CN-121978919-A - Unmanned aerial vehicle track tracking method based on grid Kalman filtering and predictive control

CN121978919ACN 121978919 ACN121978919 ACN 121978919ACN-121978919-A

Abstract

The invention relates to a four-rotor unmanned aerial vehicle track tracking method based on grid Kalman filtering and model predictive control, and belongs to the technical field of unmanned aerial vehicle control. According to the method, first, a Korobov lattice rule is adopted to generate a sample point based on Cranley-Patterson random shift, and a Kalman filtering framework constrained by a linear matrix inequality is combined, so that high-precision estimation of the pose and the speed of the unmanned aerial vehicle is realized, and the accuracy and the instantaneity of state estimation are improved. Aiming at practical constraints such as bounded disturbance and actuator saturation, a robust predictive controller is designed, and compared with a conventional model predictive control method, the problems of uncertainty of a system model, external bounded disturbance and actuator saturation can be effectively solved. And finally, carrying out simulation and track tracking experiment verification in a physical environment through an MATLAB simulation platform and an indoor optical positioning unmanned aerial vehicle experiment platform. The invention can be applied to various unmanned aerial vehicle autonomous operation scenes such as air reconnaissance, material delivery and the like through the high-precision state estimation and robust control collaborative design.

Inventors

TANG XIAOMING
ZHANG YU
TANG XIANLUN
CAI LINQIN
WANG HUIMING
YU YANG
CAI LINJUN

Assignees

重庆邮电大学

Dates

Publication Date: 20260505
Application Date: 20260107

Claims (10)

1. The unmanned aerial vehicle track tracking method based on grid Kalman filtering and predictive control is characterized by comprising the following steps of: S1, constructing a linear unmanned aerial vehicle kinematic error model; s2, establishing a state model and a measurement model of a Kalman filter according to the unmanned aerial vehicle kinematic error model obtained in the step S1; S3, generating a quasi-Gaussian sampling point according to a rank-1 lattice rule, transmitting the obtained sampling point through a linear function, and carrying out weighting treatment to obtain prior state estimation and prior error covariance; s4, constructing a linear matrix inequality optimization problem, solving the optimization problem meeting constraint conditions by considering the state constraint of the system, and updating the Kalman gain and posterior estimation of the filter; s5, constructing a track tracking robust model prediction control optimization problem based on an unmanned aerial vehicle kinematic error model, and solving a core control matrix and parameters; and S6, verifying initial feasibility, solving control input and realizing track tracking.
2. The unmanned aerial vehicle track tracking method based on the grid kalman filtering and the predictive control according to claim 1, wherein in the step S1, a linear unmanned aerial vehicle kinematic error model is built, specifically: ; ; Wherein, the , 、、、 Respectively representing a state vector of the system at the time k+1, a state transition matrix, a control matrix and a control input vector of the system, wherein, 、、 Respectively representing the position coordinates of the unmanned aerial vehicle; 、、 The speeds of the unmanned aerial vehicle on the xyz axis are respectively; 、、 respectively representing the rolling angle, the pitch angle and the yaw angle of the unmanned aerial vehicle; Representing a control input vector for the drone, 、、、 Respectively represent control inputs of the unmanned aerial vehicle, wherein, 、、、 By means of The control input transformation of (a) decouples the total thrust F from the gravity compensation term, 、、 Respectively representing the moment born by the unmanned aerial vehicle in the xyz three axes; 、、 respectively representing the rotational inertia of the unmanned aerial vehicle in the xyz triaxial; Gravitational acceleration; is unmanned aerial vehicle quality.
3. The unmanned aerial vehicle track tracking method based on the grid Kalman filtering and the predictive control according to claim 1, wherein in the step S2, a state model and a measurement model of the grid Kalman filter are established, specifically: Wherein, the To satisfy the function in the form of a linear matrix transformation, the concrete transformation is expressed as Wherein Is a priori state error; And Representing the process noise and the measurement noise at the kth step, respectively. 、、 The true value of the system state at time k, the measured true value and the function satisfying the linear matrix transformation form are represented, respectively.
4. The unmanned aerial vehicle track tracking method based on grid Kalman filtering and predictive control according to claim 1, wherein in the step S3, a quasi-Gaussian sampling point is generated according to a rank-1 lattice rule, specifically comprising the following steps: Generating low-bias points with random displacement using rank-1 lattice rule : Wherein, the The number of the sampling points is calculated; is in a unit hypercube Random displacements to ensure that the resulting data is unbiased; Is a generated vector composed of d integers , Is associated with An integer of prime numbers; An index representing the sampling point; Will have low deviation point Is converted into the mean value of Covariance is Is a quasi-Gaussian point of (2) : Wherein, the Is an inverse normal distribution function, the units are hypercube Lattice point set defined in (1) Mapping to an integration region; is by means of alignment of Obtained by Cholesky decomposition.
5. The unmanned aerial vehicle track tracking method based on grid kalman filtering and predictive control according to claim 1, wherein in the step S3, the obtained sampling points are transferred through a linear function, and the prior state estimation and the prior error covariance are obtained through weighting processing, specifically as follows: Wherein, the Estimating for a priori state; Is a priori error covariance; is process noise Is a covariance of (c).
6. The unmanned aerial vehicle track tracking method based on grid Kalman filtering and predictive control according to claim 1, wherein in the step S4, a linear matrix inequality optimization problem is constructed, the optimization problem meeting constraint conditions is solved by considering the state constraint of a system, and the Kalman gain and posterior estimation of a filter are updated, and the specific implementation method comprises the following steps: calculating a sampling point at the k moment according to the prior state estimation and the prior error covariance obtained in the step S3: ; Wherein the method comprises the steps of Sampling points at the time of k; is by means of alignment of Obtained by Cholesky decomposition; the obtained sampling points are transmitted through a linear function, and weighting treatment is carried out to obtain prediction measurement estimation, prediction measurement error covariance and cross error covariance: ; ; ; Wherein, the Is a predictive measurement estimate; Is the predicted measurement error covariance; Is the cross error covariance; To measure errors Is a covariance of (c). Selecting an objective function : Wherein, the , Is a measured value; representing an observation residual, i.e. a deviation between an observation value and a predicted value; Is Kalman gain; Representing a measurement matrix; The objective function follows the maximum likelihood derivation of recursive least squares and Kalman filtering taking into account It is possible to obtain: Combining the two formulas to obtain: ; construction of cost function : ; In the formula, Subject to the following constraints: ; The resulting constraint is converted into the form of a linear matrix inequality using Schur's complement theory: To minimize cost function To achieve this, the following optimization problem is solved, and the filter gain is calculated: Wherein, the , , Selected as a design variable, under constraint conditions such that , And at all possible And Gain to minimize cost function : Based on the obtained Kalman gain Obtaining a posterior estimated value and posterior error covariance: Wherein, the Is a posterior estimate; is the posterior error covariance.
7. The unmanned aerial vehicle track tracking method based on grid Kalman filtering and predictive control according to claim 1, wherein in the step S5, a track tracking robust model predictive control optimization problem is built based on a four-rotor unmanned aerial vehicle kinematic error model, and a core control matrix and parameters are solved. The method specifically comprises the following steps: based on four rotor unmanned aerial vehicle kinematic error model, define system state The system expression is ; Respectively representing unmanned plane states and reference target states estimated by Kalman filtering; Wherein, the I.e. , And is also provided with ; Is satisfied by the standard saturation function ; 、 Respectively represent convex hulls and are composed of L represents the number of vertexes forming the convex hull; Representing convex hull combination coefficients; To meet the bounded disturbance ; Obtained by a kalman filter; An infinite time domain 'min-max' optimization objective function is designed: Wherein, the ; Is an appropriate weighting matrix; Introduction of Lyapunov function The stability of the system is characterized by combining a secondary finite theory, inputs containing actuator saturation can be expressed as ; Representing a feedback control law; Wherein, the And (2) and ; The convex combination condition is satisfied. Forcing the lyapunov function to satisfy: The upper bound of the objective function can be obtained by accumulating the above: 。 According to the quadratic constraint theory, the disturbance vector is assumed Satisfy the following requirements For the following purposes The system quadratic constraint for the lyapunov matrix is equivalent to the following condition: ; Wherein, the Is a non-negative scalar multiplier; to minimize the upper bound of the objective function For the purpose, solving a convex optimization problem meeting the inequality constraint of the linear matrix to obtain an optimal matrix and parameters: The constraint conditions include: Obtaining a control matrix , Wherein, the method comprises the steps of, Is that Is the first of (2) A row vector; satisfying system state invariant sets 。
8. The unmanned aerial vehicle track-following method based on grid kalman filtering and predictive control according to claim 1, wherein in the step S6, initial feasibility is verified, control input is solved, track-following is performed, specifically as follows: Checking initial state of unmanned aerial vehicle Whether or not to fall into the invariant set If not, adjusting the weighting matrix 、 Or constraint parameters Returning to the step S5 again to solve the optimization problem until the initial state meets the feasible region requirement; Optimal control law matrix based on S5 、 Solving for saturation control inputs 。 And simultaneously updating the system state information in real time, entering a control flow of the next sampling period, and continuously optimizing the track tracking effect.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the unmanned aerial vehicle trajectory tracking method based on grid kalman filtering and predictive control as claimed in any one of claims 1 to 8 when executing the program.
10. A non-transitory computer readable storage medium having stored thereon a computer program, wherein the computer program when executed by a processor implements the grid kalman filter and predictive control based unmanned aerial vehicle trajectory tracking method according to any one of claims 1 to 8.

Description

Unmanned aerial vehicle track tracking method based on grid Kalman filtering and predictive control Technical Field The invention relates to the technical field of unmanned aerial vehicle control, in particular to a four-rotor unmanned aerial vehicle track tracking method based on grid Kalman filtering and model predictive control. Background The unmanned aerial vehicle track tracking control is a core component of unmanned aerial vehicle autonomous flight technology, the performance of the unmanned aerial vehicle track tracking control directly determines whether the unmanned aerial vehicle can fly safely and stably according to a preset track, and the unmanned aerial vehicle track tracking control is an important precondition for the unmanned aerial vehicle to keep reliable running in complex airspace, dynamic weather and changeable task scenes. The technology covers key links such as system kinematics modeling, flight state estimation, track tracking controller design and the like, and ensures that an unmanned aerial vehicle can finish various autonomous tasks in a high-efficiency and reliable mode through a systematic method. Although the track tracking control technology has important theoretical and application values, the practical development of the track tracking control technology still faces various restrictions. Firstly, external environment interference (such as gust and airflow disturbance) can introduce model uncertainty to influence control accuracy and stability, secondly, the control algorithm has high calculation complexity, which can cause the real-time performance of the system to be reduced, and in addition, the system state information is often difficult to directly and accurately acquire, so that the tracking performance is deteriorated. If the problems cannot be effectively solved, the flight safety and the task reliability of the unmanned aerial vehicle are directly affected. In terms of state estimation, the traditional Unscented Kalman Filter (UKF) approximates the state and observation propagation process of a nonlinear system by weighting Sigma points, has good estimation performance, but the number of sampling points is obviously increased along with the increase of the system dimension, and is not beneficial to the improvement of calculation efficiency. Furthermore, the classical Kalman Filter (KF) framework does not usually explicitly take into account system state constraints, where estimation accuracy and reliability are affected when physical or safety clipping is present in the actual system. In the aspect of track tracking control, model Predictive Control (MPC) is paid attention to because of the capability of processing constraint and optimizing performance, however, the state of the existing research multi-hypothesis system is completely measurable, and the conventional model predictive control method needs to solve the optimization problem with constraint on line, has heavy calculation load and is difficult to directly deploy on an unmanned plane platform with limited calculation resources. Aiming at the problems, the invention provides a four-rotor unmanned aerial vehicle track tracking method based on grid Kalman filtering and model predictive control, aiming at improving the tracking precision and flight stability of the unmanned aerial vehicle under interference and uncertainty. The method starts from the actual demands of external interference, model uncertainty and difficult state acquisition, and combines grid Kalman filtering, robust model predictive control and linear matrix inequality technologies. Firstly, linear matrix inequality processing state constraint is introduced into a classical Kalman filtering framework, the estimation accuracy is ensured, meanwhile, the on-line calculation amount is reduced, secondly, a robust model prediction controller is designed, bounded interference and actuator saturation constraint are considered, and finally, a set of integrated control scheme which is complete in structure and capable of realizing high-performance track tracking is formed. Through retrieval, application publication number CN118760224A, a method and a system for controlling the pose and anti-swing of a hanging unmanned aerial vehicle based on model predictive control, and relates to the technical field of anti-swing control of the hanging unmanned aerial vehicle. The method comprises the technical key points of constructing a four-rotor unmanned aerial vehicle dynamics model of a hanging load, carrying out linearization treatment on the four-rotor unmanned aerial vehicle dynamics model of the hanging load to obtain a state equation of a hanging system of a time-varying approximately linearization unmanned aerial vehicle, designing a controller based on the state equation of the hanging system of the time-varying approximately linearization unmanned aerial vehicle, designing a state estimator of the hanging system of the unmanned aerial vehicle by usin