CN117829016B - A method and device for predicting landing trajectory of large-wingspan UAV - Google Patents
A method and device for predicting landing trajectory of large-wingspan UAV Download PDFInfo
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Abstract
本发明提供一种大翼展无人机降落轨迹预测方法及装置。所述方法包括以下步骤：构建大翼展无人机突风干扰下的空气动力学模型；基于所述空气动力学模型构建卡尔曼滤波器；将实时获取的大翼展无人机降落时的观测数据输入卡尔曼滤波器，对大翼展无人机的降落轨迹进行预测。本发明通过构建大翼展无人机突风干扰下的空气动力学模型和卡尔曼滤波器，可以快速根据历史轨迹预测下一步轨迹的位置坐标和速度，可提高无人车对于无人机的回收安全性和快速性。
The present invention provides a method and device for predicting the landing trajectory of a large-wingspan UAV. The method comprises the following steps: constructing an aerodynamic model of a large-wingspan UAV under gust interference; constructing a Kalman filter based on the aerodynamic model; inputting the real-time observation data of the large-wingspan UAV during landing into the Kalman filter to predict the landing trajectory of the large-wingspan UAV. By constructing an aerodynamic model and a Kalman filter for a large-wingspan UAV under gust interference, the present invention can quickly predict the position coordinates and speed of the next trajectory based on the historical trajectory, thereby improving the safety and rapidity of the unmanned vehicle's recovery of the UAV.
Description
Technical Field
The invention belongs to the technical field of unmanned aerial vehicle control, and particularly relates to a method and a device for predicting a landing track of a large-span unmanned aerial vehicle.
Background
Compared with the aircrafts such as low-orbit satellites and high-altitude airships with the same task characteristics, the large-span unmanned aerial vehicle has the comprehensive advantages of high task height, long dead time, strong maneuverability, strong autonomy and the like, is suitable for the characteristics of informatization and autonomy of future wars, plays an important role in space attack and defense and information countermeasure, and is an important direction for unmanned aerial vehicle development. The large-span unmanned aerial vehicle has high lift-drag ratio and low flying speed, the wing has ultra-large aspect ratio and lower wing load, design indexes are deeply coupled with energy parameters, and particularly the characteristics of weak load capacity of the large-span unmanned aerial vehicle in the near space are particularly outstanding, so that great difficulty is brought to overall, aerodynamic, structural, flight control, energy, propulsion and track design. The recovery technology of the unmanned aerial vehicle is taken as an important ring of unmanned aerial vehicle combat units, and is one of key technologies in the development process of unmanned aerial vehicle weaponry. The unmanned aerial vehicle recovery technology is utilized to ensure that the unmanned aerial vehicle with the large span is accurately recovered in the effective range, and the unmanned aerial vehicle recovery technology has important significance for reducing the load of the unmanned aerial vehicle with the large span and improving the effective load.
Because the fixed wing unmanned aerial vehicle of large span inevitably can appear swinging when encountering gust disturbance in the stage of falling near ground, the flight control adjustment degree of difficulty is great this moment, causes to retrieve the route skew, increases unmanned aerial vehicle safety and reliable recovery degree of difficulty. In order to improve the real-time performance and accuracy of unmanned vehicle recovery, the invention provides a method for predicting the landing track of a large-span unmanned vehicle under the interference of gusts.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a method and a device for predicting the landing track of a large-span unmanned aerial vehicle.
In order to achieve the above object, the present invention adopts the following technical scheme.
In a first aspect, the invention provides a method for predicting a landing trajectory of a large-span unmanned aerial vehicle, comprising the following steps:
constructing an aerodynamic model of the large-span unmanned aerial vehicle under the interference of gusts;
Constructing a kalman filter based on the aerodynamic model;
and inputting the observation data obtained in real time when the large-span unmanned aerial vehicle lands into a Kalman filter, and predicting the landing track of the large-span unmanned aerial vehicle.
Further, the constructing the aerodynamic model of the large-span unmanned aerial vehicle under the gust interference comprises:
Performing approximate processing on parameters related to modeling;
listing dynamics and kinematics equations of the large-span unmanned aerial vehicle;
The decoupling simplification under a typical flight state is carried out on the transverse and longitudinal coupled motion, and a small disturbance linearization method is adopted to obtain a transverse and lateral linearization matrix equation:
wherein the state variables Δβ, Δp, Δr, Sideslip angle beta, roll rate p, yaw rate r and roll angle respectively in the lateral directionDisturbance quantity from equilibrium state; delta a、Δδr is the deflection angle disturbance quantity of the aileron and the rudder which are input by control; y β is the lateral force derivative, Y p is the roll angle speed lateral force derivative, Y r is the yaw angle speed lateral force derivative, L β is the roll static stability derivative, L p is the lateral damping derivative, L r is the lateral crossover derivative, N β is the heading static stability derivative, N p is the heading crossover derivative, N r is the heading damping derivative,As a derivative of the rudder side force,For the aileron maneuver performance derivative,For the derivative of the roll moment coefficient with respect to the rudder,For the derivative of the yaw moment coefficient with respect to the aileron,Steering efficiency derivative for rudder; alpha is the attack angle of the unmanned aerial vehicle, theta is the pitch angle of the unmanned aerial vehicle, and V is the airspeed of the unmanned aerial vehicle;
Taking the windless state as the balanced state or the undisturbed state of the unmanned plane, regarding the response of the unmanned plane to wind as disturbance motion deviating from the balanced state when the unmanned plane is windy, and linearizing the disturbance to obtain:
wherein Δβ g is the sideslip angle reference disturbance quantity under no wind disturbance, V 0 is the unmanned aerial vehicle airspeed under the balanced state, and V w is the crosswind speed;
substituting the formula (2) into the formula (1) to obtain an aerodynamic model under the condition of gust interference:
Still further, the approximating the parameters related to modeling includes the following settings:
The large-span unmanned aerial vehicle is a rigid body, and the mass is a constant;
The geographic coordinate system is an inertial coordinate system;
The plane ox bzb of the machine body coordinate system is a symmetry plane of the large-span unmanned aerial vehicle, the unmanned aerial vehicle is symmetrical in geometric appearance and symmetrical in internal mass distribution, namely the inertia product I xy＝Iyz =0;
The earth's surface is a horizontal plane;
the gravitational acceleration does not vary with the flying height.
Still further, the kalman filter is an extended kalman filter.
Still further, the constructing a kalman filter based on the aerodynamic model includes:
listing discrete nonlinear system state equations and observation equations:
X(k+1)＝f[k,X(k)]+G(k)W1(k) (4)
Z(k)＝h[k,X(k)]+W2(k) (5)
Wherein k is the current time, f [ k, X (k) ], h [ k, X (k) ] are nonlinear functions, X (k) is a state vector, Z (k) is an observation vector, G (k) is a noise input matrix, and W 1(k)、W2 (k) is a noise matrix; wherein X (k) and Z (k) are:
X(k)＝[x(k),y(k),z(k),vx(k),vy(k),vz(k),ax(k),ay(k),az(k)]T (6)
Z(k)＝[d0(k),α0(k),θ0(k)]T (7)
Wherein x (k), y (k), z (k) and v x(k)、vy(k)、vz(k)、ax(k)、ay(k)、az (k) are coordinates, speed and acceleration of the unmanned aerial vehicle under an inertial coordinate system, and d 0(k)、α0(k)、θ0 (k) is the distance, azimuth angle and pitch angle of the unmanned aerial vehicle relative to a ground observation station respectively;
f [ k, X (k) ] is determined by the formula (3), and the expression of h [ k, X (k) ] is:
wherein, (x 0,y0,z0) is the coordinates of the ground observation station;
performing first-order Taylor expansion on the nonlinear functions f [ k, X (k) ], h [ k, X (k) ] on the X (k), and omitting second-order and above to obtain a simplified state equation and an observation equation:
Z(k)＝H(k)X(k)+Y(k)+W2(k) (10)
wherein phi (k+ 1|k), H (k) and Y (k) are determined by first-order Taylor expansion;
and the position coordinates and the speed of the unmanned aerial vehicle at the k+1 moment can be predicted by using a standard Kalman filtering algorithm, so that the prediction of the landing track of the unmanned aerial vehicle is realized.
In a second aspect, the present invention provides a large-span unmanned aerial vehicle landing trajectory prediction apparatus, including:
the model construction module is used for constructing an aerodynamic model of the large-span unmanned aerial vehicle under the interference of gusts;
A filter construction module for constructing a kalman filter based on the aerodynamic model;
The track prediction module is used for inputting observation data obtained in real time when the large-span unmanned aerial vehicle lands into the Kalman filter to predict the landing track of the large-span unmanned aerial vehicle.
Further, the model building module is specifically configured to:
Performing approximate processing on parameters related to modeling;
listing dynamics and kinematics equations of the large-span unmanned aerial vehicle;
The decoupling simplification under a typical flight state is carried out on the transverse and longitudinal coupled motion, and a small disturbance linearization method is adopted to obtain a transverse and lateral linearization matrix equation:
wherein the state variables Δβ, Δp, Δr, Sideslip angle beta, roll rate p, yaw rate r and roll angle respectively in the lateral directionDisturbance quantity from equilibrium state; delta a、Δδr is the deflection angle disturbance quantity of the aileron and the rudder which are input by control; y β is the lateral force derivative, Y p is the roll angle speed lateral force derivative, Y r is the yaw angle speed lateral force derivative, L β is the roll static stability derivative, L p is the lateral damping derivative, L r is the lateral crossover derivative, N β is the heading static stability derivative, N p is the heading crossover derivative, N r is the heading damping derivative,As a derivative of the rudder side force,For the aileron maneuver performance derivative,For the derivative of the roll moment coefficient with respect to the rudder,For the derivative of the yaw moment coefficient with respect to the aileron,Steering efficiency derivative for rudder; alpha is the attack angle of the unmanned aerial vehicle, theta is the pitch angle of the unmanned aerial vehicle, and V is the airspeed of the unmanned aerial vehicle;
Taking the windless state as the balanced state or the undisturbed state of the unmanned plane, regarding the response of the unmanned plane to wind as disturbance motion deviating from the balanced state when the unmanned plane is windy, and linearizing the disturbance to obtain:
wherein Δβ g is the sideslip angle reference disturbance quantity under no wind disturbance, V 0 is the unmanned aerial vehicle airspeed under the balanced state, and V w is the crosswind speed;
substituting the formula (2) into the formula (1) to obtain an aerodynamic model under the condition of gust interference:
Still further, the approximating the parameters related to modeling includes the following settings:
The large-span unmanned aerial vehicle is a rigid body, and the mass is a constant;
The geographic coordinate system is an inertial coordinate system;
The plane ox bzb of the machine body coordinate system is a symmetry plane of the large-span unmanned aerial vehicle, the unmanned aerial vehicle is symmetrical in geometric appearance and symmetrical in internal mass distribution, namely the inertia product I xy＝Iyz =0;
The earth's surface is a horizontal plane;
the gravitational acceleration does not vary with the flying height.
Still further, the kalman filter is an extended kalman filter.
Further, the filter construction module is specifically configured to:
listing discrete nonlinear system state equations and observation equations:
X(k+1)＝f[k,X(k)]+G(k)W1(k) (4)
Z(k)＝h[k,X(k)]+W2(k) (5)
Wherein k is the current time, f [ k, X (k) ], h [ k, X (k) ] are nonlinear functions, X (k) is a state vector, Z (k) is an observation vector, G (k) is a noise input matrix, and W 1(k)、W2 (k) is a noise matrix; wherein X (k) and Z (k) are:
X(k)＝[x(k),y(k),z(k),vx(k),vy(k),vz(k),ax(k),ay(k),az(k)]T (6)
Z(k)＝[d0(k),α0(k),θ0(k)]T (7)
Wherein x (k), y (k), z (k) and v x(k)、vy(k)、vz(k)、ax(k)、ay(k)、az (k) are coordinates, speed and acceleration of the unmanned aerial vehicle under an inertial coordinate system, and d 0(k)、α0(k)、θ0 (k) is the distance, azimuth angle and pitch angle of the unmanned aerial vehicle relative to a ground observation station respectively;
f [ k, X (k) ] is determined by the formula (3), and the expression of h [ k, X (k) ] is:
wherein, (x 0,y0,z0) is the coordinates of the ground observation station;
performing first-order Taylor expansion on the nonlinear functions f [ k, X (k) ], h [ k, X (k) ] on the X (k), and omitting second-order and above to obtain a simplified state equation and an observation equation:
Z(k)＝H(k)X(k)+Y(k)+W2(k) (10)
wherein phi (k+ 1|k), H (k) and Y (k) are determined by first-order Taylor expansion;
and the position coordinates and the speed of the unmanned aerial vehicle at the k+1 moment can be predicted by using a standard Kalman filtering algorithm, so that the prediction of the landing track of the unmanned aerial vehicle is realized.
Compared with the prior art, the invention has the following beneficial effects.
According to the invention, the large-span unmanned aerial vehicle landing trajectory can be predicted by constructing the aerodynamic model under the condition of the sudden wind interference of the large-span unmanned aerial vehicle, constructing the Kalman filter based on the aerodynamic model and inputting the real-time acquired observation data of the large-span unmanned aerial vehicle during landing into the Kalman filter. According to the invention, by constructing the aerodynamic model and the Kalman filter under the interference of the large-span unmanned aerial vehicle gust, the position coordinate and the speed of the next track can be predicted relatively quickly according to the historical track, and the recovery safety and the rapidity of the unmanned aerial vehicle for the unmanned aerial vehicle can be improved.
Drawings
Fig. 1 is a flowchart of a method for predicting a landing trajectory of a large-span unmanned aerial vehicle according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a body coordinate system and an inertial coordinate system.
FIG. 3 is a schematic diagram of an air flow coordinate system and a machine body coordinate system.
Fig. 4 is a schematic view of a velocity triangle at the time of side wind.
Fig. 5 is a block diagram of a large-span unmanned aerial vehicle landing trajectory prediction device according to an embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the drawings and the detailed description below, in order to make the objects, technical solutions and advantages of the present invention more apparent. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Fig. 1 is a flowchart of a method for predicting a landing trajectory of a large-span unmanned aerial vehicle according to an embodiment of the present invention, including the following steps:
Step 101, constructing an aerodynamic model of the large-span unmanned aerial vehicle under the interference of gusts;
102, constructing a Kalman filter based on the aerodynamic model;
and 103, inputting the observation data obtained in real time when the large-span unmanned aerial vehicle lands into a Kalman filter, and predicting the landing track of the large-span unmanned aerial vehicle.
In this embodiment, the step 101 is mainly used for constructing an aerodynamic model under the influence of a large-span unmanned aerial vehicle gust. Because of the large-span structure of the large-span unmanned plane, the large-span unmanned plane has larger response to the gust interference at the landing zone and has larger influence on the flying track, so that an airplane dynamics model under the action of the gust needs to be established. The airplane dynamics model under the action of the gust mainly considers the unmanned aerial vehicle small disturbance linearization model under the existence of the side wind, does not consider the influence of wind change gradient on the torque and aerodynamic derivative of the unmanned aerial vehicle, and only researches the dynamics problem of the airplane under the action of the side wind.
In this embodiment, step 102 is mainly used to construct a kalman filter. According to the embodiment, the prediction of the landing track of the large-span unmanned aerial vehicle is realized by carrying out Kalman filtering on the observed data when the large-span unmanned aerial vehicle lands, so that the Kalman filter needs to be established first. The Kalman filtering processing aims at random signals, observed quantity of the system is taken as input quantity of a filtering algorithm, required signal estimated value is taken as output quantity of the filtering algorithm, the two quantities are closely related with an observation updating algorithm through time updating, statistical characteristics of observation noise and system noise are utilized, and the required signals are estimated according to a state equation and an observation equation of the system. The Kalman filtering algorithm is a real-time recursive filtering algorithm realized by a computer, and belongs to an optimal estimation method.
In this embodiment, step 103 is mainly used for predicting the landing track of the large-span unmanned aerial vehicle. According to the embodiment, the real-time acquired observation data such as position coordinates and speed when the large-span unmanned aerial vehicle lands are input into the Kalman filter, so that the prediction of the landing track of the large-span unmanned aerial vehicle is realized. The prediction of the unmanned aerial vehicle landing track can be used for recycling and butting of the unmanned aerial vehicle and the unmanned aerial vehicle. And substituting the predicted point in the next step as a local pre-aiming point into a course angle for solving the pre-aiming point and the current gesture of the vehicle, and performing pure tracking control.
As an alternative embodiment, the constructing the aerodynamic model of the large-span unmanned aerial vehicle under the gust interference includes:
Performing approximate processing on parameters related to modeling;
listing dynamics and kinematics equations of the large-span unmanned aerial vehicle;
The decoupling simplification under a typical flight state is carried out on the transverse and longitudinal coupled motion, and a small disturbance linearization method is adopted to obtain a transverse and lateral linearization matrix equation:
wherein the state variables Δβ, Δp, Δr, Sideslip angle beta, roll rate p, yaw rate r and roll angle respectively in the lateral directionDisturbance quantity from equilibrium state; delta a、Δδr is the deflection angle disturbance quantity of the aileron and the rudder which are input by control; y β is the lateral force derivative, Y p is the roll angle speed lateral force derivative, Y r is the yaw angle speed lateral force derivative, L β is the roll static stability derivative, L p is the lateral damping derivative, L r is the lateral crossover derivative, N β is the heading static stability derivative, N p is the heading crossover derivative, N r is the heading damping derivative,As a derivative of the rudder side force,For the aileron maneuver performance derivative,For the derivative of the roll moment coefficient with respect to the rudder,For the derivative of the yaw moment coefficient with respect to the aileron,Steering efficiency derivative for rudder; alpha is the attack angle of the unmanned aerial vehicle, theta is the pitch angle of the unmanned aerial vehicle, and V is the airspeed of the unmanned aerial vehicle;
Taking the windless state as the balanced state or the undisturbed state of the unmanned plane, regarding the response of the unmanned plane to wind as disturbance motion deviating from the balanced state when the unmanned plane is windy, and linearizing the disturbance to obtain:
wherein Δβ g is the sideslip angle reference disturbance quantity under no wind disturbance, V 0 is the unmanned aerial vehicle airspeed under the balanced state, and V w is the crosswind speed;
substituting the formula (2) into the formula (1) to obtain an aerodynamic model under the condition of gust interference:
The embodiment provides a technical scheme for constructing an aerodynamic model under the interference of large-span unmanned aerial vehicle gusts. In order to simplify a dynamics model of the large-span unmanned aerial vehicle, parameters of the large-span unmanned aerial vehicle are approximated, for example, the large-span unmanned aerial vehicle is assumed to be a rigid body, and the mass of the large-span unmanned aerial vehicle is unchanged. And then obtaining dynamics and kinematics equations of the large-span unmanned aerial vehicle based on coordinate system transformation. The present embodiments relate to inertial, aircraft body, and airflow coordinate systems. The inertial coordinate system Ox gygzg is fixed on the earth surface, the origin is located on the ground and is arbitrarily selected as a fixed point, and three coordinate axes are respectively directed north (N), east (E) and ground (D). The body coordinate system Ox bybzb is fixedly connected with the unmanned aerial vehicle and moves along with the unmanned aerial vehicle, the origin is located at the center of mass of the unmanned aerial vehicle, the x b、zb axis is located in the symmetrical plane of the unmanned aerial vehicle, the xb is parallel to the axis of the unmanned aerial vehicle, the z b axis is perpendicular to the x b axis and points downwards, the y b axis is perpendicular to the symmetrical plane and points to the right. A schematic diagram of the body coordinate system and the inertial coordinate system is shown in FIG. 2. The origin of the airflow coordinate system Ox wywzw is located at the center of mass of the unmanned aerial vehicle, the x w axis always coincides with the airspeed direction of the unmanned aerial vehicle, the z w axis is located in the plane of symmetry of the unmanned aerial vehicle, is perpendicular to the x w axis and points downwards, and the y w axis is perpendicular to the Ox wzw plane and points to the right. A schematic diagram of the air flow coordinate system and the machine body coordinate system is shown in FIG. 3. The longitudinal, transverse and heading motions of the unmanned aerial vehicle are defined under a machine body coordinate system, and three components of aerodynamic moment (rolling moment L, pitching moment M and yawing moment N) are defined relative to three axes of the machine body coordinate system, wherein the relative relation is as follows:
Wherein F x、Fy、Fz is a component of the external force along the three axes of the machine body, p, r and q are angular velocities of the machine body coordinate system relative to the geographic coordinate system, u, v and w are linear velocities of the machine body coordinate system relative to the geographic coordinate system, L, M, N are projections of external force moment on the machine body axis respectively, I x、Iy、Iz are moment of inertia of the unmanned aerial vehicle to the three axes of the machine body respectively, and I xy、Iyz、Izx are three products of inertia of the unmanned aerial vehicle to the machine body respectively. The attitude angle of the unmanned aerial vehicle is determined by the relative relation between a machine body coordinate system and an inertial coordinate system, the pitch angle theta is an included angle between a machine body axis x b and a ground plane Ox gyg, and the yaw angle ψ is an included angle between the projection of the machine body axis x b on the ground plane Ox gyg and an x g axis; the roll angle phi is the angle between the z g axis and the vertical plane containing the x b axis, and the conversion relationship is as follows:
the conversion relation between the air flow coordinate system and the machine body coordinate system is as follows:
Wherein the attack angle alpha is an included angle between the projection of the unmanned plane speed vector on the unmanned plane symmetry plane and the x b axis, and the sideslip angle beta is an included angle between the unmanned plane speed vector and the unmanned plane symmetry plane.
And finally, constructing an aerodynamic model of the large-span unmanned aerial vehicle under the interference of gusts. The large-span unmanned plane dynamics equation set and the kinematics equation set are shown in the coordinate conversion formula, decoupling of transverse and longitudinal coupled motions in a typical flight state is simplified, and a small-disturbance linearization method is adopted for transverse and lateral motion analysis to obtain a transverse and lateral linearization matrix equation, such as the formula (1). (1) Y β、Yp、Yr、Lβ、Lp、Lr、Nβ、Np、Nr in the formula andFor lateral dynamics derivatives and control derivatives, the derivatives are a visual term similar to the mathematical derivatives in which the derivative of a variable can be expressed as the product of the variable and the derivative of the variable, and the left of equation (1) is the derivative of the disturbance variable, so the right of the equation is taken as the product of the disturbance variable and the derivative parameter.
When the unmanned aerial vehicle generates side wind in the flying process, the speed triangle of the horizontal plane is shown in fig. 4. The sideslip angle of the unmanned aerial vehicle is mainly influenced by the crosswind, the windless state is used as the balanced state or the undisturbed state of the unmanned aerial vehicle, and the response of the unmanned aerial vehicle to wind can be considered as follows: and (3) the unmanned aerial vehicle deviates from the small disturbance motion of the balance state after the wind acts, so that the small disturbance linearization can be performed, and the formula (2) is obtained. Substituting the formula (2) into the formula (1) to obtain an aerodynamic model under the condition of gust interference, such as the formula (3).
As an alternative embodiment, the approximating the parameters related to modeling includes the following settings:
The large-span unmanned aerial vehicle is a rigid body, and the mass is a constant;
The geographic coordinate system is an inertial coordinate system;
The plane ox bzb of the machine body coordinate system is a symmetry plane of the large-span unmanned aerial vehicle, the unmanned aerial vehicle is symmetrical in geometric appearance and symmetrical in internal mass distribution, namely the inertia product I xy＝Iyz =0;
The earth's surface is a horizontal plane;
the gravitational acceleration does not vary with the flying height.
The present embodiment presents a method of approximating parameters related to modeling. In order to simplify the model, the present embodiment performs 5-term approximation processing on parameters related to modeling, and detailed description thereof is omitted here.
As an alternative embodiment, the kalman filter is an extended kalman filter.
In order to improve the filtering accuracy, the present embodiment employs an extended kalman filter. Standard kalman filtering is built on linear algebra and hidden markov models, and is only suitable for linear systems. However, in actual engineering practice, there are always nonlinear characteristics with different degrees in the system in the real environment, only very few systems can be approximately regarded as linear systems, and most of the systems cannot be simply processed through approximate linearization, or are difficult to quantitatively describe through linear differential equations or thread differential equations. The flying state of the large-span unmanned aerial vehicle is a nonlinear system. For this purpose, the present embodiment employs an extended kalman filter technique that can cope with nonlinear systems. The core idea of the extended Kalman filtering is that for a general nonlinear system, a nonlinear function is firstly expanded into a Taylor series around a filtering value, a second order and above term are omitted, an approximate linearization model is obtained, and then the Kalman filtering is applied to complete the prediction estimation of a target. Simulation results show that in the low-speed drop track prediction of the large-span unmanned aerial vehicle under the interference of gusts, the prediction precision of the extended Kalman filter is higher than that of the standard Kalman filter; and the real-time performance is good, and the method has certain practicability.
As an alternative embodiment, the constructing a kalman filter based on the aerodynamic model includes:
listing discrete nonlinear system state equations and observation equations:
X(k+1)＝f[k,X(k)]+G(k)W1(k) (4)
Z(k)＝h[k,X(k)]+W2(k) (5)
Wherein k is the current time, f [ k, X (k) ], h [ k, X (k) ] are nonlinear functions, X (k) is a state vector, Z (k) is an observation vector, G (k) is a noise input matrix, and W 1(k)、W2 (k) is a noise matrix; wherein X (k) and Z (k) are:
X(k)＝[x(k),y(k),z(k),vx(k),vy(k),vz(k),ax(k),ay(k),az(k)]T (6)
Z(k)＝[d0(k),α0(k),θ0(k)]T (7)
Wherein x (k), y (k), z (k) and v x(k)、vy(k)、vz(k)、ax(k)、ay(k)、az (k) are coordinates, speed and acceleration of the unmanned aerial vehicle under an inertial coordinate system, and d 0(k)、α0(k)、θ0 (k) is the distance, azimuth angle and pitch angle of the unmanned aerial vehicle relative to a ground observation station respectively;
f [ k, X (k) ] is determined by the formula (3), and the expression of h [ k, X (k) ] is:
wherein, (x 0,y0,z0) is the coordinates of the ground observation station;
performing first-order Taylor expansion on the nonlinear functions f [ k, X (k) ], h [ k, X (k) ] on the X (k), and omitting second-order and above to obtain a simplified state equation and an observation equation:
Z(k)＝H(k)X(k)+Y(k)+W2(k) (10)
wherein phi (k+ 1|k), H (k) and Y (k) are determined by first-order Taylor expansion;
and the position coordinates and the speed of the unmanned aerial vehicle at the k+1 moment can be predicted by using a standard Kalman filtering algorithm, so that the prediction of the landing track of the unmanned aerial vehicle is realized.
The embodiment provides a specific technical scheme for realizing the extended Kalman filtering. First, discrete nonlinear system state equations and observation equations are given, as in equations (4), (5), where f [ k, X (k) ], h [ k, X (k) ] are nonlinear functions. Then, expressions of a state vector X (k) and an observation vector Z (k) of the unmanned aerial vehicle are listed as (5) and (6), wherein X (k) is a 9-dimensional vector consisting of position coordinates, speed and acceleration of three components of X, y and Z, and Z (k) is a 3-dimensional vector consisting of distance, azimuth angle and pitch angle of the unmanned aerial vehicle relative to a ground observation station. f [ k, X (k) ] is determined by the unmanned aerial vehicle aerodynamic model shown in the formula (3), and the expression of h [ k, X (k) ] is shown in the formula (8). The nonlinear functions f [ k, X (k) ], h [ k, X (k) ] are subjected to Taylor expansion on X (k), namely, only one term and a constant term are reserved, and the higher-order term with more than two times is ignored, so that an approximate simple state equation and an observation equation are obtained, such as (9) and (10), wherein a matrix phi (k+ 1|k) in the formula,H (k), Y (k) are determined by a first order Taylor expansion, wherein Φ (k+ 1|k),The expression of (2) is:
Wherein Δt is the interval time of state transition, V is the airspeed of the unmanned aerial vehicle in the OXY plane, and r (k) is determined by the formula (3).
And finally, calculating a gain matrix and an error matrix according to a standard Kalman filtering algorithm, and predicting the position coordinate and the speed at the k+1 time, thereby realizing the prediction of the landing track of the unmanned aerial vehicle.
Fig. 5 is a schematic diagram of a device for predicting a landing trajectory of a large-span unmanned aerial vehicle according to an embodiment of the present invention, where the device includes:
the model construction module 11 is used for constructing an aerodynamic model of the large-span unmanned aerial vehicle under the influence of gusts;
a filter construction module 12 for constructing a kalman filter based on the aerodynamic model;
the trajectory prediction module 13 is configured to input observation data obtained in real time when the large-span unmanned aerial vehicle lands into a kalman filter, and predict a landing trajectory of the large-span unmanned aerial vehicle.
The device of this embodiment may be used to implement the technical solution of the method embodiment shown in fig. 1, and its implementation principle and technical effects are similar, and are not described here again. As well as the latter embodiments, will not be explained again.
As an alternative embodiment, the model building module 11 is specifically configured to:
Performing approximate processing on parameters related to modeling;
listing dynamics and kinematics equations of the large-span unmanned aerial vehicle;
The decoupling simplification under a typical flight state is carried out on the transverse and longitudinal coupled motion, and a small disturbance linearization method is adopted to obtain a transverse and lateral linearization matrix equation:
wherein the state variables Δβ, Δp, Δr, Sideslip angle beta, roll rate p, yaw rate r and roll angle respectively in the lateral directionDisturbance quantity from equilibrium state; delta a、Δδr is the deflection angle disturbance quantity of the aileron and the rudder which are input by control; y β is the lateral force derivative, Y p is the roll angle speed lateral force derivative, Y r is the yaw angle speed lateral force derivative, L β is the roll static stability derivative, L p is the lateral damping derivative, L r is the lateral crossover derivative, N β is the heading static stability derivative, N p is the heading crossover derivative, N r is the heading damping derivative,As a derivative of the rudder side force,For the aileron maneuver performance derivative,For the derivative of the roll moment coefficient with respect to the rudder,For the derivative of the yaw moment coefficient with respect to the aileron,Steering efficiency derivative for rudder; alpha is the attack angle of the unmanned aerial vehicle, theta is the pitch angle of the unmanned aerial vehicle, and V is the airspeed of the unmanned aerial vehicle;
Taking the windless state as the balanced state or the undisturbed state of the unmanned plane, regarding the response of the unmanned plane to wind as disturbance motion deviating from the balanced state when the unmanned plane is windy, and linearizing the disturbance to obtain:
wherein Δβ g is the sideslip angle reference disturbance quantity under no wind disturbance, V 0 is the unmanned aerial vehicle airspeed under the balanced state, and V w is the crosswind speed;
substituting the formula (2) into the formula (1) to obtain an aerodynamic model under the condition of gust interference:
as an alternative embodiment, the approximating the parameters related to modeling includes the following settings:
The large-span unmanned aerial vehicle is a rigid body, and the mass is a constant;
The geographic coordinate system is an inertial coordinate system;
The plane ox bzb of the machine body coordinate system is a symmetry plane of the large-span unmanned aerial vehicle, the unmanned aerial vehicle is symmetrical in geometric appearance and symmetrical in internal mass distribution, namely the inertia product I xy＝Iyz =0;
The earth's surface is a horizontal plane;
the gravitational acceleration does not vary with the flying height.
As an alternative embodiment, the kalman filter is an extended kalman filter.
As an alternative embodiment, the filter construction module 12 is specifically configured to:
listing discrete nonlinear system state equations and observation equations:
X(k+1)＝f[k,X(k)]+G(k)W1(k) (4)
Z(k)＝h[k,X(k)]+W2(k) (5)
Wherein k is the current time, f [ k, X (k) ], h [ k, X (k) ] are nonlinear functions, X (k) is a state vector, Z (k) is an observation vector, G (k) is a noise input matrix, and W 1(k)、W2 (k) is a noise matrix; wherein X (k) and Z (k) are:
X(k)＝[x(k),y(k),z(k),vx(k),vy(k),vz(k),ax(k),ay(k),az(k)]T (6)
Z(k)＝[d0(k),α0(k),θ0(k)]T (7)
Wherein x (k), y (k), z (k) and v x(k)、vy(k)、vz(k)、ax(k)、ay(k)、az (k) are coordinates, speed and acceleration of the unmanned aerial vehicle under an inertial coordinate system, and d 0(k)、α0(k)、θ0 (k) is the distance, azimuth angle and pitch angle of the unmanned aerial vehicle relative to a ground observation station respectively;
f [ k, X (k) ] is determined by the formula (3), and the expression of h [ k, X (k) ] is:
wherein, (x 0,y0,z0) is the coordinates of the ground observation station;
performing first-order Taylor expansion on the nonlinear functions f [ k, X (k) ], h [ k, X (k) ] on the X (k), and omitting second-order and above to obtain a simplified state equation and an observation equation:
Z(k)＝H(k)X(k)+Y(k)+W2(k) (10)
wherein phi (k+ 1|k), H (k) and Y (k) are determined by first-order Taylor expansion;
and the position coordinates and the speed of the unmanned aerial vehicle at the k+1 moment can be predicted by using a standard Kalman filtering algorithm, so that the prediction of the landing track of the unmanned aerial vehicle is realized.
The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present invention should be included in the present invention. Therefore, the protection scope of the invention is subject to the protection scope of the claims.
Claims (4)
1. The method for predicting the landing track of the large-span unmanned aerial vehicle is characterized by comprising the following steps of:
constructing an aerodynamic model under the interference of gusts of the large-span unmanned aerial vehicle;
Constructing a kalman filter based on the aerodynamic model;
Inputting observation data obtained in real time when the large-span unmanned aerial vehicle lands into a Kalman filter, and predicting the landing track of the large-span unmanned aerial vehicle;
the constructing of the aerodynamic model under the influence of the gust of the large-span unmanned aerial vehicle comprises the following steps:
Performing approximate processing on parameters related to modeling;
listing dynamics and kinematics equations of the large-span unmanned aerial vehicle;
The decoupling simplification under a typical flight state is carried out on the transverse and longitudinal coupled motion, and a small disturbance linearization method is adopted to obtain a transverse and lateral linearization matrix equation:
wherein the state variables Δβ, Δp, Δr, Sideslip angle beta, roll rate p, yaw rate r and roll angle respectively in the lateral directionDisturbance quantity from equilibrium state; delta a、Δδr is the deflection angle disturbance quantity of the aileron and the rudder which are input by control; y β is the lateral force derivative, Y p is the roll angle speed lateral force derivative, Y r is the yaw angle speed lateral force derivative, L β is the roll static stability derivative, L p is the lateral damping derivative, L r is the lateral crossover derivative, N β is the heading static stability derivative, N p is the heading crossover derivative, N r is the heading damping derivative,As a derivative of the rudder side force,For the aileron maneuver performance derivative,For the derivative of the roll moment coefficient with respect to the rudder,For the derivative of the yaw moment coefficient with respect to the aileron,Steering efficiency derivative for rudder; alpha is the attack angle of the unmanned aerial vehicle, theta is the pitch angle of the unmanned aerial vehicle, and V is the airspeed of the unmanned aerial vehicle;
Taking the windless state as the balanced state or the undisturbed state of the unmanned plane, regarding the response of the unmanned plane to wind as disturbance motion deviating from the balanced state when the unmanned plane is windy, and linearizing the disturbance to obtain:
wherein Δβ g is the sideslip angle reference disturbance quantity under no wind disturbance, V 0 is the unmanned aerial vehicle airspeed under the balanced state, and V w is the crosswind speed;
substituting the formula (2) into the formula (1) to obtain an aerodynamic model under the condition of gust interference:
The Kalman filter is an extended Kalman filter;
The constructing a kalman filter based on the aerodynamic model includes:
listing discrete nonlinear system state equations and observation equations:
X(k+1)＝f[k,X(k)]+G(k)W1(k) (4)
Z(k)＝h[k,X(k)]+W2(k) (5)
Wherein k is the current time, f [ k, X (k) ], h [ k, X (k) ] are nonlinear functions, X (k) is a state vector, Z (k) is an observation vector, G (k) is a noise input matrix, and W 1(k)、W2 (k) is a noise matrix; wherein X (k) and Z (k) are:
X(k)＝[x(k),y(k),z(k),vx(k),vy(k),vz(k),ax(k),ay(k),az(k)]T (6)
Z(k)＝[d0(k),α0(k),θ0(k)]T (7)
Wherein x (k), y (k), z (k) and v x(k)、vy(k)、vz(k)、ax(k)、ay(k)、az (k) are coordinates, speed and acceleration of the unmanned aerial vehicle under an inertial coordinate system, and d 0(k)、α0(k)、θ0 (k) is the distance, azimuth angle and pitch angle of the unmanned aerial vehicle relative to a ground observation station respectively;
f [ k, X (k) ] is determined by the formula (3), and the expression of h [ k, X (k) ] is:
wherein, (x 0,y0,z0) is the coordinates of the ground observation station;
performing first-order Taylor expansion on the nonlinear functions f [ k, X (k) ], h [ k, X (k) ] on the X (k), and omitting second-order and above to obtain a simplified state equation and an observation equation:
Z(k)＝H(k)X(k)+Y(k)+W2(k) (10)
wherein phi (k+ 1|k), H (k) and Y (k) are determined by first-order Taylor expansion;
and the position coordinates and the speed of the unmanned aerial vehicle at the k+1 moment can be predicted by using a standard Kalman filtering algorithm, so that the prediction of the landing track of the unmanned aerial vehicle is realized.
2. The method for predicting landing trajectories of a large-span unmanned aerial vehicle of claim 1, the approximating of the parameters related to modeling includes the following settings:
The large-span unmanned aerial vehicle is a rigid body, and the mass is a constant;
The geographic coordinate system is an inertial coordinate system;
The plane ox bzb of the machine body coordinate system is a symmetry plane of the large-span unmanned aerial vehicle, the unmanned aerial vehicle is symmetrical in geometric appearance and symmetrical in internal mass distribution, namely the inertia product I xy＝Iyz =0;
The earth's surface is a horizontal plane;
the gravitational acceleration does not vary with the flying height.
3. The utility model provides a big span unmanned aerial vehicle drop trajectory prediction unit which characterized in that includes:
the model construction module is used for constructing an aerodynamic model of the large-span unmanned aerial vehicle under the interference of gusts;
A filter construction module for constructing a kalman filter based on the aerodynamic model;
The track prediction module is used for inputting observation data obtained in real time when the large-span unmanned aerial vehicle lands into the Kalman filter to predict the landing track of the large-span unmanned aerial vehicle;
the constructing of the aerodynamic model under the influence of the gust of the large-span unmanned aerial vehicle comprises the following steps:
Performing approximate processing on parameters related to modeling;
listing dynamics and kinematics equations of the large-span unmanned aerial vehicle;
The decoupling simplification under a typical flight state is carried out on the transverse and longitudinal coupled motion, and a small disturbance linearization method is adopted to obtain a transverse and lateral linearization matrix equation:
wherein the state variables Δβ, Δp, Δr, Sideslip angle beta, roll rate p, yaw rate r and roll angle respectively in the lateral directionDisturbance quantity from equilibrium state; delta a、Δδr is the deflection angle disturbance quantity of the aileron and the rudder which are input by control; y β is the lateral force derivative, Y p is the roll angle speed lateral force derivative, Y r is the yaw angle speed lateral force derivative, L β is the roll static stability derivative, L p is the lateral damping derivative, L r is the lateral crossover derivative, N β is the heading static stability derivative, N p is the heading crossover derivative, N r is the heading damping derivative,As a derivative of the rudder side force,For the aileron maneuver performance derivative,For the derivative of the roll moment coefficient with respect to the rudder,For the derivative of the yaw moment coefficient with respect to the aileron,Steering efficiency derivative for rudder; alpha is the attack angle of the unmanned aerial vehicle, theta is the pitch angle of the unmanned aerial vehicle, and V is the airspeed of the unmanned aerial vehicle;
Taking the windless state as the balanced state or the undisturbed state of the unmanned plane, regarding the response of the unmanned plane to wind as disturbance motion deviating from the balanced state when the unmanned plane is windy, and linearizing the disturbance to obtain:
wherein Δβ g is the sideslip angle reference disturbance quantity under no wind disturbance, V 0 is the unmanned aerial vehicle airspeed under the balanced state, and V w is the crosswind speed;
substituting the formula (2) into the formula (1) to obtain an aerodynamic model under the condition of gust interference:
The Kalman filter is an extended Kalman filter;
The constructing a kalman filter based on the aerodynamic model includes:
listing discrete nonlinear system state equations and observation equations:
X(k+1)＝f[k,X(k)]+G(k)W1(k) (4)
Z(k)＝h[k,X(k)]+W2(k) (5)
Wherein k is the current time, f [ k, X (k) ], h [ k, X (k) ] are nonlinear functions, X (k) is a state vector, Z (k) is an observation vector, G (k) is a noise input matrix, and W 1(k)、W2 (k) is a noise matrix; wherein X (k) and Z (k) are:
X(k)＝[x(k),y(k),z(k),vx(k),vy(k),vz(k),ax(k),ay(k),az(k)]T (6)
Z(k)＝[d0(k),α0(k),θ0(k)]T (7)
Wherein x (k), y (k), z (k) and v x(k)、vy(k)、vz(k)、ax(k)、ay(k)、az (k) are coordinates, speed and acceleration of the unmanned aerial vehicle under an inertial coordinate system, and d 0(k)、α0(k)、θ0 (k) is the distance, azimuth angle and pitch angle of the unmanned aerial vehicle relative to a ground observation station respectively;
f [ k, X (k) ] is determined by the formula (3), and the expression of h [ k, X (k) ] is:
wherein, (x 0,y0,z0) is the coordinates of the ground observation station;
performing first-order Taylor expansion on the nonlinear functions f [ k, X (k) ], h [ k, X (k) ] on the X (k), and omitting second-order and above to obtain a simplified state equation and an observation equation:
Z(k)＝H(k)X(k)+Y(k)+W2(k) (10)
wherein phi (k+ 1|k), H (k) and Y (k) are determined by first-order Taylor expansion;
and the position coordinates and the speed of the unmanned aerial vehicle at the k+1 moment can be predicted by using a standard Kalman filtering algorithm, so that the prediction of the landing track of the unmanned aerial vehicle is realized.
4. A large span unmanned landing trajectory prediction apparatus according to claim 3, wherein the approximating of the modeling related parameters comprises the following settings:
The large-span unmanned aerial vehicle is a rigid body, and the mass is a constant;
The geographic coordinate system is an inertial coordinate system;
The plane ox bzb of the machine body coordinate system is a symmetry plane of the large-span unmanned aerial vehicle, the unmanned aerial vehicle is symmetrical in geometric appearance and symmetrical in internal mass distribution, namely the inertia product I xy＝Iyz =0;
The earth's surface is a horizontal plane;
the gravitational acceleration does not vary with the flying height.
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