CN115167424A - Path tracking control method of intelligent agricultural machine - Google Patents
Path tracking control method of intelligent agricultural machine Download PDFInfo
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Abstract
The invention discloses a path tracking control method of an intelligent agricultural machine, which comprises the following steps: step one, designing a control system architecture; designing an intelligent agricultural machinery dynamics model; designing an upper-layer controller architecture; step four, realizing the estimation of the transverse dynamic parameters of the intelligent agricultural machinery with constraints based on the double unscented Kalman filtering; step five, self-adaptive model prediction control based on the dynamic model; compared with the existing path tracking control method, the method improves the path tracking precision of the intelligent agricultural machine by combining the constraint double unscented Kalman filtering and the adaptive model tracking control, thereby improving the operation efficiency, the operation quality and the economic benefit of the agricultural machine; the path tracking control system provided by the invention can be deployed in actual agricultural machinery, and the requirements of reliability, instantaneity and cost of an embedded system are met on the premise of realizing good tracking precision.
Description
Technical Field
The invention relates to the technical field of intelligent agricultural machinery, in particular to a path tracking control method of an intelligent agricultural machinery.
Background
The path tracking error is defined as the shortest distance between the current position of the vehicle and the expected path, a controller for good path tracking should ensure the average deviation and the maximum deviation between the actual driving path and the expected path of the vehicle as small as possible, and the accurate path tracking of the automatic agricultural vehicle is one of effective ways for improving the agricultural production efficiency and quality. Such as manually or automatically spraying agricultural chemicals, cause gaps or overlaps in the actual working area due to inaccurate path tracking, excessive and insufficient quantities of agricultural chemicals in parts of crops, which in turn leads to a reduction in crop yield and quality. Due to the complex working environment of the agricultural vehicle and the existence of unknown noise and interference, the realization of accurate path tracking of the agricultural vehicle is challenging.
Existing path tracking methods can be divided into three major categories: geometric methods, motion control laws and optimal control, which all have respective problems in the aspects of precision, cost and the like; the existing path tracking control methods of intelligent agricultural machinery, such as a PID control method based on fuzzy logic on-line setting control parameters and a longitudinal and transverse dynamics control method based on fuzzy PID control and a Linear Quadratic Regulator (LQR), are only capable of realizing good tracking performance under a certain specific condition, and are not based on a path tracking control method of a dynamics model which can consider the dynamics characteristics of the agricultural machinery more fully and is beneficial to improving the path tracking precision; although a dynamic model is considered, the effectiveness of a control algorithm is only checked in a simulation environment, and the real-time performance, robustness and path tracking performance of a controller are not checked in an actual farmland, namely, some existing executable path tracking control methods are poor in precision, and other algorithms capable of realizing high-precision path tracking are limited by the performance and cost of an embedded system and can not be deployed on a real agricultural machine for the moment.
Disclosure of Invention
The invention aims to provide a path tracking control method of an intelligent agricultural machine, which aims to solve the problems in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme: a path tracking control method of an intelligent agricultural machine comprises the following steps: step one, designing a control system architecture; designing an intelligent agricultural machinery dynamics model; designing an upper-layer controller architecture; fourthly, realizing the estimation of the transverse dynamic parameters of the intelligent agricultural machinery with constraints based on the double unscented Kalman filtering; step five, self-adaptive model prediction control based on the dynamic model;
in the first step, the upper controller acquires current state information of the agricultural machine acquired by the sensor, carries out state estimation, calculates and generates target speed and rotation angle of the agricultural machine according to a farmland full-coverage path generated by the path planner, and finally executes corresponding actions by the lower controllers of the vehicle speed controller and the steering controller;
wherein in the second step, designing an intelligent agricultural machinery dynamics model comprises the following steps:
1) Modeling lateral and yaw motion: because the agricultural machinery is low in running speed and the non-linear dynamic characteristic is not obvious in performance, only the transverse motion and the yaw motion of the agricultural machinery can be considered, and the two motions are described by a linear two-degree-of-freedom model; the lateral and yaw motions can be described by differential equations as follows:
wherein m is the mass of the spraying machine, I z For the sprayer, u is the longitudinal velocity, β is the centroid yaw angle, γ is the yaw angular velocity, δ is the nozzle velocity f Angle of rotation of front wheel, delta r For rear wheel steering angle, C f For front wheel cornering stiffness, C r For rear wheel cornering stiffness, /) f Is the centroid to front axis distance, /) r Is the distance from the center of mass to the rear axle;
2) Modeling a steering system: the agricultural machinery adopts a steering mechanism with a hydraulic push rod and a connecting rod as main components, and under the reasonable design of a controller, the closed-loop response of a steering controller and a steering system can be approximate to the closed-loop response of a first-order system, so that the whole steering system including the controller can be modeled as follows:
where δ is the front or rear wheel steering angle, δ e Desired angle of rotation, τ, of front or rear wheels δ Is the time delay constant of the steering system;
in the third step, the upper controller structure consists of a DUKF estimator and an AMPC, the estimator fuses the vehicle state information provided by different sensors, the vehicle state and parameters from the sensors or the estimator and the reference path generated by the path planner are used as the input of the AMPC, and the estimator participates in the control quantity, namely the expected front wheel turning angle delta f,e In the calculation of (2), the expected front wheel steering angle is input into a lower controller to realize the action of a steering mechanism, and the whole process is carried out on line according to a certain period;
in the fourth step, two unscented kalman filters are adopted to estimate parameters and states respectively, corresponding to two independent state space expressions, after a group of better parameters is estimated, the parameter estimator can be temporarily shut down to reduce the calculation burden of an upper controller, and when the current estimated state is not credible, the parameter estimator can be restarted to realize accurate state estimation; meanwhile, because the estimated variables are more, the available sensor measurement quantity is relatively less, the precise estimation of the state and the parameters of the agricultural machinery is difficult to realize only by a DUKF estimator, and the estimation value without physical significance can be obtained, so that the pdf truncation method is adopted to realize the DUKF with the constraint, and the constraint is only applied to the parameters to be estimated in order to improve the calculation efficiency; the method comprises the following specific steps:
1) Obtaining a discrete state space expression of parameter estimation and state estimation: transforming the formula (1) into discrete state space expressions for parameter estimation and state estimation respectively by using a first-order forward Euler formula;
the parameter estimation state space expression is:
x p (k+1)＝x p (k)+w p (k)
z p (k)＝h p (x p (k))+v p (k)； (3)
wherein x is p ＝[C f C r ] T ，z p ＝[βγ] T ，w p And v p Process noise and observation noise for parameter estimation, respectively;
state estimation state space expression:
x s (k+1)＝f s (x s (k))+w s (k)
z s (k)＝x s (k)+v s (k)； (4)
wherein x is s ＝[βγ] T ，z s ＝[βγ] T ，w s And v s Process noise and observation noise for state estimation, respectively;
2) Constraints are applied to the parameters to be estimated: suppose that there is an unscented Kalman Filter estimate x of m parameters at time k p (k | k) with a mean value of
Covariance of P p (k | k), accordingly, there are m scalar state constraints:
wherein, LB ki ≤UB ki ，θ ki A column vector of m elements, the ith element of which is 1 and the rest elements of which are 0; under this condition, the Gaussian is truncated
And then find the mean of the truncated pdf
Sum covariance
I.e. mean and covariance of constrained parameter estimates, definition
To perform the first i post-constraint state estimation,
is composed of
The covariance of (a);
3) Estimating the state and parameters of the intelligent agricultural machine in real time by using an estimator;
in the sixth step, define A as the point where the vehicle is located, B as the point where the vehicle is closest to the reference track, and course error
The difference between the heading at point A and the heading at point B (tangential direction of the path), and the lateral error Δ y is the distance between point A and point B, and the heading error is given by the expected path
And the lateral error Δ y satisfy:
assuming that the heading error and the slip angle are always small, there are
V y ≈V x β, then the above equation can be simplified to:
wherein gamma is the transverse swing angular velocity V of the spraying machine x The running speed is beta, the centroid slip angle is beta, and rho is the curvature of the expected path;
combining the equations (1), (2) and (26), and obtaining a state equation of the discrete time system by using a first-order forward Euler formula:
x(k+1)＝A k x(k)+B k u(k)+d(k)
y(k)＝Cx(k)； (27)
the intelligent agricultural machinery under the technical scheme adopts a coordinated steering mode, and the steering angle of the front wheel is equal to the steering angle of the rear wheel, and the steering angles are opposite, namely delta r ＝-δ f And thus the state variables of the system
The control amount being a desired front wheel steering angle delta f,e I.e. u = δ f,e Output quantity of
The matrix A is:
the matrix B is:
the spatial parameters d (k) are:
the matrix C is:
in order to avoid sudden change of the control quantity and influence the precision and stability of the path tracking of the sprayer, the expected front wheel turning angle increment is adopted as the control quantity of the system, and the state equation of the system can be rewritten as follows:
wherein,
the state at time k can be obtained from the above state and parameter estimation
And parameters
In conjunction with equation (28), the optimization problem of constrained MPC with spatial parameters can be described as:
satisfy kinetics (i =0,1, \8230;, N p )
Satisfying the time domain constraint:
u min (k+i)≤u(k+i)≤u max (k+i),i＝0,1,…,N c -1
wherein,
in the above optimization problem, Ω y And Ω u Is a weighting matrix given by:
y (k +1 k) is N predicted at time k based on system (28) p A step control output defined as:
in order to avoid the situation of no solution in the solving process, a relaxation factor epsilon is introduced into the formula (29), wherein lambda is a given constant; coupled (28), (29) for obtaining the predicted N of the system p Step control output:
wherein,
because the constraint condition exists, the analytical solution of the optimization problem can not be obtained under the general condition, therefore, a numerical solving method needs to be adopted, namely the constraint optimization problem needs to be converted into quadratic programming problem description;
the standard form of the objective function of the quadratic programming problem is:
the transformation (29) is in standard form, ignoring and
independent items, get
Solve the above equation and will
The first element of (2) is used as a control quantity, and the process is repeated every period to realize complete path tracking.
Preferably, in the first step, the path planner, the upper controller, the lower controller, the RTK-GPS and the IMU of the platform all communicate with each other through the CAN.
Preferably, in the third step, the vehicle state information includes a centroid slip angle measurement β from the RTK-GPS m And vehicle speed V, yaw-rate measurement gamma from IMU m And front wheel angle delta from Hall angle sensor f The parameter to be estimated is the equivalent cornering stiffness C of the front axle and the rear axle f And C r The states to be estimated are the centroid slip angle β and the yaw rate γ.
Preferably, in the third step, the desired vehicle speed is set by the operator and is realized by the lower controller operating the actuator, and the proposed upper controller is independent of the speed, so that the controller can adaptively realize accurate path tracking at different vehicle speeds.
Preferably, in the step four 3), the operation steps of the DUKF estimator are as follows:
3.1 Setting an initial value
3.2 ) parameter prediction
Construct 2n +1 sample points:
calculating parameter prediction sample points:
calculating the mean and variance of the parameter prediction sample points:
3.3 State prediction
Construct 2n +1 sample points:
and (5) carrying the parameter prediction value in the step (2) into a formula (25) to calculate a state prediction sample point:
calculating the mean and variance of the state prediction sample points:
3.4 ) state correction
When a new measured value z is obtained s (k) Then, the state mean and variance are updated:
wherein,
3.5 Correction of parameters
When a new measured value z is obtained p (k) I.e. by
Then, updating the parameter mean and variance:
wherein,
3.6 Pdf truncation;
3.7 The real-time estimation of the state and the parameters of the intelligent agricultural machine can be realized by repeating the steps 3.2 to 3.6. Preferably, the pdf truncation in step 3.6) specifically includes the following steps:
3.6.1 Initialization)
i＝0；
Wherein,
is defined as the parameter estimation after the first i constraints are performed, the corresponding covariance is
3.6.2 Let i =1, pair
Performing Jordan standard decomposition to obtain an orthogonal matrix T ki And diagonal matrix W ki Namely:
3.6.3 Computing the m by m orthogonal matrix psi using Gram-Schmidt orthogonalization ki Which satisfies:
definition psi ki Is formed by a row vector psi ki,j (j =1, \8230;, m) i.e.:
ψ ki ＝[ψ ki,1 …ψ ki,m ] T ； (9)
then psi ki Is calculated by the following formula:
for j =2, \8230;, m, the following operations are performed:
wherein e is j Is a unit vector, i.e. e j A column vector of all 0's of m elements except the jth element being 1;
if calculated by the above equation ki,j 0, then the following formula is substituted:
re-regularization psi ki,j ：
3.6.4 Define v) definition ki Comprises the following steps:
as can be seen from formulas (3) to (5), v ki The mean of (a) is 0, and the covariance matrix is constant (unit);
lower bound LB of transform (1) ki And upper bound UB ki Obtaining:
get normalized scalar constraints:
a ki ≤[1 0…0]v ki ≤b ki ； (17)
it follows that v is before the constraints are executed ki Is N (0, 1), but the constraint requires v ki Must be located at a ki And b ki In the middle of;
3.6.5 Define a random variable v) k,i+1 V is the pdf truncated ki Namely:
pdf(v k,i+1 )＝truncated pdf(v ki )； (18)
the mean and variance of the transformation parameter estimates after the first constraint is performed are:
wherein,
the mean and variance of the parameter estimates after performing the first constraint are:
increasing i by 1 and repeating the process of steps 6.2-6.5 to obtain a parameter estimate after the next constraint is executed; it is to be noted that it is preferable that,
is an unconstrained parameter estimation at time k,
is the state of the parameter at time k after the first constraint is performed,
the parameter state at time k after the first two constraints are executed, and so on, and after the process is performed m times (once for each constraint), the final constraint state estimation and the covariance of time k are obtained:
compared with the prior art, the invention has the beneficial effects that: compared with the existing path tracking control method, the method improves the path tracking precision of the intelligent agricultural machine by combining the constraint double unscented Kalman filtering and the adaptive model tracking control, thereby improving the operation efficiency, the operation quality and the economic benefit of the agricultural machine; the path tracking control system provided by the invention can be deployed in actual agricultural machinery, and the requirements of reliability, instantaneity and cost of an embedded system are considered on the premise of realizing good tracking precision.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a control system architecture diagram;
FIG. 3 is a diagram of a two-degree-of-freedom dynamics model of an agricultural machine;
FIG. 4 is a diagram of an upper level controller architecture;
FIG. 5 is a lateral error versus heading error graph;
FIG. 6 is a graph showing an actual value of a front wheel steering angle;
FIG. 7 is a comparison plot of yaw rate;
FIG. 8 is a graph comparing centroid slip angles;
fig. 9 is a front-rear wheel cornering stiffness estimation graph;
FIG. 10 is a diagram of the agricultural machinery path converted to the UTM coordinate system;
FIG. 11 is a lateral error curve diagram during the driving of the agricultural machinery.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
Referring to fig. 1-5, an embodiment of the present invention is shown: a path tracking control method of an intelligent agricultural machine comprises the following steps: step one, designing a control system architecture; designing an intelligent agricultural machinery dynamics model; designing an upper controller architecture; step four, realizing the estimation of the transverse dynamic parameters of the intelligent agricultural machinery with constraints based on the double unscented Kalman filtering; step five, self-adaptive model prediction control based on the dynamic model;
in the first step, the upper controller acquires current state information of the agricultural machine acquired by the sensor, performs state estimation, calculates and generates a target speed and a rotation angle of the agricultural machine according to a farmland full-coverage path generated by the path planner, the lower controllers of the vehicle speed controller and the steering controller finally execute corresponding actions, the configuration of the control system sensor adopts a real-time kinematic GPS (RTK-GPS) + an inertial navigation system (IMU), two RTK-GPS receivers are respectively arranged at the head and the tail of the vehicle, the inertial navigation unit (IMU) is arranged near the mass center of the platform, and the path planner, the upper controller, the lower controller, the RTK-GPS and the IMU of the platform are communicated through CAN;
in the second step, designing an intelligent agricultural machinery dynamics model comprises the following steps:
1) Modeling lateral and yaw motion: because the agricultural machinery has low running speed and unobvious nonlinear dynamic characteristic performance, only the transverse motion and the yaw motion of the agricultural machinery can be considered, and the two motions are described by a linear two-degree-of-freedom model; the lateral and yaw motions can be described by differential equations as follows:
wherein m is the mass of the spraying machine, I z For the sprayer yaw inertia moment, u is the longitudinal speed, beta is the centroid slip angle, gamma is the yaw angular velocity, delta f Is the angle of rotation of the front wheel, delta r For rear wheel steering angle, C f For front wheel cornering stiffness, C r For rear wheel cornering stiffness, /) f Is the centroid to front axis distance, /) r Is the distance from the center of mass to the rear axle;
2) Modeling a steering system: the agricultural machinery adopts a steering mechanism with a hydraulic push rod and a connecting rod as main components, and under the reasonable design of a controller, the closed-loop response of a steering controller and a steering system can be approximate to the closed-loop response of a first-order system, so that the whole steering system including the controller can be modeled as follows:
where δ is the front or rear wheel steering angle, δ e Desired angle of rotation, τ, of front or rear wheels δ Is the time delay constant of the steering system;
in the third step, the upper controller structure consists of a DUKF estimator and an AMPC, the estimator fuses vehicle state information provided by different sensors, and the vehicle state information comprises a centroid slip angle measured value beta from an RTK-GPS m And vehicle speed V, yaw-rate measurement gamma from IMU m And front wheel angle delta from Hall angle sensor f The parameter to be estimated is the equivalent cornering stiffness C of the front axle and the rear axle f And C r The state to be estimated is the centroid slip angle β and the yaw rate γ, and the vehicle state and parameters from the sensor or estimator and the reference path generated by the path planner are taken as inputs to the AMPC, participating in the control quantity, i.e., the desired front wheel steering angle δ f,e In the calculation, the expected front wheel steering angle is input into a lower layer controller to realize the action of a steering mechanism, the whole process is carried out on line according to a certain period, the expected vehicle speed is set by an operator and is realized by operating an executing mechanism by the lower layer controller, and the provided upper layer controller is irrelevant to the speed, so that the controller can adaptively realize accurate path tracking under different vehicle speeds;
in the fourth step, two unscented kalman filters are adopted to estimate parameters and states respectively, corresponding to two independent state space expressions, after a group of better parameters are estimated, the parameter estimator can be temporarily shut down to reduce the calculation burden of an upper controller, and when the current estimated state is not credible, the parameter estimator can be restarted to realize accurate state estimation; meanwhile, because the estimated variables are more, the available sensor measurement quantity is relatively less, the precise estimation of the state and the parameters of the agricultural machinery is difficult to realize only by a DUKF estimator, and the estimation value without physical significance can be obtained, so that the pdf truncation method is adopted to realize the DUKF with the constraint, and the constraint is only applied to the parameters to be estimated in order to improve the calculation efficiency; the method specifically comprises the following steps:
1) Obtaining a discrete state space expression of parameter estimation and state estimation: transforming the formula (1) into discrete state space expressions for parameter estimation and state estimation respectively by using a first-order forward Euler formula;
the parameter estimation state space expression is:
x p (k+1)＝x p (k)+w p (k)
z p (k)＝h p (x p (k))+v p (k)； (3)
wherein x is p ＝[C f C r ] T ，z p ＝[βγ] T ，w p And v p Process noise and observation noise for parameter estimation, respectively;
state estimation state space expression:
x s (k+1)＝f s (x s (k))+w s (k)
z s (k)＝x s (k)+v s (k)； (4)
wherein x is s ＝[βγ] T ，z s ＝[βγ] T ，w s And v s Process noise and observation noise for state estimation, respectively;
2) Constraints are imposed on the parameters to be estimated: suppose that there is an unscented Kalman Filter estimate x of m parameters at time k p (k | k) with a mean value of
Covariance of P p (k | k), accordingly, there are m scalar state constraints:
wherein, LB ki ≤UB ki ，θ ki A column vector of m elements in which the ith element is 1 and the remaining elements are 0; under this condition, the Gaussian is truncated
And then find the mean of the truncated pdf
Sum covariance
I.e. mean and covariance of constrained parameter estimates, definition
To perform the first i post-constraint state estimation,
is composed of
The covariance of (a);
3) The real-time estimation of the state and the parameters of the intelligent agricultural machine by adopting the estimator specifically comprises the following steps:
3.1 Setting an initial value
3.2 ) parameter prediction
Construct 2n +1 sample points:
calculating parameter prediction sample points:
calculating the mean and variance of the parameter prediction sample points:
3.3 State prediction
Construct 2n +1 sample points:
and (3) carrying the parameter predicted value in the step (2) into a formula (25) to calculate a state prediction sample point:
calculating the mean and variance of the state prediction sample points:
3.4 ) state correction
When a new measured value z is obtained s (k) Then, the state mean and variance are updated:
wherein,
3.5 Correction of parameters
When a new measured value z is obtained p (k) I.e. by
Then, updating the parameter mean and variance:
wherein,
3.6 Pdf truncation, specifically comprising the steps of:
3.6.1 Initialization)
i＝0；
Wherein,
is defined as the parameter estimation after the first i constraints are performed, the corresponding covariance is
3.6.2 Let i =1, pair
Performing Jordan standard decomposition to obtain an orthogonal matrix T ki And diagonal matrix W ki Namely:
3.6.3 Computing the m by m orthogonal matrix ψ using Gram-Schmidt orthogonalization ki Which satisfies:
definition ofψ ki Is formed by a row vector psi ki,j (j =1, \8230;, m) i.e.:
ψ ki ＝[ψ ki,1 …ψ ki,m ] T ； (9)
then psi ki Is calculated by the following formula:
for j =2, \8230;, m, the following operations are performed:
wherein e is j Is a unit vector, i.e. e j A column vector of all 0's of m elements except the jth element being 1;
if calculated by the above equation ki,j 0, then substituted with the following formula:
re-regularization psi ki,j ：
3.6.4 Define v) definition ki Comprises the following steps:
as is clear from the formulae (3) to (5), v ki The mean of (a) is 0, and the covariance matrix is constant (unit);
lower bound LB of transformation (1) ki And upper bound UB ki And obtaining:
get normalized scalar constraints:
a ki ≤[1 0…0]v ki ≤b ki ； (17)
it follows that v is before the constraints are executed ki Is N (0, 1), but the constraint requires v ki Must be located at a ki And b ki In the middle of;
3.6.5 Define a random variable v) k,i+1 V is the pdf truncated ki Namely:
pdf(v k,i+1 )＝truncated pdf(v ki )； (18)
the mean and variance of the transformation parameter estimates after the first constraint is performed are:
wherein,
the mean and variance of the parameter estimates after performing the first constraint are:
increasing i by 1 and repeating the process of the steps 6.2-6.5 to obtain parameter estimation after the next constraint is executed; it is to be noted that it is preferable that,
is an unconstrained parameter estimation at time k,
is the state of the parameter at time k after the first constraint is performed,
is the parameter state at time k after the first two constraints are executed, and so on, after this process is performed m times (once for each constraint), the final constraint state estimate and the covariance of time k are obtained:
3.7 Repeating the steps 3.2-3.6, and then realizing real-time estimation of the state and the parameters of the intelligent agricultural machine;
wherein in the sixth step, define A as the point where the vehicle is located, B as the point where the vehicle is closest to the reference track, and course error
The heading at the point A and the heading at the point B(tangential direction of path), the lateral error Δ y is the distance between points A and B, and the heading error is given for a desired path
And the lateral error Δ y satisfies:
assuming that the heading error and the slip angle are always small, there are
V y ≈V x β, then the above equation can be simplified to:
wherein gamma is the transverse swing angular velocity V of the spraying machine x The running speed is beta, the centroid slip angle is beta, and rho is the curvature of the expected path;
combining the formulas (1), (2) and (26), obtaining a state equation of the discrete time system by using a first-order forward Euler formula:
x(k+1)＝A k x(k)+B k u(k)+d(k)
y(k)＝Cx(k)； (27)
the intelligent agricultural machinery under the technical scheme adopts a coordinated steering mode, and the steering angle of the front wheel is equal to the steering angle of the rear wheel in size and opposite to the steering angle of the rear wheel, namely delta r ＝-δ f Thus state variables of the system
The control amount being a desired front wheel steering angle delta f,e I.e. u = δ f,e Output amount of
The matrix A is:
the matrix B is:
the spatial parameters d (k) are:
the matrix C is:
in order to avoid sudden change of the control quantity and influence the precision and stability of the path tracking of the sprayer, the expected front wheel turning angle increment is adopted as the control quantity of the system, and the state equation of the system can be rewritten as follows:
wherein,
the state at time k can be obtained from the above state and parameter estimation
And parameters
In conjunction with equation (28), the optimization problem of constrained MPC with spatial parameters can be described as:
satisfy kinetics (i =0,1, \8230;, N p )
y(k|k)＝y(k)；
Satisfying the time domain constraint:
u min (k+i)≤u(k+i)≤u max (k+i),i＝0,1,…,N c -1
wherein,
in the above optimization problem，Ω y And Ω u Is a weighting matrix given by:
y (k +1 k) is N predicted at time k based on system (28) p A step control output defined as:
in order to avoid the situation of no solution in the solving process, a relaxation factor epsilon is introduced into the formula (29), wherein lambda is a given constant; coupled (28), (29) for obtaining the predicted N of the system p Step control output:
wherein,
because the constraint condition exists, the analytical solution of the optimization problem can not be obtained under the general condition, therefore, a numerical solving method needs to be adopted, namely the constraint optimization problem needs to be converted into quadratic programming problem description;
the standard form of the objective function of the quadratic programming problem is:
the transformation (29) is of standard form, ignoring and
independent items, get
Solve the above equation and will
The above process is repeated every period, and complete path tracking is realized.
The method provided in the embodiment is applied to an actual agricultural machine for testing, and an S-shaped path is adopted as a reference path for tracking the path of the agricultural machine; the test results are shown in fig. 6-11, wherein fig. 7-9 reflect the state with constraints and the working condition of the parameter estimator, and since the true value of the cornering stiffness is not known initially, the cornering stiffness of the front and rear wheels starts from a specified initial value, the estimated cornering stiffness of the front and rear wheels gradually converges to the true value along with the running of the agricultural machinery, and meanwhile, the estimated centroid cornering angle also gradually converges to the true value; the result shows that the designed state and parameter estimator with the constraint can estimate the real dynamic state and parameters of the agricultural machinery in real time, and provides reliable guarantee for model prediction control based on a dynamic model; fig. 10 and fig. 11 reflect the actual driving path of the agricultural machine and the deviation from the expected path, and it can be seen that the maximum lateral deviation does not exceed 0.03m in the whole driving process of the agricultural machine, which indicates that the controller can realize the high-precision path tracking of the intelligent agricultural machine, and further can improve the quality and efficiency of the operation.
Based on the above, the invention provides an intelligent agricultural machinery path tracking control method, and a controller suitable for intelligent agricultural machinery path tracking is designed by combining Double Unscented Kalman Filtering (DUKF) with PDF truncation and self-adaptive MPC with spatial parameters, so that the accuracy of intelligent agricultural machinery path tracking can be effectively improved.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Claims (6)
1. A path tracking control method of an intelligent agricultural machine comprises the following steps: step one, designing a control system architecture; designing an intelligent agricultural machinery dynamic model; designing an upper-layer controller architecture; step four, realizing the estimation of the transverse dynamic parameters of the intelligent agricultural machinery with constraints based on the double unscented Kalman filtering; step five, self-adaptive model prediction control based on the dynamic model; the method is characterized in that:
in the first step, the upper controller acquires current state information of the agricultural machine acquired by the sensor, carries out state estimation, calculates and generates target speed and rotation angle of the agricultural machine according to a farmland full-coverage path generated by the path planner, and finally executes corresponding actions by the lower controllers of the vehicle speed controller and the steering controller;
in the second step, designing an intelligent agricultural machinery dynamics model comprises the following steps:
1) Modeling lateral and yaw motion: because the agricultural machinery is low in running speed and the non-linear dynamic characteristic is not obvious in performance, only the transverse motion and the yaw motion of the agricultural machinery can be considered, and the two motions are described by a linear two-degree-of-freedom model; the lateral and yaw motions can be described by differential equations as follows:
wherein m is the mass of the spraying machine, I z For the sprayer, u is the longitudinal velocity, β is the centroid yaw angle, γ is the yaw angular velocity, δ is the nozzle velocity f Is the angle of rotation of the front wheel, delta r For rear wheel steering angle, C f For front wheel cornering stiffness, C r For rear wheel cornering stiffness, /) f Is the centroid to front axis distance, /) r Is the distance from the center of mass to the rear axle;
2) Modeling a steering system: the agricultural machinery adopts a steering mechanism with a hydraulic push rod and a connecting rod as main components, and under the reasonable design of a controller, the closed-loop response of a steering controller and a steering system can be approximate to the closed-loop response of a first-order system, so that the whole steering system including the controller can be modeled as follows:
where δ is the front or rear wheel steering angle, δ e Desired angle of rotation, τ, of front or rear wheels δ Is the time delay constant of the steering system;
in the third step, the upper controller structure consists of a DUKF estimator and an AMPC, the estimator fuses the vehicle state information provided by different sensors, the vehicle state and parameters from the sensors or the estimator and the reference path generated by the path planner are used as the input of the AMPC, and the estimator participates in the control quantity, namely the expected front wheel turning angle delta f,e In the calculation, the expected front wheel steering angle is input to a lower controller to realize the action of a steering mechanism, and the whole process is carried out on line according to a certain period;
in the fourth step, two unscented kalman filters are adopted to estimate parameters and states respectively, corresponding to two independent state space expressions, after a group of better parameters are estimated, the parameter estimator can be temporarily shut down to reduce the calculation burden of an upper controller, and when the current estimated state is not credible, the parameter estimator can be restarted to realize accurate state estimation; meanwhile, because the estimated variables are more, the available sensor measurement quantity is relatively less, the precise estimation of the state and the parameters of the agricultural machinery is difficult to realize only by a DUKF estimator, and the estimation value without physical significance can be obtained, so that the pdf truncation method is adopted to realize the DUKF with the constraint, and the constraint is only applied to the parameters to be estimated in order to improve the calculation efficiency; the method specifically comprises the following steps:
1) Obtaining a discrete state space expression of parameter estimation and state estimation: respectively transforming the formula (1) into discrete state space expressions for parameter estimation and state estimation by utilizing a first-order forward Euler formula;
the parameter estimation state space expression is:
x p (k+1)＝x p (k)+w p (k)
z p (k)＝h p (x p (k))+v p (k)； (3)
wherein x is p ＝[C f C r ] T ，z p ＝[β γ] T ，w p And v p Process noise and observation noise for parameter estimation, respectively;
state estimation state space expression:
x s (k+1)＝f s (x s (k))+w s (k)
z s (k)＝x s (k)+v s (k)； (4)
wherein x is s ＝[β γ] T ，z s ＝[β γ] T ，w s And v s Process noise and observation noise for state estimation, respectively;
2) Constraints are applied to the parameters to be estimated: suppose that there is an unscented Kalman Filter estimate x of m parameters at time k p (k | k) with a mean value of
Covariance of P p (k | k), accordingly, there are m scalar state constraints:
wherein, LB ki ≤UB ki ，θ ki A column vector of m elements in which the ith element is 1 and the remaining elements are 0; under this condition, the truncated Gaussian pdf
And then find the mean of the truncated pdf
Sum covariance
I.e. parameters with constraintsMean and covariance of the estimate, definition
To perform the first i post-constraint state estimation,
is composed of
The covariance of (a);
3) Estimating states and parameters of the intelligent agricultural machinery in real time by using an estimator;
wherein in the sixth step, define A as the point where the vehicle is located, B as the point where the vehicle is closest to the reference track, and course error
The difference between the heading at point A and the heading at point B (tangential direction of the path), and the lateral error Δ y is the distance between point A and point B, and the heading error is determined for a given desired path
And the lateral error Δ y satisfies:
assuming that the heading error and the slip angle are always small, there are
V y ≈V x β, then the above equation can be simplified to:
wherein gamma is the transverse swing angular velocity V of the spraying machine x The running speed is beta, the centroid slip angle is beta, and rho is the curvature of the expected path;
combining the equations (1), (2) and (26), and obtaining a state equation of the discrete time system by using a first-order forward Euler formula:
x(k+1)＝A k x(k)+B k u(k)+d(k)
y(k)＝Cx(k)； (27)
the intelligent agricultural machinery under the technical scheme adopts a coordinated steering mode, and the steering angle of the front wheel is equal to the steering angle of the rear wheel in size and opposite to the steering angle of the rear wheel, namely delta r ＝-δ f And thus the state variables of the system
The control amount being a desired front wheel steering angle delta f,e I.e. u = δ f,e Output quantity of
The matrix A is:
the matrix B is:
the spatial parameters d (k) are:
the matrix C is:
in order to avoid sudden change of the control quantity and influence the precision and stability of the path tracking of the sprayer, the expected front wheel turning angle increment is adopted as the control quantity of the system, and the state equation of the system can be rewritten as follows:
wherein,
the state at time k can be obtained from the above state and parameter estimation
And parameters
In conjunction with equation (28), the optimization problem of constrained MPC with spatial parameters can be described as:
satisfy kinetics (i =0,1, \8230;, N p )
y(k|k)＝y(k)；
Satisfying the time domain constraint:
u min (k+i)≤u(k+i)≤u max (k+i),i＝0,1,…,N c -1
wherein,
in the above optimization problem, Ω y And Ω u Is a weighting matrix given by:
y (k +1 k) is N predicted at time k based on system (28) p A step control output defined as:
in order to avoid the situation of no solution in the solving process, a relaxation factor epsilon is introduced into the formula (29), wherein lambda is a given constant; coupled (28), (29) to obtain the predicted N of the system p Step control output:
wherein,
because the constraint condition exists, the analytical solution of the optimization problem can not be obtained under the general condition, therefore, a numerical solving method needs to be adopted, namely the constraint optimization problem needs to be converted into quadratic programming problem description;
the standard form of the objective function of the quadratic programming problem is:
the transformation (29) is in standard form, ignoring and
independent items, get
Solve the above equation and will
The first element of (2) is used as a control quantity, and the process is repeated every period to realize complete path tracking.
2. The path tracking control method of the intelligent agricultural machine according to claim 1, characterized in that: in the first step, the path planner, the upper controller, the lower controller, the RTK-GPS and the IMU of the platform are communicated through CAN.
3. The path tracking control method of the intelligent agricultural machine according to claim 1, characterized in that: in the third step, the vehicle state information comprises a centroid slip angle measurement beta from an RTK-GPS m And vehicle speed V, yaw-rate measurement gamma from IMU m And front wheel angle delta from Hall angle sensor f The parameter to be estimated is the equivalent cornering stiffness C of the front axle and the rear axle f And C r The states to be estimated are the centroid slip angle β and the yaw rate γ.
4. The path tracking control method of the intelligent agricultural machine according to claim 1, characterized in that: in the third step, the expected vehicle speed is set by the operator and is realized by operating the actuating mechanism by the lower-layer controller, and the proposed upper-layer controller is independent of the speed, so that the controller can adaptively realize accurate path tracking under different vehicle speeds.
5. The path tracking control method of the intelligent agricultural machine according to claim 1, characterized in that: in the step four 3), the operation steps of the DUKF estimator are as follows:
3.1 Setting an initial value
3.2 Parameter prediction
Construct 2n +1 sample points:
calculating parameter prediction sample points:
calculating the mean and variance of the parameter prediction sample points:
3.3 State prediction
Construct 2n +1 sample points:
and (5) carrying the parameter prediction value in the step (2) into a formula (25) to calculate a state prediction sample point:
calculating the mean and variance of the state prediction sample points:
3.4 ) state correction
When a new measured value z is obtained s (k) Then, the state mean and variance are updated:
wherein,
3.5 ) correction of parameters
When a new measured value z is obtained p (k) I.e. by
Then, updating the parameter mean and variance:
wherein,
3.6 Pdf truncation;
3.7 The real-time estimation of the state and the parameters of the intelligent agricultural machine can be realized by repeating the steps 3.2 to 3.6.
6. The path tracking control method of the intelligent agricultural machine according to claim 5, characterized in that: the pdf truncation step 3.6) specifically comprises the following steps:
3.6.1 Initialization)
i＝0；
Wherein,
is defined as performing the first i post-constraint parameter estimates, with the corresponding covariance as
3.6.2 Let i =1, pair
Performing Jordan standard decomposition to obtain an orthogonal matrix T ki And diagonal matrix W ki Namely:
3.6.3 Computing the m by m orthogonal matrix ψ using Gram-Schmidt orthogonalization ki Which satisfies:
definition psi ki Is formed by a row vector psi ki,j (j =1, \8230;, m) i.e.:
ψ ki ＝[ψ ki,1 …ψ ki,m ] T ； (9)
then psi ki Is calculated by the following formula:
for j =2, \8230;, m, the following operations are performed:
wherein e is j Is a unit vector, i.e. e j Is a column vector of m elements, all 0's except the jth element being 1;
if calculated by the above equation ki,j 0, then substituted with the following formula:
re-regularization psi ki,j ：
3.6.4 Define v) definition ki Comprises the following steps:
as can be seen from formulas (3) to (5), v ki Has a mean of 0, covariance matrix of identity (unit)
Lower bound LB of transform (1) ki And upper bound UB ki Obtaining:
get normalized scalar constraints:
a ki ≤[1 0…0]v ki ≤b ki ； (17)
it follows that v is before the constraints are executed ki Is N (0, 1), but the constraint requires v ki Must be located at a ki And b ki In the middle of;
3.6.5 Define a random variable v) k,i+1 V is the pdf truncated ki Namely:
pdf(v k,i+1 )＝truncated pdf(v ki )； (18)
the mean and variance of the transformation parameter estimates after the first constraint is performed are:
wherein,
the mean and variance of the parameter estimates after performing the first constraint are:
increasing i by 1 and repeating the process of steps 6.2-6.5 to obtain a parameter estimate after the next constraint is executed; it is noted that,
is an unconstrained parameter estimation at time k,
is the state of the parameter at time k after the first constraint is executed,
is the parameter state at time k after the first two constraints are executed, and so on, after this process is performed m times (once for each constraint), the final constraint state estimate and the covariance of time k are obtained:
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