Constrained proportional navigation guided vehicle.

Abstract

A vehicle comprising at least one self-guidance device including a proportional navigation module (M331) arranged to provide a normal acceleration command ( ) based on the rotation speed ( ) of a vehicle-target line, a predictive module (M332) which receives as input the rotation speed of the vehicle-target line at each predetermined time and is arranged to provide the proportional navigation module with predicted rotation speeds of the vehicle-target line ( ) over a prediction horizon (NP) such that the proportional navigation module (M331) provides a plurality of normal acceleration commands ( ) over the prediction horizon (NP), and a control governor module (M333) arranged to modify the plurality of normal acceleration commands ( ) according to constraints applied to the prediction horizon and to provide a plurality of modified normal acceleration commands ( ) to the locomotion unit (M2). ABRIDGED FIGURE: Fig. 5.

Description

Title of the invention: Vehicle guided by proportional navigation under constraint.

[0001] The present invention relates to the field of vehicle guidance, particularly aerial vehicle guidance, and more specifically to a proportional navigation guidance law. The term "vehicle" refers to any type of machine, transporting passengers and / or goods and / or any payload whatsoever, which is equipped with a motor and a steering mechanism enabling the machine to be steered and to follow a trajectory.

[0002] BACKGROUND OF THE INVENTION

[0003] It should be noted that a guidance law is a mathematical law by which a vehicle is guided from a starting point to a destination or goal, which may be moving. It is not necessary to know the a priori position of the goal if the vehicle is equipped with a goal-detection autoguidance system, for example optronic, thermal (infrared) or radar.

[0004] Among the laws governing the guidance of a vehicle towards a moving target, the most widespread is the proportional navigation law, which consists of controlling the normal acceleration of the vehicle proportionally to the rotational speed of the line extending from the vehicle to the target (called the vehicle-target line): this law allows the vehicle-target line to rotate in a direction that favors the vehicle encountering the target and imposes on the vehicle's velocity vector a rotational speed proportional to the rotational speed of the vehicle-target line. The proportional navigation law is written as follows:

[0005] a^aV^t)

[0006] with the normal acceleration of the vehicle (perpendicular to the vehicle axis), a has a positive coefficient, Vc is the approach speed to the target, ^mb is the rotation speed of the vehicle-target line, and t is time. The coefficient a is conventionally determined according to the operational requirement. The proportional navigation law is described in particular in the documents M. Siouris, “Missile Guidance and Control Systems”, Springer-Verlag New York Inc., 2004 and Rafael Yanushevsky, “Guidance of Unmanned Aerial Vehicles”, Taylor & Francis, 2011.

[0007] Theoretically, the vehicle's encounter with the target is guaranteed, but in practice, the probability of encounter depends on the accuracy of determining the rotation speed of the vehicle-target line, the extent of the field of the target-detection autoguidance device, the exploitation of the vehicle's maximum non-linear dynamics, and other constraints concerning, for example, the behavior of the target...

[0008] To increase the probability of a meeting, augmented proportional navigation laws have been proposed in which the coefficient a is varied in real time, for example, according to the behavior of the vehicle, the field of view of the goal-detection autoguidance device taking into account its orientation relative to the goal, the estimated time before the meeting...

[0009] SUBJECT OF THE INVENTION

[0010] The invention aims to improve the probability of encountering a guidance device implementing a proportional navigation law. Summary of the invention

[0011] To this end, the invention provides a vehicle comprising at least one locomotion unit arranged to move the vehicle along a trajectory and a self-guidance device connected to the locomotion unit. The self-guidance device includes a goal detector for determining a vehicle-goal line and an electronic control unit connected to the goal detector and arranged to control the locomotion unit based on the rotational speed of the vehicle-goal line. The electronic control unit includes a proportional navigation module arranged to provide a normal acceleration command based on the rotational speed of the vehicle-goal line. The electronic control unit further comprises: - a predictive module which receives as input the rotation speed of the vehicle-target line at each predetermined instant and is arranged to provide the proportional navigation module with predicted rotation speeds of the vehicle-target line over a prediction horizon such that the proportional navigation module provides a plurality of normal acceleration commands over the prediction horizon, - a control governor module arranged to modify the plurality of normal acceleration setpoints according to constraints applied to the prediction horizon and provide a plurality of modified normal acceleration setpoints to the locomotion unit.

[0012] To increase the success rate of proportional navigation, a proportional navigation solution is proposed that explicitly takes into account vehicle-related constraints, both static and dynamic, during guidance, while retaining the architecture of standard proportional navigation. Through these constraints, the method of the invention exploits, for example, the maximum nonlinear dynamics of the vehicle and / or the nonlinear behavior of the target (if the latter is moving) in order to increase the probability of encountering the target.

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[0020]

[0021] Depending on optional features, used individually or in whole or in combination: - the predictive module implements a recursive estimation algorithm; - the recursive estimation algorithm is based on least squares; - The predictive module (M332) uses a regression model on a historical data past (Nv) and includes a neural network, such as: + D — (£)4- - • • + ^MB ( £ ~ ) where $ are the parameters of the model; - The predictive module (M332) uses a regression model on a past history (Nv) such that: ^MB(4+1)=^(^2 MB(k) + ... + ^MB(£-¼)) where $ are the model parameters, Wo is a weighting matrix of an output layer of the neural network and o is a matrix of neuron activation functions; - The parameters $ of the regression model were estimated recursively to minimize a cost function J(k) defined by: in which 2 is a factor of forgetting; - The control governor module (M333) obtains the plurality of modified normal acceleration setpoints (a^) by performing the following optimization problem: min IL- n Q(dzXk + i) -a^Àk + i) Y+H s ( X(k + i), a~Xk+i) ) under constraints that X(k+i+ 1) = f(X(k + i), az d (k + i) ) H c (X(k+i),al â (k+i)) <0 j Z = °' "' ,Np X(k) - measure of the state of the controlled loop at time kTe in which • X is a state of the vehicle piloted and controlled by the modified instructions for normal acceleration); • HC\X, - 0 is a representative function of at least one hard constraint related to the vehicle, for example the maximum acceleration of the vehicle; • Hs(X, ) is a function representing at least one soft constraint related to the vehicle; • f (X, aZd) is a state equation of the piloted locomotion unit (M2); • Q is a constant positive coefficient over the prediction horizon; • the hard constraint relates to the maximum acceleration of the vehicle; • Soft constraint is a minimization of power of at least one actuator of the locomotion unit.

[0022] Other features and advantages of the invention will become apparent from the following description of a particular, non-limiting embodiment of the invention. Brief description of the drawings

[0023] Reference will be made to the attached drawings, among which:

[0024] [Fig-1] Schematic view of a vehicle according to the invention;

[0025] [Fig.2] diagram illustrating the trajectory of a vehicle towards a goal;

[0026] [Fig.3] Diagram illustrating a vehicle control system implementing a proportional navigation law in the classic way;

[0027] [Fig.4] diagram illustrating the principle of the invention;

[0028] [Fig. 5] Diagram partially illustrating a vehicle control system implementing a proportional navigation law according to the invention. DETAILED DESCRIPTION OF THE INVENTION

[0029] With reference to figures 1 and 2, the invention is herein described in application to a vehicle M, of aircraft type, comprising a fuselage M1, at least one locomotion unit M2 arranged to move the vehicle M along a trajectory and a self-guidance device M3 connected to the locomotion unit M2 to control it so that the vehicle M reaches a goal B.

[0030] The locomotion unit M2 here comprises, for example, a turbojet engine M21 mounted in the fuselage M1 and a directional unit M22 having flight surfaces that can be steered via actuators and mounted on the fuselage M1 to extend outwards from it. The locomotion unit M2 is thus arranged to modify the magnitude and orientation of the velocity vector of the vehicle M and is known in itself: it will not be described in further detail here.

[0031] The self-guidance device M3 conventionally comprises a target detector M31, a kinematic measurement unit M32, and an electronic control unit M33. The target detector M31 is here an optronic device mounted at the front of the fuselage M1 and arranged in a manner known per se to determine a vehicle-target line MB and a speed Vc for approaching the target B. The kinematic measurement unit M32 comprises a plurality of sensors known per se (including an inertial measurement unit comprising linear inertial sensors of the accelerometer type and angular inertial sensors of the gyroscope type) and is arranged to provide the electronic control unit M33 with a set of kinematic measurements of the vehicle M (including an attitude, a speed, and a position of the vehicle). M). The electronic control unit M33 here comprises at least one processor and a memory containing a computer program executable by the processor. The electronic control unit M33 is connected to the goal detector M31 and the vehicle measuring unit M32 and is configured to control the locomotion unit M2 based on a rotational speed QMB of the vehicle-goal line MB and the speed Vc of approaching goal B in relation to vehicle M.

[0032] The computer program of the electronic control unit M33 implements a guidance loop comprising a proportional navigation module arranged to provide a normal acceleration command based on the rotation speed of the vehicle-target line and the approach speed Vc of the target B relative to to vehicle M. The proportional navigation module implements a law of Classic proportional navigation, which is written as:

[0034] In this formula, is the normal acceleration about the axis of vehicle M (here aligned (with the velocity vector v of vehicle M), a is a coefficient, and Vc is the velocity of FM approaching the goal, &mb the rotation speed of the vehicle-goal line, and t the time.

[0035] A conventional guide loop has been illustrated in [Fig.3] to better highlight the contribution of the invention compared to such a loop.

[0036] In the classical guidance loop, the goal detector M31 receives as input a difference £mb between an absolute angle of the goal B (obtained for example by processing the images provided by the optronic device of the goal detector M31) and an absolute angle of the vehicle M (from the kinematic measuring unit M32) and provides as output an estimate of the rotation speed &mb which is used directly in the guidance law to obtain the normal acceleration which constitutes a command provided to the locomotion unit M2 to orient the steerable flight surfaces in accordance with said command.

[0037] In the improved guidance loop provided for by the invention, illustrated in [Fig.4], constraints are taken into account in order to increase the probability of encounter between the vehicle M and the target B.

[0038] With reference to [Fig.5], the computer program executed by the electronic control unit M33 comprises a proportional navigation module M331 and on either side a predictive module M332 placed upstream of the proportional navigation module M331 and a control governor module M333 placed downstream of the proportional navigation module M331.

[0039] The proportional navigation module M331 is arranged to provide a normal acceleration command üz of the speed Vc of approaching the goal B relative to the vehicle M by implementing the classical proportional navigation law previously explained. ​

[0040] The predictive module M332 receives as input the rotation speed of the vehicle-target line at each predetermined instant k and is arranged to provide the proportional navigation module M331 with predicted rotation speeds of the vehicle-target line over a prediction horizon so that the proportional navigation module provides a plurality of normal acceleration commands over the prediction horizon.

[0041] The predictive module M332 performs time series prediction from a history of N v past measurements, using a recursive estimation algorithm to estimate the parameters online <l>of a model

[0042] The use of a recursive estimation algorithm exploiting a least squares approach is advantageous because this type of algorithm is easy to implement.

[0043] Thus, a regression model (linear or non-linear) of the form is trained online: [æ 44 ] $(&+!)

[0045] The model is parameterized as the vector of parameters estimated at time k.

[0046] In a purely linear approach (such as that presented in the document L. Ljung, "System Identification: Theory for the User", Prentice Hall Ptr, Upper Saddle River, NJ 07458, 1999), the regression model is written:

[0047] atm(k+1) +... ^ky^k)

[0048] In a purely non-linear approach (such as that described in the paper A. Abuduweili et al., "Robust Online Model Adaptation by Extended Kalman Filter with Exponential Moving Average and Dynamic Multi-Epoch Strategy", In: Proceedings of Machine Learning Research, vol 120:1-14, 2020), the regression model can be any universal approximator, for example a neural network: 100491 dm (*+!)=

[0050] The approximator here is a FeedForward Neural Network (FNN; see, for example, MT Hagan et al., "Neural Network Design," second edition, September 1, 2014) which has a hidden layer and an output layer. The hidden layer has the sequence of Qs as input. The approximator has Nn neurons (an arbitrary number to be set by the user): consequently, Wo is a weighting matrix of size IxNn and the $ are matrices of size Nnxl. o is a vertical vector of Nn activation functions:

[0051] o=[activation_function_l() ; activation_function_Nn()]

[0052] All the activation functions here are identical and of the sigmoid or tangent type hyperbolic. Alternatively, other neural networks can be used, for example LSTM, GRU, or radial basis function networks (RBFNNs).

[0053] $ is estimated recursively so as to minimize the cost J(k) defined by: JJ(k) - 1 ((i) - ^mb( * ) ) -2*b(z') - (vti-^y

[0055] 2 is a forgetting factor. It is recalled that the greater the number of training data As the number of data points increases, the individual weight of each new piece of data in the learning process decreases, leading to a loss of responsiveness in the learning system (more precisely, the learning capacity diminishes over time due to the increasing amount of data). Using a forgetting factor is a common practice and allows the weight of old data to be limited in order to maintain learning capacity. system learning.

[0056] The recursive solution to the cost minimization problem is known in particular from The aforementioned document is summarized here, along with one iteration:

[0057] K(.k) = P(k-\}H(k) T (H(k)P(k- {)H(k) T + rl) ' P(kH) =j(P(k)-K(k)H(k)P(k)+cT) at m (k)=f^ ) (p(kD) $(k+ 1) =$(t) +K(k)(â MB (k)

[0058] 2>0, £ > 0. r > 0 are setting parameters. The values ​​of the parameters of settings are defined empirically, it being understood that the forgetting factor will have a value close to 1 but strictly less than 1.

[0059] Once the parameters have been estimated at time k, a future numerical prediction of the rotation speed of the line MB on the future horizon N p is determined by the following principle:

[0060] 1) = f^(k}\ ^k) = [klMB(k), &MB(k-1), klMB(k-2) ...,QMB(k-Nv) ]r Qw(Æ + 2) = G (f(Æ+l)), £(£) = [l),klMB(k), (k-1).. ■ > (Æ+l-ïVj]7 7 k^MB(k + 3) — f^(^(k + 2)), ^(k) — 2 ), klMB(k+1), klMB(k) ..., QjWfi(Æ + 2-2V,,) ] àMB{k + NP) =f^k+NP-\}), ^k) = ... ]T

[0061] The prediction works continuously.

[0062] It is therefore understood that the proportional navigation module M331 does not receive at each instant k only the estimated value of the rotation speed QWB(fc) but a prediction sequence q(k + j ) j = 1 NP on the prediction horizon Np.

[0063] The M331 proportional navigation module generates a sequence of future normal acceleration commands by applying standard proportional navigation: [° 064 ] az d (k + i)=aVj^^ ...,N P

[0065] Vc is the approach velocity and a has a positive coefficient. For simplicity, we assume here that the approach velocity, like a, is constant over the future horizon, although this is not mandatory if we have assumptions about their estimates.

[0066] The M333 control governor module is arranged to modify the plurality of acceleration commands according to constraints applied to the prediction horizon and to provide a plurality of modified acceleration commands to the locomotion unit M2.

[0067] The M333 control governor module slightly modifies the acceleration setpoint Uzd (k + i), i = 1, ..., Np so as to obtain an optimal normal acceleration sequence üzd(k + i), i = 1, ..., Np allowing the vehicle M to satisfy a number of constraints (explained later) on the horizon Np, with üzd(k + i) being as close as possible to +

[0068] By virtue of the sliding horizon principle (MHC), similarly to predictive control (as for example described in the paper D. Mayne et al. "Model Predictive Control: Theory and Design", Nob Hill Publishing LLC, 2015), the M333 control governor module will apply the first value (k) of the sequence directly to the locomotion unit M2 forming the driven cell of the guidance loop, and so on...

[0069] Obtaining the optimal normal acceleration setpoint sequence a^d ( k + i), i = 1, ..., Np involves solving the following online optimization problem:

[0070] (k + i) -aZd(k + i))2 + Hs(X(k+i),(k+i)) under the constraints that X(k+i+V) =f(X(k+i),al(k + i)) ) H c (X(k + i),aï d (k + i)) <0 f°' '" ,Np X(k) - measure of the state of the controlled loop at time kTe

[0071] In this formula: X is the state of the vehicle piloted and controlled by; the function HC(X, <0 translates the hard constraints related to the vehicle, for example the maximum acceleration of the vehicle; The HS(X) function translates soft constraints related to the vehicle.

[0072] (typically minimization of a quadratic norm on certain quantities), for example minimization of the power of the actuators; - f (X, represents the state equation of the piloted locomotion unit M2. If the state X is not completely measurable, then a loop state observer is needed to reconstruct an estimate x; - Q is a constant positive coefficient over the prediction horizon. An example of a function f(X, azâ) is given below in a plane for a aircraft based on a simulation performed using MATLAB and SIMULINK software from the company MATHWORKS. The discretization is only approximate (Euler's method on the continuously controlled M2 locomotion unit) but allows us to obtain a discrete model to illustrate the invention:

[0073] rxi _ FW + s f) wir X . F TtlrfS(CxMW F Ml _ m IMF / «m L w 4 + i - + L w J a F k ' - atan \ «œ J [m +Ceg + qu] ^(k + 1) = TJ y \qSd(C ma (a, V) + Cm e! oh el (k) +C m ,q(k) ) + q(k)

[0074]

[0075]

[0076] Xk pii ( k + 1 ) — T e fKpfl ( Xk pu (.k), Y mes (k) ) + XKpu ( k ) &el ( k ) ~ grpil ( ^Xpil ( k ), Y m es (k) ) = [«?„(*) -a^(k),q(k),a(k)] T The state vector can then be written as: vt X(k) - (x(æ), ^k}, tik), t^k}, ^k}, x Kpi [k}] In this formula: - x and z are the position and altitude of the aircraft in absolute reference frame; - u and w are the aircraft's speeds in the aircraft's frame of reference; - 0 is the angular incidence of the aircraft, # is the angular velocity corresponding; - Vest the longitudinal speed of the aircraft; - xKpil is the state of the piloting corrector of the piloted locomotion unit, whose inputs are and output 5e} (actuator control).

[0077] The problem is solved using sequential quadratic programming

[0078] For this application, examples of constraints are the minimization of actuator energy and maximum acceleration.

[0079] The constraint for minimizing the energy of the actuators is written: [00801 «>0

[0081] In this equation, RQ^ represents the energy consumed by the actuators, R being a strictly positive adjustment weighting.

[0082] Assuming that the maximum acceleration Amax and the minimum acceleration Amin are such that Amin = -Amax, the maximum acceleration constraint is written:

[0083] Hc(X(z),<(z)) = |«: / ^ z = l, ..., Np

[0084] It is important to note that, in the absence of constraints, the solution implemented by the invention is transparent: standard proportional navigation (i.e., without constraints) is recovered because the problem then boils down to solving the optimization problem:

[0085] . under constraints that X(k+\)=f(X(k),aï a (k' > ), k = 0, X(0) = X(t) = measure of the state of the controlled loop at time t

[0086] The solution to the optimization problem is then:

[0087] a*d(1)=0^(1), z = 1,Np

[0088] Of course, the invention is not limited to the embodiment described but encompasses any variant falling within the scope of the invention as defined by the claims.

[0089] In particular, the vehicle may have a different structure from that described.

[0090] The locomotion unit may include one or more movable flight surfaces (rudders), one or more turbomachine or ramjet type propulsion systems, one or more propeller engines, thermal engines and / or electric motors... The engines may be fixed or steerable via actuators.

[0091] The locomotion unit can be a single entity or comprise one or more separate entities such as, for example, a propulsive entity and a directional entity.

[0092] The self-guiding unit may include an optronic sensor, a thermal sensor, a radar or other.

[0093] It is possible to use an alternative approach to the least squares approach such as a parametric estimator of the extended Kalman filter type.

[0094] Other constraints are conceivable, for example constraints aimed at reducing energy consumption, limiting current draw, limiting the risks of electromagnetic interference (EMI), limiting the deflection of steerable flight surfaces...< / l>

Claims

Demands

1. Vehicle (M) comprising at least one locomotion unit (M2) arranged to move the vehicle (M) along a trajectory and a self-guidance device (M3) connected to the locomotion unit (M2), the self-guidance device (M3) comprising a goal detector (M31) for determining a vehicle-goal line (MB) and an electronic control unit (M33) connected to the goal detector (M31) and arranged to control the locomotion unit (M2) as a function of a rotation speed (Qwb) of the vehicle-goal line (MB), the electronic control unit (M33) comprising a proportional navigation module (M331) arranged to provide a normal acceleration command (°¾) from the rotation speed (Qwb) of the vehicle-goal line (MB),characterized in that the electronic control unit (M33) further comprises: - a predictive module (M332) which receives as input the rotation speed of the vehicle-target line at each predetermined instant and is arranged to provide the proportional navigation module with predicted rotation speeds of the vehicle-target line over a prediction horizon (NP) such that the proportional navigation module (M331) provides a plurality of normal acceleration commands (0¾) over the prediction horizon (NP), - a control governor module (M333) arranged to modify the plurality of normal acceleration commands (a^) according to constraints applied on the prediction horizon and to provide a plurality of modified normal acceleration commands to the locomotion unit (M2).

2. Vehicle according to claim 1, wherein the predictive module (M332) implements a recursive estimation algorithm.

3. Vehicle according to claim 2, wherein the recursive estimation algorithm is based on least squares.

4. Vehicle according to claim 2 or 3, wherein the predictive module (M332) uses a regression model on a past history (Nv) such that: &MB ( ^ + 1 ) = ( & ) + • ■ • + ^^MB (k-Nv) where $ are the model parameters.

5. Vehicle according to claim 2 or 3, wherein the predictive module (M332) uses a past history regression model (Nv) and includes a neural network, such that: where $ are the model parameters, Wo is a weighting matrix of an output layer of the neural network and o is a matrix of neuronal activation functions.

6. Vehicle according to claim 5, wherein the parameters $ of the regression model have been recursively estimated so as to minimize a cost function J(k) defined by: in which 2 is a forgetting factor.

7. A vehicle according to any one of the preceding claims, wherein the control governor module (M333) obtains the plurality of modified normal acceleration setpoints by solving the following optimization problem: V' N p 9 min X-,û(az,(k-vi)-az,(k+i)} +HdX(k+i), aZj(k+i) ) «yjt+n.^ft+yv) i=ü ll 11 ■ / subject to the constraints that X(k + i + 1) = f(X(k + i), aZd(k+i) ) / = o V HC(X(kU), al(k+ p X(k) = measure of the state of the controlled loop at time kTe in which - X is a state of the vehicle controlled and driven by the modified normal acceleration setpoints (aZd); - Hc(X,a*d) < 0 is a representative function of at least one hard constraint related to the vehicle, for example the maximum acceleration of the vehicle; - HS(X, a* is a representative function of at least one soft constraint related to the vehicle; - f ( X.üzd ) is a state equation of the piloted locomotion unit (M2); - Q is a constant positive coefficient over the prediction horizon. 14

8. Vehicle according to claim 7, wherein the hard constraint relates to the maximum acceleration of the vehicle.

9. Vehicle according to claim 7 or 8, wherein the soft constraint is a power minimization of at least one actuator of the locomotion unit (M2).

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