Vehicle with constrained proportional navigation guidance

Abstract

The invention relates to a vehicle comprising at least one self-guidance device comprising a proportional navigation module (M331) arranged so as to provide a normal acceleration setpoint (az d) on the basis of a rotational speed (ΩMB) of a vehicle-target line, a predictive module (M332) which receives, as input, the rotational speed of the vehicle-target line at each predetermined instant and is arranged so as to provide the proportional navigation module with predicted rotational speeds of the vehicle-target line (ΩMB) over a prediction horizon (NP), such that the proportional navigation module (M331) provides a plurality of normal acceleration setpoints ((azd) over the prediction horizon (Np), and a command governor module (M333) arranged so as to modify the plurality of normal acceleration setpoints (azd) as a function of constraints applied over the prediction horizon and to provide a plurality of modified normal acceleration setpoints (azd) to the locomotion unit (M2).

Description

[0001] CONSTRAINTED PROPORTIONAL NAVIGATION GUIDANCE VEHICLE

[0002] The present invention relates to the field of vehicle guidance, particularly for aircraft, and more specifically to a guidance law using proportional navigation. The term "vehicle" refers to any type of machine, transporting passengers and / or goods and / or any payload whatsoever, equipped with a motor and a steering mechanism enabling the machine to be steered and follow a trajectory.

[0003] BACKGROUND OF THE INVENTION

[0004] A guidance law is a mathematical law that guides a vehicle from a starting point to a destination or goal, which may be moving. It is not necessary to know the destination's position beforehand if the vehicle is equipped with a destination detection system, such as optronics, thermal (infrared), or radar.

[0005] 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 vehicle's normal acceleration 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's encounter with 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:

[0006] "Z with a ZM The normal acceleration of the vehicle (perpendicular to the vehicle's axis) has a positive coefficient, Vc, and the speed of approach to the goal is £l MBThe rotation speed of the vehicle-target line, and t the time. The coefficient a is conventionally determined according to the operational need. The proportional navigation law is explained 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 view of the target-detection autoguidance system, 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.

[0011] SUMMARY OF THE INVENTION

[0012] For this purpose, 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:

[0013] - 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,

[0014] - 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.

[0015] 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 maintaining 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 it is moving) in order to increase the probability of encountering the target.

[0016] Depending on optional features, used individually or in whole or in combination:

[0017] - The predictive module implements a recursive estimation algorithm; - The recursive estimation algorithm is based on least squares;

[0018] - The predictive module (M332) uses a regression model on past history (Nv) and includes a neural network, such as: where 0 are the parameters of the model;

[0019] - The predictive module (M332) uses a regression model on a past history (Nv) such that: where 0 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;

[0020] - The parameters 4> of the regression model were estimated recursively in order to minimize a cost function J(fc) defined by: in which  is a factor of forgetting;

[0021] - The command governor module (M333) obtains the plurality of modified normal acceleration setpoints (o.z'a') by performing the following optimization problem: o X is a state of the vehicle piloted and controlled by the modified instructions for normal acceleration Oh C (X, < 0 is a function representing at least one hard constraint related to the vehicle, for example the maximum acceleration of the vehicle; o H S (X, is a function representing at least one soft constraint related to the vehicle; of(X,a Zd ) is a state equation of the piloted locomotion unit (M2); o Q is a constant positive coefficient over the prediction horizon;

[0022] - the hard constraint relates to the maximum acceleration of the vehicle;

[0023] - soft constraint is a minimization of power of at least one actuator of the locomotion unit.

[0024] Other features and advantages of the invention will become apparent from the following description of a particular and non-limiting embodiment of the invention.

[0025] BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Reference will be made to the attached drawings, including:

[0027] [Fig. 1] Schematic view of a vehicle according to the invention;

[0028] [Fig. 2] diagram illustrating the trajectory of a vehicle towards a goal;

[0029] [Fig. 3] diagram illustrating a vehicle control system implementing a proportional navigation law in a classical way;

[0030] [Fig. 4] diagram illustrating the principle of the invention;

[0031] [Fig. 5] diagram partially illustrating a vehicle control system implementing a proportional navigation law according to the invention.

[0032] DETAILED DESCRIPTION OF THE INVENTION

[0033] 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.

[0034] The locomotion unit M2 here includes, for example, a turbojet engine M21 mounted in the fuselage M1 and a directional unit M22 with steerable flight surfaces, controlled by actuators and mounted on the fuselage M1 to extend beyond it. The locomotion unit M2 is thus configured to modify the magnitude and orientation of the vehicle's velocity vector M and is known in itself: it will not be described in further detail here. The autoguidance system 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 configured in a manner known in itself to determine a vehicle-target line MB and a target approach velocity Vc.The kinematic measuring unit M32 comprises a plurality of sensors known in themselves (including an inertial measuring unit with 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 its attitude, velocity, and position). The electronic control unit M33 includes at least one processor and 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 arranged to control the locomotion unit M2 based on a rotational speed QMB of the vehicle-goal line MB and the velocity V. capproaching target B relative to vehicle M. 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 target B relative to vehicle M. The proportional navigation module implements the classical proportional navigation law, which is written:

[0035] In this formula, a Zd is the normal acceleration to the axis > of the vehicle M (here aligned with the velocity vector V) M of vehicle M), a is a coefficient, Vc is the speed of approach to the goal, Cl MB the rotation speed of the vehicle-target line, and t the time.

[0036] Figure 3 illustrates a conventional guide loop to better highlight the contribution of the invention compared to such a loop.

[0037] In the conventional guidance loop, the M31 goal detector receives an input deviation s MB between an absolute angle of the target B (obtained, for example, by processing the images provided by the optronic device of the target detector M31) and an absolute angle of the vehicle M (from the kinematic measurement unit M32) and provides as output an estimate of the rotational speed Σl MB which is directly exploited in the guidance law to obtain the normal acceleration a Zd which constitutes an instruction given to the locomotion unit M2 to orient the steerable flight surfaces in accordance with said instruction.

[0038] In the improved guidance loop provided by the invention, illustrated in Figure 4, constraints are taken into account in order to increase the probability of encounter between vehicle M and target B.

[0039] With reference to Figure 5, the computer program executed by the electronic control unit M33 includes 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.

[0040] The M331 proportional navigation module is arranged to provide a normal acceleration command to Zd from the rotation speed of the vehicle-goal line and the speed Vc of approaching the goal B relative to the vehicle M by implementing the classical proportional navigation law previously explained.

[0041] 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.

[0042] The M332 predictive module performs time series prediction from a historical N v past measurements, using a recursive estimation algorithm to estimate online the parameters 4> of a model f$. 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, we train online a regression model (linear or non-linear) of the form:

[0044] The model is parameterized as the vector of parameters estimated at time k.

[0045] 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:

[0046] In a purely non-linear approach (such as that presented 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:

[0047] The approximator here is a FeedForward Neural Network (FNN; see, for example, MT Hagan et al., "Neural Network Design," second edition, September 1, 2014) with a hidden layer and an output layer. The hidden layer takes 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: c = [activation_function_l(); ...; activation_function_Nn()]. All activation functions are identical and of sigmoid or hyperbolic tangent type. Alternatively, other neural networks can be used, such as LSTM, GRU, or radial basis function networks (RBFNNs).

[0048] We estimate 4> recursively so as to minimize the co

[0049] ΂ is a forgetting factor. It's worth remembering that as the number of training data points increases, the individual weight of each new data point 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 number of data points). Using a forgetting factor is a common practice and allows us to limit the weight of older data in order to maintain the system's learning capacity.

[0050] The recursive solution to the cost minimization problem is known in particular from the aforementioned document, and one iteration is summarized here:

[0051] $(fc + 1)= $(k)+ K(k)(ft MB (k)- a MB (kj)

[0052] A > 0, e > 0, r > 0 are tuning parameters. The values ​​of the tuning parameters are defined empirically, it being understood that the forgetting factor will have a value close to 1 but strictly less than 1.

[0053] Once the parameters are estimated at time k, a future numerical prediction £L is determined. MB of the rotation speed of the line MB on the future horizon N P by the following principle: The prediction is always working.

[0054] 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 O MB (k) but a prediction sequence £l MB (k+f),j= 1,...,N p on the prediction horizon N p .

[0055] The M331 proportional navigation module develops a sequence of future normal acceleration commands by applying standard proportional navigation: a Zd (. k + 0 = aV c ü MB (k + ï),i= 1,...,N p

[0056] Vc is the approach velocity and 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.

[0057] The M333 control governor module is arranged to modify the plurality of acceleration commands based on constraints applied to the prediction horizon and provide a plurality of modified acceleration commands to the M2 locomotion unit.

[0058] The M333 command governor module slightly modifies the acceleration setpoint. Zd (k + ï),i= 1,...,N pso as to obtain an optimal normal acceleration sequence a* d (k + i), i = l, ..., N p allowing vehicle M to satisfy a number of constraints (explained later) on horizon N pr has Zd (k + i) being closest to a Zd (k + ï).

[0059] Under the sliding horizon principle (MHC), similar to predictive control (as described, for example, in D. Mayne et al., "Model Predictive Control: Theory and Design," Nob Hill Publishing LLC, 2015), the M333 command governor module will apply the first value from the sequence directly to the locomotion unit M2 forming the piloted cell of the guidance loop, and so on...

[0060] Obtaining the optimal normal acceleration command sequence has Zd (k + i), i = 1, N p This involves solving the following online optimization problem:

[0061] In this formula:

[0062] - X is the state of the vehicle piloted and controlled by o£ d ;

[0063] - the H function c (X,c4 d )< 0 translates the hard constraints related to the vehicle, for example the maximum acceleration of the vehicle;

[0064] - the H function s (X,c4 d ) translates soft constraints related to the vehicle (typically minimization of a quadratic norm on certain quantities), by minimizing the power of the neurons; represents the state equation of the piloted locomotion unit M2. If the state X is not fully measurable, then a loop state observer is needed to reconstruct an estimate X;

[0065] - Q is a constant positive coefficient over the prediction horizon.

[0066] An example of a function f(X,a ZdThe discretization is given below in a plan for an aircraft based on a simulation performed using MATLAB and SIMULINK software from MATHWORKS. The discretization is only approximate (Euler's method on the continuously piloted M2 locomotion unit) but allows us to obtain a discrete model to illustrate the invention.

[0067] The state vector can then be written as:

[0068] In this formula:

[0069] - x and z are the position and altitude of the aircraft in absolute reference frame;

[0070] - u and iv are the aircraft's speeds in the aircraft's frame of reference;

[0071] - 0 is the angular incidence of the aircraft, q is the corresponding angular velocity;

[0072] - V is the longitudinal speed of the aircraft;

[0073] - x Kp n is the state of the steering controller of the piloted locomotion unit, whose inputs are Y mesand exit 8 ei (actuator control).

[0074] The problem is solved using sequential quadratic programming.

[0075] For this application, examples of constraints are minimizing actuator energy and maximum acceleration.

[0076] The constraint for minimizing the energy of the actuators is written as:

[0077] In this equation, RÔgi represents the energy consumed by the actuators, R being a strictly positive adjustment weighting.

[0078] Assuming that the maximum acceleration Amax and the minimum acceleration Amin are such that Amin = - Amax, the maximum acceleration constraint is written:

[0079] 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:

[0080] The solution to the optimization problem is then:

[0081] 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.

[0082] In particular, the vehicle may have a different structure than that described.

[0083] The locomotion unit may include one or more movable flight surfaces (control surfaces), one or more turbomachine or ramjet propulsion systems, one or more propeller engines, internal combustion engines, and / or electric motors. The engines may be fixed or steerable via actuators. The locomotion unit may be a single entity or comprise one or more separate entities, such as a propulsion unit and a steering unit. The self-guidance unit may include an optronic sensor, a thermal sensor, a radar, or other sensors.

[0084] It is possible to use an alternative approach to the least squares approach such as a parametric estimator of the extended Kalman filter type.

[0085] Other constraints are conceivable, such as those aimed at reducing energy consumption, limiting current draw, limiting the risks of electromagnetic interference (EMI), limiting the range of motion of steerable flight surfaces...

[0086] The invention applies to any type of vehicle, moving in the air and / or space, in or on water, in or on land...

Claims

DEMANDS 1. A 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) according to a rotational speed (fl MB ) of the right vehicle-goal (MB), the electronic control unit (M33) comprising a proportional navigation module (M331) arranged to provide a normal acceleration command starting from the rotational speed (fl MB ) of the right vehicle-goal (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 (Ü MB ) on a prediction horizon (Np) so that the proportional navigation module (M331) provides a plurality of normal acceleration commands ( a z d 'l on the prediction horizon (Np), - a control governor module (M333) arranged to modify the plurality of normal acceleration setpoints depending on constraints applied to the prediction horizon and provide a plurality of modified normal acceleration setpoints (a Zd ) 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: where c|) are the parameters of the model.

5. Vehicle according to claim 2 or 3, wherein the predictive module (M332) uses a regression model on past history (Nv) and comprises a neural network, such as: in which are the parameters of the model, 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 4> of the regression model have been recursively estimated so as to minimize a cost function J(k~) defined p in which  is a factor of forgetting.

7. Vehicle according to any one of the preceding claims, wherein the control governor module (M333) obtains the plurality of modified normal acceleration commands (a^) en leading to the following optimization problem solution: in which - X is a state of the vehicle piloted and controlled by the modified instructions for normal acceleration )— 0 is a representative function of at least n hard constraint related to the vehicle, for example maximum vehicle acceleration; ) is a representative function of at least n soft constraint related to the vehicle; is a state equation of the piloted locomotion unit (M2); - Q is a constant positive coefficient over the prediction horizon.

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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