Abstract:
A method and apparatus for controlling the steering of a trailing section of a multi-sectioned vehicle is described. The trailing section follows the path of the first section. Data is acquired by a controller from sensors on the various sections. The controller then processes this data, generating a configuration needed for the controller-steered wheels to follow a path approximately equivalent to the path taken by the first steered section. Power is then applied by some means to steer these controller-steered wheels, forcing them into the desired configuration. The complexity of the control system can be varied with different algorithms providing alternative steering patterns as desired. This system can be extended with more trailing sections without necessitating more than minor changes to the control algorithms.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]    This application claims the benefit of provisional patent No. 60/204,513, filed Jun. 4, 2001. 
     
    
     
       TECHNICAL FIELD  
         [0002]    This invention relates generally to the steering of the various sections of mobile articulated machines, and particularly to the steering of a section that is steered as a robot by a non-human control system. The preferred embodiments of the invention demonstrate a way of applying the principles of the invention to over-the road tractor-trailer combinations. A driver controls the steering of a lead tractor, which carries the first trailer.  
         BACKGROUND OF THE INVENTION  
         [0003]    Over-the-road transport companies find it difficult at times to compete with other freight haulers due to labor costs. Labor costs could be decreased if each tractor-trailer rig could carry more weight, but weight limits have been placed on roads and bridges for structural reasons. Multi-trailer arrangements have been seen as a possible solution to this problem because they spread the load over a longer stretch of pavement and reduce the columnar loading on bridges. These arrangements generally involve long combination vehicles, a semi-trailer carried by the tractor with one or more full trailers composed of semi-trailers carried by dollies, called “doubles” and “triples”.  
           [0004]    These long combination vehicles face the two interconnected problems of instability and lack of maneuverability, with each following dolly (with trailer attached) becoming less stable at speed and, also, each following dolly “cutting the corner” more than the vehicle segment in front of it during cornering. The standard Type A dolly has achieved some degree of success over the years by striking a point between the two problems. It hitches to the towing vehicle or first trailer using a single point hitch. The standard Type A dolly provides steering for the trailer it is carrying by allowing the entire dolly to steer relative to its semi-trailer about the fifth wheel vertical axis on the dolly as well as relative to the towing trailer about the single point hitch vertical axis. The dolly tires however, do not steer relative to the dolly frame.  
           [0005]    Commercial vehicles of either truck and full trailer or multi-trailer configurations which employ the standard Type A dollies generally possess undesirable characteristics such as limited maneuverability and instabilities caused by rearward amplification. Rearward amplification, sometimes described as a crack-the-whip phenomenon, implies that in rapid evasive maneuvers such as emergency lane changes, the rearward elements of the vehicle train such as the dolly and the trailer carried by the dolly experience motions which are substantially amplified compared to the motions of the towing tractor and first trailer. Rearward amplification is known to be the basic cause of many accidents in which roll over of the last trailer or second trailer occurs while the remaining elements of the vehicle remain unscathed.  
           [0006]    A second general class of dollies known as Type B dollies represents an improvement over standard Type A dollies. Type B dollies are generally characterized by a double tow bar arrangement, which eliminates steering of the dolly with respect to the towing vehicle, most commonly the first trailer. The Type B dollies have been effective to a degree against some of the instability problems and are slightly more maneuverable than the standard Type A dollies. However, they cause other problems such as introducing other types of instabilities, causing stresses on the rear of the forward trailer, and increasing unloading delays due to difficulty in accessing the back of the forward trailer for some configurations.  
           [0007]    Steerable Type A dollies address the stability problems, but are even less maneuverable than Standard Type A dollies.  
           [0008]    The long dolly of provisional patent No. 60/204,513 addressed these problems by switching between a stability and a cornering or maneuverability mode. The application of drive power to the dolly axles, provisional patent No. 09/776,211 did not change the steering but did allow the long dolly (with its trailer attached) to swing wider around a corner in the path dictated by steering modes that demanded a closer emulation of the behavior of the tractor.  
           [0009]    Although an improvement, these modes of steering for the long dollies, stability and cornering, did not truly track the path of the tractor, but only traced a path that represented a typical expected path for a given maneuver. Clearly a mode of steering is needed for these long combination vehicles that would ensure that the following vehicle tracked the path of the forward vehicle as closely as possible, especially during critical cornering maneuvers in tight places.  
           [0010]    A similar problem exists in narrow city streets where equipment must be delivered to an emergency site such as a fire, or where the delivery of other materials is required. A sectioned vehicle in which each short section followed the path of the first section would be better able to negotiate such streets than a single long vehicle. Similarly, in a convoy of RV&#39;s traveling together, each vehicle requires a driver. If a mode of path tracking steering existed which would assure that successive vehicles followed the same path as the lead vehicle, a single driver might steer a convoy of several vehicles.  
         SUMMARY OF THE INVENTION  
         [0011]    The present invention advances the concept of a robotic vehicle that is capable of tracking the path of a lead vehicle. At this point the device can no longer be considered a mere dolly but must more properly be called a robotic vehicle or robotic tractor, because it is filly capable of steering itself in response to input and of propelling itself during cornering. It is also capable of selecting other desired steering modes, including, for example, a mode in which the stability is enhanced at a slight expense to its tracking capability.  
           [0012]    The details of this robotic tractor include mathematical equations and algorithms, electronic hardware, and a mechanical system.  
         OBJECTIVES OF THE INVENTION  
         [0013]    It is an objective of this invention to advance the concept of a robotic vehicle that is capable of tracking the path of a lead vehicle, and that is fully capable of steering itself in response to input, of propelling itself during cornering, and of selecting other desired steering modes, including, for example, a mode in which the stability is enhanced at a slight expense to its tracking capability.  
           [0014]    It is an objective of this invention to present a mathematical model that would allow a multiplicity of path-tracking and non-path-tracking steering algorithms to be combined in a coherent manner using a variety of weighting factors, and to point toward even more complex control algorithms.  
           [0015]    It is an objective of this invention to provide a plurality of mathematical algorithms based on physical principles and on the geometry of the vehicle configurations, each of which is compatible with the above system for combining algorithms, for steering a robotic vehicle to track the path of a lead vehicle.  
           [0016]    It is an objective of this invention to present an electronic control system, preferably including hardware such as sensors, actuators, and other I/O devices, RAM, ROM, and other data storage devices, and digital processors, that is capable of acquiring data from these sensors, using that data as input to algorithms to generate control signals, and using these control signals to activate steering and other control components to enable a robotic vehicle to track the path of a lead vehicle.  
           [0017]    It is an objective of this invention to present a mechanical system that is capable of being controlled by the actuators to track the path of the lead vehicle, thereby eliminating the need for a second operator for the second vehicle.  
         ADVANTAGES OF THE INVENTION  
         [0018]    The first advantage of this invention is the increase in maneuverability for shorter sectioned delivery or emergency vehicles in places such as narrow city streets. The long wheelbases of standard trucks and tractor-trailer combinations cause them to “cut the corner” during tuns. In narrow city streets such as those found in many European cities, this behavior could be disastrous. A vehicle composed of a number of shorter sections that were steered so that each section tracked the first section could solve some of the problems in these types of situations.  
           [0019]    Another advantage of this invention is the savings in labor costs in applications such as over-the-road freight transport. The length of the robotic tractor spreads the load and permits more weight to be carried by a single long combination vehicle driven by a single driver. A robotic tractor “double” eliminates one driver, and a robotic tractor “triple” eliminates two drivers. At the same time, because of the ability of the robotic tractor(s) to track the path of the lead tractor while carrying its own trailer, the loss of maneuverability is minimal. Because of the length and because of the capability for using a more stable mode at higher speeds, there is also no appreciable loss of stability as compared to a single tractor-trailer rig.  
           [0020]    Another advantage of this invention is that it requires minimal supervision from the driver. The controller is programmed to steer using input from its sensors (such as speed of travel or quickness of a turn), and by taking clues from the normal control activities of the driver. To set up the long combination vehicle, the driver has only to adjust the length of the tongue and input the length of the tractor and the trailers.  
           [0021]    Another advantage of this invention is that the robotic tractor embodiment can carry standard semi-trailers with only very minor modifications. Standard tractors could also be used as lead tractors with only slightly more substantial modifications, such as the addition of the appropriate sensors.  
           [0022]    This invention offers the stability of the steerable Type A dollies but with better cornering capabilities than the Type B dolly. It also takes advantage of the reduction in cost and the rapid growth in the capabilities of electronic computing hardware. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0023]    [0023]FIG. 1 is a diagrammatic view of a tractor-trailer long combination rig  
         [0024]    [0024]FIG. 2 is a diagrammatic perspective plan view of a robotic tractor according to one embodiment of the articulated machine of the present invention  
         [0025]    [0025]FIG. 3 is a diagrammatic back plan view of a robotic tractor according to one embodiment of the articulated machine of the present invention  
         [0026]    [0026]FIG. 4 is a diagrammatic top view taken along the lines  4 - 4  of FIG. 3 of a robotic tractor according to one embodiment of the articulated machine of the present invention  
         [0027]    [0027]FIG. 5 is a diagrammatic top view of a robotic tractor according to one embodiment of the articulated machine of the present invention  
         [0028]    [0028]FIG. 6 is a diagrammatic close up of the rear section of atop view of a robotic tractor according to one embodiment of the articulated machine of the present invention  
         [0029]    [0029]FIG. 7 is a diagrammatic view of a tractor partial circular track with associated sensors  
         [0030]    [0030]FIG. 8 is a diagrammatic back view of a second embodiment of the present invention  
         [0031]    [0031]FIG. 9 is a diagrammatic top view of a second embodiment of the present invention  
         [0032]    [0032]FIG. 10 is a diagrammatic top view detail of a stinger  
         [0033]    [0033]FIG. 11 is a diagrammatic end view detail of a transverse axle and axle hanger assembly  
         [0034]    [0034]FIG. 12 is a diagrammatic back view detail of a transverse axle hanger assembly and traction kinking air motor assembly  
         [0035]    [0035]FIG. 13 is a diagrammatic view of a double-axle wagon according to one embodiment of the articulated machine of the present invention  
         [0036]    [0036]FIG. 14 is a diagrammatic representation of a lead tractor and trailer making a turn  
         [0037]    [0037]FIG. 15 is a diagrammatic representation of a robotic tractor and trailer making a turn 
     
    
     DETAILED DESCRIPTION  
       [0038]    A system for steering a trailing section of an articulated machine is shown as embodied in a tractor-trailer combination rig, but other articulated machines are considered equivalents and within the scope of the invention. In FIG. 1 a tractor-trailer combination rig having first, second, third and fourth pivotally connected articulated machine sections is shown as a tractor  30 , forward trailer  40 , robotic tractor  50 , and rear trailer  80 . Information is obtained from the various sensors and input to a controller  49 , which can be a processor or computer. The controller  49  uses algorithms to extract necessary information about orientation, speed, etc. from the input data, and then determines the necessary action to obtain the desired steering result  
         [0039]    Three steering algorithms are described. The relative angle steering mode and the rate of orientation change steering mode are methods of path tracking steering. The third method, variable ratio with oversteer from provisional patent No. 60/204,513 is an independent mode. The traction kinking system is included from provisional patent No. 09/776,211. Full redundancy for all the electronic components would be desirable to minimize the consequences of failures, but for simplicity such redundancy is not included in this description of the invention. Energy must be supplied to power the robotic tractor  50  steering system and traction kinking system. Various means, including air, hydraulic, or electric power or a combustion engine would suffice. In this embodiment compressed air and pressurized hydraulic fluids are utilized as energy sources.  
         [0040]    Three embodiments are described. A simpler embodiment is shown in FIGS. 1 through 7 as a robotic tractor with a single steering mode, the relative angle path-tracking mode. The second, more complex, embodiment utilizes both the relative angle path tracking mode and the rate of orientation change path tracking mode as well as the independent ratio with oversteer steering mode, shown in  1 ,  7 ,  8 ,  9 ,  11 ,  12 , and  13 . This embodiment also uses traction kinking to assist in swinging wide around corners. The third embodiment, a double axle wagon, towed behind a pickup truck or other small vehicle, is shown in FIG. 14.  
         [0041]    [0041]FIG. 1 illustrates a typical application of a robotic tractor with its attached trailer towed behind a tractor-trailer combination rig, as in the first and second embodiments. A lead tractor  30  of a tractor-trailer combination has a first trailer  40  coupled thereto via a pair of fifth wheels  36  L, R. Behind this first trailer  40  is attached the steerable machine section that we refer to as the robotic tractor  50 . A second trailer  80  is mounted on the robotic tractor  50  by another pair of fifth wheels  67  L, R.  
         [0042]    Two sensors are mounted on the tractor  30  to determine reference steering information about the path the lead tractor  30  has traveled in the first embodiment. This reference steering information for the path tracking steering modes comes from a sensor θ R0    42  (FIG. 7) mounted on the tractor partial circular track  250  between the tractor  30  and the front trailer  40  to determine the angle θ R0  between the tractor  30  and the front trailer  40 , and linear motion sensor ΔT  34  (FIG. 1) mounted on the tractor  30  in order to determine the distance traveled by the tractor  30 . The rotation of the tractor drive shaft is utilized to obtain this measurement, but other methods could be used to obtain it. In the second embodiment a third sensor, θ F  (FIG. 1), is located to sense the angle θ F  between the tractor  30  centerline and the centerline of the front wheels of the tractor  30 .  
         [0043]    First Embodiment:  
         [0044]    The first embodiment of the invention has a long rigid main robotic tractor frame or tongue  55 , which is the central rigid structural member. The front of the tongue  55  is attached at hitch latch  108  to the forward trailer  40 .  
         [0045]    At the rear of the robotic tractor there are three sections which each pivot in relation to each other, with a single vertical pivot point, best seen in FIG. 3. The uppermost section is a trailer mounting bar  66  with its two attached fifth wheels  67  L, R. The middle section is the robotic tractor frame or tongue  55 . The lowest section is a steering axle assembly  60  with attached running wheels  70  L, R.  
         [0046]    In the uppermost section, the trailer mounting bar  66  is free to swivel around the trailer mounting bar central pivot  65  (FIG. 3). This trailer mounting bar  66  pivots above the tongue  55  and around the same line as the steering axle assembly central pivot  58 . Mounted on this trailer mounting bar  66  are the two fifth wheel latches  67  L, R by which the rear trailer  80  will be coupled to the robotic tractor in this embodiment, instead of the single fifth wheel coupling that is usually used. The trailer mounting bar  66  and the rear trailer  80  (FIG. 1) are allowed to pivot above the main robotic tractor frame  55  as the rear trailer  80  (FIG. 1) swings from side to side with respect to the robotic tractor. This movement is accurately measured and communicated to the processor  49  by the movement of the optical rotation encoder θ R1    43  mounted adjacent to an upper partial-circular track  140 .  
         [0047]    The upper partial-circular track  140  attaches at an attachment assembly  141  at its endpoints to the trailer mounting bar  66  and pivots with it during turns. Bearing plates provide stability for this pivot  65 . This upper partial-circular track  140  is mounted sufficiently above a rear partial-circular track  75  to easily clear it during operation and to allow unobstructed operation of both rotational systems.  
         [0048]    The middle pivotal section of the robotic tractor  50  is the frame or tongue  55  (FIG. 3). Both the steering axle assembly  60  below the tongue  55 , and the trailer mounting bar  66  above the tongue  55  are mounted on pivots extending downward and upward respectively from the tongue  55 , and pivot with respect to the tongue  55 . The tongue  55  is attached to the forward trailer  40  by a of some type. A front pivot orientation sensor θ D1    44  (FIGS. 4,5) is mounted on the front partial circular track  100  to measure the angle θ D1  between the robotic tractor tongue  55  and the front trailer  40  centerline. The front partial circular track  100  is attached as shown in FIG. 4 and  5  by ball type hitch latches  106  L, R that are attached to the front of the partial circular track  100 , but other methods could be used.  
         [0049]    The axle assembly central pivot  58  (FIG. 3) is mounted on the bottom of the robotic tractor tongue, and a corresponding trailer mounting bar central pivot support  65  above the tongue  55  and in line vertically with the axle assembly pivot support  58  is the pivoting attachment for the trailer mounting bar  66 . The axle assembly  58  pivots in relation to the robotic tractor tongue  55  in response to torque applied by a hydraulic steering motor  68  via a chain  69  (FIGS. 4, 6). The angle between the robotic tractor tongue  55  and the axle assembly  60  is read by a sensor θ S1    53  (FIG. 4). The sensor θ S1    53  obtains the angle between the robotic tractor tongue  55  and the axle assembly central pivot support  58  as shown in FIG. 4 by measuring the rotation of the lower partial circular track  75 .  
         [0050]    The tongue  55  of the robotic tractor will be longer than the typical dolly tongue  55 , because if it is to correct for the deviation the trailer ahead of it caused it will need to be roughly on par with the length of the front trailer  40 . The degree of similarity in length will depend on various factors; the longer the robotic tractor tongue  55 , the easier it will be to correct the course deviation, but the more awkward the assembly will be. A short tongue would allow a degree of course correction, and how short the tongue can be made will depend on how accurately the robotic tractor  50  is desired to follow the path of the main trailer  40 . The long tongue provides an advantage in that the length of the tongue would allow the vehicle to carry more weight, because the weight characteristics would be more like two tractor-trailer rigs in close convoy, rather than one tractor towing two trailers. By spreading the load over a longer span, this extra length has the highly desirable benefits of reducing the stresses on the pavements and reducing the columnar loading on the bridges of our highway systems, thus allowing a heavier load to be pulled.  
         [0051]    The lower pivotal section is a steering axle assembly  60  with attached running wheels  70  L, R. The steering axle assembly  60  is mounted on the vertical axle central pivot  58  (FIG. 3) which extends below the main robotic tractor frame or tongue  55  and is able to swivel around on this axle central pivot  58  (FIG. 3). Bearing plates provide stability for this axle central pivot  58 .  
         [0052]    The steering axle assembly  60  and two spaced pairs of running wheels  70 R and  70 L, which it carries, are mounted beneath the main robotic tractor frame  55  along with any conventional suspension system components that may be needed. In this embodiment the suspension system is omitted for clarity of illustration since it is composed of standard assemblies. A double-axle steering section that turns as a unit, two independent steering axles, or any other suitable configuration would be possible, but, for simplicity, this embodiment of the invention is shown with a single axle.  
         [0053]    The sensor assemblies and the hydraulic motor assemblies, which enable the controlling processor to steer the steering axle assembly  60 , are mounted generally above the main robotic tractor frame  55  and in front of the transverse axle  72 . These assemblies include the upper partial circular track  140 , a lower rear partial-circular track  75 , one hydraulic motor  68 , two optical rotation encoders θ R1    43  and θ S1    53  or some such sensors, and several additional components. Mounted on the axle drive shaft  202  (FIG. 12) of the robotic tractor  50 , sensors ΔS 1     —     LEFT    52 L and ΔS 1     —     RIGHT    52 R measure the rotation of the axle of the robotic tractor  50  in order to determine the distance traveled by the robotic tractor  50 . The average of the sensors ΔS 1     —     LEFT    52 L and ΔS 1     —     RIGHT    52 R is ΔS 1 . Mounted on the steering axle  72  are two air motors  170  L, R, (FIG. 12) which provide power to the wheels  70  L, R of the robotic tractor as needed.  
         [0054]    The steering axle assembly  60  (FIG. 3) has an attachment at the top via a track attachment assembly  73 L and  73 R near the extremities of a rear partial-circular track  75 . The partial-circular track  75  is somewhat longer than a semicircle to allow for turns of greater than 90 degrees. The attachment assemblies  73 L and  73 R are designed solidly, but they attach behind the steering axle assembly  60  so that the space directly above the steering axle assembly  60  and forward is empty. This allows above 180 degrees of rotation of the steering axle assembly  60  about the transverse age central pivot  58  (FIG. 3) in response to the torque applied by the rear partial-circular track  75 .  
         [0055]    The bottom of the rear partial-circular track  75  is in the same plane with the top of the main robotic tractor frame  55 . The front of the rear partial-circular track  75  contains a channel with a heavy roller chain  216 . The two ends of the heavy roller chain  216  are attached at the extreme rear points of the rear partial-circular track  75  on each side. At the point where the heavy roller chain  216  passes over the main robotic tractor frame  55 , the heavy roller chain  216  forms a loop forward around a heavy main sprocket  77 , consisting of two coaxial sprockets. Below the heavy roller chain on the main sprocket  77  is a roller chain  69 , which connects the main sprocket with the power output sprocket  76  from the hydraulic steering motor assembly  68 , providing the torque for steering the robotic tractor.  
         [0056]    In a separate channel of the rear partial-circular track  75 , just below the channel for the roller chain  216 , a flexible steering cable (inside track  75 , not shown) resides. This steering cable is also attached at the rearmost part of the rear partial-circular track  75  on each side and is pulled tight by a short heavy spring on one of the attachment points. At a point slightly to the side of where this steering cable passes over the main robotic tractor frame  55 , it forms a twisted loop around a flat-bottomed pulley on a shaft rotating around a vertical axis located directly above an optical encoder θ S    53 . As it turns, this shaft rotates the input shaft of this optical rotation encoder θ S    53  mounted on the main robotic tractor frame  55 . This optical rotation encoder θ S    53  provides information to the processor  49  about the orientation of the transverse axle  72  and of the running wheels  70 L and  70 R of the robotic tractor with respect to the main robotic tractor frame/tongue  55 .  
         [0057]    Two raised bumps just to each side of the center point on the top of the rear partial-circular track  75  will assist the processor  49  in keeping track of the axle orientation. These raised bumps will activate switches  236  L, R on rollers as they pass underneath the rollers. When both switches  236  L, R are simultaneously activated, the processor  49  will set the orientation of the track  75  to zero degrees.  
         [0058]    A forward partial-circular track  100  attaches near its endpoints to the hitching points  106  L, R on the forward trailer  40  and pivots with the forward trailer  40  during turns. A narrow channel on the back of the forward partial-circular track  100  contains a flexible steering cable (inside track  100 , not shown). This steering cable is attached at the front most part of the forward partial-circular track  100  on each side and is pulled tight by a short heavy spring on one of the attachment points. At the center of the tongue, where this steering cable pass over the main robotic tractor frame  55 , it forms a twisted loop around a flat-bottomed pulley on a shaft rotating around a vertical axis. As it turns, this shaft rotates the input shaft of an optical rotation encoder θ D1    44  mounted on the robotic tractor tongue  55 . The pulses from this optical rotation encoder θ D1    44  are transferred via pulse counting circuits to the microprocessor or computer  49 , providing information about the orientation of the forward trailer with respect to the centerline of the main robotic tractor frame  55 .  
         [0059]    Two raised bumps just to each side of the center point on the top of the forward partial-circular track  100  will assist the processor  49  in keeping track of the track  100  orientation. These raised bumps will activate switches  854  L, R on rollers as they pass underneath the rollers. When both switches  854  L, R are simultaneously activated, the processor  49  will set the orientation of the track  100  to zero degrees.  
         [0060]    The forward partial-circular track  100  is attached to the forward trailer  40  at its extremities via some sort of hitching device that allows some amount of pivoting around horizontal axes while preventing vertical or horizontal movement at the point of hitching to provide support and pulling force. In this embodiment, we will use standard ball hitch type latches  106 L and  106 R to represent the hitch arrangements for the partial-circular track  100 . The heavy central member of the robotic tractor frame  55  attaches to a larger hitching point using a similar, but larger, hitching device that will be represented by hitch latch  108  which will allow pivoting around a vertical axis and some pivoting around horizontal axes while preventing vertical or horizontal movement at the point of hitching. The forward trailer  40  (FIG. 1) must be modified to have hitching points compatible with the robotic tractor hitch latches, which in this embodiment we will represent with hitch balls mounted solidly directly to each side of a heavy central hitch ball. The side hitch balls must be mounted slightly higher than the central ball to line up with their respective ball hitch latches  106 L and  106 R. Note that the partial-circular track  100  is not solidly attached to the main robotic tractor frame, but travels across it, in contact with it, during turns.  
         [0061]    [0061]FIG. 5 is a top view of the robotic tractor showing details of the upper partial-circular track  140 , with FIG.  6  being a close up of the rear section of FIG. 5. The upper partial-circular track  140  attaches at its endpoints to the trailer mounting bar  66  and pivots with it during turns. This upper partial-circular track  140  is mounted sufficiently above the rear partial-circular track  75  to easily clear it during operation and to allow unobstructed operation of both rotational systems. A narrow channel on the front of the upper partial-circular track  140  contains a flexible steering cable (inside track  140 , not shown). This steering cable (inside track  140 , not shown) is attached at the rearmost part of the upper partial-circular track  140  on each side and is pulled tight by a short heavy spring on one of the attachment points (in channel, not shown). At of the point where this steering cable (inside track  140 , not shown) passes over the main robotic tractor frame  55 , it forms a twisted loop around a flat-bottomed pulley on a shaft rotating around a vertical axis located directly above the optical encoder θ R1    81 . As it turns this shaft rotates the input shaft of an optical rotation encoder θ R1    81  mounted on the main robotic tractor frame  55 . Pulse counting circuits process the pulses from this encoder θ R1    81  and then pass the data on to the microprocessor or computer  49 , providing information about the orientation of the rear trailer  80  with respect to the main robotic tractor frame  55 .  
         [0062]    Two raised bumps just to each side of the center point on the top of the upper partial-circular track  140  will assist the processor  49  in keeping track of the track  140  orientation. These raised bumps will activate switches  242  L, R on rollers as they pass underneath the rollers. When both switches  242  L, R are simultaneously activated, the processor  49  will set the orientation of the track to zero degrees.  
         [0063]    In this embodiment of the invention, the two fifth wheel latches  67  L, R on the trailer mounting bar  66  provide the means to transfer the torque between the upper partial-circular track  140  and the rear trailer  80 . Unless some means for transferring this torque was provided, the trailer mounting bar  66  would simply rotate around the kingpin of the rear trailer  80  and any measurement of the orientation of the upper partial-circular track  140  would not be representative of the orientation of the rear trailer  80 .  
         [0064]    [0064]FIG. 7 is a detail of the lead tractor partial-circular track  250  for measuring the orientation of the forward trailer with respect to the lead tractor. This diagram will apply for both the first and the second embodiments of the invention. The tractor partial-circular track  250  attaches near its endpoints to the forward trailer mounting bar  501  above the rear wheels of the tractor  30  and pivots with it during turns. A narrow channel on the front of the tractor partial-circular track  250  contains a flexible steering cable (inside track, not shown). This steering cable (inside track, not shown) is attached at the rearmost part of the tractor partial-circular track  250  on each side and is pulled tight by a short heavy spring on one of the attachment points. Near the point where this steering cable passes over the centerline of the tractor  30 , it forms a twisted loop around a flat-bottomed pulley on a shaft rotating around a vertical axis. As it turns, this shaft rotates the input shaft of an optical rotation encoder θR 0   42  mounted on the frame of the tractor  30 . Pulse counting circuits then process the pulses from the encoder θ R0    42  R, L, providing the microprocessor or computer  49  with information about the orientation of the forward trailer  40  with respect to the centerline of the tractor  30 ).  
         [0065]    Two raised bumps just to each side of the center point on the top of the tractor partial-circular track  250  will assist the processor  49  in keeping track of the track orientation. These raised bumps will activate switches  256  L, R on rollers as they pass underneath the rollers. When both switches  256  L, R are simultaneously activated, the processor  49  will set the orientation of the track  250  to zero degrees.  
         [0066]    In this embodiment of the invention, the two fifth wheel latches  36  L, R on the forward trailer mounting bar  501  provide the means to transfer the torque between the tractor partial-circular track  250  and the forward trailer  40  (FIG. 1). If no method for transferring this torque was provided, the forward trailer mounting bar  501  would simply rotate around the kingpin of the trailer  40  and any measurement of the orientation of the tractor partial-circular track  250  would not be representative of the orientation of the forward trailer  40  (FIG. 1). Alteratively, a stinger  500  (FIG. 13), or other device, could be used to prevent rotation around the trailer kingpin.  
         [0067]    An optical rotation encoder ΔT  34  (on the tractor  30  itself), mounted in a manner that allow it to sense the rotation of the drive shaft of the tractor  30 , provides information via pulse processing circuits to the microprocessor or computer  49  about movement and speed of the tractor  30 . Note that this encoder must be mounted behind any twospeed axle gearbox(es) in order to give a true representation of the rotation of the tractor drive wheels.  
         [0068]    Preferred Second Embodiment of Invention  
         [0069]    [0069]FIG. 8 and  9  show a robotic tractor with path tracking steering, variable ratio with oversteer steering, and traction kinking that is a preferred embodiment of the invention. This embodiment differs from the simpler robotic tractor with path tracking of the first embodiment in several ways. The robotic tractor length can be adjusted in this embodiment. The robotic tractor tongue is split into two parts,  55   a  and  55   b , and  55   b  can be extended or retracted at the joint  144 , with the pin and lock set  146  holding it in place. This embodiment also uses traction kinking to assist in turning corners. This embodiment uses two separate path tracking modes, relative angle path tracking mode and rate of orientation change path tracking mode, instead of only the relative angle path tracking mode used in the first embodiment of the invention. Also, the variable ratio with oversteer steering mode is included in the combination of steering modes to allow the path-tracking modes to be combined with either a more stable version of the variable ratio with oversteer mode or a more maneuverable version of the variable ratio with oversteer mode. The traction kinking will be disabled when the robotic tractor is traveling in a straight line in order to conserve air pressure.  
         [0070]    As described in the operations, the reference steering information for the relative angle path tracking mode comes mainly from sensor θ R0    42  (FIG. 7) mounted on the tractor partial circular track  250  (FIG. 5) between the tractor  30  and the front trailer  40  (FIG,  1 ), and sensor ΔT mounted to sense the rotation of the tractor drive shaft. This information is compared to sensors θ R1 , θ S1  and ΔS 1 . The details of the tractor partial circular track can be seen in FIG. 7.  
         [0071]    The steering information for the variable ratio with oversteer robotic mode comes from θ D1 , θ R1 , θ S1 , and ΔS 1     —   LEFT  52L and ΔS   1     —     RIGHT    52 R.  
         [0072]    The rate of orientation change path tracking mode will use sensor θ F    31 , the angle of the front tractor steered wheels and sensors θ D1 , θ R1 , θ S1 , and ΔS 1 .  
         [0073]    Full redundancy is desirable for all the electronic components so that consequences of failures would be minimized, although this is optional to the invention, and not shown, for simplicity.  
         [0074]    The rear partial-circular track  75  and the front partial circular track  100  are configured in the sane way as in the first embodiment  
         [0075]    This complex embodiment includes a traction kinking system for assistance in cornering. The operation of this system is described in the operations.  
         [0076]    The arrangement of the rear partial-circular track  75  and the front partial circular track  100 , along with the associated sensors and switches is essentially identical to the arrangement of the equivalent structures of the first embodiment described above, and will not be repeated at this point.  
         [0077]    To allow the main frame  55  to be manually adjusted, there is a joint  144 . At this joint  144 , a smaller main robotic tractor frame  55   b  section slides into a larger main robotic tractor frame  55   a  section and is secured by some type of mechanism such as a pin and lock set  146  to prevent slippage or movement during operation.  
         [0078]    The arrangement of the upper partial-circular track  140 , along with its sensors and switches is essentially identical to the arrangement of the equivalent structures of the simpler embodiment described above, however, in this embodiment of the invention, an articulated stinger assembly  500  is used instead of the second fifth wheel latch  67  L, R on the first embodiment of the invention. This stinger assembly  500  extends backward from the trailer mounting bar  66  to provide the means for transferring the torque between the upper partial-circular tack  140  and the rear trailer  80 . A detailed treatment of this stinger  500  will be presented in FIG. 13. The stinger  500  is used to prevent the rotation of the trailer mounting bar  66  around the kingpin of the trailer, in order to obtain an accurate measurement of the orientation of the rear trailer  80 .  
         [0079]    As mentioned above, optical rotation encoders ΔS 1     —     LEFT    52 L and ΔS 1     —     RIGHT    52 R (FIG. 12) will record the rotation of the drive shaft for each robotic tractor wheel  70  L, P The software in the microprocessor or computer  49  will use this information in two ways. The average of the distance traveled by the left and right wheels  70  L, R will yield the distance traveled by the robotic tractor in any given time interval. The difference in the distance traveled by the left and right wheels  70  L, R will be scaled to yield a measure of the amount of cornering that the robotic tractor wheels  70  L, R are undergoing. This difference will be used with the ratio with oversteer mode. The details of this operation will be covered in the Operations section.  
         [0080]    The primary microprocessor or computer  49  would be in control at any time with the secondary microprocessor or computer continually performing a check on the operation of the primary microprocessor or computer  49  and taking control of the operation if the situation warranted it. Any significant discrepancies could be reported to the driver as a warning. Since each microprocessor or computer  49  has access to all the sensors, errors can be detected and corrective actions taken.  
         [0081]    Below the main robotic tractor frame  74  a heavy axle hanger central pivot  58  supports and allows pivoting of the steering axle assembly  60  and of the transverse axle  72  with its associated components. Bearing plates provide stability for this pivot. The traction kinking motors can be seen inside the steering axle assembly  
         [0082]    [0082]FIG. 11 shows an end view of a detail of the transverse axle  72  inside the axle hanger assembly  75 . Since the input to the kinking system is the sideways force on the robotic tractor axle  72 , we must have some way of measuring this force. In this embodiment of the invention, the transverse axle  72 , together with the air motors for the traction kinking system, is mounted in an axle hanger assembly  75  that allows some movement from side to side in response to a sideways force. This movement is used to activate air regulator switches  183 ,  184  (FIG. 12) (or some such device) on each side, which then power the kinking system.  
         [0083]    The axle  72  is mounted in the center of an inverted U-shaped channel  172  in the axle hanger assembly  75 . The weight on the axle  72  is supported by a number of vertical arms  174  each of which attach via a pivot  176  at the top to the axle  72  and via a pivot  177  at the bottom to the lower sides of the U-shaped channel  172 . When a sideways force is applied to the axle  72 , the vertical arms  174  swing somewhat to the side in response to the force. At the top and bottom of the channel  172 , roller bearings  180 ,  181  in partial-circular races  182 ,  183  stabilize the axle  72  against forward and/or backward forces and against twisting movement.  
         [0084]    [0084]FIG. 12 is a detail of the location of regulator switches or pressure transducers  183 ,  184  on the axle hanger assembly  75 . The axle  72  is shown passing through the axle hanger assembly  75 , which rotates on the vertical axle central pivot  58 . The air motors for the traction kinking system, mounted on the axle  72 , are also located inside the axle hanger assembly  75 . The movement of the axle  72  in response to the sideways forces upon it activates a regulator valve or pressure transducer  183 ,  184  placed on each side of the axle  72 . Full air pressure from the truck air system is applied to the input side of these switches  183 ,  184 . The switches  183 ,  184  are designed to send increasing pressure to the traction kinking system as the sideways force increases, in just the opposite manner to the way the force on the brake pedal reduces the pressure to the brakes in an air brake system. During a turn, if the sideways pressure tries to push the robotic tractor to the inside of the turn, air pressure is sent to the air motors in the traction kinking air motor assembly  170  L, R (FIG. 6) to push the robotic tractor wheels  70  L, R (FIG. 8) forward, relieving the pressure. If the sideways pressure tries to push the robotic tractor to the outside of the turn, air pressure is sent to the brake activation system to slow the robotic tractor  72  and eliminate the risk of jackknifing.  
         [0085]    The traction kinking air motor assemblies  170  R, L that comprise the power source for the traction kinking drive system are mounted below the transverse axle  72  on each side. Each air motor assembly  170  R, L includes gearing to slow the rotation to the appropriate speed and to increase the torque. The output from each air motor assembly  170  R, L is applied via a gear  200  on a drive shaft  202  that extends out through the center of each wheel  70  R, L. The wheels  70  R, L and the shafts are mounted on bearings in a similar manner to the drive wheels on the back of a truck tractor. No differential is needed, because the two air motors  170  R, L have a common air supply and will apply equal torques to the shafts  200  they are driving. Two optical rotation encoders, one on each drive axle  202  (FIG. 12), Δ S1     —     Left , Δ S1     —     Right    53 L, R record the rotation of the shafts  202  and transfers the information via pulse processing circuits to the microprocessor or computer  49 .  
         [0086]    [0086]FIG. 12 is a detail of the traction kinking air motor assembly  170  R located on the transverse axle inside the axle hanger assembly. The two similar air motor assemblies  170  L, R convert the air pressure sent by the regulator switches  183 ,  184  (FIG. 12) into torque to drive the robotic tractor wheels  70  L, R (FIG. 3). Each assembly  170  L, R includes a system of gears to reduce the speed and increase the torque of the air motors  171  L, R When the air motor  171  R is activated, the shaft  204  R and gear  206  R carrying the output rotation from the air motor assembly  170  R engages a gear  200  R on the end of the axle shaft  202  R that extends out through the center of the wheels  70  R (FIG. 7) on the side of the robotic tractor. This shaft  202  R then causes the wheels  70  R (FIG. 7) to drive forward in a manner similar to the way the drive wheels of the truck tractor operate. Since the two air motor assemblies  170  L, R share a common air pressure source, no differential gears are needed to equalize the torques on the wheels  70  L, R.  
         [0087]    [0087]FIG. 13 shows a detailed view of the articulated stinger assembly  500  that is attached to the back of the trailer mounting bar  66 . The heavy central bar  546  of the stinger assembly is designed to withstand substantial sideways forces. The locking arms  544  slide freely forward and backward along the heavy central bar  546 , but are prevented by a stop from sliding off the end. Each locking arm  544  consists of three actuating arms  541 ,  542 ,  543 , the back two of which are parallel, and a contact bar  540  with a heavy solid rubber pad that remains parallel to the heavy central bar  546  during deployment. The entire stinger assembly  500  is mounted to the trailer mounting bar  66  via a spring-supported hinge  548  so that it can be easily positioned during hitching operations.  
         [0088]    In this embodiment of the invention, this articulated stinger assembly  500  provides the means to prevent the rotation of the trailer mounting bar  66  around the kingpin of the rear trailer  80 . The stinger locking arms  544  can be slid backward or forward into position between the trailer structural members or between the two legs of the trailer landing gear. The locking arms  544  can then be opened tightly outward against the structural members or the legs of the landing gear to lock the trailer mounting bar  66  rigidly into place with respect to the rear trailer  80 . If the trailer has no solid structures on which to lock the stinger assembly, an adapter can be provided which will allow the stinger to lock to the sides of the trailer itself, with supporting straps going over the top of the trailer.  
         [0089]    Third Embodiment:  
         [0090]    [0090]FIG. 14 shows a double-axle trailer or wagon that utilizes path tracking and variable ratio with oversteer mode steering with traction kinking. This wagon is designed to be pulled in a “Multiple Wagon Train” configuration behind a three-quarter ton pickup or some such vehicle, so it will be accordingly sized down somewhat from the robotic tractor with path tracking steering, variable ratio with oversteer and traction kinking discussed as the complex embodiment above. As was true for the robotic tractor however, this wagon will require three hitch balls on the towing vehicle. The second wagon in the train will use as input the orientation information from the upper  140  and lower partial circular tracks  75  of the first wagon in the train. The steering system for this wagon is identical to that for the robotic tractor except that control and shifting by the driver and the controlling microprocessor or computer  49  will utilize 12 volt solenoids and/or 12 volt DC motors instead of the air motors used by the robotic tractor. Ratios used for the variable ratio with oversteer mode of steering may also be somewhat different for the wagon than for the robotic tractor. The mounting of the partial circular tracks and the sensors will be similar to that for the robotic tractor, but since the back portion of the wagon  554  will be permanently attached to the wagon mounting bar  555  on the front section of the main wagon frame  552 , there will be no need for the two fifth wheels or for the articulated stinger that were present on the robotic tractor.  
         [0091]    The traction kinking system must also be modified to operate on 12 volt DC power, and an extra battery may be needed to supply the additional current Again, the traction kinking system will be disabled when the steered wheels of the wagon are aligned with the centerline of the wagon tongue. The hydraulic steering motor  68  steering wheels will use an electric motor to drive the hydraulic pump.  
         [0092]    [0092]FIG. 14 is a diagrammatic representation of a lead tractor and trailer making a turn. The angles, lengths, and distances demonstrated in this diagram will be used in the operations section to derive the mathematical equations relating to the rate of orientation change mode of steering.  
         [0093]    [0093]FIG. 15 is a diagrammatic representation of a robotic tractor and trailer making a turn. The angles, lengths, and distances demonstrated in this diagram will be used in the operations section to derive the mathematical equations relating to the rate of orientation change mode of steering.  
         [0094]    Operations  
         [0095]    The primary goal of this path tracking steering system is to have the pivot point at the front of the second semi-trailer follow the same path as the pivot point at the front of the first semi-trailer. In the preferred embodiment, two different path tracking modes and one non-path-tracking mode, variable ratio with oversteer mode, are combined in order to steer the robotic tractor. The modes will be combined based on the steering characteristics desired. In most cases, the modes will provide very similar steering output. But in some cases, for example, if the wheels of the vehicle slip sideways, the steering output can differ to a greater degree, depending on the degree of the slippage. The ability to combine a number of different path tracking modes, and even non-path tracking modes such as the non-path-tracking “variable ratio with oversteer” steering mode, will contribute significantly to the reliability of the final product, since errors in one mode are offset by the contributions of other modes.  
         [0096]    Full redundancy for all electronic components would be desirable to minimize the consequences of failures, but since ease of understanding is a priority here, redundancy was not included in this embodiment.  
         [0097]    A secondary controller is used to check on the operation of the primary controller  49  and could take control if the situation warranted it. Any significant discrepancies between the two controllers could be reported to the driver as a warning.  
         [0098]    Output from the Controller to Steer the Robotic Tractor Axles  
         [0099]    The robotic tractor is steered by rotating the steering axle assembly about its central pivot  58  (FIG. 3) by applying the steering correction needed for a particular travel interval. This steering correction is generated by the steering algorithms. Each stewing algorithm independently generates a parameter that represents this steering correction needed for a particular travel interval. This parameter is named Δ. Each steering algorithm generates a Δ of its own. For example, the rate of orientation mode generates a ΔPath 1     —     Rate     —   of   —     Orientation . This value Δ indicates the magnitude and direction of the steering angle change that the axle needs to undergo according to the particular steering mode or combination of modes generating the Δ. A positive value of Δ would cause the wheels to be steered more to the right of the robotic tractor centerline, and a negative Δ would cause them to be steered more to the left of the robotic tractor centerline. A larger magnitude of Δ would cause more rapid steering movement.  
         [0100]    In this embodiment, a reversible hydraulic motor  68  geared down to a moderate speed will provide the energy for turning the axle when the software detects that movement is required. This hydraulic motor  68  is provided with automatic braking mechanisms that lock the gear train into position at times when no action is required of the hydraulic motor  68 . The hydraulic valves that are activated by the controller  49  to control the flow of the hydraulic fluid to this motor act as a secondary hydraulic braking system. Low air pressure or low hydraulic pressure will cause the motor to move the axle to a straightforward position and then activate the braking mechanisms. The hydraulic motor operates from a reservoir of fluid in a pressure chamber where the hydraulic fluid is separated from a compressed gas by a diaphragm, This hydraulic and, located in the steering motor assembly, will provide a reservoir of energy for emergency positioning if all power is lost. The fluid in the chambers is continuously replenished during operation by an air motor or electric motor operating a high-pressure hydraulic pump in the steering motor assembly.  
         [0101]    The Traction Kinking System  
         [0102]    The traction kinking section is used to prevent sideways sliding of the robotic tractor wheels either when the pull on the tongue causes the robotic tractor to be pulled to the inside of the corner or when excessive forward forces cause the robotic tractor to be pushed to the outside of the corner. This system uses the forward or backward traction of the robotic tractor wheels to control the “kinking” behavior of the robotic tractor.  
         [0103]    The traction inking system functions in two modes. If excessive sideways force toward the inside of the curve is sensed, the system acts to accelerate the robotic tractor and rear trailer to prevent the robotic tractor wheels from slipping toward the inside of the turn. To do this, traction kinking system activates its air motors  170  L, R (FIG. 12), driving the robotic tractor wheels forward. The same air pressure is supplied to both of the air motors  170  L, R, assuring that the torque on the two sides is equal. The pressure of the air that is supplied will be increased as the amount of sideways pull that is being experienced by the axle increases.  
         [0104]    If excessive force toward the outside of the curve is sensed, the traction kinking system applies the brakes to the second trailer and to all sections behind the second trailer, acting as a jackknife prevention device. The brakes on the robotic tractor itself will not be activated by the kinking braking system.  
         [0105]    The primary input used by the controller to manage the traction kinking system is the sideways force on the robotic tractor axle  72  (FIG. 12). The design of the robotic tractor axle hanger assembly  75  (FIG. 12) allows the magnitude of this sideways force to be sensed directly by the regulator valves  183 ,  184  (FIG. 12). The regulator valves are directly activated by the sideways force and act as the control valves, sending air pressure to the traction kinking motors or activating the automatic braking system as appropriate.  
         [0106]    The controlling microprocessor or computer  49  also keeps up with the orientation of the rear partial-circular track  512  and uses algorithms to determine the direction and/or the amount of torque needed for proper traction kinking of the robotic tractor and the back trailer. If the tractor-trailer combination rig is making a left turn, a pull to the left on the axle will indicate that the drive wheels of the robotic tractor should be speeded up, so air pressure will be applied to the traction kinking air motors  170  L, R (FIG. 12) to cause the robotic tractor to move forward faster. If the axle experiences a pull to the right during a left turn, it indicates that the trailer is moving too fast, trying to push the robotic tractor along. In this case, the brakes will be applied on both the robotic tractor and on the trailer it is supporting to slow the trailer back down and prevent the robotic tractor wheels from being pushed sideways. In a similar fashion, a pull to the left during a right turn will cause the brakes to be applied, while a pull to the right during a right turn will cause air pressure to be sent to the air motors powering the wheels.  
         [0107]    When the robotic tractor wheels  70  R, L are close to alignment with the robotic tractor centerline, the application of forward traction will be ineffective. In this situation, the controller will reduce the amount of air pressure sent to the traction kinking motors to reduce wear and tear on the system. The traction kinking braking system need not be disabled in these situations, but could serve to activate the rear trailer braking system if the rear trailer started applying significant forward pressure to the forward trailer.  
         [0108]    A pressurized air tank located on the robotic tractor will provide a reservoir of energy for the traction kinking system. This reservoir can store the substantial amounts of power that will be required by the air motors of the traction kinking system to accelerate the robotic tractor in tracking and cornering maneuvers. The air pressure in the tank is continuously replenished during operation by a direct supply from the tractor compressor, by a separate internal combustion engine located on the robotic tractor operating an air compressor, and/or by electric motors operating air compressors.  
         [0109]    This traction kinking system is incorporated from Provisional Patent No. 60/179,745.  
         [0110]    Operation of the Articulated Stinger Assembly (FIG. 10)  
         [0111]    In the more complex embodiment of the invention, the articulated stinger assembly  500  (FIG. 10) extending backward from the trailer mounting-bar  66  (FIG. 10) provides the means to prevent the rotation of the trailer mounting-bar  66  (FIG. 10) around the kingpin of the trailer. Without some mechanism for preventing this rotation around the trailer kingpin, the readings from the sensors for the orientation of the trailer-mounting bar with respect to the robotic tractor tongue would be meaningless. This stinger  500  (FIG. 10) has locking arms  544  (FIG. 10) that can be slid backward or forward into position between the trailer structural members or between the two legs of the trailer landing gear. The locking arms  544  (FIG. 10) are then opened tightly outward against the structural members or the legs of the landing gear to lock the trailer mounting-bar  66  (FIG. 10) rigidly into place with respect to the trailer. If the configuration of the trailer is such that no substantial structural members are available, an adapter (not shown) can be provided which will allow the stinger to latch onto the sides of the trailer, with a strap going over the top of the trailer to hold the adapter in place.  
         [0112]    [0112]FIG. 10 shows a detailed view of the articulated stinger assembly  500  (FIG. 10) that is attached to the back of the trailer mounting bar  500  (FIG. 10). The heavy central bar  546  (FIG. 10) of the stinger assembly is designed to withstand substantial sideways forces. The locking arms  544  (FIG. 10) slide freely forward and backward along the heavy central bar  546 , but are prevented by a stop from sliding off the end. Each locking arm  544  (FIG. 10) consists of three actuating arms  541 ,  542 ,  543  (FIG. 10), the back two of which are parallel, and a contact bar  540  (FIG. 10) with a heavy solid rubber pad that remains parallel to the heavy central bar  546  (FIG. 10) during deployment. The entire assembly is mounted to the trailer mounting-bar  66  (FIG. 10) via a spring-supported hinge  548  (FIG. 10) so that it can be easily positioned during hitching operations.  
         [0113]    Two raised bumps just to each side of the center point on the top of each of the three partial-circular tracks mentioned above will assist the processors in keeping track of the orientation of the tracks. These raised bumps will activate switches on rollers as they pass underneath the rollers. When both switches for a given track are simultaneously activated, the processor will set the orientation to zero degrees for that track.  
         [0114]    Physical Basis and Details of Algorithms for Path Tracking Modes, Variable Ratio with Oversteer Mode, and Combinations of Steering Modes  
         [0115]    At this point we will attempt to describe the physical basis and the details of the algorithms that will control the steering behavior of the robotic tractor.  
         [0116]    The data from each of the input sensors to the steering system can be transferred to the controller  49  at either fixed time intervals or fixed travel intervals. For the purposes of the algorithms used here, the data from both the lead tractor  30  and the robotic tractor is obtained on the basis of fixed travel intervals.  
         [0117]    The data could be acquired at time intervals, then converted by the controller  49  using interpolation between data points to plot, or reference, each piece of data acquired to a pseudo-travel interval of either the lead tractor  30  drive wheels or of the steered wheels of the robotic tractor as required. Thus, each piece of data would be converted from a time basis to either a lead tractor  30  travel interval basis or a robotic tractor travel interval basis, but this system is not used in this invention.  
         [0118]    For each travel interval, the controller  49  will acquire data from each sensor on the lead tractor  30  and/or the robotic tractor. The data from the angle sensors will be scaled to radians of rotation of the angle being measured, and the distance sensors will be scaled to feet traveled by the wheels being measured.  
         [0119]    Calculations based on data from the lead tractor  30  will use the data that has been placed on a lead tractor  30  travel interval basis, and calculations based on data from the robotic tractor will use the data that has been placed on a robotic tractor travel interval basis. The separate reference for the linear movement of the lead tractor  30  and of the robotic tractor  50  is not a requirement of this invention, but is only used to obtain a higher degree of control.  
         [0120]    Now the controller  49  has a set of data from each sensor, stored either on a basis of lead tractor  30  travel intervals or on a basis of robotic tractor  50  travel intervals depending on where the data originated. These numbers represent the movement of a particular encoder or the reading of a particular sensor during that travel interval. The remainder of the processing will take the form of mathematical manipulation of these numbers. The sensors used are listed here.  
         [0121]    The angle θ R0 , between the lead tractor and the lead tractor&#39;s trailer will be positive when the lead tractor is rotated clockwise of the straight-ahead position with respect to the trailer carried by the lead tractor and negative when the lead trailer is rotated counterclockwise of the straight-ahead position. Sensor θ R0    44  will be on a lead tractor travel interval basis.  
         [0122]    The angle θ F , which derives the angle between the lead tractor and the lead tractor steering axle from how sharply the steering wheel of the lead tractor is turned, will be positive when the steering axle is clockwise of the straight-ahead position with respect to the lead tractor and negative the steering axle is counterclockwise of the straight-ahead position. Sensor θ F    44  will be on a lead tractor travel interval basis.  
         [0123]    The angle θ D1    44 , between the robotic tractor and the trailer in front of it, will be positive when the trailer is rotated clockwise of the straight-ahead position with respect to the tongue of the robotic tractor and negative when the trailer is rotated counterclockwise of the straight-ahead position. Sensor θ D1    44  will be on a robotic tractor travel interval basis.  
         [0124]    The angle θ R1    81 , between the tongue of the robotic tractor and the trailer towed by the robotic tractor, will be positive when the robotic tractor tongue is rotated clockwise of the straight-ahead position with respect to the trailer carried by the robotic tractor and negative when the robotic tractor axle assembly is rotated counterclockwise of the straight-ahead position. Sensor θ R1    44  will be on a robotic tractor travel interval basis.  
         [0125]    The angle θ S1    53 , between the robotic tractor tongue and the robotic tractor sting axle, will be positive when the steering axle assembly is rotated clockwise of the straight-ahead position with respect to the tongue and negative when the steering axle assembly is rotated counterclockwise of the straight-ahead position. Comparable sign conventions will be used for the lead tractor sensors. Sensor θ S1    44  will be on a robotic tractor travel interval basis.  
         [0126]    The distance sensor ΔS 1     —     LEFT  measures the distance the left wheel of the robotic tractor travels. It is obtained from the rotation of the left axle shaft of the robotic tractor.  
         [0127]    The distance sensor ΔS 1     —     RIGHT  measures the distance the right wheel of the robotic tractor travels. It is obtained from the rotation of the right axle shaft of the robotic tractor.  
         [0128]    The distance sensor Δ S1 , measures the distance the robotic tractor travels, and is the source of the robotic tractor travel intervals. It is the average of ΔS 1     —     LEFT  and ΔS 1     —     RIGHT .  
         [0129]    The distance sensor Δ T , measures the distance the robotic tractor travels, and is the source of the lead tractor travel intervals. It is obtained from the rotation of the drive shaft of the lead tractor.  
         [0130]    At the completion of each travel interval, the processor will also use the distance traveled during the interval by the robotic tractor, ΔS 1  to complete the following calculation:  
           SPD=[AV*SPD*DIFF   TIME   +ΔS   1 ]/[( AV +1)  DIFF   TIME ] 
         [0131]    Where SPD is the average running speed, ΔS 1  is the distance traveled during the latest interval by the robotic tractor, and DIFF TIME  is the number of seconds of time since the last travel interrupt. The number AV is representative of the number of intervals over which the average speed is calculated. A larger AV will produce a SPD that varies more slowly with momentary velocity changes.  
         [0132]    When the robotic tractor  50  is operating in the relative angle path tracking mode or the rate of orientation change path tracking mode, the value of each piece of data obtained from the lead tractor  30  sensors will be stored in memory in a manner that references each value to the linear position of the lead tractor  30  drive wheels at the time the value was acquired. These numbers will be recalled from memory after the robotic tractor  50  wheels have traveled a distance equal to the linear separation of the robotic tractor  50  wheels and the lead tractor  30  drive wheels.  
         [0133]    Relative Angle Mode  
         [0134]    In general, the relative angle mode detects the angle between the lead tractor and the first trailer at the fifth wheel, delays this angle, and causes the angle between the robotic tractor steering axle and the second trailer at the fifth wheel to match what the angle between the lead tractor and the first trailer was when they passed that point.  
         [0135]    As shown in FIGS. 2, 3,  4 ,  5 , and  6 , relative angle mode steering utilizes three angle sensors and two distance measures. The angle sensors are θ R1    81 , θ S1    53 , and θ R0    42 . The linear motion sensors are sensor ΔT  34  and sensor ΔS 1 . The ΔT&#39;s and ΔS 1 &#39;s are each summed in DIST T  and DIST S1 , respectively. The combined length of the first trailer  40  and the robotic tractor tongue  55  are input into the controller  49  before starting, and the difference between DIST T  and DIST S1  is initialized to be equal to this combined length. The angle θ R0  is saved with an associated reading from DIST T . When the value of DIST S1  reaches the value that DIST T  had when the angle θ R0  was stored, the controller will compare the value of the angle θ S1 +θ R1 , between the steering axle assembly and the trailer being towed by the robotic tractor, to the stored value of the angle θ R0  in order to determine how much steering correction is needed. Then the hydraulic steering motor  68  will adjust the angle θ S1 +θ R1  in order to make it equal to the value that angle θ R0  had when the lead tractor passed that point.  
         [0136]    The difference between θ R0  and θ S1 +θ R1  becomes a parameter ΔPATH 1     —     Relative     —     Angle  that will be used to correct the robotic tractor steering axle orientation to mach the orientation of the lead tractor  30  drive axle(s) when they passed the same point. The controller  49  will determine the steering necessary at each robotic tractor travel interval due to this steering mode by the following calculation:  
         Δ PATH   1     —     Relative     —     Angle =θ R0     —     Delayed −(θ S1 +θ R1 )  
         [0137]    For subsequent robotic tractors, the steering correction will be calculated in a very similar manner. The same equation is used. The sensors on the robotic tractor being considered are used in the equation, and the data from the lead tractor sensors is delayed an amount equivalent to the distance between the lead tractor and the robotic tractor being considered before it is used.  
         [0138]    Rate of Orientation Change Mode  
         [0139]    The second method of path tracking, rate of orientation change mode, measures the rate of orientation change with respect to distance traveled by the lead tractor in a horizontal plane. This information is delayed and compared to the rate of orientation change with respect to distance traveled by the robotic tractor and used for steering.  
         [0140]    This method, as shown in FIG.&#39;s  14  and  15 , utilizes the fact that derivative with respect to distance traveled of the absolute orientation of the steering axle assembly of the robotic tractor must be equal to the derivative with respect to distance traveled of the absolute orientation of the lead tractor at the same linear position if the robotic tractor is following the path of the lead tractor. Even when we do not know the actual value of the absolute orientation of the lead tractor, this derivative can be extrapolated from the data obtained by sensor θ F    31  that detects the angle between the tractor centerline and the direction of travel of the front wheels of the lead tractor.  
         [0141]    In rate of orientation change path-tracking mode the controller  49  calculates the change in the angle of the lead tractor  30  axle in the horizontal plane during each lead tractor travel interval. This reference information is then stored and delayed an amount equal to the number of travel intervals between the lead tractor  30  drive wheel assembly and the robotic tractor steering axle assembly  60 . The controller  49  also calculates the change in the range of the robotic tractor axle in the horizontal plane during each robotic tractor travel interval. Then the controller  49  steers the robotic tractor to cause the rate of orientation change of the steering wheels of the robotic tractor to equal the rate of orientation change of the drive wheels of the lead tractor.  
         [0142]    The equations for this mode can be derived using Ackerman geometry. In FIG. 14, the following variables are measured: ΔT, the distance traveled by the lead tractor in one travel interval and θ F , the angle of the front steered wheels of the lead tractor  30  with respect to the centerline of the lead tractor  30 . The LENGTH T , the distance from the center of the front steering axle of the lead tractor  30  to the center of the rear drive axle (or equivalent average drive axle if the lead tractor  30  has more than one drive axle), is known. Using the fact that we know the two measured variables and the length, we can obtain (Δθ T )/ΔT, which is the rate of orientation change of the entire tractor with respect to distance traveled by the drive wheels of the lead tractor. The following is the derivation for (Δθ T )/ΔT:  
         cos                   θ   F       =       R   T       R   F                 R   T     =       R   F        cos                   θ   F                 Δ                   θ   T          R   F       =     Δ                 F               R   F     =       Δ                 F       Δθ   T                   Δθ   T          R   T       =       Δ                 T     =     Δ                 θ                   R   F        cos                   θ   F                   Δ                 F     =       Δ                 T       cos                   θ   F                   sin                   θ   F       =       LENGTH   T       R   F                 R   F     =         LENGTH   T       sin                   θ   F         =       Δ                 F       Δθ   T                   Δθ   T     =         Δ                 F                 sin                   θ   F         LENGTH   T       =       Δ                 T                 tan                   θ   F         LENGTH   T                   R   T     =         R   F        cos                   θ   F       =       LENGTH   T       tan                   θ   F                       Δθ   T       Δ                 T       =       tan                   θ   F         LENGTH   T                             
 
         [0143]    Therefore, if the travel intervals are small, the change in the angle of the lead tractor  30  drive axle is given by the equation:  
           Δθ   T       Δ                 T       =       [     tan                   (     θ   F     )       ]       LENGTH   T                             
 
         [0144]    Since this calculation is performed for each travel interval, the linear distance ΔT will be equal to the length of the lead tractor  30  travel interval.  
         [0145]    The equivalent derivation using Ackerman geometry for the robotic tractor is shown in FIG. 22. The following variables are measured: ΔS 1 , the distance traveled by the steering axle of the robotic tractor; θ D1 , the angle between the centerline of the forward trailer and the centerline of the robotic actor tongue; θ S1 , the angle between the centerline of the robotic tractor or tongue and the centerline of the robotic tractor steering axle assembly  60 ; and LENGTH D1 , the length of the robotic tractor tongue from the hitch point of the first robotic tractor  50  to the center of the steering axle assembly as measured along the centerline of the, robotic tractor  50 . Using the four known variable values, you can obtain (ΔΓ S1 )/ΔS 1  which is the rate of orientation change of the robotic tractor with respect to distance traveled by the robotic tractor steering axle assembly. The following is the derivation for (Δθ S1 )/ΔS 1 :  
         m   +     π   2     -     θ   D1     +     π   2     +     θ   S1       =   π             m   -     θ   D1     +     θ   S1       =   0           m   =       θ   D1     -     θ   S1                   LENGTH   D1       sin                 m       =         LENGTH   D1       sin        (       θ   D1     -     θ   D1       )         =       R   R       sin        (       π   2     +     θ   S1       )                     R   R   ′     =     (         LENGTH   D1     *     sin        (           π           2         +     θ   S1       )           sin        (       θ   D1     -     θ   S1       )         )               R   D   ′     =         LENGTH   D1     *     sin        (       π   2     -     θ   D1       )           sin        (       θ   D1     -     θ   S1       )                   Δθ   S1     =       Δθ   D1     =         Δ                   S   1         R   D   ′       =     Δ                   S   1     *     [       sin        (       θ   D1     -     θ   S1       )           [     LENGTH   D1     ]     *     sin        (       π   2     -     θ   D1       )           ]                     Δθ   S1     =         Δ                   S   1         LENGTH   D1       *     [       sin        (       θ   D1     -     θ   S1       )         cos                   θ   D1         ]                             
 
         [0146]    If the travel intervals are small between samples, the equation for the change in the angle of the robotic tractor  50  steering axle assembly is:  
           Δθ   S1       Δ                   S   1         =       ⌊     sin        (       θ   D1     -     θ   S1       )       ⌋         (     LENGTH   D1     )     *     cos        (     θ   D1     )                                 
 
         [0147]    where ΔS 1  is the linear distance traveled by the wheels of the first robotic tractor  50 , LENGTH D1  is the length between the first robotic tractor  50  hitch point and the center of the steering axle assembly as measured along the robotic tractor  50  centerline, θ D1  is the angle between the centerline of the first trailer and the centerline of the first robotic tractor  50 , and θ S1  is the angle between the perpendicular to the first robotic tractor  50  steering axles and the centerline of the robotic tractor  50 . Again, since the data is referenced to each robotic tractor  50  travel interval, the value of ΔS 1  will be equal to the robotic tractor  50  travel interval. Now, since the value of θ S1  is under the direct control of the controller  49 , it can be directly adjusted until the value of Δθ S1  matches the value Δθ T  had at that point in its linear travel.  
         [0148]    Let θ F,DEL =the delayed θ F  then Δθ T,DEL =Δθ S1  (to make dolly steering axle track drive wheels of tractor)  
           Δ                 T   *   tan                   θ     F   ,   DEL           LENGTH   T       =         Δ                   S   1         LENGTH   D1       *     [       sin        (       θ   D1     -     θ   S1       )         cos                   θ   D1         ]                   Δ                 R       R   R   ′       =       Δ                   S   1         R   D   ′                       Δ                 R     =       Δ                   S   1     *     (       R   R   ′       R   D       )       =     Δ                   S   1     *     [         LENGTH   D1     *     sin        (       π   2     +     θ   S1       )             LENGTH   D1     *     sin        (       π   2     -     θ   D1       )           ]                     =     Δ                 S   *     (       cos        (     -     θ   S1       )         cos                   θ   D1         )                       sin        (       θ   D1     -     θ   S1       )       =       (       LENGTH   D1       LENGTH   T       )     *     (       Δ                 T       Δ                   S   1         )     *   tan                   θ     F   ,   DEL       *   cos                   θ   D1                 θ   S1     =       θ   D1     -     arcsin              [       (       LENGTH   D1       LENGTH   T       )     *   tan                   θ     F   ,   DEL       *   cos                   θ   D1       ]                             
 
         [0149]    The delta needed to steer the dolly Δ Rate     —     of     —     Orientation  is then  
         θ S1     —     calculated −θ S1     —     measured =Δ Rate     —     of     —     Orientation    
         [0150]    [0150]               Δ     Rate                 _                 of                 _                 Orientation       =                  θ   D1     -     θ   S1     -     arcsin              [       (       LENGTH   D1       LENGTH   T       )     *                                  tan                   θ     F   ,   DEL       *   cos                   θ   D1                                     
         [0151]    After having determined the rate of orientation change with respect to distance traveled for both the lead tractor (FIG. 21) and robotic tractor (FIG. 22), the controller  49  will determine the steering correction provided by this rate of orientation change mode necessary at each first robotic tractor  50  travel interval by the following calculation:  
               Δ                   PATH     Rate                 _                 of                 _                 Orientation         =                  θ   D1     -     θ   S1     -     arcsin              [       (       LENGTH   D1       LENGTH   T       )     *                                    (     tan                   θ     F                 _                 Delayed         )     *     (     cos                   θ   D1       )       ]                               
 
         [0152]    θ F     —     DELAYED  is the angle between the front steered wheels of the lead tractor  30  and the lead tractor  30  centerline [delayed an amount equal to the linear distance between the lead tractor  30  drive wheels and the robotic tractor  50  wheels (empirically corrected with a response time correction, if needed)], and where θ S1 , and θ D1  are defined as above. For subsequent robotic tractors, the steering correction will be calculated in a very similar manner. The same equation is used. The sensors on the robotic tractor being considered are used in the equations, and the data from the lead tractor sensors is delayed an amount equivalent to the distance between the lead tractor and the robotic tractor being considered before it is used.  
         [0153]    Variable Ratio with Oversteer mode  
         [0154]    The variable ratio (with oversteer) mode of steering is an non-path-tracing mode that has been derived in a way that allows it to be used in combinations with the path tracking modes. This steering method is disclosed in provisional patent No. 60/167077. This method does not rely on any information from the tractor sensors, but only on sensors on the robotic tractor itself. This method compliments the path tracking modes, each compensating for possible weaknesses in the other. This alternate steering mode can be used to factor into one or more of the path tracking modes. The variable ratio steering algorithm reacts more strongly the farther out of line the wheels slip, thereby automatically correcting the path back to the approximate path of the first trailer. The variable ratio (with oversteer) mode uses sensors θ S1 , θ D1 , ΔS 1     —     LEFT  and ΔS 1     —     RIGHT , and θ R1 .  
         [0155]    The difference between the counts for the two wheels will be scaled to yield a measure of the amount of cornering that the robotic tractor wheels are undergoing. This difference is accumulated and then decayed at a prescribed rate per linear foot of travel, and is used along with the input from sensor θ R1  as input to the oversteer logic system. The controller  49  will maintain two decayed running totals of the difference between the travel of the left wheel and the travel of the right wheel.  
           DIFF   L     —     R   =DIFF   L     —     R +(Δ S   1     —     LEFT   −ΔS   1     —     RIGHT )−DECREMENT  
         [0156]    And  
           DIFF   R     —     L =DIFF R     —     L +(ΔS 1     —     RIGHT   −ΔS   1     —     LEFT )−DECREMENT  
         [0157]    Where DIFF L     —     R  is the decayed running total of the difference between the travel of the left wheel  71  L minus the travel of the right wheel  71  R, and DIFF R     —     L  is the decayed running total of the difference between the travel of the right wheel  71  R minus the travel of the left wheel  71  L. Also, ΔS 1     —     LEFT  is the travel of the left wheel  71  L in the latest travel interval and ΔS 1     —     RIGHT  is the travel of the right wheel  71  R in the latest travel interval. The number DECREMENT represents the amount of decay in each travel interval and can be adjusted as needed to change the oversteer characteristics of the system. Generally any accumulation in the delayed running totals DIFF L     —     R  and DIFF L     —     R  should decay within less than 100 feet or so to zero. At the end of any travel interval in which DIFF L     —     R  is less than zero, we will set DIFF L     —     R =0. At the end of any travel interval in which DIFF L     —     R  is less than zero, we will set DIFF L     —     R =0.  
         [0158]    The steering ratio for the variable ratio mode could be varied as a function of turning angle, speed, or any other such variable, but for simplicity, we will demonstrate how the steering ratio would be varied continuously by the processors as the speed of the robotic tractor changes. At higher speeds, the controller  49  will automatically control the robotic tractor in a manner that is more stable (a more positive steering ratio), and at lower speed, the processors will automatically control the robotic tractor in a manner the has better cornering ability (a more negative steed ratio). In order to accomplish this we will choose a correction factor, CORR, which is dependent upon the average speed of the robotic tractor. A steering ratio of −4 produces very responsive steering and a steering ratio of about +0.6 (depending upon the ratio of the robotic tractor length to the length of the robotic tractor and the rear trailer  80  together) produces very stable steering. If we wanted to vary the correction factor CORR linearly between −4 and +0.6 as the speed increased from 8 ft/sec to 30 ft/sec, we would use the equation:  
         [0159]    CORR=(0.2091* SPD)−5.673 whenever 8&lt;SPD&lt;30 ft/sec.  
         [0160]    If SPD was less than 8, then we would set:  
         [0161]    CORR=−4 for SPD&lt;8 ft/sec.  
         [0162]    And if SPD was greater than 30, we would set:  
         [0163]    CORR=0.6 for SPD&gt;30 ft/sec.  
         [0164]    CORR could also be a constant, or varied according to any method desired.  
         [0165]    ΔRATIO 1  is the steering output from the variable ratio (with oversteer) mode, the processor will then determine the steering output at each robotic tractor travel interval by the following calculation:  
           ΔRATIO   1 =[θ D1 +( FAC   1 )(θ R1 )+( FAC   2 )( DIFF   L-R   −DIFF   R-L )]*( CORR )−θ S1    
         [0166]    where FAC 1  and FAC 2  are the oversteer factors for the trailer orientation system and the accumulated robotic tractor wheel delayed difference system respectively, and ΔRATIO 1  1 is the amount of movement determined by the variable ratio component of the steering algorithms to be needed by the axle steering system.  
         [0167]    Methods for Combining Modes, and Advantages of Such Combinations  
         [0168]    For the preferred embodiment of the invention, a non-path-tracking steering mode, the variable ratio (with oversteer) mode will be combined with the path tracking modes. This combination will help to assure that any errors that enter into the steering operation are not propagated in a way that will cause instabilities or offsets.  
         [0169]    The variable ratio (with oversteer) mode (incorporated from Provisional Patent number No. 60/204513), is actually a non-path tracking mode of steering that can be combined with the path tracking modes of steering. In this capacity it will help to ensure that any errors that enter the system through wheel slippage, inaccuracies in measurements, or anything else are quickly and smoothly eliminated before problems develop. The variable ratio type of steering is particularly fuel for eliminating any offset between the centerlines of the lead tractor-trailer combination and the robotic tractor-trailer combination.  
         [0170]    The contribution from this variable ratio (with oversteer) mode of steering has a somewhat different character at different speeds. As the speed increases, the steering ratio will become positive and the contribution from the variable ratio with oversteer mode will become a more stable type of ratio steering, like a steerable type A dolly, increasing steering stability. As the speed decreases, the steering ratio will become negative to produce a cornering type of ratio steering including oversteer.  
         [0171]    The controller  49  can be programmed to use any combination of the Path Tracking, and/or cornering or stability ratio steering modes under various speed and/or cornering conditions. The mixture can easily be adjusted to obtain the desired steering characteristics.  
         [0172]    This variable ratio with oversteer mode of steering from U.S. Pat. No. 60/204513 can be easily integrated with the path tracking modes of steering, since the modes all have output in the form of a Δ which is the correction to the steering angle that is needed. For example, if equal weight was given to each of the two path tracking modes (relative angle mode and rate of orientation change mode) and to the Variable Ratio with oversteer mode of steering, each type of steering would contribute roughly one-third of the total steering character. When the robotic tractor  50  is operating in this combined mode, the controller  49  will determine the steering necessary at each first robotic tractor travel interval by a calculation similar to the following:  
         Δ FINAL=[ΔRATIO   1   +ΔPATH   1     —     Relative     —     Angle   +ΔPATH   1     —     Rate     —     of     —     Orientation ]/3  
         [0173]    where ΔRATIO 1 , ΔPATH 1     —     Relative     —     Angle , and ΔPath 1     —     Rate     —     of     —     Orientation  are defined as above. Also, any of the modes can easily be combined with any of the other modes. For example, a simple combination of the two path tracking modes with equal weightings could be obtained by setting  
         Δ FINAL =(Δ PATH   1     —     Relative     —     Angle   +ΔPath   1     —     Rate     —     of     —     Orientation )/2  
         [0174]    The output from the steering modes could be weighted according to the speed of the vehicle, the steering angle of the lead tractor, the angle between any two section, under the control of the driver of the lead tractor, or using input from many different systems. The output from the steering modes could be combined using many methods, and it is expected that they would all be covered under this invention.  
         [0175]    Referring to the equations that were derived for the variable ratio (with oversteer) portion of the above controlling equation, we can see how this combination contributes to the stability of the system at high speeds. When CORR is near 0.6 the two path-tracking modes will be combined with a very stable form of the variable ratio mode (steering ratio positive). When CORR is closer to −4 the more maneuverable cornering mode (steering ratio negative) will be combined with the path-tracking modes.  
         [0176]    As above, ΔFINAL is the amount of steering correction needed by the axle steering system.  
         [0177]    During operation, the steering motors should act to maintain ΔFINAL near zero. The value of ΔFINAL controls the activation of hydraulic control valves that cause the hydraulic motor  68  (FIGS. 4, 5) to rotate the steering axle assembly  60  about its central pivot support point  58  (FIG. 3). A positive value of ΔFINAL will cause the wheels to be steered more to the right of the robotic tractor centerline, and a negative ΔFINAL will cause them to be steered more to the left of the robotic tractor centerline. A larger magnitude of ΔFINAL will cause the valves to be opened wider or will cause more than one valve to be opened, producing more rapid steering movement.  
         [0178]    Miscellaneous Topics  
         [0179]    Smoothing Steering Behavior  
         [0180]    It should be noted that if experimental error in the measurements was causing the steering to become erratic during operation, the steering response could be smoothed by simply averaging ΔFINAL over several travel intervals.  
         [0181]    Improving General Steering Response  
         [0182]    It should also be noted that in each of the above cases, steering response could be improved by having an algorithm for the controller  49  to predict the value of the variables in the next travel interval by extrapolation of the input values for the last two or three travel intervals. It could then control the steering motors so that when the actual data for the interval was obtained, the value of ΔFINAL would be minimized. Obviously, the steering response will also be improved if the controller  49  uses the smallest travel interval that it is able to use. The travel interval size could be changed occasionally as the speed changed in order to improve the response of the system at lower speeds.  
         [0183]    Backing mode  
         [0184]    The behavior of the robotic tractor with path tracking steering modes, variable ratio (with oversteer) mode, and traction kinking during backing operations is of particular interest. Normally a double is almost impossible to back, but if the robotic tractor is shifted into a special stability mode (corresponding to fill control by the stability portion of the variable ratio steering mode), the robotic tractor with its trailer will behave much like a single-axle trailer with a very long wheelbase. The double string will then become only slightly harder to back than a single trailer.  
         [0185]    Multiple Robotic tractors  
         [0186]    It should be noted that, while the analysis presented here applies to all robotic tractors in a given truck-tractor string. In general, with the robotic tractors incorporating the improvements of this invention, one tractor will pull and control several robotic tractors with their trailers. The algorithms for the various modes of path tracking for the second robotic tractor function the same as those for the first robotic tractor, with the sensor readings from the main tractor must be delayed longer due to the greater distance between the robotic tractor and the lead tractor.  
         [0187]    Most of the algorithms could also be made to function for more robotic tractors by taking the readings off of the robotic tractor in front of the one being considered, instead of the lead tractor, but that would cause errors to propagate more readily. The ratio with oversteer mode must take readings from the unit directly in front of it, however combining this method with the other modes will correct for that additional error.  
         [0188]    Length Adjustments  
         [0189]    The length of the robotic tractor may need to be adjusted to accommodate rear trailers  58  of different lengths. This may be accomplished by loosening the pins and locks  146  and  148 , sliding the inner section of the frame  74   b  into or out of the outer frame section  74   a  at joint  144 , and then re-tightening the pins and locks  146  and  148 .  
         [0190]    Generality of Concepts  
         [0191]    The concepts involved in this invention are most easily explained by describing specific devices that embody or exemplify these concepts. The construction of the various sensors and control components shown in the preferred embodiment of the invention was chosen more with the intention of making each part of the invention understandable than for practicality of construction and use. More compact angle sensors and rotation sensors are readily available, and an expert in the field will quickly see that, in almost all cases, the invention could easily be constructed using any device that performs the desired function. The description of any particular embodiment of the invention is not intended in any way to limit the invention to some particular embodiment, but only to assist the reader in understanding the concepts involved in this invention. It is, therefore, to be understood that the present invention includes any embodiment that is within the scope of the claims rather than as specifically described.