AIRCRAFT GUIDANCE SYSTEM

Abstract

The present invention relates to an aircraft guidance system (102i), comprising: - an external constraint calculation module designed, for at least one obstacle (102m), to define an envelope (E'm) surrounding the obstacle (102m), and calculate an external constraint for bypassing the envelope (E'm); and - a predictive control module designed to implement predictive control while respecting the external constraint.The definition of the envelope (E'm) used for calculating the external stress includes: - a definition of an initial envelope (Em) surrounding the obstacle (102m); - obtaining a relative velocity (Δv) of the aircraft (102i) with respect to the obstacle (102m); and - at least when the aircraft (102i) approaches the obstacle (102m), an enlargement of the initial envelope (Em) along at least one direction (DΔv) of the relative velocity (Δv) to obtain the envelope (E'm) used for calculating the external stress, the enlargement being greater the higher the absolute value of the relative velocity (Δv). Figure for the abbreviation: Fig. 3.

Description

Title of the invention: AIRCRAFT GUIDANCE SYSTEM Technical field of the invention

[0001] The present invention relates to an aircraft guidance system, in particular a fixed-wing aircraft, such as an airplane, an aircraft comprising such a guidance system, a formation of such aircraft and a method of guiding an aircraft. Technological background

[0002] The article "Safe formation control using constrained linear model predictive control", by P. Feyel, ICINCO, 2020 (hereafter referred to as FEYEL), describes an aircraft guidance system comprising: - an external constraint calculation module designed for at least one obstacle: • obtain a box surrounding the obstacle, and • calculate an external constraint for bypassing the box; and - a predictive control module designed to implement predictive control while respecting the external constraint.

[0003] This article focuses more specifically on the case of a training program for rotary-wing drones. These drones are aircraft capable of hovering in mid-air and are highly maneuverable. Furthermore, each drone is modeled using a linear model.

[0004] On the contrary, for fixed-wing aircraft, the difficulty is that they are very non-linear, fast, and not very maneuverable. Thus, even with the external obstacle avoidance constraint described above, there remains a risk of collision with the obstacle.

[0005] It may therefore be desirable to provide a guidance system that makes it possible to overcome at least some of the aforementioned problems and constraints. Summary of the invention

[0006] A guidance system for an aircraft is therefore proposed, comprising: - an external constraint calculation module designed, for at least one obstacle, to: • define an envelope surrounding the obstacle, and • calculate an external constraint for bypassing the envelope; and - a predictive control module designed to implement predictive control while respecting the external constraint; characterized in that the definition of the envelope used for calculating the external stress includes: - a definition of an initial envelope surrounding the obstacle; - obtaining a relative speed of the aircraft with respect to the obstacle; and - at least when the aircraft approaches the obstacle, an enlargement of the initial envelope at least in one direction of the relative velocity to obtain the envelope used for the calculation of the external stress, the enlargement being all the more important as an absolute value of the relative velocity is high.

[0007] The invention may further include one or more of the following optional features, according to any technically possible combination.

[0008] Optionally, the initial envelope is a box.

[0009] Optionally also, the box has edges oriented along three directions of an orthogonal frame and, the relative velocity having three components in the orthogonal frame, each edge is enlarged according to an absolute value of the component of the relative velocity along the direction of that edge.

[0010] Optionally, each edge is also enlarged proportionally to the absolute value of the relative velocity component along the direction of that edge with a predefined proportionality coefficient.

[0011] Optionally also, the proportionality coefficient is the same for all edges.

[0012] Optionally, the guidance system also includes an internal constraint supply module, the internal constraints including at least that an aerodynamic longitudinal speed remains above a predefined threshold, and the predictive control module is further designed to implement predictive control while respecting the internal constraints.

[0013] Optionally also, the predictive control module is designed to determine, at each instant, a sequence of commands over a horizon, the predictive control module includes a linear prediction module designed to implement a process of successive linearization from a measurement of a state of the aircraft for a current instant and the command sequence determined at the previous instant, to provide, at each instant of the horizon, a linear model of the aircraft, and the predictive control module is designed to use the linear models to determine the sequence of commands over the horizon for the current instant.

[0014] Optionally, the external stress calculation module is also designed to calculate the external constraint of bypassing the envelope, in order to: - estimate future positions of the aircraft at respective future times; - find the future time(s) when an envelope of the aircraft is within the envelope of the obstacle; and - for each future instant found: • estimate a future speed of the aircraft at that instant, this estimated future speed having components along three directions of an orthogonal coordinate system, • determine the direction of the orthogonal coordinate system in which the component of the estimated future velocity is highest, • the envelope having two sides along the determined direction, determine which of these sides is closest to the estimated position, and • define as an external constraint of the envelope that the aircraft envelope remains on the determined side of the envelope along the determined direction.

[0015] An aircraft comprising a guidance system according to the invention is also proposed.

[0016] An aircraft formation according to the invention is also proposed, in which, for each aircraft, the guidance system includes a reference computing module designed to calculate future reference states and future reference commands using a reference trajectory of the formation, a model of the aircraft and an offset of the aircraft in the formation.

[0017] A method for guiding an aircraft is also proposed, comprising: - a calculation of external constraints including, for at least one obstacle: • a definition of an envelope surrounding the obstacle, and • a calculation of an external constraint for bypassing the envelope; and • the implementation of a predictive control system that respects the external constraint; characterized in that the definition of the envelope used for calculating the external stress includes: - a definition of an initial envelope surrounding the obstacle; - obtaining a relative speed of the aircraft with respect to the obstacle; and - at least when the aircraft approaches the obstacle, an enlargement of the initial envelope at least in one direction of the relative velocity to obtain the envelope used for the calculation of the external stress, the enlargement being all the more important as an absolute value of the relative velocity is high. Brief description of the figures

[0018] The invention will be better understood with the aid of the following description, given solely by way of example and made with reference to the accompanying drawings in which: - Fig. 1 is a top view of a formation of aircraft, - [Fig.2] is a schematic view of one of the aircraft in [Fig.1], - Figure 3 is a functional view of an aircraft guidance system. [Fig.2], - Figure 4 illustrates two aircraft and an enlargement of an envelope around one of them. - [Fig.5] is similar to [Fig.4], but with an oval rather than a parallelepiped shape, - Figure 6 illustrates the aircraft with their respective envelopes, - Figure 7 illustrates the result of a combination of the two envelopes around one of the aircraft, the other being considered as a point mass, and - [Fig.8] is a view similar to [Fig.7], illustrating a workaround rule. Detailed description of the invention

[0019] In the following description, the different elements of the invention will be located in space by means of a frame R which is orthogonal and thus presents three directions X, Y, Z.

[0020] Furthermore, time will be discretized with a sampling period Te to give instants denoted with = 1,2, ...,

[0021] Figure 1 illustrates a formation of 100 aircraft 102i (i = 1...Na) implementing the invention. In the illustrated example, the number Na of aircraft 102i is six. Each aircraft 102i has a reference point c, such as a center of gravity of the aircraft 102i.

[0022] The formation 100 has a reference point c, the reference points ci of the aircraft 102i being offset from this reference point c by desired respective offsets ÔYCi(k), which can change over time, in order to change the geometry of the formation 100 dynamically.

[0023] The formation 100 is designed to move along a desired trajectory. This trajectory is thus established in the form of a reference trajectory consisting of a sequence of positions Yc(k) of the reference point c of the formation 100: .....

[0024] With reference to [Fig.2], aircraft 102i will be described in more detail.

[0025] The aircraft 102i has a fixed wing 202i, in particular wings. It is, for example, an airplane.

[0026] The aircraft 102i further comprises a measurement system 204i designed to provide, at each instant k, measurements M(k)- The measurements M(k) include, for example: a measurement of a position / \ / \ / \ r of the reference point cî of Y^k) = [x^k), y^k], z t \k]] aircraft 102i in frame R, a measurement of the longitudinal aerodynamic speed of aircraft 102i (i.e., the speed along the longitudinal axis of the aircraft) 102i), and a measurement of the Euler angles of aircraft 102i (roll pitch 0 / and heading Wi).

[0027] The aircraft 102i further comprises a communication system 206i, in particular wireless, designed to receive R data and transmit E data.

[0028] For example, the transmitted data E includes the measured position Y^k and, optionally, a derivative dY^k of this position Y^k, and is transmitted to other aircraft 102m. The received data R thus includes, from the other aircraft 102m, their positions Y / (k) and, optionally, the derivatives dYj(k) of these positions Yj{k}. The received data R may also include the positions and, optionally, the associated derivatives of obstacles other than those of the other aircraft 102m.

[0029] The aircraft 102i further comprises a guidance system 208i designed to calculate, at each instant k, a command u^k) from the measurements M and possibly the received data R. The command ut(k) groups commands for several parameters to be regulated, that is, the values ​​that these parameters must take. For example, the command u^k) groups a longitudinal aerodynamic speed command VCj, a pitch control 9^ and a roll control: ( k ) = VCi ( k ), 9Cj. ( k ), <pCi ( k ) ]. Le système de guidage 208i sera décrit plus en détail par la suite.

[0030] The aircraft 102i further comprises a displacement system 210i designed to receive, at each instant k, the command u^k), in order to implement the latter to move the aircraft. For example, the displacement system 210i comprises a propulsion system to achieve the aerodynamic longitudinal speed control Vq and control surfaces for achieving the pitch control 0c, and roll control ^c. Furthermore, the displacement system 210i may include, for each parameter of the command u^k), a control loop to regulate this parameter to the value indicated by the command. Each control loop behaves, for example, as a first-order filter with a certain bandwidth. For example, the aircraft 102i comprises three control loops for respectively the aerodynamic longitudinal speed control Vch, the pitch control 9Ci and the roll control $Cj, with respectively the bandwidths ky., k0( and k^,.

[0031] In general, the aircraft 102i can be represented by a model, for example continuous, that is to say variables linked together by mathematical equations, in particular differential equations of time.

[0032] For example, the aircraft model 102i may be the following: Or : - Vi is the aerodynamic longitudinal speed of aircraft 102i, "(wr. wy is a wind speed, considered null thereafter, - g is gravity, - Y{ = (x^ y ? z^ is the position of aircraft 102i, - ( "n, 1 are the Euler angles of aircraft 102i (respectively roll, pitch

[0033] and cape), and - (ky. kg. are 'cs Passing commands of the aircraft attitude control loops 102i modeled by first-order filters. In this example, aircraft 102i exhibits a measured state X'(k\ — \x- v 7 V- f)- (bw 1T- The k command) of aircraft 102i is noted

[0034]

[0035]

[0036]

[0037] by the vector y. ( £ ) — yc Qc $ j which therefore represents the output of the guidance system 208i. Subsequently, the speed of aircraft 102i will be denoted by a vector jy^ = j, T. Generally, the function f is nonlinear, so the model is nonlinear. With reference to [Fig. 3], the guidance system 208i will now be described in more detail. The 208i guidance system includes, firstly, a reference calculation module 302 designed to provide, for each current instant, a sequence of future states reference point on the horizon; - l)rf and a series of future reference orders on the Nf horizon;

[0038] For example, with the 102i aircraft model above, each future state of reference 3 on the Nf horizon is as follows: and each subsequent reference order:

[0039] To calculate future reference states and future orders of

[0040] reference yf(kÿ 'C reference calculation m°dule 302 is for example designed to use the reference trajectory of formation 100, the model of aircraft 102i and the offset 5YCi(k) of aircraft 102i in formation 100. For example, the reference calculation module 302 is primarily designed to calculate an overall reference heading... fri at each instant k of the horizon from the reference trajectory of formation 100 and the aircraft model 102i. Using the previous model example, this calculation is as follows: tp c [k] = atan2 y^ky-y^k-ty1 xjky-Xtfk-ï) /

[0041]

[0042]

[0043] VL ^) = L s ^sn(y c (.k) -y c (kl) ) six c (k) -x c (k- l) =0 -V c (k-six c (k) -x c (k-1) -Oety^k)-y c (k-1) ~0 Furthermore, it is chosen, for example, that each aircraft 102i must orient itself according to the global reference heading (jX) such that the reference heading / , \ of the aircraft W / WrtjjK} 102i at each instant k of the horizon Nt- is taken equal to this global reference heading at this instant k; / \ Wr e f{k) = For example, the reference calculation module 302 is also designed to calculate the reference coordinates x^f.(k), y^j (k), zref.(k) from the global reference heading, for example, in the following way: Xref.Çk') -x c (k) + Ôx Ci (k)cos( ^ c (k) ) -Ôy c \k)sin( w c(k) ) y ref (k) = y c (k')+ ôx C; (k)sin( ip c (k) ) + ôy Ci (k)cos( ip c (k) ) Zref. (k) = Z c (k) + ÔZc^k] For example, the reference calculation module 302 is also designed to calculate the reference aerodynamic longitudinal speed Vref.(k), the attitude of reference OrejAk) and the reference roll (k) from the reference coordinates xref_(k), yrej (k), zref (k), for example in the following way: with : y?v1'C* ' C

[0044] The guidance system 208i may further include a module for supplying internal constraints 304, for example expressed by two matrices AiJtt_aVion.., Bintjmon. such that future commands on the horizon satisfy the following equation: i “^int_avioni

[0045] The internal constraints Aintawon., Bint_avù»i. of the aircraft 102i reflect in particular the fact that the fixed wing 202i has low maneuverability and the difficulty of guidance compared to other machines such as those with rotary wings.

[0046] For example, the internal constraints considered are as follows: v. < speed < V r mini rt\njr max^ ^min; ^max j

[0047] As the command „ (1A is as follows: t \ ( \ i \ / \ this This amounts to imposing the following constraints on the order: 1 zr \ F zjX ... „ 5 W) < yf -3J L -màïtà- with : and therefore to impose the following constraints on future orders 1¾ over the horizon Nor to be determined:

[0048] Thus, in this example, the internal constraints are expressed by the matrices Aint avion., Bint avion. following: ~ l — l

[0049] The internal constraints Aint_avûm., Bitlt avion, can, as in the example above, be independent of the aircraft model 102i and in this case be calculated beforehand. Thus, the internal constraint supply module 304 can simply include a memory in which the internal constraints Aita_aviont, Bint avio^ are stored.

[0050] The guidance system 208i further includes an external constraint calculation module 306 for obstacle avoidance, these external constraints being expressed for example by two matrices Aext_obst., Bext (,bsi. so that future commands Y; on the horizon N; satisfy the following equation: AgXt_obst^i — Bext_obst.

[0051] Obstacles include, for example, other aircraft in formation 100 and / or other obstacles.

[0052] The external stress calculation module 306 will be described in more detail later, with reference to Figures 4 to 8.

[0053] The guidance system 208i further comprises a predictive control module 308 designed to implement predictive control in order to calculate, at each instant, the command to be given to the movement system 210i so as to follow the sequence of future reference states and the sequence of commands future references, respecting the internal constraints Am avion., Bint_avi(m. and the external constraints Aext obst., Bext — J — (

[0054] The predictive control module 308 includes, for example, firstly, a linear prediction module 309 designed to provide, at each time k of the horizon, a linear model of the aircraft 102i in the form: (^+1) = AiXi (k) + ( k ) + VZOÛ is a prediction of the aircraft's state 102i.

[0055] More precisely, starting from the continuous nonlinear model, the linearization around a control Wq = [ T and a state Xo = yo, Vo, followed by discretization leads to the following discrete linear model: X((k + 1) = 4((^ / ^)^(¾) 4- + with

[0056] Thus, the linear prediction module 309 is designed to construct the prediction matrices on the horizon using the successive linearization process from the measurement of the state X, (k) at time k and the optimal control sequence W obtained at the previous time k-1; [17(0), <0,,.^ 1) Àg — .A0A > for j “1 ; M “c - W” 1) Â .(,■ - 1) = ,4,(¾.. u0) ^(J ~ 1) - &A- Mo) di(j -1) = 0, --0 end for j

[0057] From the measurement of the state X^k), the linear prediction module 309 is designed to compute the following augmented prediction matrices which are useful to other modules, unfolding the prediction over the horizon Ni.

[0058] The linear prediction module 309 uses, for example, the following sequences on the horizon N j; rs ni R(i)' [ ^(0) ] diCû) ' Wi ^(2) fW) fj = ( ---- O).¾ = IW) = d<(2) Ll4(M - 1). .^( / ¾ ™ 1],

[0059] So: K# = + :¾¾ + Similarly with the position:

[0060]

[0061]

[0062] Y^k): SO : With : 'W =CX t (k), C=(I } I $3x4 ) , CAj(O) C4£(i)4(0) Od2)âXiM(o) cn i U® CBiOl OMP# U») C^(2)44IM(0) cj^Mœ j® 3 râjw i)

[0063] The predictive control module 308 includes, for example, a shaping module 310 designed to shape an optimization problem consisting of minimizing®' » given, for example, by: * +n - (Ow*+ / ) - ^œ))] while respecting the constraints, for example given by: so that the formatted optimization problem is compatible with commercial quadratic solvers.

[0064] Thus, the formatting module 310 is designed to put the optimization problem in the following form: minimize: ®i) = respecting: Qüj < $

[0065] For example, the parameters Lf, -, Ci, and ci are given by: % = % hf = ..^4¾¾. — RJ

[0066] Indeed, it is easy to see that: Î(W), W -1 ~ ~+ ('^n® ~ ” UO] Oj - ~ diag^i)

[0067] And using the outputs of the reference calculation module 302 and the linear prediction module 309, and assuming the matrices are -¾ and diagonal to simplify the calculations: JP - 2 [fe ~ - 1¾ * (u^x^) - - M e¥( - ï^^U) - ^<4 •“ w^U)

[0068] By expanding everything, we show that: = ^10^(¾¾ + + (-2¾¾ -2^^)¾)¾ + +

[0069] And minimizing 1^,.(¾^¾) is equivalent to minimizing: = 1¾¾¾ e + HM- m*AM

[0070] Regarding the constraints:

[0071] The tuning matrices Ri and Qi are used to weight the importance to be given to each variable. In the case where the commands are in speed and angle, the low-level piloting loops (modeled by first-order low-pass filters) use aerodynamic data of the aircraft 102i (thrust, etc.), so that the guidance system 208i does not use this aerodynamic data and is relatively independent of this data.

[0072] Preferably, the weighting of the heading ^Pi in the tuning matrices Ri and Qi is chosen to be zero. This is because the heading ^P is measured between -pi and pi, whereas the model (in particular the reference ^ref) assumes it to be unbounded. Therefore, to avoid excessively large false angular tracking errors that could make the solution too complicated, it is advisable to disregard this term and thus weight it to zero.

[0073] Typical orders of magnitude for adjustments of other factors that can be fine-tuned around these values ​​may be: Q, = dàî5(4.1Q~st 4.1O^O.ÛS,O.OÜLQ.ÛM^^ R; = dLi^(0.01,5.1O^ 7^ — 0.1 s

[0074] The predictive control module 308 further includes, for example, a solver 312 designed to solve the optimization problem, for example that formatted by the formatting module 310, to provide sW commands on the horizon

[0075] For example, Solver 312 uses one of two well-known techniques: the interior-point technique and the active-set technique. For problems For large dimensions, such as when the horizon A,- is large, then the interior point technique is preferable. Another advantage of the interior point technique is that it can be initialized even with an impractical starting point.

[0076] Another usable technique is that of warm start (from the English "warmstrat", described in "model predictive control: theory, computation and design" by Rawlings et al., published in Nob Hill Publishing, 2017, which consists of initializing the resolution with the sequence obtained at the previous instant but shifted by one step.

[0077] The predictive control module 308 further includes, for example, a memory module 314 designed to store the commands determined by the solver 312.

[0078] With reference to figures 4 to 8, the operation of the external stress calculation module 306 will now be described in more detail.

[0079] In [Fig.4], the case where the obstacle to be avoided is another aircraft 102m from formation 100 is illustrated.

[0080] The aircraft 102i is fast and not very maneuverable. In particular, it cannot stop in flight. Furthermore, it reacts with a certain dynamics, i.e., a certain delay, which depends in part on the dynamics of the guidance loop. This delay should preferably be taken into account and anticipated. This delay is, for example, represented by a constant, denoted and judiciously chosen by a person skilled in the art.

[0081] In order to avoid colliding with the obstacle, it is therefore proposed to take into account a relative speed Av of the aircraft 102i with respect to the obstacle 102m.

[0082] This relative velocity Av is directed along a certain direction DAv and has a certain absolute value IAvl.

[0083] The external stress calculation module 306 is thus designed to first obtain an initial envelope Em surrounding the obstacle 102m. The external stress calculation module 306 is further designed to enlarge the initial envelope Em, at least along the direction DAv of the relative velocity Av, the enlargement increasing with the absolute value IAvI of the relative velocity Av.

[0084] For example, as in the illustrated example, the initial envelope Em is an initial box in the shape of a rectangular parallelepiped having edges LXm, Lym, and LZm oriented respectively along the three directions X, Y, and Z of the frame R (only the edges LXm and Lym are visible in Figure 4). Since the relative velocity Av has three components in the frame R: At, Af, and Avz, each edge LXm, Lym, and LZm is enlarged according to an absolute value of the associated component Avx, Ay, and Avz of the relative velocity Av. For example, the initial box is enlarged along each direction of the frame R by the absolute value of the relative velocity Av along that direction of the frame.

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091] R multiplied by the constant Tdyn^ which therefore forms a proportionality coefficient for the enlargement. This gives, for each other aircraft 102m from the formation 100, the following edge increases: ALxm — | Avx | Tdy^ — | (k)-Xm(k) | Tdy^ NLym = | Avj | Tdyn. = | y. (k)-ym(k) | Tdyn. = i AvJ Tdyn. = IZi(k)-zm(k) | Tdy^ xm kx jn «F ALXm L’y — Ly + AZ>v L’Zm = LZm + ALZm The initial envelope Em, when enlarged, thus forms a new envelope E'm used to define the external constraints. Figure 5 illustrates a case where the initial envelope Em is a sphere, enlarged only in the direction of the direction DAv of the relative velocity Av to give the envelope E'm. Thus, the external constraint calculation module 306 is further designed to calculate the external constraints Aext_obst., Bext obst. so that the aircraft 102i bypasses the envelope E'm. For this, with reference to figure 6, the external stress calculation module 306 is preferably designed to define an envelope Ei surrounding the aircraft 102i and to calculate the external stresses Aextobst Bext_obst. so that the envelope Ei of the aircraft 102i bypasses the envelope E'm of the obstacle 102m. For example, the envelope Ei of aircraft 102i is a box in the shape of a rectangular parallelepiped with edges LXi, Ly., LZi oriented according respectively to the three directions X, Y, Z of the frame R. Under these conditions, the avoidance constraint can be expressed by the following equation: [xt-(&) >xm(k) + and [y^kï-^yjjcï+^r and [ z^k)>zm(k)+^ Or Or Or x^k) + ^ <xm(k) yi(k)+T<ym(k)-^ z^k} +^<ym{k}-^ Or m = 1, ..., N mi equivalently, as illustrated in [Fig.7], by the following equation: And And OR < Xw®) [ML) >ÎOA) or ^(L) <-ym(k) %(&) > or m. = 1... ÿ#,j» * i with : _ , Z»dA) - (^ ) F —7^ + V 1% L. or ïrtt(k) = xm(k)--- -77 — Z or ÿyi) = yw(k) -Z - y1 £f. L. or - ^(k) —

[0092] To avoid a collision, the external stress calculation module 306 is thus, for example, designed to determine the instant(s) k of the horizon N, at which there is a risk of collision.

[0093] For this purpose, the external stress calculation module 306 is designed to estimate, at least roughly, on the horizon N, the predicted future positions of the aircraft 102i, denoted xi(k), y.(k), Zj(k), and the predicted future positions of the obstacle 102m, denoted xm(k\ ym(k), zm(k) ■

[0094] For example, it is possible to use for this purpose the method described in the article by Yajing Wang et al., “A Hierarchical Collision Avoidance Architecture for Multiple Fixed-Wing UAVs in an Integrated Airspace”, IF AC PapersOnLine 53-2 (2020) 2477-2482, which shows that dynamic obstacles can be avoided by constructing the xm(k), y(k), zm(k) with a linear prediction from the measured velocities of the agents and their position at time k: Xm ( j ) — Xm (k) + jTg

[0095] The same applies to aircraft 102i: Xi(j) ^X^k) + jTeXi(k) ' ^yi(k)+jTey (k) ; = 1 . ZiUÏ =Zi(k) y^^k)

[0096] The external stress calculation module 306 is further designed to search for the instant(s) ^derhonzorAi where the aircraft envelope 102i is within the envelope of the obstacle 102m, for example by checking if the estimated positions satisfy the previous equation. These are for example the instants k^ k2 and ^on the [Fig.8].

[0097] The external constraint calculation module 306 is then designed, for each instant k found (where there is therefore a risk of collision), to define a constraint on the position of the aircraft 102i allowing to satisfy the previous equation.

[0098] To define the constraint on the position of the aircraft 102i, it is necessary to implement a bypass rule to determine which side to bypass the obstacle 102m.

[0099] One possible circumvention rule is, for example, that described in FEYEL. According to this circumvention rule, an attempt is first made to circumvent the obstacle along the X direction, defining as a constraint that the position Xj(k) of the aircraft must be on the side closest to the X axis. If the position x{(k) is equidistant from both sides, the same is attempted along the Y direction, and then along the Z direction.

[0100] However, the Feyel avoidance rule is not suitable for a low-maneuverability aircraft such as fixed-wing aircraft like the 102i because, even with the envelope enlargement proposed above, the optimization problem remains very difficult. Therefore, it is preferable to help solve it by deciding on the avoidance direction.

[0101] Thus, preferably, for each instant ^found (where a risk of collision has been detected), the external constraint calculation module 306 is designed to favor avoidance along the X, Y or Z direction in which the stop L'Xm, L'y , L'Zm is the smallest.

[0102] The workaround rule can for example be put in the expected form Aextobst ^i ~ Bextobst. as will now be explained.

[0103] The workaround rule can be written as follows: iiG) > < *m < / ) iW) > Ma( / ) PiO) < ÎOO HAS > « on pHdwî Center in m ^^0) >%Ü) ee^iW < W / ); |^Q) - x^û)| < lif( / ) - & y itiv:. ^<0. / )“'“^ otherwise if |.î^Q) - ^( / )| > IO) S £% Otherwise sî [jMj ) ” 3¾¾ 0) | Lyiü) -'jjnU / l sî '^ * tt , £ A0)<£ffl4-T s^wt |O) ™-^( / )] > l&C / ) £ Vy^ < -sa) -Zi Z Otherwise Sî |e s G) - £mü)| < I^0) - ^Ü) IW^SW-^-y Otherwise SJ l^s'U.) “■;sm01| I.) “ ^si: V) I / fn 3j / <« if end if / in if / in si / in si

[0104] This last workaround rule can also be written in the following form:

[0105] In the case where all aircraft 102m other than aircraft 102i are taken into account, we obtain, with the values ​​of n ( / ) ~ ( / ) ~ ^7 ( j) '•

[0106] Considering the equation v, = X4(fc) 4 4- from the modulus of Calculating linear prediction 309, the external constraints A^xt^obst^ Bext obst. are then as follows: ■ r »?aU)n(0 - feiùMi i Av jl; l&jj ■" | *i;v (Av J |i. ;^J .:¾¾.¾)Kea(A)) [i^(Afj)k'il. (yWt) + ^d)

[0107] In other embodiments, it is also possible to control aircraft 102i by thrust, instead of speed. Robustness is reduced, but the control interfaces become identical to those of a rotary-wing aircraft, which can be advantageous. In this case, the equation of state for aircraft 102 can be the following (which is a point mass model): i; ™ M:ss SS y, ™ ss Î as L ...,¾ ■C^ sa Côs(ti) ,^ ” si&(v)3y — tàn(v)

[0108]

[0109]

[0110] Or : Tc. is the controlled thrust Dj = Rd Vf is 'a drag, with Ro. related to the aircraft's aerodynamics the command u. = [ ] T mi is the mass of the aircraft. Since the definition of the state does not change, the different modules simply adapt, for example in the following way. Adaptation of the 302 reference calculation module The thrust reference is given by: [YES]

[0112]

[0113]

[0114] Te, (k) = mi------+ RDyCi (k) + s^Hig The order reference is then / x / x / x / xT. Vref[k)= [T^k), (^k)] The rest of the module is unchanged. Adaptation of the linear prediction calculation module 309 Starting from the new continuous nonlinear model, the linearization around a control Uq = [7^ T and a state Xo = [Xq, yQ, V(), 0(> ^0]r followed A discretization leads to the following discrete linear model: As(fc T 1) = 4~ "h} with .

[0115]

[0116] (¾ w) - I» O 0 0 0 0 0 0 0 0 îni Q 0 0 0 0 0 2¾¾ 0 ' Q G & 0 0 -¾¾ O » 0 0 0 0 û ^(^ + 0 ©' 0 / y 0 0 0 0 oh 0 0 0 0 We simply add the calculation of the predicted velocity necessary for calculating the constraints on velocity: Vi(k) = CyX^kY Cv= (0 0 0 1 0 0 0) SO : £ = W^Cfe) A: 0 jss») £^S;(O) €^(1)^(0) €^(3)4^1)^(6)

[0117] The rest of the module is unchanged.

[0118] Adaptation of the internal stress calculation module 304

[0119] An additional constraint on the thrust must be added: 0 •

[0120] And so this time: max; ~ TniaXp Omaxp $maXi j , nûf^ ~ ^minf ®min*

[0121] We always have:

[0122] Since we are controlling by thrust, then we must add the constraint relating to the velocity through the predicted state. The velocity is written as: V^k) “ (0 0 0 10 00)X,-(fc) ^CyX^k)

[0123] And so:

[0124] Considering the predicted speed over the horizon, then:

[0125] And: V; = +

[0126] Finally, the global constraint on u is the following union:

[0127] Which is of the form:

[0128] Adaptation of the formatting module 310

[0129] The adaptation only relates to the settings, which are for example the following: & = d^(440-s, 4.10"5,0.015, (HMH, 0.002,1.1Q-4 Q) (0.001,5.10-4.0.01) M = ^£0^(40), Tg = 0.1 s-

[0130] In conclusion, it should be noted that the invention is not limited to the embodiments described above. It will indeed be apparent to those skilled in the art that various modifications can be made to the embodiments described above, in light of the information just disclosed to them.

[0131] In the detailed presentation of the invention given above, the terms used shall not be interpreted as limiting the invention to the embodiments set forth in this description, but shall be interpreted as including all equivalents whose prediction is within the reach of the person skilled in the art by applying their general knowledge to the implementation of the teaching that has just been disclosed to them.

Claims

Demands

1. A guidance system (208i) for an aircraft (102i), comprising: - an external constraint calculation module (306) designed, for at least one obstacle (102m), to: • define an envelope (E'm) surrounding the obstacle (102m), and • calculate an external constraint (Aint_avimt., Bittijnwn.) for circumventing the envelope (E'm); and - a predictive control module (308) designed to implement predictive control while respecting the external constraint (Aint_avimt., Bittijnwn.); characterized in that the definition of the envelope (E'm) used for calculating the external constraint (Aint_avimt., Bittijnwn.), Bintavion) ​​includes: - a definition of an initial envelope (Em) surrounding the obstacle (102m); - obtaining a relative velocity (Av) of the aircraft (102i) with respect to the obstacle (102m); and - at least when the aircraft (102i) approaches the obstacle (102m), an enlargement of the initial envelope (Em) at least along one direction (DAv) of the relative velocity (Av) to obtain the envelope (E'm) used for the calculation of the external stress , Bint avion), the enlargement being all the more important as an absolute value of the relative velocity (Av) is high.

2. Guidance system (208i) according to claim 1, wherein the initial envelope (Em) is a box.

3. A guidance system (208i) according to claim 2, wherein the box has edges (Lx^ Lym) oriented respectively along three directions (X, Y, Z) of an orthogonal frame (R) and wherein, the relative velocity (Av) having three components in the orthogonal frame (R), each edge (LXm, Ly^ is enlarged according to an absolute value of the component of the relative velocity (Av) along the direction (X, Y, Z) of that edge (LXm, Ly^,

4. Guidance system (208i) according to claim 3, each edge (LXm, Lym) is enlarged proportionally to the absolute value of the relative velocity component (Av) along the direction (X, Y, Z) of that edge (LXm, Lym) with a predefined proportionality coefficient.

5. Guiding system (208i) according to claim 4, wherein the proportionality coefficient is the same for all edges (Lxm, ^ym).

6. Guidance system (208i) according to any one of claims 1 to 5, further comprising an internal constraint supply module (304), the internal constraints comprising at least that an aerodynamic longitudinal velocity remains above a predefined threshold, and wherein the predictive control module (308) is further designed to implement predictive control while respecting the internal constraints.

7. Guidance system (208i) according to any one of claims 1 to 6, wherein the predictive control module (308) is designed to determine, at each instant, a sequence of commands over a horizon, wherein the predictive control module (308) comprises a linear prediction module (309) designed to implement a method of successive linearization from a measurement of a state of the aircraft (102i) for a current instant and the command sequence determined at the previous instant, to provide, at each instant of the horizon, a linear model of the aircraft (102i), and wherein the predictive control module (308) is designed to use the linear models (309) to determine the sequence of commands over the horizon for the current instant.

8. A guidance system (208i) according to any one of claims 1 to 7, wherein the external stress calculation module (306) is designed to calculate the external stress (Ait aircraft, Bit aircraft) for bypassing the envelope (E'm), in order to: - estimate future positions of the aircraft (102i) at respective future times; - find the future time(s) when an envelope (Ei) of the aircraft (102i) is within the envelope (E'm) of the obstacle (102m); and - for each future time found: • estimate a future velocity of the aircraft (102i) at this instant, this estimated future velocity having components along three directions (X, Y, Z) of an orthogonal frame (R), • determine the direction of the orthogonal frame (R) in which the component of the estimated future velocity is the highest, • the envelope (E'm) having two sides along the determined direction, determine which of these sides is closest to the estimated position, and • define as an external constraint (A^ / aircraft., Büit_aircraft) of circumvention of the envelope (E'm) that the envelope (Ei) of the aircraft (102i) remains on the determined side of the envelope (E'm) along the determined direction.

9. Aircraft (102i) comprising a guidance system (208i) according to any one of claims 1 to 8.

10. Aircraft (100) formation (102i) according to claim 9, wherein, for each aircraft (102i), the guidance system (208i) comprises a reference computing module (302) designed to calculate future reference states and future reference commands using a reference trajectory of the formation (100), a model of the aircraft (102i) and an offset (5^,.(k)) of the aircraft (102i) in the formation (100).

11. A method for guiding an aircraft (102i) (208i), comprising: - a calculation of external constraints (306) including, for at least one obstacle (102m): • a definition of an envelope (E'm) surrounding the obstacle (102m), and • a calculation of an external constraint (Aint_avion, Bint_avion) ​​for circumventing the envelope (E'm); and - an implementation of a predictive control respecting the external constraint (Aint_avion, Bint_avion); characterized in that the definition of the envelope (E'm) used for calculating the external constraint (Aint_avion, Bint_avion) ​​includes: a definition of an initial envelope (Em) surrounding the obstacle (102m); obtaining a relative speed (Av) of the aircraft (102i) with respect to the obstacle (102m); and at least when the aircraft (102i) approaches the obstacle (102m), an enlargement of the initial envelope (Em) at least along one direction (DAv) of the relative velocity (Av) to obtain the envelope (E'm) used for the calculation of the external stress (Ai„t_avion., Bint arion), the enlargement being all the more important as an absolute value of the relative velocity (Av) is high.

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