Abstract:
A rollover risk assessment system includes sensors and a processor for estimating rollover risk associated with maneuvering on varying terrain.

Description:
TECHNICAL FIELD  
       [0001]    The disclosure is generally related to the field of rollover warning systems and methods for autopilot-guided agricultural vehicles. 
       BACKGROUND  
       [0002]    About 50% of agricultural accident fatalities occur in tractor rollovers. The end can come quickly for an unsuspecting farmer as the time from “point of no return”, when rollover is inevitable, to impact takes less than one second. D. J. Murphy et al. (Applied Ergonomics 1985, 16.3, 187-191) describe a plausible rollover scenario: 
         [0003]    “A tractor operator is baling hay with a large round baler. He is operating the tractor at 4 mph on ground that starts out with a 5% slope at the outer edges of the field. The windrows on the outside of the field are sufficiently rounded, so he hasn&#39;t had to slow down to make turns. But as he moves toward the center of the field, the slope has gradually increased to 20% and the turns have grown slightly tighter.” 
         [0004]    “He hasn&#39;t cut his speed yet, but he has noticed that there is less time to correct his steering after the turn to stay on the windrow. On the next round, a narrow rise, where the inside rear tire travels, raises the slope to 23% and the turning angle is tightened once again. Unbeknownst to the operator, the slight increase in slope, decrease in radius, and constant speed put his tractor right on the brink of overturn.” 
         [0005]    “As he starts into the turn of this new round, the operator, from previous experiences, senses that he needs to slow down. But just as he reaches for the throttle, his eye catches sight of a groundhog hole that the front wheel is about to drop into. The presentation of this new bit of stimuli causes the slightest hesitation as it is transmitted to the brain and analyzed. Almost instinctively, the operator quickly yanks the steering wheel tighter to avoid the hole. This final act results in the tractor rolling over.” 
         [0006]    Tractor stability is a widely studied topic because of its importance to farm safety. Static stability refers to the effect of tractor attitude (pitch, roll, and yaw) and the projection of the center of gravity inside or outside a stability baseline. Dynamic stability takes into account effects of motion, speed and turning maneuvers. 
         [0007]      FIG. 1  shows a rear view of a tractor  105  on slope  110 . The position of the tractor&#39;s center of gravity (CG)  115  is marked by a circle with a cross inscribed in it. Arrow  120  is drawn along a vertical line coincident with the center of gravity; i.e. it shows the direction from the center of gravity to the center of the earth. In  FIG. 1  arrow  120  crosses the slope just inside the tractor&#39;s rear wheel. If the tractor were to tip such that the arrow lay outside the wheel, the tractor would roll over in the direction of curved arrow  125 . 
         [0008]      FIG. 2  is a tractor stability baseline diagram. The diagram shows a top view of a tractor&#39;s wheels ( 200 ,  205 ) and center of gravity  210 . Dotted trapezoid  215  connects points at the outside, center of each wheel where the wheel touches the ground. This trapezoid is called the stability baseline. If a line (such as arrow  120  of  FIG. 1 ) drawn from the center of gravity toward the center of the earth passes within the stability baseline, the tractor is stable. On the other hand if the line passes outside the baseline, the tractor is unstable and will roll over. 
         [0009]    Rollovers may occur to the side, rear or front. Most often, side rollovers are the result of driving on too steep a slope while rear rollovers are caused by trying to pull an object with a hitch point located too high on the tractor. Front rollovers are rare. However, rollovers may occur for any number of reasons that contribute to an accident chain. 
         [0010]      FIG. 3  lists common hazards that increase rollover risk. These hazards include driving on too steep a slope and encounters with bumps or ditches. Some maneuvers, such as uphill turns, are safe at slow speed, yet pose significant rollover risk at higher speeds. Sharp turns increase risk compared to gradual turns. The position of a tractor&#39;s center of gravity affects rollover risk greatly. High center of gravity conditions caused by unusual loads (e.g. spray tanks) or lifted implements (e.g. buckets) increase rollover risk. Driving with a flat tire can make an otherwise tolerable slope traverse impassable. 
         [0011]    A common theme among rollover hazards is that it is not always easy for a tractor operator to perceive the level of rollover risk associated with a particular maneuver. Driving along a particular path may be safe sometimes and dangerous at other times depending on speed, center of gravity location, type of tractor and other factors. Therefore, what are needed are systems and methods for warning tractor operators of rollover hazards as far in advance as possible. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS  
         [0012]      FIG. 1  shows a rear view of a tractor on a slope. 
           [0013]      FIG. 2  is a tractor stability baseline diagram. 
           [0014]      FIG. 3  lists common hazards that increase rollover risk. 
           [0015]      FIG. 4  shows schematically a tractor and autopilot system. 
           [0016]      FIG. 5  lists modes of operation of a rollover warning system. 
           [0017]      FIG. 6  is a flow chart for calculating tractor CG position. 
           [0018]      FIG. 7  shows a tractor on a slope and parameters used to determine CG height from tire pressure measurements. 
           [0019]      FIGS. 8A and 8B  illustrate how elevation data is collected in “Mapping/Recording” mode. 
           [0020]      FIG. 9A and 9B  illustrate two kinds of terrain maps. 
           [0021]      FIG. 10  lists warnings for conditions leading to increased rollover risk. 
           [0022]      FIG. 11  shows an example of a stability display. 
           [0023]      FIG. 12  shows an example of a roll angle display. 
           [0024]      FIG. 13  shows an example of a map with a planned path and warnings. 
           [0025]      FIGS. 14A and 14B  show planned paths with methods to reduce rollover risk. 
           [0026]      FIG. 15  shows another example of a map display. 
           [0027]      FIG. 16  illustrates “cruise” mode operation. 
           [0028]      FIG. 17  is a flow chart showing when rollover risk warnings are issued. 
           [0029]      FIG. 18  shows a rollover warning system automatically calling for help in the event of a rollover. 
       
    
    
     DETAILED DESCRIPTION  
       [0030]    Farm tractors are increasingly driven by autopilot. Current autopilot systems primarily control tractor steering, but in the future throttle, brakes and implement operations may all be controlled by autopilot systems. Autopilots help farmers complete field application faster, more accurately, safely and comfortably, and with less operator fatigue than ever before. With autopilots, tractors can work at night or in dusty and low-visibility conditions to avoid losing valuable field time. Autopilots also save time by allowing operators to drive faster with better precision and no field call-backs. 
         [0031]    A tractor may also be driven by a human operator but guided by an autopilot; i.e. the human operator executes commands issued by the autopilot. Throughout this disclosure systems and methods are applicable to both autopilot-driven and autopilot-guided operations. Further, the systems and methods are not restricted to tractors; they are also applicable to a wide range of agricultural vehicles and other vehicles. 
         [0032]    Inertial sensors, continuously calibrated by state-of-the-art global navigation satellite system (GNSS, e.g. GPS, GLONASS, Galileo, etc.) receivers, enable autopilot systems to guide a farm tractor with one-inch accuracy. This capability translates into smaller overlaps between passes across a field, and increases the efficiency of precision operations like drip tape irrigation and strip tillage. 
         [0033]    An operator in an autopilot-driven tractor is not necessarily aware of how close the tractor is to its rollover point. Distractions, such as monitoring the farm work being performed, may prevent the operator from noticing an unsafe situation develop. Even when full attention is available, an operator may not realize how close to rollover he is. Experience is not always an accurate guide as a path driven slowly may become unsafe at higher speeds. (Flying an aircraft by reference to instruments, rather than visually, is similar in that human senses may be unreliable guides for controlling a machine.) The rollover warning system described here uses autopilot sensors to monitor and/or predict rollover risk. Risk information and rollover warnings can save lives, train operators to recognize unsafe conditions, and prevent equipment damage. 
         [0034]    In the future, human operators may not be present in every tractor. Fleets of tractors may operate in formation with a human present in only the lead tractor, for example. Or single tractors may be controlled remotely. Whether or not a human is present, an autopilot driving a tractor must be aware of rollover risk. The autopilot may provide a rollover warning to a local operator (e.g. tractor driver), a remote operator (e.g. a person monitoring an autonomous tractor from a remote location), or both. In this application “operator” may refer to either a local or a remote operator. In addition to, or instead of, providing a warning the autopilot may take preventive action when present or future rollover risk exceeds an acceptable threshold. For example, based on a planned path of operation the autopilot may reduce the speed of tractor when reaching high-risk terrain or a high-risk maneuver. The autopilot may also change the planned path, or suggest such changes to an operator, in order to reduce rollover risk. 
         [0035]      FIG. 4  shows schematically a tractor and autopilot system. In  FIG. 4 , farm tractor  405  is equipped with GNSS receiver  410 , radio/cell phone  415 , display, 3-D map and path processor  420 , pitch, roll and yaw sensors  425 , accelerometers  430 , steering sensor and steering control  435 , weight sensor  440 , and throttle sensor and throttle control  445 . Of these items, radio/cell phone  415 , weight sensor  440  and throttle sensor and throttle control  445  are optional. The system may also include an aural warning system such as a horn, buzzer, etc. 
         [0036]    GNSS receiver  410  may use the NAVSTAR GPS constellation, Galileo, GLONASS or other global navigation satellite system. The receiver may include the capability to use DGPS radio beacons, space based augmentation systems (such as WAAS, EGNOS, or MSAS), or L-band differential services (such as Ominstar™ or Landstar™). The receiver may also use real-time kinematic (RTK) techniques in conjunction with RTK base stations and/or RTK networks. The receiver also includes appropriate antennas to receive GNSS and correction signals. 
         [0037]    Optional radio/cell phone  415  transmits voice and/or data to a base station. Display, 3-D map and path processor  420  includes a microprocessor, volatile and non-volatile memory, and input/output devices including buttons, trackballs, speakers, USB ports, etc. Pitch, roll and yaw sensors  425  may be MEMS based or use other technologies, and may include both orientation (pitch, roll, yaw) and rate (pitch rate, roll rate, yaw rate) sensors. Accelerometers  430  may be MEMS based or use other technologies. Steering sensor and steering control  435  monitors wheel angle information and controls hydraulic steering valves. Optional weight sensor  440  measures the tractor&#39;s total weight. The weight sensor may use tire pressure measurements or rely on sensors in wheel hubs or use other technologies. Optional throttle sensor and throttle control  445  measures throttle position and opens and closes the throttle as needed to control tractor speed. The throttle control may also control a continuously variable transmission. Steering, weight, throttle and other sense and/or control functions may be implemented via a data bus, such as an ISO 11783 bus, for example. 
         [0038]    The autopilot system of  FIG. 4  provides many capabilities including steering a tractor along a predetermined path, providing light-bar course guidance, mapping hazards in a field, controlling variable rate application of sprays. The system also monitors the risk of tractor rollover. When rollover risk exceeds a critical threshold—or, based on knowledge of a planned path over mapped terrain, will exceed a critical threshold in the future—the autopilot may take control of the tractor to prevent rollover (e.g. by slowing down) or warn the tractor operator and provide suggestions (e.g. slow down, turn in a particular direction), or both. The capability to provide warnings of immediate and/or future rollover hazards improves both safety and efficiency of a tractor operation. 
         [0039]    The autopilot system has several modes of operation  500 , some of which are shown in  FIG. 5 . The system may operate in more than one mode simultaneously. In the “CG Determination” mode  505  the system calculates or measures the location of the tractor&#39;s center of gravity (or changes in the center of gravity location from a known starting point). In the “Mapping/Recording” mode  510  the system records tractor position and attitude and uses that information to create detailed topographic maps. In the “Advance Terrain Warning” mode  515  the system combines pre-existing maps and knowledge of planned maneuvers to warn an operator of future rollover risks. In “Cruise” mode  520  the system monitors rollover risk without pre-existing map information. In this mode the system may assume that the terrain slope ahead is the same as in the present location, for example. Each of these modes is now described in more detail. 
         [0040]    Center of Gravity Determination 
         [0041]    CG can be calculated for various tractor configurations or input manually by an operator if the location is already known.  FIG. 6  is a flow chart for calculating tractor CG position. First the system is defined in step  605  by the type of tractor, attached implements, and accessories. The position and weight of each of these components is determined in step  610 . Positions and weights may be obtained from manufacturer&#39;s data, a model, or user input, or a combination of sources. Finally, center of gravity is calculated in step  615 . As an example, the weight and center of gravity position for a base model tractor may be known. The weight and position of accessories (e.g. spray tanks, ballast weights, fuel, etc) and implements (e.g. defined by hitch position and weight) may then be input by an operator. This data is combined with the basic tractor CG. First the moment (weight times arm) of each item is calculated. Then the sum of the moments is divided by the total weight to find the CG arm of the tractor with all its accessories and implements. 
         [0042]    The CG height can also be determined from tire pressure measurements as shown in  FIG. 7 . These measurements may be used to determine CG height directly or to find changes in CG from a known starting position.  FIG. 7  shows a rear view of tractor  705  on slope  710 . The location of the CG is marked with circle inscribed with a cross  715 . The slope angle θ is the angle between vertical  720  and tractor z-axis  725 . The pressures in the uphill and downhill rear tires are p 1  and p 2 , respectively. 
         [0043]    Angle θ is measured by the tractor&#39;s roll angle sensors while pressures p 1  and p 2  are measured by pressure sensors in each tire. Appropriate pressure sensors include MEMS pressure sensors mounted in tire valve stems. Such sensors may send pressure data wirelessly. The difference in tire pressure, p 1 -p 2 , for a given roll angle depends on CG height. At a given roll angle, p 1 -p 2  is greater when the CG is higher, i.e. farther away from the slope. Total tractor weight, tire footprint, level (θ=0) tire pressure differential, distance between tires and other data are used to complete the calculation. 
         [0044]    Suppose, for example, that p 1 =p 2  when θ=0, that the contact area between each tire and the slope is A, and that the distance between the rear tires is W. Then, the height of the center of gravity above the rear axle of the tractor is given approximately by 
         [0000]    
       
         
           
             L 
             = 
             
               
                 Δ 
                  
                 
                     
                 
                  
                 pWA 
               
               
                 2 
                  
                 
                     
                 
                  
                 Mg 
                  
                 
                     
                 
                  
                 sin 
                  
                 
                     
                 
                  
                 θ 
               
             
           
         
       
     
         [0000]    where Δp is the increase in pressure in the downhill tire, M is the mass of the tractor, g is the acceleration due to gravity and θ is the slope angle as shown in the figure. The relationship between L, Δp and θ may be used during turning maneuvers to find L (or changes in L) even when a slope is not available. 
         [0045]    Thus, user input, moment arm calculations, and tire pressure differences may all be used, separately or in combination, by an autopilot system to determine the location of the center of gravity (or changes in the location of the center of gravity) of a tractor. This information combined with tractor attitude (pitch, roll, yaw) and velocity may be used to assess tractor stability and rollover risk. 
         [0046]    Mapping/Recording 
         [0047]    In the “Mapping/Recording” mode the autopilot system records tractor position and attitude and uses that information to create detailed topographic maps.  FIGS. 8A and 8B  illustrate how elevation data is collected in “Mapping/Recording” mode. The autopilot system records latitude, longitude and elevation as a tractor drives over a field and stores that information for later use by itself or another tractor. 
         [0048]    In  FIG. 8A  path  805  represents a track along which an autopilot controlled tractor is operating. Points  807 ,  808 ,  809  are examples of position fixes along the track where the autopilot system records position (x, y, z) and attitude (pitch, roll, yaw) of the tractor.  FIG. 8B  shows how data at position fixes obtained in  FIG. 8A  can be used to create triangular segments of a topographic map. The positions of fixes  807 ,  808 ,  809  determine the slope of a plane intersecting all three points. The unit normal  820  to the plane is shown in the Figure. Attitude measurements at each position fix may be used to improve the accuracy of normal vectors such as  820 . 
         [0049]      FIGS. 9A and 9B  illustrate two kinds of terrain maps that can be generated by the autopilot system.  FIG. 9A  shows a map created from a network of points ( 905 ,  910 ,  915 ,  920 ,  925 ,  930 ) while  FIG. 9B  shows a contour map  940  rendering of the same kind of data. 
         [0050]    Usually, “mapping/recording” implies that the terrain ahead is not known. Therefore mapping/recording may take place at slow speed to reduce rollover risk. Alternatively mapping/recording may be done by a high stability vehicle having a wide wheel separation and a low center of gravity. Map data recorded by a high stability vehicle may later used by tractors traversing the same ground. 
         [0051]    Advance Terrain Warning 
         [0052]    In the Advance Terrain Warning mode the autopilot system has a terrain map available. The map may be one generated earlier in mapping/recording mode by the same tractor or another vehicle. The map may also be obtained from other sources such as satellite imagery. In the Advance Terrain Warning mode the autopilot system provides operator warnings for conditions leading to increased rollover risk such as those listed in  FIG. 10 . The warnings include: CG near the limit of a stability baseline; high pitch or roll angle; and, planned turn dangerous at current speed or planned turn dangerous at any speed. The autopilot can provide such advance warnings because it has knowledge of both the terrain ahead and the tractor&#39;s planned maneuvers. 
         [0053]      FIG. 11  shows an example of a stability display. In the Figure, dotted line  1105  represents the stability baseline of a tractor. Symbols  1110 ,  1112 ,  1114 , and  1116  represent the position of the tractor&#39;s CG at different times. In  FIG. 11 , the CG is shown inside the baseline; i.e. in a stable condition. The CG symbol may change color depending on its position inside the baseline. For example the CG may be depicted in green near the center of the baseline and red close to the baseline limits. The current CG position may be depicted brighter while older CG positions are depicted dimmer. When the tractor is not moving, the display shows the static stability situation. When the tractor is moving the display includes effects of centrifugal force. For example, the CG is shown moving to the right in a hard left turn on level ground. An aural warning horn may be provided when CG gets close to baseline limits. 
         [0054]      FIG. 12  shows an example of a roll angle display. In  FIG. 12  tractor  1205  is traversing a slope  1210 . The tractor&#39;s center of gravity is marked by symbol  1215 . Roll angle display  1220  is shown both inside the tractor cab and separately outside the tractor for clarity. The display includes a miniature tractor  1225  and tractor z-axis indicator  1235 , a vertical indicator  1230  and horizon  1232 , and a roll limit indicator  1240 . The display gives a tractor operator an intuitive picture of the current roll angle of the tractor. Warning lines (e.g.  1240 ) indicate limits of safe operation. The warning lines may move depending on tractor speed. High roll angles may be tolerable at low speed, for example. Although the display of  FIG. 12  is limited to roll angle information, it could easily be extended to show pitch as well, much like an aircraft attitude indicator. 
         [0055]      FIG. 13  shows an example of a map with a planned path and warnings. Conventional autopilots show maps of planned paths, but without terrain information or rollover risk warnings. In  FIG. 13  planned tractor path  1310  is shown on topographic map  1305 . The autopilot may warn an operator if the planned path will result in high rollover risk. For example, the autopilot may change the path color (e.g. to red) where the path makes uphill turns in steep terrain. Turn  1315  is an example of such a high risk turn. Path warnings may also be speed dependent. A path shown in green (low risk) at low speed may be shown in red (high risk) at higher speeds. 
         [0056]    The autopilot system may change a tractor&#39;s path to reduce rollover risk or suggest to the operator that he change the path manually.  FIGS. 14A and 14B  show planned paths with methods to reduce rollover risk. In  FIG. 14A  a path is shown in which tractor speed is reduced approaching a turn and increased leaving the turn. In a fully automatic system the autopilot commands these speed adjustments through throttle control. (In this disclosure “throttle” or “throttle control” refer to any of a variety of systems or methods for controlling and/or sensing engine and/or vehicle speed including: a throttle valve, a fuel flow control system, an RPM governor, a continuously variable transmission control, etc.) In a system with a human operator the autopilot may issue maximum speed recommendations to the operator and/or prevent the operator from selecting too high a speed. As an alternative to slowing down, the autopilot may command the tractor (or suggest to its operator, if an operator is present) to increase turn radius as shown in  FIG. 14B . In a field with many parallel rows, this may be accomplished by skipping rows, for example. 
         [0057]      FIG. 15  shows another example of a map display. In  FIG. 15 , display  1500  depicts panes such as map pane  1510  and status pane  1540 . Other panes display buttons for marking hazards or controlling autopilot functions, for example. In pane  1510  a tractor is depicted by symbol  1520 . Also displayed are paths  1525  that the tractor has already traversed and planned path  1530 . 
         [0058]    A rollover warning system uses knowledge of the planned path and the terrain over which the path passes to determine levels of future rollover risk. If the planned path includes high rollover risk maneuvers, such as traverses across steep grades or high speed turns, then the system may provide a warning to local or remote operator. For example, the planned path may be depicted in a different color, or as a dashed or flashing line in areas where rollover risk is high. Other visual or aural warnings may be issued. 
         [0059]    In addition to, or instead of, a warning the system may also initiate preventive action to prevent a high rollover risk situation from developing. For example, the system may command a speed decrease or complete stop, or it may change the path. As an example, when working a field with many parallel rows, it may be safer to skip one or more rows when turning around at the edge of the field than to turn to the closest adjacent row. The tractor may return to skipped rows later in the job. 
         [0060]    Cruise 
         [0061]      FIG. 16  illustrates “cruise” mode operation. In this mode, the autopilot does not have the benefit of prerecorded terrain information. Therefore the terrain slope ahead is assumed to be the same as the terrain slope in the present position. In cruise mode the autopilot evaluates the risk of a planned turn assuming that the turn will occur on ground with the same slope as the present slope. Cruise mode may be used simultaneously with mapping/recording mode. 
         [0062]    In both “Advance Terrain Warning” and “Cruise” modes the autopilot issues warnings when the risk of rollover exceeds a critical threshold. Liu&#39;s stability index, S, is one way to quantify rollover risk (see J. Agricultural Safety and Health, Special Issue (1):171-181, 1998, incorporated herein by reference). S=100 for when stability is maximum; i.e. for a tractor at rest on a level plane. S=0 indicates that a stability limit has been reached and rollover is imminent. Thus, a reduction in stability index corresponds to an increased rollover risk. 
         [0063]    Static stability is a function of tractor attitude (pitch, roll, and yaw), center of gravity position and wheel geometry. Dynamic stability depends also on linear and angular tractor velocities. 
         [0064]    A static stability index may be defined as: 
         [0000]    
       
         
           
             
               S 
               stat 
             
             = 
             
               
                 [ 
                 
                   1 
                   - 
                   
                     
                       
                         
                           θ 
                           2 
                         
                         
                           θ 
                           c 
                           2 
                         
                       
                       + 
                       
                         
                           ϕ 
                           2 
                         
                         
                           ϕ 
                           c 
                           2 
                         
                       
                     
                   
                 
                 ] 
               
               × 
               100 
             
           
         
       
     
         [0065]    Here θ is the tractor&#39;s pitch angle and φ is its roll angle. The tractor&#39;s static pitch and roll overturn angles are θ c  and φ c  respectively. 
         [0066]    A dynamic stability index may be defined as: 
         [0000]    
       
         
           
             
               S 
               dyn 
             
             = 
             
               
                 [ 
                 
                   1 
                   - 
                   
                     V 
                     
                       V 
                       c 
                     
                   
                 
                 ] 
               
               × 
               100 
             
           
         
       
     
         [0067]    Here V is the tractor&#39;s tangential speed along a turn and V c  is Liljedahl&#39;s critical speed for a tractor in a steady state circular turn (see Tractors and Their Power Units, Liljedahl et al., p. 272-313, Van Nostrand Reinhold, New York, 1989, incorporated herein by reference). The critical speed is: 
         [0000]    
       
         
           
             
               V 
               c 
             
             = 
             
               
                 
                   
                     gA 
                     ϕ 
                   
                    
                   R 
                 
                 
                   
                     Z 
                     cg 
                   
                    
                   
                     cos 
                      
                     
                       ( 
                       γ 
                       ) 
                     
                   
                 
               
             
           
         
       
     
         [0068]    Here A φ  is the shortest horizontal distance in the plane between the center of gravity and the vertical plane going through the tipping axis; R is the turn radius; Z cg  is the center of gravity height; γ is the angle between the tipping axis and the longitudinal plane; and, g is the acceleration due to gravity near the earth&#39;s surface. Turn radius, R, may be calculated by processor  420  using wheel angle information obtained from steering sensor  435 . In a side rollover, the tipping axis is approximately the line between the points where the front and rear wheels of the tractor, on the side toward which the tractor is rolling, touch the ground. 
         [0069]      FIG. 17  is a flow chart showing when rollover risk warnings are issued. Processor  420  performs the functions in objects  1705 ,  1710  and  1715  and issues warnings pertaining to current and future rollover risk as specified in objects  1720  and  1725 . 
         [0070]    In object  1705  the processor determines the tractor&#39;s current attitude and velocity from: GNSS receiver  410 ; pitch, roll and yaw sensors (which may output angle and rate information)  425 ; and, accelerometers  430 . In object  1710  the processor obtains terrain information such as the ground slope along the planned path of the tractor from a topographic map, if available. The map may be one that has been recorded earlier by the autopilot, obtained from a similar autopilot on a different vehicle, derived from satellite imagery, or obtained from some other source. In object  1715  the processor calculates the radius of turn for maneuvers on the planned path along which the autopilot is steering the tractor, if a planned path has been entered into the autopilot. Objects  1705 ,  1710 , and  1715  run independently; sometimes not enough information is available to run objects  1710  and/or  1715 . 
         [0071]    In object  1720  the processor uses the information obtained in objects  1705 ,  1710 , and  1715 , as available, to calculate the current static and dynamic stability indices, S stat  and S dyn , described above. If either of these indices is less than a threshold value, the autopilot issues a warning to the tractor operator. The warning may be an aural warning such as a bell or horn, or a visual warning such as a red light or warning message on a display. The threshold value for current stability indices is typically about 10 but may be anywhere between about 5 and about 50 based on operator preferences. 
         [0072]    In object  1725  the processor uses the information obtained in objects  1705 ,  1710 , and  1715 , as available, to calculate the future static and dynamic stability indices, S stat  and S dyn , described above. If either of these indices is less than a threshold value, the autopilot indicates the future danger by highlighting the tractor&#39;s planned path on the display. The path may be highlighted by changing its color (e.g. to red), depiction (e.g. dashed or dotted), or making part of the path blink. The threshold value for future stability indices is typically about 10 but may be anywhere between about 5 and about 50 based on operator preferences. The threshold for future stability may be set to a different value than that for current stability. 
         [0073]    Objects  1720  and  1725  run independently; sometimes not enough information is available to run object  1725 . Objects  1705 - 1725  are continually updated by the processor. In object  1710  the autopilot assumes that the ground slope at points ahead along the tractor&#39;s planned path is the same as the current ground slope if no map is available. 
         [0074]      FIG. 18  shows a rollover warning system automatically calling for help in the event of a rollover. The autopilot may send out a distress signal via a communications link (e.g. cell phone, radio, satellite link, wi-fi, wi-max, etc.) whenever a rollover event is detected; e.g. whenever the roll angle exceeds a critical angle. 
         [0075]    The autopilot system described here combines tractor state information obtained from autopilot sensors with the autopilot&#39;s knowledge of planned maneuvers to evaluate rollover risks. A fully automatic implementation of the system makes speed or heading corrections autonomously. When a human operator is present the system issues warnings and suggestions to operator. 
         [0076]    As one skilled in the art will readily appreciate from the disclosure of the embodiments herein, processes, machines, manufacture, means, methods, or steps, presently existing or later to be developed that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized according to the present invention. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, means, methods, or steps. 
         [0077]    The above description of illustrated embodiments of the systems and methods is not intended to be exhaustive or to limit the systems and methods to the precise form disclosed. While specific embodiments of, and examples for, the systems and methods are described herein for illustrative purposes, various equivalent modifications are possible within the scope of the systems and methods, as those skilled in the relevant art will recognize. The teachings of the systems and methods provided herein can be applied to other systems and methods, not only for the systems and methods described above. 
         [0078]    In general, in the following claims, the terms used should not be construed to limit the systems and methods to the specific embodiments disclosed in the specification and the claims, but should be construed to include all systems that operate under the claims. Accordingly, the systems and methods are not limited by the disclosure, but instead the scope of the systems and methods are to be determined entirely by the claims.