomous control as the robot lawnmower navigates the lawn is shown in  FIG. 9B . In the method  3000 , the robot lawnmower continuously collects its location data and constructs a virtual map of labeled grid cells as described above (steps  3002  and  3004 ). If the robot determines that it is located in a MOWABLE or safe cell, the robot lawnmower continues driving forward at its current speed (step  3006 ) and heading (step  3008 ). When the robot is in this safe zone, it drives at full autonomous speed (0.5 m/s). If the robot lawnmower  10  determines that is in a NEAR BOUNDARY cell indicating the caution zone, it slows (to, e.g., 0.15 m/s), in step  3010 . The two speeds can be determined by the update rate of the localization algorithm and the response time of the low-level motor control. In some examples, a ratio of the full autonomous speed to the near boundary speed can be between about 5:1 and about 2:1, e.g., about 5:1, about 4:1, about 3:1, about 2:1. When the robot reaches a BOUNDARY cell it adjusts its course to remain within the mowable area. For example, the robot lawnmower  10  can stop and back up immediately (step  3012 ). The robot then selects a random target point from MOWABLE cells in the mowable area. The target is selected so that it is at least a minimum distance from the nearest BOUNDARY cell and so that the path from the robot to the target passes through no more than a specified number of BOUNDARY or NON-MOWABLE cells. The robot then turns to face the target and resumes forward motion. In some preferred implementations, the resumed motion resumes with the robot lawnmower  10  following along a path close to the boundary, e.g., at a constant distance from the boundary. The robot lawnmower  10  can follow the boundary until a complete perimeter is mowed. The robot lawnmower  10  then may move a constant distance inside the MOWABLE area and complete another circuit, continuing on decreasing circuits until the lawn  20  is mowed. Alternatively, the robot may mow a complete perimeter, and then follow a series of parallel, adjacent lines until the MOWABLE area inside the boundary is completely traversed. 
         [0075]    In a further embodiment, a method of smoothing the path of the robot lawnmower for later traversing of a boundary, can use the suspension of teaching mode feature discussed above. For example, when the user pulls the robot backwards to reposition the robot during teaching, a jagged path (such as jag  28  in  FIG. 6E ) results. As described above, this can place the robot lawnmower in an unteachable state, where teaching mode is automatically suspended. Teaching mode resumes when the robot lawnmower  10  detects it is moving forward again (within a threshold period of time). 
         [0076]      FIG. 10  describes an implementation of a method  4000  for teaching a robot lawnmower the perimeter of an area within the lawn allows the robot to autonomously mow the lawn at a later time which uses this suspension of teach mode. Prior to implementing method  4000 , the robot lawnmower  10  follows steps similar to those described in  FIG. 7 , checking if handle  116  is attached and, if it determines that the handle  116  is not attached, prompting the user to attach the handle  116  (by, e.g., beeping, or flashing a light on the operator feedback unit). Once the robot lawnmower has determined that handle  116  is attached, the emitter communicates with the beacons or boundary markers, and determines if the beacons are UWB beacons. If so, the UWB calibration sequence (as described above with respect to  FIG. 2B ) is executed. 
         [0077]    At this point the robot lawnmower then determines its initial location relative to the beacons  810  and the dock  12 , and initializes a virtual 2D grid of cells around its initial location, to represent lawn (step  4010 ). The robot lawnmower  10  is ready to begin teachable mode motion by the operator and prompts the operator to push the robot lawnmower  10  around the perimeter  21  of the lawn  20  (step  4012 ). As the robot lawnmower  10  is pushed by the operator, the controller  150  is in communication with the beacons  810  and collects location data (step  4014 ). Each cell of the 2D grid corresponding to a detected position of the robot during this motion is set to a value marking it as a BOUNDARY cell (step  4016 ). The robot continuously checks if it is moving forward (step  4017 ). If so, the robot continues to collect location data and set each cell traversed to boundary (steps  4014  and  4016 ). If not, the robot checks whether it has received operator input indicating completion, or whether a length of non-mobile time greater than a stored threshold time has elapsed (step  4018 ) and again checks whether the robot is moving forward (step  4017 ). If so, the robot resumes collecting location data. Otherwise the robot determines (step  4018 ) whether the operator has indicated completion (or that time has run out), in which case the robot lawnmower  10  determines that the mapping of the perimeter  21  is complete and prompts the operator to move to a mowable, interior area of the lawn (i.e., the space to be mowed, step  4020 ). The controller then selects the outermost locations of the boundary cells in the map (step  4022 ) and performs the smoothing operation on selected cells (step  4024 ) to calculate a final, smoothed boundary. The controller then uses a filling function to assign all locations inside the calculated boundary as inside/mowable area (step  4026 ). 
         [0078]    In some examples, the grid established with MOWABLE, NONMOWABLE, and BOUNDARY cells can additionally be used to determine where the mobile robot should travel while mowing the lawn. For example, during a particular run of the robot (or over multiple different runs), the system can record information about coverage-type states for the robot. For example, the system can keep track of the number of time the robot has visited the cell (to mow it) during a particular run or across multiple runs. For example, the system could determine a pose of the robot and identify the associated location on the grid. Information associated with that grid location could then be updated to indicate that the robot had mowed the location. The robot could then identify cells that had either not been mowed during the current run or that had been mowed less frequently over a series of past mowing runs (e.g., over the past 3 runs) and mow those areas prior to mowing other areas. This would be helpful for covering areas adequately before moving to other areas. 
         [0079]    While at least some of the examples above have been discussed in relation to the use of UWB beacons, the methods described herein can be used in systems having other beacon-based localization systems where distance is measured from the mobile asset (robot) to the beacons. Such technologies include but are not limited to time-of-flight (TOF), time distance of arrival (TDOA), or signal strength based systems. 
         [0080]    While this specification contains many specifics, these should not be construed as limitations on the scope of the disclosure or of what may be claimed, but rather as descriptions of features specific to particular implementations of the disclosure. Certain features that are described in this specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable sub-combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination. 
         [0081]    Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multi-tasking and parallel processing may be advantageous. Moreover, the separation of various system components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products. 
         [0082]    Accordingly, other embodiments are within the scope of the following claims.