EP1552355A1 - Systeme de maintien de position de vehicule - Google Patents

Systeme de maintien de position de vehicule

Info

Publication number
EP1552355A1
EP1552355A1 EP02750141A EP02750141A EP1552355A1 EP 1552355 A1 EP1552355 A1 EP 1552355A1 EP 02750141 A EP02750141 A EP 02750141A EP 02750141 A EP02750141 A EP 02750141A EP 1552355 A1 EP1552355 A1 EP 1552355A1
Authority
EP
European Patent Office
Prior art keywords
vehicle
formation
rate
maneuver
commanded
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP02750141A
Other languages
German (de)
English (en)
Inventor
Christine Haissig
Paul Samanant
Dale Enns
Eric Euteneuer
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Honeywell International Inc
Original Assignee
Honeywell International Inc
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Honeywell International Inc filed Critical Honeywell International Inc
Publication of EP1552355A1 publication Critical patent/EP1552355A1/fr
Withdrawn legal-status Critical Current

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Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • G05D1/104—Simultaneous control of position or course in three dimensions specially adapted for aircraft involving a plurality of aircrafts, e.g. formation flying

Definitions

  • the present invention relates to position keeping and, more particularly, to position keeping for vehicles traveling in formation.
  • C-130 and KC-135 military transport aircraft frequently travel in formation.
  • the C-130 is a medium-range, tactical airlift aircraft designed primarily for transporting personnel and cargo.
  • the KC-135 is an aircraft dedicated to air refueling, it also flies command post and reconnaissance missions.
  • other aircraft such as the B-52, the B-2, the B-l, the C-17, and the C-141 also fly in formation.
  • FIG 1 A typical in-trail position keeping formation is illustrated in Figure 1.
  • the formation consists of multiple three-aircraft cells.
  • the wings follow their cell leader, while each of the cell leaders follows the leader of the cell that immediately precedes it in the formation.
  • three cells are illustrated in Figure 1, formations of thirty cells or more are possible.
  • other types of formations are possible.
  • a box formation is illustrated in Figure 2, and a fluid trail formation is illustrated in Figure 3.
  • the box formation is formed from two cells of aircraft flying in line-abreast formation.
  • the follower wing aircraft stay along a fixed radius of the leader, never passing forward of the leader, and avoiding the position directly behind the leader.
  • VFR visual flight rules
  • IFR instrument flight rules
  • the first type is a commanded maneuver involving, for example, speed, heading, and/or altitude changes to the aircraft trajectory as the aircraft performs position keeping missions.
  • a drop command is a commanded maneuver to initiate drops of cargo or personnel. Commanded maneuvers can be either simultaneous or sequential, depending on the type of maneuver and mission requirement. For example, speed changes should always be simultaneous, while altitude changes can be either simultaneous or sequential. Both leader and follower aircraft perform commanded maneuvers.
  • the second type of maneuver is a position keeping maneuver.
  • Follower aircraft perform position keeping maneuvers in order to maintain a desired relative position to the leader aircraft or other aircraft in the formation.
  • Position keeping maneuvers can be performed alone, or in conjunction with commanded maneuvers. For example, during a commanded turn, the follower attempts to maintain the desired separation with the leader while simultaneously executing the commanded turn maneuver.
  • a typical formation flight might proceed with the aircraft initially taking off at fixed intervals and climbing to 2000 feet or the lowest altitude to clear the terrain. During this interval, each of the aircraft joins the formation. Following formation, the aircraft then climb at 180 knots to 20,000 feet. The aircraft cruise at 20,000 feet and at 190 knots making speed, heading, and altitude changes as required in order to reach a designated location such as a drop point. If the mission is to drop personnel or cargo, the aircraft typically slow to 125 knots for a personnel drop and 130 knots for a cargo drop and descend simultaneously to the drop altitude, which usually ranges from 700 feet to 1500 feet above the ground depending upon whether the drop is a personnel drop or a cargo drop. The exact altitude is selected based on the highest terrain within five miles of the formation centerline.
  • the lead aircraft provides its drift angle ten to fifteen minutes from the drop zone so that the follower aircraft can compensate for the difference between heading and track angle.
  • the drift angle is the angle between the aircraft's heading and the aircraft's actual ground track.
  • the drift angle is required so that the aircraft can fly the same ground track over the Earth.
  • the follower aircraft calculate the lateral offset required to compensate for the drift, and input this offset into the position keeping equipment.
  • the follower aircraft reset their lateral offset to the nominal value, all aircraft climb to 20,000 feet, and all aircraft accelerate to 180 knots. During such cruising, speed, heading, and altitude changes may be required during the return to base.
  • the aircraft formation longitudinal spacing is changed to 6000 feet.
  • the aircraft land about 60 seconds apart.
  • Some of the changes that can occur while the aircraft are en route include rerouting, a change in drop zone, a change in leader, and a change in formation as members leave the formation and others move up.
  • Current position keeping systems use radar to measure the actual relative positions in the formation and use this relative position measurement to maintain the desired relative positions in the formation.
  • Such systems can be unreliable, expensive, and do not take advantage of data from on-board navigation systems for position keeping. Also, they do not use wind direction in maintaining position in the formation. Therefore, these systems cannot automatically fly a track instead of a heading. Also, current position keeping systems cannot combine some maneuvers, such as altitude changes and turns .
  • a method of keeping position of a vehicle in a vehicle formation comprises the following: acquiring a track velocity input; acquiring a formation position error input; and, determining a velocity output for the vehicle based on the track velocity input and the formation position error, wherein the velocity output indicates a velocity required to maintain the vehicle in the vehicle formation.
  • a method of keeping a position of a vehicle in a vehicle formation comprises the following: receiving leader information over a communication link; acquiring relative position information from a relative position measurement system; selecting at least one of the leader information and the relative position information so as to provide selected information; and, determining guidance corrections based on the selected information, wherein the guidance corrections indicate corrections that are required to place the vehicle in the vehicle formation.
  • a method of keeping position of a follower in a vehicle formation comprises the following: acquiring a rate of the vehicle; converting the vehicle rate to a directional vehicle rate; acquiring a directional formation position error rate dependent upon an error in the position of the vehicle in the vehicle formation; determining a desired vehicle rate based on the directional vehicle rate and the directional formation position error rate, wherein the desired vehicle rate indicates a rate required to maintain the vehicle in the vehicle formation; converting the desired vehicle rate to a vehicle acceleration input; acquiring a commanded acceleration; and, determining guidance corrections for the vehicle based on the vehicle acceleration input and the commanded acceleration, wherein the guidance corrections indicate guidance corrections required to maintain the vehicle in the vehicle formation and to respond to the commanded acceleration.
  • a method of keeping position of a vehicle in a vehicle formation comprises the following: receiving a track velocity input comprising track, Xt r a c , and Yt r ac k /" receiving a commanded maneuver comprising V dott rack, Xdottrack and Y d ot r ack'- and, determining guidance corrections based on the track velocity input and the commanded maneuver during position keeping only, during a simultaneous altitude change maneuver, during a simultaneous speed change maneuver, during a simultaneous turn maneuver, during a sequential altitude change maneuver, during a sequential speed change maneuver, during a sequential turn maneuver, during a simultaneous altitude and speed change maneuver, during a simultaneous altitude change and turn maneuver, during a simultaneous turn and speed change maneuver, during a simultaneous turn and altitude and speed change maneuver, during any and all pending maneuvers maneuver, during sequential altitude and speed change maneuvers, during a sequential altitude change and turn maneuver, during a sequential turn and speed
  • a method of determining a formation error vector e in a position of a vehicle with respect to a leader L in a vehicle formation comprises the following: determining a position vector ⁇ x based upon a position x v of the vehicle and a position x L of the leader; comparing the position vector ⁇ x to a desired relative position vector ⁇ x re f, wherein the desired relative position vector ⁇ x ref designates a desired relative position between the vehicle and the leader; and, determining the formation error vector e based on a result of the comparison.
  • a method of executing a sequential maneuver by a follower F following a leader L in a vehicle formation comprises the following: once the leader begins execution of the sequential maneuver, waiting to execute the sequential maneuver; during the waiting, guiding the follower to a location occupied by the leader at the time that the leader began the sequential maneuver; and, initiating execution of the sequential maneuver when the follower arrives at the location.
  • a method of keeping a position of a vehicle in a vehicle formation comprises the following: determining air mass related quantities; determining inertial related quantities; selecting one of the air mass related quantities and the inertial related quantities as selected quantities; and, determining guidance corrections based on the selected quantities.
  • a method of keeping position of a vehicle in a vehicle formation comprises the following: determining guidance corrections to execute a combined maneuver of the vehicle in the vehicle formation, wherein the combined maneuver comprises a combination of at least two simple maneuvers, and wherein the combined maneuver is commanded by a leader of the vehicle formation; and, guiding the vehicle through the combined maneuver based on the guidance corrections.
  • a method of keeping a position of a vehicle in a vehicle formation comprises the following: determining guidance corrections to execute a commanded maneuver of the vehicle in the vehicle formation and to maintain the position of the vehicle in the vehicle formation; and, displaying the guidance corrections on a primary flight display to an operator of the vehicle.
  • Figure 1 illustrates a typical in-trail position keeping formation useful in understanding the present invention
  • Figure 2 illustrates a box formation useful in understanding the present invention
  • Figure 3 illustrates a fluid trail formation useful in understanding the present invention
  • Figure 4 illustrates an overview of a position keeping guidance system in accordance with an embodiment of the present invention
  • Figure 5 illustrates the position keeping guidance law block of Figure 4 in greater detail
  • Figure 6 illustrates a simultaneous commanded altitude change maneuver useful in understanding the present invention
  • Figures 7 and 8 illustrate a commanded sequential altitude change
  • Figures 9 and 10 illustrate a commanded sequential turn
  • Figure 11 is a block diagram illustrating the position guidance law calculations performed by the position keeping guidance law block of Figures 4 and 5;
  • Figure 12 is a diagram illustrating a position keeping reference frame PK useful in performing the position guidance law calculations;
  • Figure 13 illustrates three possibilities for defining a reference heading ⁇ PK for the PK frame
  • Figure 14 illustrates a NED (north, east, down) inertial reference frame
  • Figure 15 summarizes the tracking state and maneuver track rate calculations for simple maneuvers
  • Figure 16 summarizes the tracking state and maneuver track rate calculations for combined maneuvers
  • Figure 17 illustrates vectors ⁇ x, ⁇ x raf , and e where e is a formation tracking error vector
  • Figure 18 provides a translation of the components of ⁇ x, ⁇ x r ⁇ f, and e to make their visualization easier;
  • Figure 19 illustrates a summary of guidance tracking error calculations
  • Figure 20 illustrates maneuver commands in general form as may be applied in the present invention
  • Figure 21 illustrates a primary flight display (PFD) that is operating in position keeping mode
  • Figure 22 illustrates a traffic control display (such as TCAS) modified to operate in a position keeping mode .
  • TCAS traffic control display
  • Position keeping guidance uses formation geometry, maneuver commands, and/or aircraft states in order to calculate position keeping tracking errors and to provide traffic and guidance to the pilot.
  • a position keeping guidance system 10 in accordance with an embodiment of the present invention is shown in Figure 4.
  • the position keeping guidance system 10 includes a position keeping guidance law block 12 that calculates the maneuver mode and maneuver commands for an aircraft, that calculates the track velocity and tracking position error of an aircraft, and that computes the position keeping guidance commands for display or for input to a flight management system (FMS) or autopilot of the aircraft.
  • FMS flight management system
  • the position keeping guidance law block 12 accepts leader state and maneuver command inputs from a leader state and maneuver command block 14 and formation geometry from an aircraft state and formation geometry block 16.
  • the formation geometry may be specified by the flight crew, or may be provided via a data link from the lead vehicle, another vehicle, or a ground station.
  • the aircraft state and formation geometry block 16 outputs a selected formation geometry to the position keeping guidance law block 12.
  • the position keeping guidance law block 12 computes various tracking related errors and position keeping guidance instructions, and provides these to a traffic and guidance display block 18 that displays the necessary errors and instructions to a pilot 20 so that the pilot 20 can maintain the aircraft 22 in its correct position within the formation.
  • the output of the position keeping guidance law block 12 can be supplied directly to an FMS or automatic pilot 24 so that adjustments can be made automatically to maintain the aircraft 22 in its correct , formation position.
  • FIG. 5 illustrates the position keeping guidance law block 12 of Figure 4 in additional detail.
  • the position keeping guidance law block 12 includes a maneuver mode and maneuver command calculation block 30, a track velocity and tracking position error calculation block 32, and a position keeping guidance command calculation block 34 each of which receives aircraft state and formation geometry information from the aircraft state and formation geometry block 16.
  • the maneuver mode and maneuver command calculation block 30 receives the maneuvers commanded by the leader from the leader state and maneuver command block 14, and the track velocity and tracking position error calculation block 32 receives the leader state information from the leader state and maneuver command block 14.
  • the position keeping guidance command calculation block 34 supplies the tracking related errors and position keeping guidance instructions to the traffic and guidance display block 18 and/or to the FMS or automatic pilot 24.
  • the formation aircraft are or are not performing commanded maneuvers, they are maintaining a formation geometry.
  • the follower aircraft are responsible for monitoring their positions relative to the leader aircraft and for making the necessary guidance adjustments, which can be done visually or with the aid of a traffic or guidance display.
  • speed v is used to compensate for longitudinal errors
  • bank angle ⁇ is used to compensate for lateral errors
  • flight path angle ⁇ is used to compensate for vertical errors.
  • Commanded maneuvers generally fall into two categories - simultaneous maneuvers and sequential maneuvers.
  • Simultaneous commanded maneuvers are maneuvers where the leader and follower initiate the maneuver at the same time. For example, speed, heading, and altitude changes may be made simultaneously.
  • each pilot is required to adjust the throttle and angle of attack or to input a speed command in order to track the new commanded speed.
  • Each follower pilot is responsible for monitoring the lateral and longitudinal tracking errors with respect to the leader and monitoring altitude to ensure that the formation geometry remains constant.
  • a simultaneous commanded altitude change maneuver is illustrated in Figure 6.
  • the leader and follower aircraft initiate the altitude change at the same time, tracking to a predetermined climb or descent rate.
  • the follower aircraft adjust their speeds and bank angles to maintain the longitudinal and lateral formation separations.
  • Simultaneous commanded turns typically have not in the past been performed by military transport aircraft because it is more difficult to maintain the formation geometry during a simultaneous turn. These aircraft .have instead performed commanded turns sequentially. However, to perform a commanded turn simultaneously, the leader aircraft turns to a predetermined bank angle and the follower aircraft maintain their longitudinal positions by speeding up or slowing down depending on whether the follower aircraft are on the outside or inside of the turn. Bank angles may be used to perform the turn and to compensate for any lateral position errors. Both the leader and the follower aircraft also track to the appropriate altitude. Combined simultaneous commanded maneuvers can also be performed.
  • Sequential commanded maneuvers are maneuvers that the follower aircraft perform after the leader aircraft.
  • the leader initiates the commanded sequential maneuver, and the follower aircraft wait a predetermined amount of time so that they can initiate the same commanded maneuver at the same longitudinal location where the leader aircraft initiated that same maneuver.
  • a commanded maneuver of a follower is pending from the time that the leader initiates the sequential commanded maneuver until the follower reaches the location at which the leader initiated the sequential commanded maneuver.
  • a commanded sequential altitude change is illustrated in Figure 7.
  • the formation geometry changes.
  • the leader is climbing and the follower maneuver is pending (i.e., the delay time t de iay has not completely elapsed)
  • the delay time t de iay has not completely elapsed
  • the leader is getting closer longitudinally. That is, because the longitudinal component of speed decreases during the climb, the leader and follower are flying to different longitudinal components of speed.
  • the longitudinal relative position increases again because the follower is into its climb.
  • the leader climbs while tracking to a predetermined climb rate.
  • the follower initiates its climb, it tracks to the same predetermined climb rate.
  • the follower has the additional task of maintaining the appropriate longitudinal and lateral separation. The lateral separation is tracked as for a simultaneous altitude change, and errors are compensated for with bank angle corrections.
  • the longitudinal separation cannot be tracked as for a simultaneous altitude change. As mentioned previously, the longitudinal separation changes as the leader and follower maneuvers progress. Instead of tracking to the current position of the leader, the follower can track to the delayed or ghost position of the leader, as illustrated in Figure 8.
  • the ghost leader is next to the follower so that, when tracking the ghost position of the leader, the follower keeps the longitudinal relative position to zero.
  • a commanded sequential turn maneuver is performed as follows.
  • the leader initiates its turn by banking to a predetermined bank angle until the desired heading or track angle is reached.
  • the follower waits a delay time t de iay to start the turn maneuver at the same longitudinal location that the leader was in when the leader started its turn maneuver.
  • the goal during the sequential turn is for the leader and follower aircraft to follow concentric arcs, as shown in Figure 9.
  • the follower banks to a bank angle that is smaller (or larger) than the predetermined bank angle that the leader uses in order to compensate for being on the inside (or outside) of the turn.
  • the follower also decreases (or increases) speed to compensate for being on the inside (or outside) of the turn.
  • the longitudinal separation between the leader and follower is specified as a separation distance.
  • the longitudinal separation between the leader and follower could also be specified in terms of a separation time ⁇ t n om.
  • ⁇ t nom can be converted to an equivalent separation distance by multiplying it by the follower's commanded speed.
  • the delay time t de ⁇ ay is the same as ⁇ t nom -
  • the position keeping guidance law block 12 calculates guidance commands for display to the pilot based on formation tracking position error and track velocity.
  • the guidance commands can also be automatically provided to the flight management system (FMS) or autopilot.
  • the purpose of the position keeping guidance system 10 is to provide guidance so that the pilot can perform mission- maneuvers while maintaining the desired formation geometry.
  • the calculation of the position keeping guidance commands uses a technique called dynamic inversion.
  • Figure 11 is a block diagram illustrating the position guidance law calculations performed by the position keeping guidance law block 12.
  • the primary input is the track velocity comprising the ground speed vtr ac / the track angle ⁇ rackr the flight path angle Ytack/ and the formation guidance tracking position error e NED .
  • NED designates a North, East, and down reference frame.
  • the track velocity is dependent upon information supplied by or about the leader and any maneuver commands. This information may be supplied over a communication link from the leader, from another aircraft, or from a ground station, and/or by an on-board relative position determining system such as radar, TCAS, etc.
  • the formation tracking position error e NED is calculated using the relative position between the leader and follower, the formation geometry, and the commanded altitude.
  • the relative position between the leader and follower can be provided by a relative position determining device or calculated using the leader position and follower position, or calculated using a combination of the two.
  • the source of the information is usually the on-board navigation system, which could be an inertial navigation system (INS) , a global positioning system (GPS) -based navigation system, or a combined GPS/INS or other system.
  • the navigation data could be augmented by other on-board system data, such as air data, as needed.
  • the leader data could be linked directly to the followers, be linked via other aircraft, or be linked through a ground station.
  • the commanded maneuvers can be specified in terms of either air speed or ground speed, either heading or track angle, and/or either geometric or barometric altitude, and converted as needed.
  • the ground speed v tra ckf the track angle Xt ack , and the flight path angle Ytrac are used by a block 40 to calculate a North position rate ⁇ o t an East position
  • ⁇ do 11 Xtrack COS (Ytrack) Sin (Xtrack) (2)
  • An adder 42 adds the North position rate ⁇ dot the East
  • ⁇ ot d ⁇ dot fc + K ⁇ e ⁇ ( 5 )
  • the North tracking error rate K ⁇ e ⁇ , the East tracking error rate K ⁇ e ⁇ , and the vertical tracking error rate K h ⁇ h are supplied by a gain block 44 based on the formation tracking error e NED .
  • the gains K ⁇ , ⁇ ⁇ , and K h may be 0.25 rad/s, 0.25 rad/s, and 0.125 rad/s, respectively.
  • the formation errors e ⁇ , e n , and e h are the North, East, and down components of e NED .
  • the position error rates ⁇ do t d , ⁇ ot d , and h do t d are input into the inverted dynamic equations implemented by a block 46 in order to calculate the ground speed v c , track angle ⁇ c , and flight path angle ⁇ c that are required to follow the desired ground speed, track angle, and geometric altitude while at the same time maintaining the formation geometry.
  • the block 46 implements dynamic inversion by calculating the ground speed v c , track angle ⁇ c , and flight path angle ⁇ c according to the following equations:
  • the quadrant checks in equations (8) and (10) are necessary to prevent the aircraft from turning in order to slow down.
  • the aircraft should use speed only if it is too close longitudinally; it should not use bank angle or a combination of speed and bank angle if it is too close longitudinally.
  • the ground speed v c , the track angle ⁇ c , and the flight path angle ⁇ c represent the state that the aircraft should be following in order to simultaneously maintain the formation shape and follow the track velocity.
  • a summer 48 subtracts the current ground speed v, the current track angle x, and the current flight path angle ⁇ from the required states v c , ⁇ c , and ⁇ c calculated by the block 46.
  • the current ground speed v, the current track angle ⁇ , and the current flight path angle ⁇ are provided by the on-board navigation system.
  • Gains K v , K x , and K Y are applied by a gain block 50 to the results of these subtractions and are limited by a limiter 52 in order to produce a ground speed rate V ot a track rate Xdot and a flight path angle rate Ydot 1 according to the following equations:
  • K v , K x , and K Y may have values, for example, of 0.5 rad/s, 0.25 rad/s, and 0.5 rad/s, respectively. If the current ground speed v, the current track angle ⁇ , and the current flight path angle ⁇ are the same as the required states v c , ⁇ c , and ⁇ c , then dot XdotS and Ydot* will be zero.
  • the speed rate Vot the heading or track rate dot 12 / and the flight path angle rate Ydot* are added to the commanded maneuver speed rate ottrac k / the commanded maneuver track rate Xdott r ack r and the commanded maneuver flight path angle rate Ydottrack by an adder 54 according to the following equations:
  • Vdot V ot + Vdottrack (15)
  • the commanded maneuver speed rate v do ttrack the commanded maneuver heading or track rate Xott r acr and the commanded maneuver flight path angle rate Ydottrack comprise commanded maneuver accelerations, which may be supplied by the leader over a communication link to its followers, and are zero during nominal position keeping but can be nonzero if a commanded maneuver, such as a speed change, a turn, or an altitude change, is commanded.
  • a commanded maneuver such as a speed change, a turn, or an altitude change
  • Xdot d / and Ydot d are passed to the autopilot or are used to calculate display outputs, they are limited by a limiter 56.
  • the limits on the commanded accelerations could be constants or they could be calculated using a dynamic model for the aircraft.
  • the limits on the commanded accelerations Vdot d / dot d / and Yot d are calculated using a model of the autopilot and expected performance limits on the bank angle ⁇ , the thrust T, and the angle of attack .
  • the aircraft equations of motion are given by the following equations:
  • ⁇ c tan _1 (v cos ( ⁇ ) ⁇ dot d ) / (v Ydot + g cos ( ⁇ ) ) (21)
  • T c (m v do t d + D + g sin ( ⁇ ) ) /cos ( ⁇ c )
  • tan( ⁇ c ) ( (m v ⁇ do t d + m g cos (y) ) /cos ( ⁇ c ) - L) / (m v dot d + D + m g sin( ⁇ ) ) (23)
  • q dynamic pressure available from an air data system
  • S surface area of the wing
  • C L is the coefficient of lift
  • C D is the coefficient of drag
  • C L ⁇ 0 is the lift curve y intercept
  • C L ⁇ is the lift curve slope
  • Co m i ⁇ is the drag polar minimum
  • K is the drag polar coefficient
  • attack ⁇ are or min _ limit and ⁇ max -iimit - Let it further be
  • ⁇ c is calculated from equation (21)
  • ⁇ c is outside the bank angle limits of ⁇ m n-iiit and ⁇ max - ⁇ i t it may be assumed that the bank angle limit is exceeded due to an excessive desired track angle rate (i.e., turn rate) Xot d rather than to an excessive climb rate Ydot d -
  • the turn rate Xdot d is calculated by rearranging equation (21) and by substituting ⁇ im for ⁇ according to the following equation:
  • ⁇ c is calculated using equation (21) with Xdot d as given above according to the following equation:
  • ⁇ c tan _1 (v cos ( ⁇ ) ⁇ do t d ) / (v ⁇ do t d + g cos (y) ) ( 32 )
  • ⁇ c ' ( (m v ⁇ dot d + m g cos (Y) ) /cos ( ⁇ c ) -
  • Equation (18) can be solved for the limited acceleration v dot d using equations (25), (26), and (27), where c is substituted for and T ⁇ m is used for T to produce the following equation:
  • T ⁇ m n- ⁇ m t t J-c " ⁇ Tmin-li it
  • dynamic pressure q is provided by the air data computer.
  • the mass m is determined as W/g, where W is a default weight of the aircraft.
  • the commanded accelerations v do t d / Xdot d / and Yot d represent the corrections that are necessary to maintain formation and track state and to implement any commanded maneuver.
  • the commanded accelerations v do t d / Xo d ; and Y do d as limited by the limiter 54, and the vertical position rate h dot fc from the block 4T j , are passed to the guidance display 18 or they may be passed to the autopilot 24 for automatic corrections.
  • the commanded accelerations v dot d / Xdot d and ⁇ do t d as limited by the limiter 54 are also supplied to a block 58 for calculation of other display outputs .
  • a commanded speed guidance v c and a commanded flight path angle guidance ⁇ c are calculated by integrating v do t d and Ydot d according to the following equations :
  • commanded bank angle guidance ⁇ c , thrust T c , and angle of attack ⁇ c are calculated according to equations (21), (22), and (23) .
  • the commanded accelerations v do t d / Xdot d / and Ydot / the bank angle guidance ⁇ c , the thrust guidance T c , the angle of attack guidance ⁇ c , the ground speed guidance v c , and the flight path angle guidance ⁇ c ( Figure 11) can be combined with the maneuver commands (the commanded track angle ⁇ CO m or the commanded heading ⁇ CO the commanded ground speed v com or the commanded air speed vas com , and the commanded geometric altitude h COm or the barometric altitude hbaro com ) , the lateral, longitudinal and vertical deviations from the leader position or commanded altitude e d is / the track climb rate hot 1 / and other information in order to provide guidance to
  • the calculation of the displayed tracking error command e d i S p is described below.
  • a description of how the display outputs can be used to fly position keeping missions There are a number of possible outputs from the position keeping guidance law block 12. These outputs may be used in different ways, depending on how the position keeping mission and maneuvers are flown.
  • a pilot has three options when flying, which are referred to herein as flight modes.
  • flight modes In general, a pilot has three options when flying, which are referred to herein as flight modes.
  • the pilot flies manually using guidance cues to track the desired speed, heading, and altitude while also maintaining the formation shape.
  • Second, in the autopilot select mode, speed, heading, or altitude are provided to the autopilot or autothrottle which controls the speed of the aircraft automatically.
  • each of these flight modes can be used for any combination of the turn, speed change, and altitude change maneuvers. How each maneuver will be flown depends on the equipment of the aircraft, flight crew preferences, and aircraft role. For example, an aircraft that does not have an autothrottle cannot command speed in the autocoupled flight mode. Similarly, an aircraft in the leader role may be flying the maneuvers using the autocoupled flight mode while a follower tracks using the flight director. Currently, most position keeping maneuvers are flown manually.
  • the position keeping guidance display can be used for both manual flight and to provide the necessary values for the autopilot during autopilot select flight. It may also be useful during autocoupled flight to maintain situational awareness.
  • the guidance display (s) can include one or more of the following: the longitudinal formation tracking error component of e d i SP/ the ground speed guidance v c , and the acceleration guidance v do t d -
  • the guidance display (s) can include one or more of the following: the lateral formation tracking error component of e d i Sp/ the bank angle guidance ⁇ c , and the commanded track angle, x com or commanded heading ⁇ COm -
  • the guidance display (s) can include one or more of the following: the commanded altitude h CO m/ the target climb rate hot and the flight path angle guidance ⁇ c . Which variables will be displayed depends on pilot preferences and display limitations. If desired, the inertial quantities can be converted to air mass referenced quantities. For example, the ground speed guidance v c can be converted to an air speed guidance.
  • the pilot In the autopilot select flight mode, the pilot flies by providing commands to the autopilot and/or autothrottle.
  • the pilot can manually input the ground speed guidance v c (or converted air speed guidance) from the guidance display.
  • the pilot could input the commanded heading ⁇ com or the commanded track angle ⁇ com into the autopilot.
  • the pilot can input a heading or track angle to make the aircraft match the commanded bank angle guidance ⁇ c .
  • the bank angle or turn rate cannot be specified in addition to the commanded heading and track angle.
  • the follower cannot track perfectly during a turn when using the autopilot for lateral guidance.
  • the pilot inputs the commanded altitude h com into the autopilot.
  • the target climb rate or flight path angle guidance may also be specified.
  • the automatic guidance could be provided to the autopilot directly or through the FMS as follows: longitudinal/speed guidance can be provided to the autothrottle by v c ; lateral guidance can be provided to the autopilot by ⁇ c ; and, vertical guidance can be provided to the autopilot with h c and hdot 1 (or the equivalent flight path angle ⁇ c ) .
  • the interface details depend on each autopilot or FMS implementation.
  • the track velocity (v tra ck/ Xtrack/ and Ytrack) / the commanded maneuver track rates (v do ttrack/ Xdottrack/ and Ydottrack) / and the formation tracking error (e) are inputs to the position guidance law calculations performed by the position keeping guidance law block 12.
  • the track velocity, the commanded maneuver track rates, the formation tracking error, and other variables need to be expressed with consistent reference frames and clear definitions relative to the formation geometry.
  • Military transport aircraft in formation fly with respect to the leader.
  • the nominal formation separation distance is defined as vector ⁇ x nom (with components ⁇ x nom ,
  • this vector represents the formation separation distance that is desired during nominal position keeping and commanded simultaneous maneuvers.
  • this distance vector should be defined with respect to a reference frame.
  • the reference frame for this purpose is called the position keeping reference frame and is denoted () p ⁇ .
  • the position keeping reference frame is centered on the follower and its x axis is along a reference angle designated as ⁇ PK , which is measured clockwise from North.
  • the nominal longitudinal separation ⁇ x nom p ⁇ is defined as the distance between the leader and follower along the position keeping frame x axis (x p ⁇ ) . This distance is defined as positive if the leader is ahead of the follower.
  • the nominal lateral separation ⁇ y ⁇ m PK is defined as the distance between the leader and follower along the PK frame y axis (y p ⁇ ) . This distance is defined as positive if the leader is to the right of the follower.
  • the nominal vertical separation ⁇ z n0m PK is defined as the distance between the leader and follower along the PK frame z axis (z p ⁇ ) . This distance is defined as positive if the leader is below the follower.
  • the definition of the reference heading ⁇ PK for the PK reference frame is important. Figure 13 illustrates three possibilities: using the leader heading
  • ⁇ PK ⁇ F
  • the tracking errors are referenced along the heading of the follower aircraft.
  • ⁇ PK ⁇ Fref/ the tracking errors are referenced to the heading that the follower should be tracking.
  • ⁇ PK ⁇ / the tracking errors are referenced to the heading that the leader is tracking.
  • ⁇ P K ⁇ Lef/ the tracking errors are referenced to the heading that the leader should be tracking.
  • ⁇ PK ⁇ L
  • ⁇ PK ⁇ ref
  • Definition (1) is used in current position keeping systems.
  • Using definition (2) eliminates the variation in the lateral and longitudinal tracking errors that come with small changes in heading as the follower maneuvers to maintain the formation shape.
  • Definition (3) requires knowledge of the leader's heading.
  • Using definition (4) eliminates the variation in the lateral and longitudinal tracking errors that arise with small changes in heading as the leader maneuvers.
  • Definition (4) requires knowledge of the leader's intended heading, and is frequently the same as definition (2) because the leader and follower usually track the same reference heading.
  • Definition (5) requires knowledge of the follower's track angle.
  • definition (6) eliminates the variation in the lateral and longitudinal tracking errors that come with small changes in track as the follower maneuvers to maintain the formation shape.
  • Definition (7) requires knowledge of the leader's track angle.
  • definition (8) eliminates the variation in the lateral and longitudinal tracking errors that come with small changes in track as the follower maneuvers to maintain the formation shape, and requires knowledge of the leader's intended track angle.
  • definition (2) or definition (6) is used depending on whether the aircraft are tracking to a commanded heading or to a commanded track angle.
  • a fixed reference that is independent of the variations in heading of the leader or follower, cleaner tracking can be expected.
  • using these definitions should be beneficial during formation join-up.
  • definition (3) or definition (7) is instead used depending on whether the aircraft are tracking to a commanded heading or to a commanded track angle. If the leader track or heading angle is not available, it can be estimated based on the time the maneuver started and the desired turn rate.
  • definition (3) or definition (7) is used depending on whether the aircraft are tracking to a commanded heading or to a commanded track angle.
  • the other reference frame that is used frequently is the North East Down (NED) reference frame.
  • NED North East Down
  • the formation tracking error e NED that is input into the position keeping guidance laws at the gain block 44 as shown in Figure 11 is expressed in the NED frame.
  • the NED frame is an inertial reference frame, with the x-axis along North, the y-axis along East, and the z-axis pointing down. It is the reference frame in which GPS velocity is often represented.
  • the track errors may be transformed to the NED frame prior to being input to the guidance equations described above in relation to Figure 11. In the dynamic
  • the PK frame is the frame used to compute the lateral, longitudinal, and vertical tracking errors.
  • the x-axis and the y-axis are in a locally level plane, and the z-axis is down.
  • the angle between the x- axis of the PK frame and the x-axis of the NED frame is ⁇ PK
  • the PK frame is related to the NED frame by rotation about the z NED by ⁇ P ⁇ -
  • the track velocity and maneuver track rate calculations are summarized in Figure 15 for simple maneuvers and in Figure 16 for combined maneuvers.
  • the subscript "com” designates a commanded value
  • the subscript "dotcom” designates a time derivative of a commanded value.
  • the commanded values are transmitted to the followers by the leader, by another aircraft, or by a ground station.
  • the time derivatives may be transmitted by the leader, may be input by the followers, or may be a system default.
  • Xdottrack is calculated from a default bank angle ⁇ COm and a commanded ground speed v com .
  • Simple maneuvers are individual maneuvers, like a speed change or a heading change or an altitude change. Combined maneuvers are combinations of simple maneuvers.
  • the track velocity components are v track/ Xtrack/ and Ytrack-
  • the values of the track velocity depend on whether the commanded maneuvers are simultaneous or sequential, and whether a sequential maneuver is pending or executing.
  • v tE ack is the commanded ground speed v com .
  • v tr ac k is the leader ground speed v L that is provided over a communication link.
  • v rack is the leader ground speed v rack.
  • tdeiay ⁇ X nom ( t s tartman) Vcom ( tstartman) ( 48 ) and where t star t m a n i the time at which the leader starts the maneuver and ⁇ x nom P is the longitudinal formation separation. If the longitudinal formation spacing is specified as the time ⁇ t n0 m / then
  • ⁇ y n0m PK is zero, and there is no speed adjustment. Since the leader is expected to turn to a predetermined bank angle ⁇ COm/ there is no need to transmit the leader bank angle, and ⁇ v tU rn is given by the following equation:
  • vtum ⁇ y n0 m PK g tan (turn_direction* ⁇ com ) /v ( 51 )
  • ⁇ Vtum ⁇ y nom p ⁇ g tan(turn_direction* ⁇ CO m) /v L (t - tdeiay) (52)
  • the track angle Xtrac is set to the commanded track angle ⁇ com when the aircraft is not executing a commanded turn maneuver or a drop maneuver.
  • the track angle is the leader track angle as given by the following equation:
  • the track angle is the delayed leader track angle as given by the following equation:
  • ⁇ tr ack X w ayp o i nt
  • X aypoint is given by the following equation :
  • the flight path angle ⁇ tr ack is nonzero during altitude change maneuvers and, for simple maneuvers, is calculated from the commanded climb or descent rate h dotcom and the commanded speed v COm according to the flowing equation:
  • the commanded maneuver track rates are the feedforward information that is input to the summer 54 in order to improve tracking performance for commanded maneuvers.
  • the predetermined commanded acceleration v do tcom is provided as an input.
  • the predetermined commanded track angle (turn) rate X otcom is provided as an input.
  • the leader and follower should have the same turn rate.
  • the turn rate Xdot can be expressed according to the following equation:
  • Xdotcom tan(turn_direction* ⁇ CO m) (v L ⁇ do tL + g cos ( ⁇ L ) / (v L cos ( ⁇ L ) ) (59)
  • the formation tracking error e is the error between the aircraft position and the desired aircraft position.
  • the relative position between the leader and the follower aircraft in the formation is calculated as
  • the formation tracking error vector e is calculated as
  • ⁇ x re f is the desired relative position vector between the aircraft and the leader.
  • the vectors ⁇ x, x r e f/ and e are illustrated in Figure 17.
  • the leader is too far ahead and to the left for the desired formation geometry.
  • the follower is too far behind and to the right.
  • Figure 18 translates the components of these vectors into directions to make visualization easier, assuming that the vectors are represented in the position keeping reference frame.
  • Figure 19 summarizes the guidance tracking error calculations.
  • the relative position is calculated by determining the difference between the leader and follower positions.
  • the relative position is calculated using the position of the leader at the start (t star tman) of its corresponding maneuver.
  • the relative position is computed using the delayed leader position.
  • the reference relative position vector ⁇ x raf in the formation geometry is the same as the nominal relative position vector ⁇ x nom (which is composed of the components ⁇ x n ⁇ m/ ⁇ y n ⁇ m/ and ⁇ z nom ) when there are no pending maneuvers or there are no simultaneous maneuvers being executing.
  • the ⁇ x ⁇ om component of the reference longitudinal relative position vector ⁇ x ref is calculated using the vehicle position and the position of the leader at the start of the maneuver, as given by the following equation:
  • a pending maneuver designates the waiting of the follower before the follower begins its part of a sequential maneuver that was previously started by the leader. For executing sequential commanded maneuvers
  • the formation tracking error vector used by the guidance calculations is e 1 TM 0 , which is calculated from the vector e p ⁇ by a coordinate transformation that is discussed above in relation to Figure 14.
  • the lateral tracking error e y is always calculated using the following equation:
  • the longitudinal tracking error e x is calculated using the following equation: PK _ ⁇ x PK PK
  • the longitudinal tracking error e x is zero because tracking is based only on speed, not on a longitudinal position. Accordingly, during a pending maneuver, while the follower is waiting to execute a commanded maneuver, the follower is guided to the exact longitudinal location where the leader started that maneuver. If there are no commanded altitude changes, the vertical tracking error e z is computed using the current altitude and commanded altitude as given by the following equation:
  • the vertical tracking error e z is zero since tracking is based only on vertical rate, not on vertical position.
  • the position keeping reference angle ⁇ PK is set to the commanded track or heading angle if there are no commanded turns or drop maneuvers executing.
  • ⁇ P ⁇ is set to the leader heading or track angle.
  • ⁇ PK is set to the delayed leader heading or track angle.
  • ⁇ P ⁇ ⁇ waypoint-
  • maneuver commands may take the general form shown in Figure 20.
  • the default acceleration, bank angle, and climb or descent rate could be set by the crew, transmitted by the leader, or come from another source.
  • maneuvers there are a variety of maneuvers that can be commanded, and many of the position keeping guidance calculation inputs are based on the type of maneuvers being executed.
  • the position keeping guidance calculations described herein use maneuver modes that are also calculated with an associated maneuver mode logic to aid in calculating the track states, formation tracking error, and maneuver track rates.
  • the maneuver mode logic proceeds as follows:
  • displays may be used by the position keeping system 10 to convey information back to the pilots and operators.
  • These displays can reside on a variety of hardware devices.
  • the TA/VSI display is a dedicated display device that accompanies traditional TCAS systems.
  • the specific output is determined by the control unit and can include guidance cues as well as formation traffic information.
  • the position keeping system generates a wealth of information that could be displayed to the pilot.
  • This information includes the following: (i) the lateral, longitudinal and vertical deviations from the leader position or commanded altitude; (ii) the maneuver commands such as the commanded track angle ⁇ com or the commanded heading ⁇ C om / the commanded ground speed v COm or the commanded air speed vas com , and the commanded geometric altitude h CO m or the barometric altitude hbaro COm ; (iii) the track climb rate hdot ; (iv) the bank angle guidance ⁇ c , the thrust guidance T c , the angle of attack guidance cr the ground speed guidance v c , or the flight path angle guidance ⁇ c ; (v) the ground speed guidance v c converted to air speed guidance vas c ; (vi) the leader ground speed, air speed, heading, track angle, bank angle, geometric and/or barometric altitude; (vii) the relative speed between the leader
  • Guidance information can be conveyed to the pilot many different ways.
  • One approach is to use the flight director, which can be part of the primary flight display (PFD) or part of a separate attitude direction indicator (ADI) .
  • Figure 21 shows a PFD that is operating in position keeping mode.
  • Guidance cues such as speed
  • ground speed v c air speed vas c , command ground speed
  • V com/ or command air speed vas CO m) / altitude (h com or h L ) , and heading targets ( ⁇ CO m or ⁇ com ) are displayed.
  • Vertical and lateral guidance bars are available to inform the pilot of lateral and longitudinal position errors.
  • the longitudinal position error is not displayed graphically on the PFD in Figure 21 because it does not fit naturally into the framework of current PFD's. If desired, however, such graphical displays can be added to the position keeping mode of the PFD/EADI.
  • Guidance information can also be displayed on the dedicated TCAS TA/VSI display.
  • the display format may be different from that of a traditional PFD, but the equivalent information can be displayed.
  • Traffic displays provide a plan form view of other aircraft with respect to a pilot's own ship. This display may be shown on the secondary display unit of an electronic flight information system, or it may be shown as one of the display modes of the TA/VSI.
  • the default mode of operation is to have the pilot's own ship at the center of the display, although other modes may be implemented instead.
  • Symbols enable pilots to distinguish between formation aircraft and other aircraft. If an aircraft is a follower, its lead aircraft will be designated. Range rings assist pilots in determining relative horizontal ranges. Default but adjustable range scales may be provided. For vertical reference, numbers and arrows adjacent to the symbols display relative altitude and altitude rates of the other aircraft. Figure 21 shows an example of such a formation display. Miscellaneous information related to position keeping (such as the computer air release point for a drop maneuver) may also be displayed.
  • the formation can track a virtual or imaginary leader whose position or trajectory is calculated or provided by another vehicle or ground station.
  • the virtual leader desired position could be calculated based on a weighted average of the position of all vehicles in the formation. This calculation could be made so as to minimize the adjustments required to maintain a formation shape.
  • the virtual leader could be a four- dimensional trajectory (three dimensions related to position and one dimension for time points) that is provided before flight or that is datalinked from another vehicle or a ground station.
  • maneuvers discussed above include speed changes, altitude changes, turns, drop maneuvers, and combinations of the preceding.
  • present invention can be extended to include any type of maneuver that can be specified in terms of an action or actions that should be performed in conjunction with a position and/or a position change, a velocity and/or a velocity change, and/or an acceleration and/or an acceleration change.
  • the guidance logic that calculates t the thrust T c , the bank angle ⁇ c , and the angle of attack ⁇ c is based on dynamically inverting a set of equations of motion for an aircraft. Similar equations are used to calculate the limit logic of the block 56. These equations of motion do not include the effects of wind.
  • that vehicle's equations of motion would be substituted for the aircraft equations of motion, and the associated controls for the guidance block 58 would be calculated by inverting those equations of motion.
  • the equations of motion for a land vehicle are different than for an aircraft, since the principles of motion are different.
  • a land vehicle's controls would include throttle, which is analogous to thrust, and steering angle, which is analogous to bank angle, but not vertical control like flight path angle since the vehicle follows the ground.
  • the invention described above could be implemented so that each vehicle computes its own guidance corrections.
  • the guidance corrections could be calculated on the ground or on board other aircraft, and these guidance corrections could be transmitted as guidance commands via a datalink.
  • much of the above description is based on inertial quantities. However, if desired, inertial quantities can be converted easily to air mass referenced quantities. Therefore, inertial referenced quantities and air mass referenced quantities are used interchangeably herein.
  • the position keeping guidance system 10 may be implemented in software executed by a computer, in hardware such as programmable logic arrays or other digital processing circuitry, etc.
  • Each aircraft in a formation is equipped to make the calculations described above.
  • each aircraft in the formation can act as a leader and a follower. Accordingly, the description of the present invention is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the best mode of carrying out the invention.
  • the details may be varied substantially without departing from the spirit of the invention, and the exclusive use of all modifications which are within the scope of the appended claims is reserved.

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  • Engineering & Computer Science (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Radar, Positioning & Navigation (AREA)
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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
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Abstract

L'invention concerne un système de maintien de position de véhicule utilisable pour maintenir la position d'un véhicule dans une formation de véhicules, de sorte que tous les éléments de la formation volent à une vitesse et à une altitude spécifiées, et que des manoeuvres commandées soient effectuées. Ledit système détermine des corrections de guidage en fonction d'un état de route référencé par rapport à un leader ou à un leader virtuel de la formation et d'une erreur de position du véhicule dans la formation, indiquant l'erreur de position du véhicule dans la formation. Les corrections de guidage sont nécessaires pour le maintien des véhicules dans la formation.
EP02750141A 2002-07-16 2002-07-16 Systeme de maintien de position de vehicule Withdrawn EP1552355A1 (fr)

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FR2924505B1 (fr) 2007-12-04 2015-12-11 Thales Sa Methode de decouplage du mode de suivi automatique du profil lateral et du mode de suivi automatique du profil vertical
CN105912020B (zh) * 2016-05-26 2018-10-09 北京航空航天大学 一种弱稳定边界区域内航天器编队飞行方法
KR20190075221A (ko) * 2017-12-21 2019-07-01 현대자동차주식회사 차량 및 그 제어 방법
CN109324636B (zh) * 2018-10-24 2021-08-20 中北大学 基于二阶一致性和自抗扰的多四旋翼主从式协同编队控制方法
KR102903581B1 (ko) * 2020-10-30 2025-12-24 한화에어로스페이스 주식회사 무인 추종 차량
CN112678182A (zh) * 2021-01-13 2021-04-20 北京航空航天大学 一种无人机的编队回收装置及回收方法

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