Abstract:
Disclosed a towbarless airplane tug and method of operating thereof. The tug comprises a chassis mounted on a plurality of tug wheels, at least some of said tug wheels being steerable tug wheels and at least some of said tug wheels being drivable tug wheels; an airplane wheel support turret assembly, rotatably mounted in connection with said chassis and operative to support at least one wheel of a nose landing gear of an airplane; at least one rotation sensor connected to said wheel support turret assembly and operative to sense rotation of said wheel support turret assembly relative to said chassis, said rotation resulting at least from steering control induced movement of the nose landing gear caused by pilot-controlled ground steering of said airplane, and to generate an output indicating a direction of said pilot-controlled ground steering of said airplane; at least one tug wheel driver unit operative to drive said drivable tug wheels; at least one tug wheel steering mechanism operative to steer said steerable tug wheels thereby providing steering of said chassis; and at least one tug controller operative to control operation of at least said tug wheel steering mechanism at least in response to said output of said rotation sensor, so as to cause steering said steerable tug wheels such that said chassis moves in the direction indicated in said output of said rotation sensor.

Description:
This is a Continuation of Application No. PCT/IL2008/000459 filed Apr. 2, 2008, which claims the benefit of U.S. patent application Ser. No. 11/798,777 filed May 16, 2007 and International Patent Application No. PCT/IL2008/000036, filed Jan. 8, 2008. The disclosure of the prior applications is hereby incorporated by reference herein in its entirety. 
     This is also a Continuation-in-Part of application Ser. No. 11/798,777 filed May 16, 2007, which in turn is a Continuation-in-Part of application Ser. No. 11/528,647, filed Sep. 28, 2006. The disclosure of the prior applications is hereby incorporated by reference herein in its entirety. 
     REFERENCE TO RELATED APPLICATIONS 
     The following unpublished patent applications are related to the present application and the disclosures thereof are hereby incorporated by reference: 
     U.S. patent application Ser. No. 11/528,647, filed Sep. 28, 2006, entitled SYSTEM AND METHOD FOR TRANSFERRING AIRPLANES; U.S. patent application Ser. No. 11/798,777, filed May 16, 2007, entitled SYSTEM AND METHOD FOR TRANSFERRING AIRPLANES; and PCT Patent Application No. IL2008/000036, filed Jan. 8, 2008, entitled SYSTEM AND METHOD FOR TRANSFERRING AIRPLANES. 
     Priority is hereby claimed under 37 CFR 1.78(a)(4) and (5)i from: U.S. patent application Ser. No. 11/798,777, filed May 16, 2007, entitled SYSTEM AND METHOD FOR TRANSFERRING AIRPLANES; and PCT Patent Application No. IL2008/000036, filed Jan. 8, 2008, entitled SYSTEM AND METHOD FOR TRANSFERRING AIRPLANES. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to systems for airplane ground movement and more particularly to ground vehicles operative to move airplane in an airport. 
     BACKGROUND OF THE INVENTION 
     The following patent publications are believed to represent the current state of the art: 
     U.S. Pat. Nos. 6,945,354; 6,739,822; 6,675,920; 6,751,588; 6,600,992; 6,405,975; 6,390,762; 6,357,989; 6,352,130; 6,305,484; 6,283,696; 6,209,671; 5,860,785; 5,680,125; 5,655,733; 5,562,388; 5,549,436; 5,516,252; 5,511,926; 5,480,274; 5,381,987; 5,346,354; 5,314,287; 5,308,212; 5,302,076; 5,302,075; 5,302,074; 5,261,778; 5,259,572; 5,219,033; 5,202,075; 5,176,341; 5,151,003; 5,110,067; 5,082,082; 5,078,340; 5,054,714; 5,051,052; 5,048,625; 5,013,205; 4,997,331; 4,976,499; 4,950,121; 4,923,253; 4,917,564; 4,917,563; 4,913,253; 4,911,604; 4,911,603; 4,836,734; 4,810,157; 4,745,410; 4,730,685; 4,658,924; 4,632,625; 4,482,961; 4,375,244; 4,225,279; 4,113,041 and 4,007,890; 
     U.S. Patent Publication Number 2003/095854; 
     PCT Patent Publication Numbers WO 93/13985; WO 89/03343 and WO 98/52822; and 
     Patent publication numbers RU 2302980; RU 2271316; EP 1623924; EP 1190947; JP 2279497; JP 4138997; JP 57070741; JP 56002237; GB 1249465; DE 3844744; DE 4446048; DE 4446047; DE 4131649; DE 4102861; DE 4009419; DE 4007610; DE 19734238; DE 3534045; DE 3521429; DE 3327629; DE 3327628; DE 4340919; FR 2581965 and FR 2675919. 
     SUMMARY OF THE INVENTION 
     The present invention seeks to provide novel robotic tugs for taxiing airplanes. 
     There is thus provided in accordance with a preferred embodiment of the present invention a towbarless airplane tug including a chassis mounted on a plurality of tug wheels, at least some of the plurality of tug wheels being steerable tug wheels, a base assembly, mounted on the tug chassis, an airplane nose wheel support turret assembly, rotatably mounted on the base assembly, for supporting wheels of nose landing gear of an airplane, at least one force sensor operative to sense force applied to the nose landing gear of the airplane in at least one generally horizontal direction resulting from at least one of airplane pilot-controlled braking, deceleration and acceleration of the airplane, at least one tug wheel driver unit operative to drive the plurality of tug wheels in rotation to provide displacement of the chassis, at least one tug wheel steering mechanism operative to steer the steerable tug wheels during airplane taxiing and at least one tug controller operative at least partially in response to an output of the at least one force sensor indicating airplane pilot-controlled braking of the airplane to operate the at least one tug wheel driver unit so as to reduce the force applied to the nose landing gear of the airplane as the result of the airplane pilot-controlled braking. 
     Preferably, the towbarless airplane tug also includes at least one rotation detector operative to sense rotation of the airplane nose wheel support turret assembly relative to the chassis resulting at least from pilot-controlled ground steering of the airplane and the at least one tug controller is also operative to control operation of at least the at least one tug wheel steering mechanism, the at least one tug controller being operative at least partially in response to an output of the at least one rotation detector indicating pilot-controlled steering of the airplane to operate the at least one tug wheel steering mechanism so as to steer the steerable tug wheels such that the chassis moves in a direction indicated by the pilot-controlled steering. 
     There is also provided in accordance with another preferred embodiment of the present invention a towbarless airplane tug including a chassis mounted on a plurality of tug wheels, at least some of the plurality of tug wheels being steerable tug wheels, an airplane nose wheel support turret assembly, rotatably mounted on the chassis, for supporting rotatable wheels of a nose landing gear of an airplane, at least one rotation detector operative to sense rotation of the airplane nose wheel support assembly relative to the chassis, resulting at least from pilot-controlled ground steering of the airplane, at least one tug wheel driver operative to drive the plurality of tug wheels in rotation to provide displacement of the chassis, at least one tug wheel steering mechanism operative to steer the steerable tug wheels and at least one tug controller operative to control operation of at least the at least one tug wheel steering mechanism, the at least one tug controller being operative at least partially in response to an output of the at least one rotation detector indicating airplane pilot-controlled steering of the airplane to operate the at least one tug wheel steering mechanism so as to steer the steerable tug wheels such that the chassis moves in a direction indicated by the pilot-controlled steering. 
     Preferably, the airplane nose wheel support turret assembly is rotatably mounted on the chassis by bearings. Preferably, the towbarless airplane tug also includes at least one energy absorber assembly mounted between the airplane nose wheel support turret assembly and the chassis for absorbing energy resulting from inertial forces of the tug which would otherwise be applied to the nose landing gear of the airplane. 
     Preferably, the towbarless airplane tug also includes at least one airplane wheel engagement assembly for placement of the airplane wheels on the airplane nose wheel support turret assembly such that a center of horizontal rotation of the nose landing gear of the airplane lies at a center of rotation of the airplane nose wheel support turret assembly relative to the chassis. Additionally, the at least one airplane wheel engagement assembly is also operative for retaining the airplane nose landing gear wheels in place at a location such that a center of horizontal rotation of the nose landing gear wheels of the airplane lies at the center of rotation of the airplane nose wheel support turret assembly relative to the chassis. Additionally or alternatively, the at least one airplane wheel engagement assembly is adaptive to airplane wheel size for placement of the airplane wheels on the airplane wheel support assembly and retaining the airplane wheels in place at the location such that the nose landing gear wheels of the airplane lie at the center of rotation of the airplane nose wheel support turret assembly relative to the chassis. 
     Preferably, the airplane nose wheel support turret assembly is pivotably mounted relative to the chassis, for accommodating tilt of the airplane nose landing gear wheels during airplane movement. Additionally or alternatively, the towbarless airplane tug has a tug driver-controlled mode of operation for airplane pushback and an airplane pilot-controlled mode of operation for airplane movement during taxiing following at least one of pushback and landing. 
     Preferably, the towbarless airplane tug has an autonomous mode of operation for airplane movement during taxiing following at least one of pushback and landing. Additionally, in the autonomous mode of operation, the tug controller is responsive to commands received from an airport command and control center. Additionally or alternatively, in the autonomous mode of operation, the tug controller is responsive to pre-programmed driving pathways and speed limits and to tug location information received from tug mounted tug location functionality. 
     Preferably, the towbarless airplane tug has an autonomous mode of operation for tug return from a take-off area to a pre-pushback location. 
     Preferably, the towbarless airplane tug has tug speed control functionality allowing the tug to travel at speeds up to different speed limits at different locations in the airport. 
     Preferably, the at least one tug controller is operative to control acceleration and deceleration of the tug, thereby to limit the force applied to the nose landing gear of the airplane, the at least one tug controller employing at least one force feedback loop utilizing an input from the at least one force sensor and at least one of the following inputs: an indication of known slopes at various locations along an airplane travel surface traversed by the tug, the locations being identified to the at least one tug controller by tug location and inclination sensing functionality, an indication of wind forces applied to the airplane, an indication of known airplane and tug rolling friction force at various locations along airplane travel surface traversed by the tug, the locations being identified to the at least one tug controller by location sensing functionality and an obstacle detection indication. In another preferred embodiment the at least one force feedback loop utilizes an input from the at least one sensor and the following inputs: an indication of known slopes at various locations along an airplane travel surface traversed by the tug, the locations being identified to the at least one tug controller by tug location and inclination sensing functionality, an indication of wind forces applied to the airplane, an indication of known airplane and tug rolling friction force at various locations along airplane travel surface traversed by the tug, the locations being identified to the at least one tug controller by location sensing functionality and an obstacle detection indication. 
     Preferably, the at least one tug controller is operative to control speed of the tug and employs at least one speed feedback loop utilizing at least one of the following inputs: an indication of known desired speed at various locations along an airplane travel surface traversed by the tug, obtained by the at least one tug controller using tug location sensing functionality and a predetermined map of the airplane travel surface indicating speed limits therealong and desired speed information supplied to the at least one tug controller from an airplane main controller. 
     Preferably, the at least one tug controller is operative to control steering of the tug by employing at least one position feedback loop utilizing at least an indication of rotation of the airplane nose landing gear wheels provided by the at least one rotation detector. 
     There is further provided in accordance with yet another preferred embodiment of the present invention a towbarless airplane tug including a chassis mounted on a plurality of tug wheels, at least some of the plurality of tug wheels being steerable tug wheels, an airplane wheel support assembly, mounted on the chassis, for supporting rotatable wheels of a nose landing gear of an airplane, at least one force sensor operative to sense force applied to the nose landing gear of the airplane in at least one generally horizontal direction, at least one tug wheel driver operative to drive the plurality of tug wheels in rotation to provide displacement of the chassis, at least one tug controller operative to control acceleration and deceleration of the tug thereby to limit the force applied to the nose landing gear of the airplane, the at least one tug controller employing at least one force feedback loop utilizing an input from the at least one force sensor and at least one of the following inputs: an indication of known slopes at various locations along an airplane travel surface traversed by the tug, the locations being identified to the at least one tug controller by tug location and inclination sensing functionality, an indication of wind forces applied to the airplane, an indication of known airplane and tug rolling friction force at various locations along airplane travel surface traversed by the tug, the locations being identified to the at least one tug controller by location sensing functionality and an obstacle detection indication. 
     Preferably, the at least one tug controller employs at least one feedback loop utilizing an input from the at least one force sensor and at least two of the following inputs: an indication of known slopes at various locations along an airplane travel surface traversed by the tug, the locations being identified to the at least one tug controller by tug location and inclination sensing functionality, an indication of wind forces applied to the airplane, an indication of known airplane and tug rolling friction force at various locations along airplane travel surface traversed by the tug, the locations being identified to the at least one tug controller by location sensing functionality and an obstacle detection indication. 
     Preferably, the at least one tug controller employs at least one feedback loop utilizing an input from the at least one force sensor and all of the following inputs: an indication of known slopes at various locations along an airplane travel surface traversed by the tug, the locations being identified to the at least one tug controller by tug location and inclination sensing functionality, an indication of wind forces applied to the airplane, an indication of known airplane and tug rolling friction force at various locations along airplane travel surface traversed by the tug, the locations being identified to the at least one tug controller by location sensing functionality and an obstacle detection indication. 
     Preferably, the towbarless airplane tug also includes at least one energy absorber assembly mounted on the chassis for absorbing forces resulting from inertia of the tug which would otherwise be applied to the nose landing gear of the airplane. Additionally or alternatively, the airplane nose wheel support turret assembly is rotatably mounted on the chassis by bearings. 
     Preferably, the towbarless airplane tug also includes at least one airplane wheel engagement assembly for placement of the airplane wheels on the airplane wheel support assembly such that the nose landing gear of the airplane lies at a center of rotation of the airplane wheel support assembly relative to the chassis. Additionally, the at least one airplane wheel engagement assembly is also operative for retaining the airplane wheels in place at a location such that the nose landing gear wheels of the airplane lie at a center of rotation of the airplane wheel support turret assembly relative to the chassis. Additionally or alternatively, the at least one airplane wheel engagement assembly is adaptive to airplane wheel size for placement of the airplane wheels on the airplane wheel support assembly and retaining the airplane wheels in place at the location such that the nose landing gear of the airplane lies at the center of rotation of the airplane wheel support assembly relative to the chassis. 
     Preferably, the at least one energy absorber assembly includes multiple pistons which absorb energy upon acceleration or deceleration of the tug relative to the airplane. 
     Preferably, the at least one tug controller is responsive to input signals from an airport command and control system. 
     There is even further provided in accordance with still another preferred embodiment of the present invention a towbarless airplane tug including a chassis mounted on a plurality of tug wheels, at least some of the plurality of tug wheels being steerable tug wheels, an airplane wheel support assembly, mounted on the chassis, for supporting rotatable wheels of a nose landing gear of an airplane, at least one tug wheel driver operative to drive the plurality of tug wheels in rotation to provide displacement of the chassis and at least one tug controller operative to control speed of the tug, the at least one tug controller employing at least one feedback loop utilizing a mapping of speed limits along a travel path traversed by the tug and the airplane at the airport as well as an indication of the instantaneous location of the tug and the airplane along a travel path. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will be understood and appreciated more fully from the following detailed description, taken in conjunction with the drawings in which: 
         FIG. 1A  is a pictorial illustration of a towbarless airplane tug constructed and operative in accordance with a preferred embodiment of the present invention; 
         FIG. 1B  is a sectional illustration of a towbarless airplane tug constructed and operative in accordance with a preferred embodiment of the present invention, taken along the lines  1 B- 1 B in  FIG. 1A ; 
         FIG. 1C  is a top view illustration of the towbarless airplane tug of  FIGS. 1A &amp; 1B ; 
         FIGS. 2A ,  2 B,  2 C,  2 D,  2 E,  2 F,  2 G,  2 H,  2 I and  2 J are respective pictorial illustrations of various stages in the pre-pushback and pushback operation of the towbarless airplane tug of  FIGS. 1A-1C ; 
         FIGS. 3A ,  3 B,  3 C,  3 D and  3 E are respective pictorial illustrations of various stages in pilot controlled taxiing operation of the towbarless airplane tug of  FIGS. 1A-1C  in accordance with one embodiment of the present invention; 
         FIGS. 4A ,  4 B,  4 C,  4 D and  4 E are respective pictorial illustrations of various stages in autonomous taxiing operation of the towbarless airplane tug of  FIGS. 1A-1C  in accordance with an alternative embodiment of the present invention; 
         FIGS. 5A ,  5 B,  5 C,  5 D and  5 E are respective pictorial illustrations of various stages in the autonomous return operation of the towbarless airplane tug of  FIGS. 1A-1C ; and 
         FIGS. 6A ,  6 B and  6 C are respective diagrammatical illustrations of steering functionality of the towbarless airplane tug of  FIGS. 1A-1C . 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     The present invention relates to novel robotic tugs for taxiing airplanes from a gate to a take-off runway without using the aircraft jet engines. In accordance with a preferred embodiment of the present invention, the robotic tugs preferably operate in an airplane pilot-controlled taxi mode wherein the airplane pilot steers and brakes as if the airplane were moving under its own engine power and the tug speed is controlled by a controller. Upon completion of the airplane taxi the tug preferably returns autonomously to a pre-pushback location at the gate, controlled by an airport command and control system. Preferably, a tug driver performs the pushback operation, after which he leaves the tug and the airplane pilot controls the tug during taxi. In accordance with an alternative embodiment of the present invention, the tug may operate in an autonomous mode of operation during airplane taxi. The term “autonomous” is used throughout in a broad sense to include operation under the control of an airport command, control and communication system, preferably subject to airplane pilot override. 
     Reference is now made to  FIGS. 1A ,  1 B and  1 C which illustrate a towbarless airplane tug  100  constructed and operative in accordance with a preferred embodiment of the present invention. As seen in  FIGS. 1A ,  1 B and  1 C, the towbarless tug  100  preferably comprises a chassis  102  supported on six wheels, including forward steerable wheels  104  and  106 , rearward steerable wheels  108  and  110  and intermediate non-steerable wheels  112  and  114 . It is appreciated that wheels  112  and  114  may alternatively be steerable as well. The centers of rotation of steerable wheels  104 ,  106 ,  108  and  110 , respectively indicated by reference numerals  115 ,  116 ,  117  and  118 , preferably define vertices of a rectangle, whose length A is defined by the separation between the centers of rotation of respective forward and rearward wheels on the same side of the tug  100  and whose width B is defined by the separation between the centers of rotation  115  and  116  of respective forward wheels  104  and  106  and between the centers of rotation  117  and  118  of respective rearward wheels  108  and  110 . 
     Each of wheels  104 ,  106 ,  108 ,  110 ,  112  and  114  is preferably controllably driven by a corresponding hydraulic motor (not shown) powered by a corresponding hydraulic pump (not shown) driven by the vehicle diesel engine (not shown) in response to speed and torque control signals from a controller  119 . Each of the steerable wheels  104 ,  106 ,  108  and  110  is preferably steerable by one or more steering pistons (not shown) in response to steering control signals from controller  119 . 
     A driver control interface assembly, preferably including a steering wheel  120 , brakes (not shown) and optionally other controls, preferably interfaces with controller  119  to enable a driver to govern the operation of the towbarless airplane tug  100  prior to and during pushback, and/or in the event of an emergency or a tug control system malfunction. In accordance with a preferred embodiment of the present invention, the towbarless airplane tug  100  operates under airplane pilot in control (PIC), via controller  119  to taxi to or near a take-off point. Near the take-off point, the controller  119  automatically disengages the tug  100  from the airplane, in response to a command received from an airport Command and Control Center or from a tug location sensor  121 , such as a GPS sensor or any other suitable tug location sensor, and the tug  100  operates under control of controller  119 , to return autonomously from the take-off point to a desired pre-push back location. Tug  100  is also preferably equipped with a wind sensor  122 , one or more obstacle detection sensors  123 , such as radar and/or laser sensors, for example a Velodyne HDL-64E laser scanner, which output to controller  119 , and one or more driving cameras  124 , which enable remote driving of tug  100 , such as by a remote command and control center. Driving cameras  124  may be rotatable to have selectable pan and tilt so as to enable an operator to view various locations on or near the tug  100 . 
     In accordance with a preferred embodiment of the present invention, a rotatable airplane nose landing gear wheel support turret  125  is pivotably and rotatably mounted on a horizontal base assembly  126 . The steady state center of rotation of the turret  125 , designated by reference numeral  127 , is preferably at the geometrical center of the rectangle defined by the centers of rotation  115 ,  116 ,  117 , and  118  of respective steerable wheels  104 ,  106 ,  108  and  110 . 
     Horizontal base assembly  126  is connected to the chassis  119  in a manner which allows a limited amount of freedom of movement of horizontal base assembly  126  relative to chassis  102 , and is engaged by an energy absorber assembly preferably comprising a plurality of energy absorbing pistons  128 , each of which is pivotably coupled to the chassis  102  and to horizontal base assembly  126 . Force sensors, preferably load cells  129 , are preferably associated with each of energy absorbing pistons  128 , which output to controller  119 , and are used by controller  119  in controlling vehicle acceleration and deceleration. 
     Horizontal base assembly  126  preferably comprises a circumferential base element  130 , which is pivotably mounted onto chassis  102  by being suspended from a transversely extending support rod  131  on a pair of forward hanging supports  132 , and suspended on a pair of rearward hanging supports  132 ′ which are pivotably mounted onto chassis  102 . Rearward hanging supports  132 ′ are engaged by pivotably mounted energy absorbing pistons  128 . Mounting of circumferential base element  130  onto rearward hanging supports  132 ′ is preferably by means of pivotable axles  133 , which may or may not be integrally formed with circumferential base element  130 . 
     Turret  125  is preferably pivotably and rotatably mounted onto base  126  by a pair of pivot rods  134  extending outwardly therefrom into engagement with high load capacity bearings  135 , which in turn, engage a 360 degree circumferential bearing race  136  formed in base  126 . This arrangement provides both relatively low friction rotatability and tiltability of turret  125  relative to the base element  130 , the horizontal base assembly  126 , and chassis  102 . 
     An upstanding frame  140  is fixedly mounted onto turret  125  for aligning the airplane nose landing gear wheel on the turret  125 . An airplane nose landing gear wheel stop bar  142  is preferably selectably positioned with respect to upstanding frame  140  by a stop bar positioning piston  144 , anchored on turret  125 , for adapting turret  125  to different sizes of airplane nose landing gear wheels. The rotational orientation of the turret  125  is preferably sensed by a rotation sensor  145 , such as a potentiometer, which provides a turret rotational orientation input to controller  119 . Rotational orientation of the turret  125  may be governed by a turret rotation motor  146 . 
     A selectably positionable clamp assembly  147  is preferably mounted on turret  125  and connected to upstanding frame  140  and is operative to selectably clamp airplane nose landing gear wheels onto turret  125  such that the center of rotation of the airplane nose landing gear wheels lies, insofar as possible, exactly at the center of rotation  127  of turret  125 , which, as noted above, lies at the geometrical center of the rectangle defined by the centers of rotation of steerable wheels  104 ,  106 ,  108  and  110 . 
     Preferably, force sensors, such as load cells  148 , are mounted onto a forward facing surface of selectably positionable clamp assembly  147  and onto a rearward facing surface of stop bar  142 , so as to engage the airplane nose landing gear wheels to sense forces in the horizontal plane which are being applied to airplane nose landing gear wheels and thus to the airplane nose landing gear, such as due to differences in acceleration and/or deceleration of the tug  100  relative to acceleration and/or deceleration of an airplane being towed thereby. 
     An inclined airplane nose landing gear wheel ramp  150  is preferably mounted onto base element  130 . A pair of airplane nose landing gear wheel engaging piston assemblies  152  is preferably provided for pushing and lifting the airplane nose landing gear and positioning the airplane nose landing gear wheels onto turret  125 . 
     It is a particular feature of the present invention that the force sensors, such as load cells  148 , are operative to sense forces applied to the nose landing gear in at least one generally horizontal direction resulting at least from airplane pilot-controlled braking of the airplane, producing tug deceleration, and resulting from tug acceleration. The controller  119  is operative at least partially in response to an output of a force sensor indicating inter alia airplane pilot-controlled braking, resulting in deceleration of the airplane to provide speed and torque control signals to the hydraulic motors which drive the wheels of the tug  100 . The control is such as to reduce and limit the force applied to the nose landing gear of the airplane, to a maximum allowed force which will not damage the nose landing gear of the airplane as a result of airplane pilot-controlled braking resulting in tug deceleration and/or tug acceleration. 
     It is additionally a particular feature of the present invention that the rotation sensor  145  is operative to sense rotation of the turret  125  relative to base assembly  126 , which is produced by airplane pilot steering via the nose landing gear of the airplane, and the controller  119  is operative to control steering of steerable wheels  104 ,  106 ,  108  and  110  based on the output of rotation sensor  145  and thus in response to airplane pilot steering commands. 
     It is a further particular feature of the present invention that the force sensors, such as load cells  129  and  148 , are operative to sense forces applied to the nose landing gear in at least one generally horizontal direction resulting such that the controller  119  is operative to control acceleration and deceleration of the tug by employing at least one force feedback loop utilizing an output of at least one force sensor, sensing pilot-controlled braking and at least one of the following inputs: 
     an indication of force induced by known slopes at various locations along an airplane travel surface traversed by the tug  100 , the locations being identified to the controller by location sensing functionality; 
     an indication of wind forces applied to the airplane, information regarding the wind forces being supplied to the controller from airport and/or tug mounted wind sensors; and 
     an indication of known tug and airplane rolling friction forces at various locations along the airplane travel surface traversed by the tug, the locations being identified to the controller by location sensing functionality. 
     It is a further particular feature of the present invention that the controller  119  is operative to control the speed of the tug  100  by employing at least one speed feedback loop based on known speed limits along a travel path traversed by the tug and the airplane, preferably utilizing a suitable airport map embedded in the controller  119 , and an output of a tug location sensor, indicating the position of the tug  100  along the travel path of the tug  100  and the airplane. 
     In accordance with an embodiment of the invention a pair of laser range finders  154  are mounted on chassis  102  of tug  100  for ascertaining the angular relationship between the longitudinal axis of the airplane and the longitudinal axis of the tug  100 . The angular relationship between the longitudinal axis of the airplane and the longitudinal axis of the tug  100  is employed particularly in an autonomous taxiing mode of operation such as that described hereinbelow in  FIGS. 4A-4E . 
     Reference is now made to  FIGS. 2A ,  2 B,  2 C,  2 D,  2 E,  2 F,  2 G,  2 H,  21  and  2 J, which are respective pictorial illustrations of various stages in the pre-pushback and pushback operation of the towbarless airplane tug of  FIGS. 1A-1C , preferably under tug driver control. 
     As seen in  FIG. 2A , towbarless airplane tug  100 , constructed and operative in accordance with a preferred embodiment of the present invention, is moved, under the control of a tug driver, in a direction indicated by an arrow  200 , towards an airplane  202  awaiting pushback.  FIG. 2B  show the nose landing gear wheels  204  located on ramp  150 .  FIG. 2C  shows nose landing gear wheel engaging piston assemblies  152  positioned in engagement with nose landing gear wheels  204  for pushing and lifting the airplane nose landing gear and positioning the airplane nose landing gear wheels onto turret  125 .  FIG. 2D  shows suitable positioning of airplane nose landing gear wheel stop bar  142  with respect to upstanding frame  140  by a stop bar positioning piston  144  to accommodate the specific airplane nose landing gear wheels  204  of the specific airplane  202 .  FIG. 2E  shows nose landing gear wheels  204  being pushed onto turret  125 . 
       FIG. 2F  shows the airplane nose landing gear wheels  204  pushed by piston assemblies  152  against suitably positioned stop bar  142 , such that the axis of rotation of the airplane nose landing gear wheels  204  preferably lies insofar as possible exactly at the center of rotation  127  of turret  125 , which, as noted above, lies at or close to the geometrical center of the rectangle defined by the centers of rotation of steerable wheels  104 ,  106 ,  108  and  110 . 
       FIGS. 2G and 2H  shows a sequence of retraction of individual piston assemblies  152  out of engagement with airplane nose landing gear wheels  204  and engagement of individual clamps of selectably positionable clamp assembly  147  with airplane nose landing gear wheels  204  to clamp airplane nose landing gear wheels onto turret  125  such that the center of rotation of the airplane nose landing gear wheels lies insofar as possible exactly at the center of rotation  127  of turret  125 .  FIG. 21  shows pushback of the airplane  202  by tug  100  under control of the driver of the tug.  FIG. 2J  shows the tug driver leaving the tug  100  following completion of pushback. According to an alternative embodiment of the invention, the driver remains on tug  100  during all or part of taxiing and may participate in disengagement of the tug from the airplane following engine start up. 
     Reference is now made to  FIGS. 3A ,  3 B,  3 C,  3 D and  3 E, which are pictorial illustrations of various stages in the taxiing operation of the towbarless airplane tug  100  of  FIGS. 1A-1C  under airplane pilot control with the assistance of controller  119 . 
       FIG. 3A  shows rotation of the airplane nose landing gear wheels  204  by the airplane pilot using the conventional airplane steering tiller  206  or pedals (not shown), producing corresponding rotation of turret  125  relative to base element  130 . Rotation of turret  125  is immediately sensed by rotation sensor  145  which provides an output to controller  119  resulting in immediate rotation of steerable wheels  104 ,  106 ,  108  and  110  of tug  100 , as described hereinbelow in greater detail with reference to  FIGS. 6A-6B . 
     Controller  119  preferably performs steering of tug  100  in accordance with a feedback control loop which receives an input from rotation sensor  145  indicating an angle α between the direction of the wheels  204  of the nose landing gear as steered by the airplane pilot, and thus of turret  125 , with the longitudinal axis of the tug  100 , here designated by reference numeral  210 . The controller  119  rotates tug steerable wheels  104 ,  106 ,  108  and  110  at respective angles β 1 , β 2 , β 3  and β 4 , as described hereinbelow with reference to  FIGS. 6A-6C , and drives tug  100  such that angle α goes to zero. 
       FIG. 3B  shows an intermediate stage during movement of tug  100  to orient the tug  100  such that the airplane  202  is pulled by the tug  100  in the direction indicated by the airplane pilot. At this stage the angle α between the turret  125  and the longitudinal axis  210  of tug  100  is shown to be one-half of that shown in  FIG. 3A . An angle γ is indicated between the longitudinal axis  210  of the tug  100  and the longitudinal axis of the airplane  202  being towed by tug  100 , here designated by reference numeral  220 , due to turning of the tug  100  relative to the airplane  202 . 
       FIG. 3C  shows the tug  100  oriented with respect to the wheels  204  of the nose landing gear of the airplane  202  such that α is zero. It is noted that the angles β 1 , β 2 , β 3  and β 4  of the tug steerable wheels  104 ,  106 ,  108  and  110 , respectively, are typically not zero. At this stage the angle γ between the longitudinal axis  210  of the tug  100  and the longitudinal axis  220  of the airplane  202  being towed by tug  100  is less than γ in  FIG. 3B , inasmuch as the airplane  202  has begun to turn. 
       FIG. 3D  shows braking of the airplane  202 , by the airplane pilot pressing on pedals  222 . Braking of the airplane  202  is performed by brakes on the main landing gear (not shown) of the airplane  202  and immediately causes the application of a force sensed by the load cells  148  on clamps  147 , the output of which is received by controller  119 , which immediately decelerates the tug  100 . Inasmuch as there is a time lag between braking of the airplane  202  and corresponding deceleration of the tug  100 , forces are applied to rearward energy absorbing pistons  128  which are immediately sensed by load cells  129 . Rearward energy absorbing pistons  128  absorb the energy produced by braking of the airplane  202  relative to the tug  100 . At this stage load cells  129  serve as a back up to load cells  148 . 
       FIG. 3E  shows controlled acceleration of the tug  100  governed by controller  119  in response, inter alia, to inputs received from force sensors such as load cells  148  and  129 , to provide airplane taxi velocity which is within predetermined speed limits at predetermined locations along an airplane travel path and to ensure that forces applied to the nose landing gear do not exceed predetermined limits, taking into account one or more, and preferably all of the following factors: 
     force induced by known slopes at various locations along an airplane travel surface traversed by the tug  100 , the locations being identified to the controller  119  by location sensing functionality, such as GPS functionality, here provided by a tug mounted tug location sensor  121  ( FIGS. 1A-1C ); 
     wind forces applied to the airplane  202 , information regarding the wind forces being supplied to the controller  119  from airport or tug-mounted wind sensors, such as tug mounted wind sensor  122 , and preferably also via airport command and control functionality; and 
     tug  100  and airplane  202  rolling friction forces at various locations along the airplane travel surface traversed by the tug  100 , the locations being identified to the controller  119  by the location sensing functionality provided by tug location sensor  121 , and preferably also via airport command and control functionality. 
       FIG. 3E  also contemplates controlled deceleration of the tug  100  responsive not only to airplane pilot braking of the airplane  202 , but also to detection of an obstacle sensed by an obstacle sensor  123  ( FIGS. 1A-1C ). The tug deceleration is governed by controller  119  in response, inter alia, to inputs received from force sensors, such as load cells  148  and  129 , to ensure a coordinated deceleration ratio between the airplane and the tug, thereby to limit the forces applied to nose landing gear of the airplane  202  to within predetermined force limits. 
     In order to distinguish between normal traction forces on the nose landing gear and forces applied by the pilot braking, the controller  119  takes into account one or more, and preferably all of the factors described above, which are indicated by data from the various sensors, such as sensors  120 ,  121 ,  122  and  123  and cameras  124 . 
     Controller  119  is operative to govern acceleration and deceleration of tug  100  so as to maintain a desired tug speed preferably by employing a speed control feedback loop. The controller  119  has an embedded map of the airport indicating relevant tug speed limits at various regions of the tug travel path. This speed limit information is coordinated with information indicating instantaneous location of the tug  100 , which is preferably provided by tug location sensor  121 . The controller  119  preferably includes an inertial navigation system which indicates the instantaneous speed of the tug  100 . The feedback loop operates to cause the actual speed to be as close as possible to and not to exceed the speed limit for the instantaneous location of the tug  100 . 
     Controller  119  is also operative to govern acceleration and deceleration of tug  100  so as to limit the horizontal forces applied to the nose landing gear of the airplane  202  to an acceptable limit, which is currently 6% of the airplane gross weight, preferably by employing a force control feedback loop. Controller  119  receives inputs from load cells  148  and  129 , which indicate the sum of the forces applied to the nose landing gear of the airplane  202 , resulting from, inter alia, wind, slopes, rolling friction and acceleration or deceleration of the airplane  202  and/or the tug  100 . The force feedback loop is operative to accelerate or decelerate the tug  100  such as to maintain the forces sensed by load cells  148  and  129  sufficiently below the acceptable limit, so as to leave a margin for unexpected accelerations or decelerations of either the airplane  202  or the tug  100 . 
     Reference is now made to  FIGS. 4A ,  4 B,  4 C,  4 D and  4 E, which are pictorial illustrations of various stages in autonomous taxiing operation of the towbarless airplane tug  100  of  FIGS. 1A-1C  in accordance with an alternative embodiment of the present invention. The autonomous taxiing operation may be initiated by a driver of the tug  100  or automatically in response to a command from the airport command and control center following completion of pushback. 
     In autonomous taxiing operation, a function of turret  125  is to reduce the forces which are applied to the nose landing gear in the horizontal plane, specifically torque, to zero, by maintaining the position of the nose landing gear wheels  204  in the position last selected by the airplane pilot, typically parallel to the longitudinal axis  220  of the airplane. As a result the nose landing gear remains in that position while the tug  100  changes its heading along its travel path. This means that in most of the steering maneuvers of the tug  100  the turret will be turned in a direction opposite to that of the tug  100 . 
     Autonomous tug control may be overridden immediately by the airplane pilot by operating the airplane brakes on the main landing gear, which is immediately sensed by load cells  148  and  129 . 
     Autonomous taxiing preferably employs enhanced C4 functionality of an airport command and control center which coordinates and optimizes the taxi travel path and speed of all of the taxiing airplane in the airport, utilizing the following inputs: 
     Positions of all the airplanes taxiing in the airport; 
     Calculation of all airplane taxi clearances and taxi travel pathways; and 
     Airfield meteorological conditions and taxiway ground travel conditions. 
     This enhanced C4 functionality preferably provides the following functions: 
     avoidance of runway incursions; 
     calculating optimal taxiing speeds for all the airplanes to insure minimal starts and stops during taxiing; 
     minimizing traffic jams on the taxiways; and 
     enabling immediate pilot control in the event of a malfunction or emergency. 
       FIG. 4A  shows an initial orientation of the tug  100  and the airplane  202  at the beginning of autonomous taxiing operation. The airplane nose landing gear wheels  204  lie parallel to the longitudinal axis  210  of the tug  100  and to the longitudinal axis  220  of the airplane. The steerable wheels  104 ,  106 ,  108  and  110  of the tug  100  also lie parallel to axes  210  and  220 . 
       FIG. 4B  shows initial turning of the tug  100  under control of controller  119 , preferably responsive to traffic control instructions received from an airport command and control system  250  which may be based on a C4 (command, control &amp; communication center) system. As seen in  FIG. 4B , in this embodiment, the airplane pilot does not use the conventional airplane steering tiller  206  or pedals (not shown), except for emergency braking. Desired steering of the tug  100  is produced in response to suitable instructions from controller  119  by rotation of steerable wheels  104 ,  106 ,  108  and  110  of tug  100 . In order to avoid application of torque to the nose landing gear of the airplane  202 , turret  125  is rotated by turret rotation motor  146  by an angle −α equal and opposite to the angle α between the longitudinal axis  210  of the tug and the longitudinal axis  220  of the airplane. Rotation of turret  125  is sensed by rotation sensor  145  which provides a feedback output to controller  119 . 
     Controller  119  preferably performs steering of tug  100  by steering steerable wheels  104 ,  106 ,  108  and  110  and rotation of the turret  125  by turret rotation motor  146  in accordance with two feedback control loops. One feedback loop ensures that the heading of the tug  100  follows a predetermined travel path established by the airport command and control system  250 . The second feedback loop employs laser range finders  154  to ensure that the nose landing gear wheels  204  are aligned parallel to the longitudinal axis  220  of the airplane. The laser range finders  154  ascertain the angle α between the longitudinal axis  210  of the tug  100  and the longitudinal axis  220  of the airplane  202 . Controller  119  ensures that the turret  125  is rotated relative to the longitudinal axis  210  by an angle −α, so as to ensure that the nose landing gear wheels  204  remain aligned with the longitudinal axis  220  of the airplane at all times. 
       FIG. 4C  shows a further stage of rotation of the tug  100  At this stage the angle α between the longitudinal axis  210  of the tug  100  and the longitudinal axis  220  of the airplane  202  and the angle −α between the turret  125  and the longitudinal axis  210  of tug  100  are shown to be twice the angles shown in  FIG. 4B . 
       FIG. 4D  shows overriding of the autonomous mode of operation by the airplane pilot, preferably by the airplane pilot pressing on braking pedals  222 . This overriding may be for emergency braking and/or to enable the airplane pilot to control steering of the tug  100 , as described hereinabove with reference to  FIGS. 3A-3E . Braking of the airplane  202  is performed by brakes on the main landing gear (not shown) of the airplane  202  and immediately causes the application of a force sensed by the load cells  148  on clamps  147 , the output of which is received by controller  119 , which immediately decelerates the tug  100 . 
     Controller  119  automatically terminates autonomous mode operation of the tug  100  and returns the tug to airplane pilot control operation, as described above with reference to  FIGS. 3A-3E . 
     Inasmuch as there is a time lag between braking of the airplane  202  and corresponding deceleration of the tug  100 , forces are applied to rearward energy absorbing pistons  128  which are immediately sensed by load cells  129 . Rearward energy absorbing pistons  128  absorb the energy produced by braking of the airplane  202  relative to the tug  100 . At this stage load cells  129  serve as a back up to load cells  148 . 
     A return to autonomous mode operation typically requires an input from the airport command and control system  250  or a pilot command transmitted via an Electronic Flight Book (EFB), commercially available from Astronautics Ltd. of Israel. 
       FIG. 4E  shows controlled acceleration of the tug  100  in the autonomous mode of operation, governed by controller  119  in response, inter alia, to inputs received from airport command and control center  250  and from force sensors, such as load cells  148  and  129 , to provide airplane taxi velocity which is within predetermined speed limits at predetermined locations along an airplane travel path and to ensure that forces applied to the nose landing gear do not exceed predetermined limits, taking into account one or more, and preferably all, of the following factors: 
     force induced by known slopes at various locations along an airplane travel surface traversed by the tug  100 , the locations being identified to the controller  119  by location sensing functionality, such as GPS functionality, here provided by a tug mounted tug location sensor  121  ( FIGS. 1A-1C ); 
     wind forces applied to the airplane  202 , information regarding the wind forces being supplied to the controller  119  from airport or tug-mounted wind sensors, such as tug mounted wind sensor  122  and preferably also via airport command and control functionality; and 
     tug and airplane roiling friction forces at various locations along the airplane travel surface traversed by the tug  100 , the locations being identified to the controller  119  by the location sensing functionality provided by tug location sensor  121 , and preferably also via airport command and control functionality. 
       FIG. 4E  also contemplates controlled deceleration of the tug  100  responsive not only to airplane pilot braking of the airplane  202 , but also to detection of an obstacle sensed by an obstacle sensor  123  or one of driving cameras  124  ( FIGS. 1A-1C ) or to control instructions received from airport command and control center  250 . The tug deceleration is governed by controller  119  in response, inter alia, to inputs received from force sensors, such as load cells  148  and  129 , to ensure a coordinated deceleration ratio between the airplane and the tug, thereby to limit the forces applied to nose landing gear of the airplane  202  to within predetermined force limits. 
     In order to distinguish between normal traction forces on the nose landing gear and forces applied by the pilot braking, the controller  119  takes into account one or more, and preferably all, of the factors described above, which are indicated by data from the various sensors, such as sensors  120 ,  121 ,  122  and  123 . 
     Controller  119  is operative to govern acceleration and deceleration of tug  100  so as to maintain a desired tug speed preferably by employing a speed control feedback loop. The controller  119  has an embedded map of the airport indicating relevant tug speed limits at various regions of the tug travel path. This speed limit information is coordinated with information indicating instantaneous location of the tug  100 , which is preferably provided by tug location sensor  121 . The controller  119  preferably includes an inertial navigation system which indicates the instantaneous speed of the tug  100 . The feedback loop operates to cause the actual speed to be as close as possible to and not to exceed the speed limit for the instantaneous location of the tug. 
     Controller  119  is also operative to govern acceleration and deceleration of tug  100  to as to limit the horizontal forces applied to the nose landing gear of the airplane  202  to an acceptable limit, which is currently 6% of the airplane gross weight, preferably by employing a force control feedback loop. Controller  119  receives inputs from load cells  148  and  129 , which indicate the sum of the forces applied to the nose landing gear of the airplane, resulting from, inter alia, wind, slopes, rolling friction and acceleration or deceleration of the airplane  202  and/or the tug  100 . The force feedback loop is operative to accelerate or decelerate the tug  100  such as to maintain the forces sensed by load cells  148  and  129  sufficiently below the acceptable nose landing gear force limit, so as to leave a margin for unexpected accelerations or decelerations of either the airplane  202  or the tug  100 . 
     It is a particular feature of the present invention when operative in the autonomous taxiing mode of operation illustrated in  FIGS. 4A-4E , where the taxi speeds of tug  100  and the towed airplane  202  are typically those of the airplane pilot controlled taxiing mode of operation, that the airplane pilot can override the autonomous system to switch to an airplane pilot-controlled mode of operation by applying the airplane brakes and resuming tug steering by the airplane tiller  206 . The airplane pilot may also apply the airplane brakes in emergency situations. 
     Efficient taxiing operation is provided in the autonomous taxiing mode of operation due to the fact that the ground movements of all airplanes in the airport are managed by the command and control system  250  in an integrated manner, thus avoiding lines of airplanes waiting to take off. As seen in  FIG. 4E , the command and control system  250  integrates the movement of all airplanes such that airplanes maintain desired spacing therebetween during taxiing and avoid start and stop movements, insofar as possible. 
     Reference is now made to  FIGS. 5A ,  5 B,  5 C,  5 D and  5 E, which are respective pictorial illustrations of various stages in the autonomous mode of operation of the towbarless airplane tug  100  of  FIGS. 1A-1C  under the control of a command and control system in the airport tower, via controller  119  for tug taxiing movement and for return of the tug  100  from the take-off area to a pre-pushback location. 
       FIGS. 5A ,  5 B and  5 C show disengagement of the tug  100  from the airplane nose landing gear wheels  204 . It is appreciated that disengagement of the tug  100  from the airplane is typically carried out after the engines of the airplane have been started by the airplane pilot. In one embodiment of the invention, the command and control system  250  commands the tug  100  to perform disengagement. Alternatively, disengagement by the tug is automatically actuated by the sensed location of the tug at a predetermined disengagement location adjacent the take off point. The disengagement instructions are preferably communicated wirelessly to the controller  119 . In response to an instruction to disengage the tug, selectably positionable clamp assembly  147  is disengaged from clamping engagement with the airplane nose landing gear wheels  204  and tug  100  is moved forwardly, while the airplane pilot brakes the airplane  202  and controls the airplane tiller  206 , allowing the airplane nose landing gear wheels to roll down the ramp  150  and keeping the nose landing gear parallel to the longitudinal axis of the airplane  220 , as the ramp  150  is moved forward relative thereto. 
     According to an alternative embodiment of the invention, (not illustrated) where a safety driver is present on the tug  100 , the disengagement can be carried out by the safety driver in a conventional manner and is usually accompanied by disconnection of a voice communications cord, by the safety driver. 
       FIG. 5D  shows controlled acceleration and steering of the tug governed by controller  119  to provide tug travel speed which is within predetermined speed limits at predetermined locations along a predetermined tug autonomous travel path from the take off area to a pre-pushback location, taking into account one or more, and preferably all, of the following factors: 
     instantaneous location of the tug  100  as indicated by tug location sensor  121 ; 
     obstacle detection information received from sensors  123  or cameras  124 ; 
     real time information on the locations of other vehicles along the tug travel path which is provided by the airport command and control system  250 ; and 
     information indicating one or more predetermined travel paths of the tug  100  from the take-off location to the pre-pushback location. This information may be stored in controller  119  or provided in real time by the airport command and control system  250 . 
       FIG. 5E  shows controlled deceleration and parking of the tug governed by controller  119  at a pre-pushback location. 
     Reference is now made to  FIGS. 6A ,  613  and  6 C, which are respective diagrammatical illustrations of steering functionality of the towbarless airplane tug  100  of  FIGS. 1A-1C , which provides Ackerman steering of the airplane  202 . 
     Turning to  FIG. 6A , which illustrates the airplane  202  with its nose landing gear wheels  204  steered straight ahead along the longitudinal axis  220  of the airplane  202 , the following designations of parameters are noted: 
     L=Distance along the longitudinal axis  220  of the airplane  202  between the axis of rotation  302  of the nose landing gear wheels  204 , and a line  304  joining the main landing gear, here designated by reference numerals  306  and  308 ; 
     A=Longitudinal distance between a line  310  connecting the centers of back steerable wheels  108  and  110  and a line  312  connecting the centers of front steerable wheels  104  and  106  of tug  100 ; 
     B=Transverse distance between centers of wheels  108  and  110  and between centers of wheels  104  and  106  of tug  100 ; and 
     C=Distance between main landing gear  306  and  308  along line  304 . 
       FIG. 6B  shows airplane  202  with its nose landing gear wheels  204  turned by an angle α, in response to airplane pilot steering using tiller  206  producing corresponding rotation of turret  125  relative to the chassis  102  of tug  100 . Controller  119  causes rotation of tug steerable wheels  104 ,  106 ,  108  and  110  in order to cause reoriention of the tug  100  such that a goes to zero, as described hereinabove with reference to  FIGS. 3A-3E . Controller  119  also controls the motion of the tug  100  such that Ackerman steering of the airplane  202  is produced, as illustrated in  FIG. 6B , in accordance with the following parameters: 
     R+C/2=instantaneous radius of rotation of airplane  202 ; 
     α=angle of rotation of the nose landing gear wheels  204  relative to the longitudinal axis  220  of the airplane  202 ; and 
     β i =Steering angle of the wheels of tug  100  (i=104, 106, 108 and 110). 
     Preferably, the calculation of β i  as a function of α is as follows:
 
 L/[R+C/ 2]=tan α&gt;&gt;&gt;&gt; R=L /tan α− C/ 2
 
tan β 108   =[L−A/ 2 cos α− B/ 2 sin α]/[ L /tan α+ A/ 2 −B/ 2 sin α]
 
tan β 110   =[L−A/ 2 cos α+( A/ 2 tan α+ B/ 2)sin α]/[ L /tan α+( A/ 2 tan α+ B/ 2)cos α]
 
tan β 104   =[L+A/ 2 cos α+ B/ 2 sin α]/[ L /tan α−λ/2 +B/ 2 sin α]
 
tan β 106   =[L+A/ 2 cos α−( A/ 2 tan α+ B/ 2)sin α]/[ L /tan α−( A/ 2 tan α+ B/ 2)cos α]
 
       FIG. 6C  illustrates the operation of tug  100  in accordance with a preferred tug steering algorithm whereby the tug  100  is reoriented relative to the airplane  202  such that α is zero. As noted above with reference to  FIGS. 3A-3E , controller  119  reorients the tug  100  by rotating steerable tug wheels  104 ,  106 ,  108  and  110  as described hereinabove so as to reduce the angle α, sensed by rotation sensor  145 , to zero. Controller  119  is preferably operative to cause orientation of the tug  100  such that the instantaneous radius of rotation, R+C/2, of the tug-towed airplane  202  is identical to the instantaneous radius of rotation R+C/2 of the airplane  202 , itself, such that in the embodiment of  FIGS. 3A-3E , the pilot of the airplane steers the airplane in the same way whether or not it is pulled by the tug  100  or proceeds under its own power. 
     It will be appreciated by persons skilled in the art that the present invention is not limited by what has been particularly shown and described hereinabove. Rather the invention includes both combinations and subcombinations of various features described hereinabove as well as modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not in the prior art.