CN114879490A

CN114879490A - Iterative optimization and control method for unmanned aerial vehicle perching maneuver

Info

Publication number: CN114879490A
Application number: CN202210337063.0A
Authority: CN
Inventors: 何真; 周紫君
Original assignee: Nanjing University of Aeronautics and Astronautics
Current assignee: Nanjing University of Aeronautics and Astronautics
Priority date: 2022-03-31
Filing date: 2022-03-31
Publication date: 2022-08-09

Abstract

The invention provides an iterative optimization and control method of an unmanned aerial vehicle perching maneuver, which is characterized by firstly establishing a longitudinal nonlinear dynamic model of the fixed wing unmanned aerial vehicle perching maneuver. Secondly, in order to obtain an ILMPC strategy initial feasible track with the end point state quantity meeting expected requirements, a constraint iterative quadratic form regulator (CILQR) algorithm is used for optimizing the perch maneuvering track, and the optimal track is used as the initial feasible track of the ILMPC strategy. And then defining the unmanned aerial vehicle perching maneuver process as an iterative task, designing a sampling safety set and a terminal cost function related to the perching maneuver trajectory, and designing a perching maneuver ILMPC strategy by utilizing the sampling safety set and the terminal cost function. Finally, the numerical simulation result shows that the iteration cost is gradually reduced along with the increase of the iteration times, and the perch maneuver trajectory is gradually converged to the optimal trajectory, so that the effectiveness of the designed controller is proved.

Description

Iterative optimization and control method for unmanned aerial vehicle perching maneuver

Technical Field

The invention relates to an iterative optimization and control method for unmanned aerial vehicle perching maneuver.

Background

Birds have an advantage in landing that artificial aircrafts currently cannot achieve. By observing the process of bird descent, it was found that when approaching the target, they spread the wings and tail and adjust the entire body to a large angle of attack, using the air resistance after stalling to decelerate quickly. Researchers have introduced the concept of perching maneuvers in the inspired birds' maneuvers. If fixed wing unmanned aerial vehicle also can realize fast descending through perching down the mobile mode like birds, no longer need taxiway or other supplementary landing device, its application will be widened greatly.

Currently, in the research on the perch maneuver control, the control target is basically to minimize the tracking error, i.e., assuming that the reference trajectory is known in advance, the feedback controller is designed to track the reference trajectory. How to deploy the control design for the perch maneuver system is a further problem to be solved when the reference trajectory is unknown. Existing studies on perch maneuver optimization do not take full advantage of historical data to optimize control performance through iteration.

Disclosure of Invention

The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides an iterative optimization and control method for perching and landing maneuver of a fixed-wing unmanned aerial vehicle. The technical scheme is as follows: in order to achieve the purpose, the invention adopts the following technical scheme:

step 1, establishing an unmanned aerial vehicle perching maneuver longitudinal nonlinear dynamics modeling;

step 2, planning state quantities such as position, speed, pitch angle and the like at the motor terminal point of the perch by adopting a Constrained Iterative Linear Quadratic Regulator (CILQR) to obtain an optimal track;

and 3, taking the optimal track obtained in the step 2 as an initial feasible track of an Iterative Learning Model Predictive Control (ILMPC) strategy, and designing an iterative learning model predictive controller.

Preferably, the perch maneuver longitudinal nonlinear dynamical model described in step 1 is:

in the formula, V represents the flying speed of the unmanned aerial vehicle, theta is a pitch angle, alpha is an attack angle, q is a pitch angle speed, x is a horizontal displacement, h is a height,

The derivative of V is indicated. m is the mass of the aircraft and g isLocal gravitational acceleration, T engine thrust, I _y Is unmanned aerial vehicle every single move inertia. M is aerodynamic moment, L and D represent lift and resistance that unmanned aerial vehicle receives respectively, and the expression equation is respectively:

where ρ is the air density, S is the aerodynamic area of the drone, C _L 、C _D And C _M The lift, the resistance and the moment coefficient of the fixed-wing unmanned aerial vehicle are respectively expressed, and the expression equations are respectively as follows:

in the formula, S _e Denotes the surface area of the elevator, l _e Representing the distance, delta, of the aerodynamic centre of gravity of the elevator to the centre of mass of the aircraft _e Is the elevator yaw angle.

Preferably, step 2 comprises the steps of:

step 2-1, formulating the constrained perch maneuver trajectory planning problem into the following form, and recording as problem 1:

s.t.x _k+1 ＝f(x _k ,u _k ),k＝0,1,…,N-1 (4b)

x ₀ ＝x _start (4c)

g _uk (u _k )<0,k＝0,1,…,N-1 (4d)

g _xk (x _k )<0,k＝0,1,…,N (4e)

wherein x in the formula (4a) _k And u _k Respectively is a perching maneuver state variable and a control input variable when the time step number is k, N is the time step number required by the unmanned aerial vehicle to complete one perching maneuver, x _N Is the amount of the end point state,φ(x _N ) Is the end-of-line phase cost, L _k (x _k ,u _k ) Is the stage cost when the time step number is k, argmin represents the independent variable value when the function value is minimum, x ^* And u ^* The state quantity sequence and the control input sequence when the cost function takes the minimum value.

s.t. is an abbreviation for subject to, indicating that it is subject to …. Formula (II)

(4b) F (·, ·) in (a) represents the perch maneuver dynamics equation;

x in the formula (4c) ₀ Is an initial state quantity, x _start Is the set initial state quantity;

g in formula (4d) _uk (u _k ) Representing control input constraints;

g in formula (4e) _xk (x _k ) Representing a constraint on a state quantity;

step 2-2, to handle the constraints in problem 1, introduce a logarithmic barrier function b (x, u):

in the formula, q >0 is a parameter, and g (x, u) represents a state quantity and a control input constraint.

The step 2-3 specifically comprises the following steps:

step 2-3-1: given a perch maneuver initial control sequence

The initial value of the parameter q is q ₀ >0, coefficient of proportionality μ>1,0<α<1, forward simulation to obtain an initial feasible track

Step 2-3-2: converting inequality constraints (4d) and (4e) into cost functions by using a logarithmic barrier function, and adding the cost functions into the objective function in the step (4a) to obtain an unconstrained optimization problem;

step 2-3-3: solving the problem of the step by using an iterative LQR algorithm2-3-2 and obtaining a control sequence u of the next iteration, wherein the control sequence is a sequence formed by control input variables at all time points in one iteration, namely u ═ u { (u) } ₁ ,…,u _k ,…,u _N-1 }；

Step 2-3-4: and judging whether the current control sequence u can enable the habitat trajectory to meet the constraint condition by using straight line search, if so, performing the step 2-3-5, and if not, enabling u to be alpha u until the habitat trajectory meets the constraint condition.

Step 2-3-5: forward simulation to obtain the current state sequence

Judging whether the iteration cost is converged, if so, ending the iteration, and if not, ordering

q ═ μ q, and return to step 2-3-2.

Preferably, step 3 comprises the steps of:

step 3-1, aiming to make the unmanned aerial vehicle perch the maneuvering track from the starting point x _S Reaches the end point x _F And solve the problem of the limited time domain optimal control as described below, which is denoted as problem 2:

x ₀ ＝x _S (6d)

wherein, in the formula (6a)

Represents the optimal cost, x _t And u _t Respectively representing the perch maneuver state variable and the control input variable, h (x) at time t _t ,u _t ) Is the stage cost; u. of _t And u _T It does not mean that T is a value of one of the set {0, …, T }, and when T is T, u is _t ＝u _T 。

F (·,) in formula (6b) represents the perch maneuver dynamics equation;

in formula (6c)

Representing state and control input constraints, respectively;

x in formula (6d) ₀ Is an initial state quantity, x _S Is the initial state quantity of the setting.

Defining one iteration as that the unmanned aerial vehicle successfully completes one perching maneuver, and storing the closed-loop track of the perching maneuver; in the jth iteration, vector x ^j And u ^j Respectively storing the state quantities and the corresponding control inputs of the jth iteration of the perch maneuver:

in the formula (I), the compound is shown in the specification,

and

respectively representing the state quantity and the control input of the habitat mobile at the jth iteration T moment, wherein the T value is 0-T ^j ；T ^j Representing the time at which the jth iterative perch maneuver closed-loop trajectory reaches the endpoint, i.e.

Respectively representing the state quantity and the control input at the time of the j-th iteration 0.

Setting each iteration perch maneuvering closed-loop track to start from the same initial state, namely:

setting a local optimal solution to the problem 2, and recording as:

wherein x is ^* ,u ^* Respectively represent the optimum state quantity and the series of control inputs,

respectively representing the optimal state quantity and control input at the moment T, wherein the value of T is 0-T ^j 。

Respectively, the optimum state quantity and the control input at time 0.

And 3-2, designing the iterative learning model predictive controller.

Further, step 3-2 comprises:

step 3-2-1, constructing a sampling safety set of the perch maneuvering track: the unmanned aerial vehicle perch maneuvering closed-loop system is defined as follows:

wherein the content of the first and second substances,

respectively representing the state quantity of the habitat mobile at the time of the jth iteration t +1 and the state quantity at the time of t,

represents a closed-loop control strategy;

at the jth iteration, a sample security set is defined

Comprises the following steps:

wherein i ∈ M ^j ，t∈[0,T ^j ]，M ^j Is an index set in which iteration tasks are successfully completed in the previous j iterations, and is defined as:

then sample the security set

A set of perch maneuver state trajectories representing successful completion of the iterative task in the previous j iterations.

3-2-2, establishing an iterative cost function of the perch maneuvering track: at time t of the jth iteration, a cost function associated with the perch maneuver closed-loop trajectory (17) and the input sequence (18)

Is defined as: :

wherein，

And

respectively representing the real state quantity and the input quantity of the jth iteration of the perch maneuver,

is the stage cost, and k is T-T ^j 。

Using a cost function, the number of values Q for a sample security set ^j (x) Is defined as:

step 3-2-3, obtaining an iterative learning model predictive controller ILMPC:

at the time t of the jth iteration, the iterative learning model predictive controller ILMPC strategy will solve the following rolling time domain optimal control problem, which is denoted as problem 3:

wherein, in the formula (17a)

Is the optimum cost, h (x) _k|t ,u _k|t ) Is the stage cost, Q ^j-1 (x _t+N|t ) Is a function of the value described in equation (16); formula (17d) represents maneuvering the habitat in the time domain [ t, t + N ]]The terminal state of (2) is constrained to the perch maneuver sampling security set defined by formula (13)

In (1).

Setting that the problem 3 has an optimal solution at the jth iteration t, and recording as:

wherein the content of the first and second substances,

respectively representing the time periods t, t + N of the solution at time t]The optimal state quantity and control input series;

the optimal control input at the moment k is shown, and the value of k is t-t + N-1;

expressing the optimal state quantity at the moment k, wherein the value of k is t-t + N;

then, at the time t of the j-th iteration, the

The first element of (a) is applied to the perch maneuver dynamics equation, i.e.:

wherein the content of the first and second substances,

as described in equation (12), a closed-loop control strategy is represented. At this time, the state quantity of the habitat mobile at the t +1 moment can be obtained

Then in a new state

On the basis of (1), solving the problem 3 at the time of t +1 until the end point of the iteration is reached, namely

Has the advantages that: the method takes the perching maneuver of the unmanned aerial vehicle as a repeatedly executed task, adopts a Constrained Iterative Linear Quadratic Regulator (CILQR) to plan state quantities such as the position, the speed, the pitch angle and the like at the final point of the perching maneuver, and provides an initial feasible track for an LMPC control strategy. And (3) researching the track optimization and control problem of the perching maneuver on the premise of meeting the state and input constraints by using a data-driven ILMPC strategy and using the optimal track obtained by a CILQR algorithm as an initial feasible track of the ILMPC strategy. By the method, the unmanned aerial vehicle can perch at a specified position and obtain an perch track which enables the cost function to be optimal on the premise of meeting the state and input constraint.

Drawings

The foregoing and/or other advantages of the invention will become further apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.

FIG. 1 is an iterative cost diagram of the CILQR algorithm.

Fig. 2a, 2b, 2c, 2d, 2e and 2f are schematic speed change curves of the CILQR algorithm with different iteration times.

Fig. 3a and 3b are schematic diagrams of control quantity change curves of different iteration times of the CILQR algorithm.

Fig. 4a is a schematic diagram of the LMPC predicted trajectory at the time when the 2 nd iteration t is 0, and fig. 4b is a schematic diagram of the LMPC predicted trajectory at the time when the 2 nd iteration t is 1.

Fig. 5 is a diagram illustrating the variation of iteration cost of the ILMPC strategy with the number of iterations.

Fig. 6a, 6b, 6c, 6d, 6e and 6f are schematic diagrams of state quantity change curves of different iteration times of the LMPC strategy.

Fig. 7a and 7b are schematic diagrams of control quantity change curves of different iteration times of the LMPC strategy.

FIG. 8 is a schematic diagram of the method of the present invention for obtaining an optimal trajectory.

Detailed Description

The invention provides an iterative optimization and control method for perching and landing maneuver of an unmanned aerial vehicle, which comprises the following steps:

1. modeling of unmanned aerial vehicle perching mobile dynamics

The research object of the invention is a conventional fixed wing unmanned aerial vehicle. In order to simplify the model of the research object, the invention only carries out dynamic modeling aiming at the longitudinal motion of the unmanned aerial vehicle, and sets that the transverse motion, the transverse force and the moment of the unmanned aerial vehicle do not influence the longitudinal motion of the unmanned aerial vehicle. The set state variables and control inputs are respectively:

x＝[V,θ,α,q,x,h] ^T ,u＝[T,δ _e ] ^T

in the formula: v, theta, alpha and q respectively represent the flight speed, the pitch angle, the attack angle and the pitch angle speed of the unmanned aerial vehicle; x and h represent the horizontal position and vertical height of the drone, respectively; t and delta _e Thrust and elevator deflection angles generated by the unmanned aerial vehicle engine are provided. [] ^T Representing the transpose of the matrix. The longitudinal motion equation of the fixed-wing drone is as follows:

in the formula (I), the compound is shown in the specification,

representing the derivative of VM is the mass of the aircraft, g is the local gravitational acceleration, I _y Is unmanned aerial vehicle pitching moment of inertia; m is the aerodynamic moment, and L and D represent the lift and the resistance that unmanned aerial vehicle receives respectively. The expression equations are respectively:

in the formula: ρ is the air density, S is the aerodynamic area of the drone, C _L 、C _D And C _M The lift, the resistance and the moment coefficient of the fixed-wing unmanned aerial vehicle are respectively expressed, and the expression equations are respectively as follows:

in the formula, S _e Denotes the surface area of the elevator, l _e Representing the distance of the aerodynamic center of gravity of the elevator from the center of mass of the aircraft.

2. Constrained iteration LQR trajectory optimization algorithm

2.1 constrained iterative LQR Algorithm

An Iterative Linear Quadratic Regulator (ILQR) is an algorithm based on the LQR and can solve the problem of unconstrained optimal control of nonlinear system power. Its greatest advantage is time efficiency, but its disadvantage is that constraints cannot be handled. A Constrained Iterative Linear Quadratic Regulator (CILQR) effectively solves the constraint problem in ILQR by adding a barrier function to convert constraint into an additional cost function item and adding the additional cost function item into an original cost function. Therefore, the section plans the state quantities of the terminal position, the speed, the pitch angle and the like of the perch maneuver in advance by using a CILQR algorithm aiming at the perch maneuver system constrained by the state and the control input, and takes the state quantities as the initial feasible track of the LMPC control strategy. The constrained perch maneuver trajectory planning problem is formulated into the following form and is denoted as problem 1:

problem 1 (constrained perch maneuver trajectory planning problem):

s.t.x _k+1 ＝f(x _k ,u _k ),k＝0,1,…,N-1 (4b)

x ₀ ＝x _start (4c)

g _uk (u _k )<0,k＝0,1,…,N-1 (4d)

g _xk (x _k )<0,k＝0,1,…,N (4e)

wherein x in the formula (4a) _k And u _k Respectively is a perching maneuver state variable and a control input variable when the time step number is k, N is the time step number required by the unmanned aerial vehicle to complete one perching maneuver, x _N Is the end point quantity of state, phi (x) _N ) Is the end-of-line phase cost, L _k (x _k ,u _k ) Is the stage cost when the time step number is k, argmin represents the independent variable value when the function value is minimum, x ^* And u ^* The state quantity sequence and the control input sequence when the cost function takes the minimum value. s.t. is an abbreviation for subject to, indicating that it is subject to …. F (·, ·) in formula (4b) represents the perch maneuver dynamics equation. X in the formula (4c) ₀ Is an initial state quantity, x _start Is the initial state quantity of the setting. G in formula (4d) _uk (u _k ) G in equation (4e) representing a control input constraint _xk (x _k ) Representing a constraint on the state quantity.

The ILQR algorithm cannot be used directly because of the state constraints and control input constraints present in problem 1. The control-limited differential dynamic programming algorithm adds constraints in (4a), but is limited to control inputs and cannot work with state constraints. Another way to deal with constraints is to introduce penalties, the basic idea of which is to convert the constraint functions (4d) and (4e) into barrier functions and add them to the original objective function. The invention will use a logarithmic barrier function:

in the formula: q >0 is a parameter, and g (x, u) represents state quantities and control input constraints. The logarithmic function has several good properties. First, it ensures hard constraints by definition. Second, by increasing q, it will asymptotically converge to the indicator function. And the logarithmic barrier function is quadratic and differentiable, the derivative of which is easy to calculate.

The section is based on a logarithm barrier function, and a main body structure of a perch maneuver constrained iterative linear quadratic regulator CILQR algorithm is constructed. The basic idea is to construct outer loop and inner loop iterations. The outer loop uses barrier function to convert the constraint into punishment, and the inner loop uses ILQR algorithm to solve the problem of no constraint after transformation. The pseudo code of the CILQR algorithm is shown in table 1.

TABLE 1

The three core components of the algorithm are:

outer ring: the algorithm starts from the initial feasible track and the initial parameter q of the perch maneuver ⁽⁰⁾ >0 starts. In each iteration, constraints (4d) and (4e) are first converted into penalties using the barrier function of equation (5) and added to the objective function in (4a), and then the converted problem is passed to the inner loop for solution. After each iteration, the parameter q will be increased by a scalar μ>0。

An inner ring: the inner ring solves the conversion problem introduced by the outer ring. Since it is now an unconstrained problem, the unconstrained ILQR algorithm can be used to solve the problem.

Straight line searching: in the ILQR calculation, a straight line search is generally used to ensure convergence. Although the barrier function can guarantee hard constraints, constraints may still be violated during the ILQR trace update process. To solve this problem, a straight line search is performed iteratively to check whether the updated perch trajectory violates the constraint until it completely satisfies the constraint.

2.2 simulation and analysis

Firstly, an open-loop controller is used for calculating an initial feasible locus of a perching and falling motor, and definition is carried out

And

respectively representing the state quantity and the control input when the jth iteration time step number of the perch maneuver is k, and the initial state of the initial track is

The end point state is

Since it is desirable that the terminal velocity, pitch angle and altitude are as small as possible during perching, but the velocity, pitch angle and altitude may not be reduced at the same time considering some characteristics of the perching maneuver model itself, while the pitch angle of the terminal state of the initial trajectory is already relatively small, the terminal target is set to

End point phase cost

And phase cost in k time steps

Respectively expressed as:

wherein the content of the first and second substances,

representing the state quantity with the j iteration time step number of the perch maneuver being N,

is the set end point target, Q _f And the end point weight matrix, Q and R respectively represent the weight matrix of the state quantity and the control quantity.

Since the simulation plans the end point state quantity of the perching mobile track, that is, the error between the end point of the perching track and the set target end point is expected to be smaller and better in each iteration, the optimization index does not limit the state quantity, and the weight of the control quantity is not required to be too large, so that the Q is set to be diag [0,0,0,0]，R＝diag[0.01,0.01](ii) a In the perching process, the speed, the pitch angle and the height of the terminal point are more concerned, the weight occupied by the corresponding state quantity in the weight matrix of the terminal point is set to be relatively larger, and Q is set _f ＝diag[100,1,0.01,0.01,0.01,100](the diag function is used in FreeMatlab, FreMat to construct a diagonal matrix). The state quantities and constraints of the control inputs are shown in table 2.

TABLE 2

The conditions for the end of the iterative algorithm are:

i.e. the state quantities of the ith iteration

State quantities from the i-1 th iteration

The maximum deviation between the two is less than the tolerance gamma of 10 ^-8 The trajectory of the ith iteration is referred to as the optimal trajectory at this time. As shown in fig. 8.

The sampling time for setting the discretization of the unmanned aerial vehicle continuous system in the simulation is delta T equal to 0.01s, and the time step number N required by the unmanned aerial vehicle to finish one-time perching maneuver is 150, so that the time required by the one-time perching maneuver is T equal to 1.5 s.

The simulation results are shown in fig. 1, fig. 2a, fig. 2b, fig. 2c, fig. 2d, fig. 2e, fig. 2f, fig. 3a, and fig. 3 b. In fig. 1, the blue curve represents the cost of each iteration, and the red dotted line represents the optimal cost, so that the cost gradually decreases as the number of iterations increases until the cost converges to a stable value, and the cost function converges to the optimal value when the number j of iterations is 51.

Fig. 2a, 2b, 2c, 2d, 2e, and 2f show state quantity change curves for different numbers of iterations. Where the blue dashed line is the initial feasible trajectory for the perch maneuver and the red solid line is the optimal trajectory. It can be seen that under the action of the CILQR controller, as the number of iterations increases, the end values of the speed and the height gradually approach the set target end values, and all the state quantities satisfy the set constraints. Fig. 3a and 3b show control amount variation curves for different iteration numbers. Wherein the blue dotted line is the control quantity corresponding to the initial feasible trajectory of the perch maneuver, and the red solid line is the control quantity corresponding to the optimal trajectory. The figure shows that the thrust and the rudder deflection angle both meet the set constraint, and the validity of the CILQR algorithm is proved.

3. Design iterative learning model predictive controller

The method is used for researching the optimization and control problem of the trail of the perch maneuver on the premise of meeting the state and input constraints by using a data-driven ILMPC strategy aiming at the condition that the perch maneuver reference trail is unknown, and using the optimal trail obtained by the previous section of CILQR algorithm as the initial feasible trail of the ILMPC strategy.

3.1 problem formulation

The kinetic model (1) was discretized and abbreviated as follows:

x _t+1 ＝f(x _t ,u _t ) (9)

the state constraints and input constraints are:

the goal of this section is to make the unmanned aerial vehicle perch the maneuver trajectory from the starting point x _S Reaches the end point x _F And solve the problem of the finite time domain optimal control, which is denoted as problem 2, as follows:

problem 2 (finite time domain global optimal control problem):

x ₀ ＝x _S (11d)

wherein, in the formula (11a)

Represents the optimal cost, x _t And u _t Respectively representing the perch maneuver state variable and the control input variable, h (x) at time t _t ,u _t ) Is the stage cost. F (·, ·) in formula (11b) represents the perch maneuver dynamics equation. In formula (11c)

Representing state and control input constraints, respectively. X in formula (11d) ₀ Is an initial state quantity, x _S Is the initial state quantity of the setting.

Setting the phase cost h (·,) in equation (11a) is continuous and satisfies:

and defining one iteration as the unmanned plane successfully completing one perching maneuver, and storing the closed-loop track of the perching maneuver. In the jth iteration, vector x ^j And u ^j Respectively storing the state quantities and the corresponding control inputs of the jth iteration of the perch maneuver:

in the formula:

and

respectively representing the state quantity and the control input of the habitat mobile at the jth iteration T moment, wherein the value of T is 0-T ^j ；T ^j Representing the time at which the jth iterative perch maneuver closed-loop trajectory reaches the endpoint, i.e.

Setting each iteration perch maneuvering closed-loop trajectory to start from the same initial state, namely:

setting a local optimal solution to the problem 2, and recording as:

3.2 controller design

This section first introduces how to design a sampling security set and a terminal cost function using historical data; next, a design method of the ILMPC controller is introduced.

3.2.1 sampling safety set

This subsection will utilize the iterative nature of the control problem to construct a sampled safety set of perch maneuver trajectories and use it in the design of perch maneuver ILMPC controllers. Defining an unmanned aerial vehicle perching maneuvering closed-loop system:

wherein the content of the first and second substances,

respectively representing the state quantities of the jth iteration t +1 time and the t time of the perch maneuver,

representing a closed-loop control strategy, and f (·,) representing a perch maneuver dynamics equation.

At the jth iteration, a sample security set is defined as:

in the formula:

representing the state quantity of the i-th iteration t moment of the perch maneuver, wherein i belongs to M ^j ，t∈[0,T ^j ]，M ^j Is an index set in which iteration tasks are successfully completed in the previous j iterations, and is defined as:

thus, the security set is sampled

3.2.2 iterative cost function

The subsection introduces the sampling value function of the perch maneuver and takes the sampling value function as the terminal cost of the iterative learning model predictive control, and the iterative performance of the perch maneuver closed-loop system can be gradually improved.

At time t of the jth iteration, a cost function associated with the perch maneuver closed-loop trajectory (16) and the input sequence (17)

Is defined as:

in the formula:

and

is the stage cost, and k is T-T ^j . Using said cost function to function Q the values of the security set with respect to the sample ^j (x) Is defined as:

value function will perch mobile sampling safety set

The minimum cost function of the stored data is assigned to each point therein, namely:

in the formula:

is a function of x, taking the minimum of equation (22), i.e.:

3.2.3 ILMPC controller design

This subsection will design an Iterative Learning Model Predictive Controller (ILMPC) for an unmanned aerial vehicle perching mobile system. And storing the closed-loop track of the perch mobile system in each iteration, constructing a sampling safety set and a value function, and designing the ILMPC controller of the perch mobile for the next iteration by using the sampling safety set and the value function.

At the time t of the jth iteration, the rooming maneuver ILMPC strategy records the following rolling time domain optimal control problem as problem 3.

Problem 3 (rolling time domain local optimum control problem):

wherein, in the formula (25a)

Is the optimum cost, h (x) _k|t ,u _k|t ) Is the stage cost, Q ^j-1 (x _t+N|t ) Is a function of the value described by equation (22); f (·,) in formula (25b) represents the perch maneuver dynamics equation; in formula (25c)

Representing state and control input constraints, respectively; formula (25d) mobilizes the perch in the time domain [ t, t + N [ ]]The terminal state of (1) is constrained to the perch maneuver sampling security set defined by formula (19)

In (1).

Suppose that problem 3 has an optimal solution at the jth iteration t, which is recorded as:

wherein the content of the first and second substances,

respectively representing the time periods t, t + N of the solution at time t]The series of optimal state quantities and control inputs,

respectively representOptimal control input at the moment k, the value of k is t-t + N-1,

respectively representing the optimal state quantity at the moment k, wherein the value of k is t-t + N.

Then, at the time t of the j-th iteration, the

wherein the content of the first and second substances,

Then in a new state

At iteration 1, SS is set ^j-1 ＝SS ⁰ Is a non-empty set, and the initial perch maneuver trajectory is x ⁰ ∈SS ⁰ And can reach an end point x _F . FIGS. 4a and 4b illustrate the operation of the perch maneuver LMPC controller, using iteration 2 as an example. In the figure, blue points represent perch maneuver sampling safety sets shown in an expression (19), and green stars represent N time-domain perch maneuver optimal prediction tracks given by the optimal solution of the problem 3. Finally, the red squares represent the perch maneuver closed-loop trajectory. Note that at time t-0, the state of the system is equal toInitial state x _S And at the time t equal to 1, the state of the system is equal to the first state quantity in the perching maneuver predicted track at the time t equal to 0.

4. Numerical solving method for designing perch maneuvering ILMPC

4.1 roosting and landing maneuvering model pretreatment

Since the perch maneuver nonlinear model (1) is complex, if the original model is directly used in the solution of the problem 3, the solution difficulty is increased, and even a feasible solution cannot be obtained. In order to reduce the difficulty of the operation, the perch maneuver nonlinear model (1) is simplified as follows:

the input of the simplified four-dimensional model is thrust T and pitch angle acceleration eta, and the state quantities are the flight speed V, track angle mu, attack angle alpha and pitch angle speed q of the fixed-wing unmanned aerial vehicle. Compared with the original six-dimensional model, the horizontal position x and the vertical height h are reduced, and because the two state quantities are only related to the speed V and the track angle mu and are not directly connected with the control input, the two state quantities can not participate in optimization in each iteration, and the horizontal position x and the vertical height h are directly obtained by using the speed V and the track angle mu of the last iteration after the optimization is finished. Since these two state quantities do not participate in the optimization, it may not be guaranteed that the end position of the perch maneuver trajectory in the last iteration coincides with the end position of the initial trajectory, but the end position may coincide with the end position of the initial trajectory by translating the start position of the perch maneuver trajectory in the last iteration.

Furthermore, for a real drone perch maneuver, the control inputs should also be thrust T and rudder deflection angle δ _e Eta is only a virtual control input, and the constraint range of eta needs to be calculated in order to make the eta conform to the physical law of the actual six-dimensional perch maneuvering system. The constraint of η is not a fixed value but varies at each instant, and the magnitude of the value depends on the velocity V, the angle of attack α at that instant and on the value of the velocity V, the angle of attack α at that instantAnd rudder deflection angle delta _e The constraint range of (2) is shown as formula (29):

the specific algorithm for computing the η constraint is therefore: make the rudder declination angle delta _e Has a constraint range of [ -pi/3, pi/3]Each time is at delta _e Is in the range of [ -pi/3, pi/3]Get X from above ₁ (generally 1000) one thousand points, and then the velocity V and the angle of attack alpha at that moment are taken together with X ₁ Delta _e Carry over the value of (1) to calculate X ₁ Taking the value of X ₁ The maximum value and the minimum value of the values are respectively used as an upper limit value and a lower limit value of eta, namely a constraint range of the eta at the moment.

4.2 solving of the perch maneuver optimization problem

The solution of the optimization problem 3 mainly utilizes the Yalmip tool box. The Yalmip tool box is a free optimization solving tool box based on a Matlab platform, has a set of modeling solving languages for solving an optimization problem, and integrates a plurality of external optimization solvers, wherein the external optimization solvers comprise Gurobi, Cplex, Ipopt and the like. When the Yalmip external optimization solver is used, a user does not need to learn the use methods of the external solvers independently, only needs to learn the modeling solving sentences of the Yalmip, and only needs to specify which external optimization solver is used in the grammar of the Yalmip. The Yalmip really realizes the separation of modeling and algorithm, and effectively reduces the learning cost of learners. If the user does not know which solver is suitable, the Yalmip can automatically detect the type of the problem solved by the user and select a suitable solver. The modeling syntax of Yalmip is also simple, with only the four most basic commands:

(1) creating decision variables

Yalmip provides three types of decision variables that can be created, respectively: real number type decision variables, integer type decision variables and 0/1 type decision variables, and the corresponding statements are sdp var, intbar and binvar respectively.

The solution of optimization problem 3 herein requires the creation of 2 real decision variables: the state variable x, the input variable u, and the modeling statement are respectively: x ═ sdp var (6, N); u ═ binvar (2, N). Wherein, N is a prediction time domain.

(2) Adding constraints

The constraints of Yalmip are written very intuitively: for such constraints, for example, it can be written directly as: constraints ═ x (1) + x (2) + x (3)<＝3]. If new constraints are to be added, e.g. x ₂ 1, then can be written as: constraints, x (2) 1]。

In the invention, the solution of the optimization problem 3 needs to create 5 constraint conditions, namely a habitat mobile system dynamic model represented by a formula (25b), a state quantity and control quantity constraint represented by a formula (25c), a terminal state constraint represented by a formula (25d) and an initial condition constraint represented by a formula (25 e).

(3) Parameter configuration

The parameter configuration statement of Yalmip is: options ═ sdp settings (option1, value1, option2, value2, … …). The purpose of parameter setting is mostly to set the solver. For example, if the solver used in the present invention is an interior point non-linear solver (Ipopt), then the configuration statements are sdp settings ('solver', 'Ipopt').

(4) Solving for

The solution statement for Yalmip is: optimize (constraints, cost, options). Wherein constraints are constraints in step (2), optiones are parameter configurations in step (3), and cost is a solution target. The solution objective of optimization problem 3 is shown in equation (33). After the solution is completed, the optimal solution of the corresponding variables can be extracted through statements value (x), value (u).

5. Simulation and analysis

To construct an initial sampling safety set SS ⁰ And an initial cost function Q ⁰ Firstly, an open-loop controller is used for calculating an initial feasible locus x of the perch maneuver meeting the constraints of state quantity and input quantity ⁰ ∈SS ⁰ The specific constraints are shown in table 1.

Optimization problem 3 middle stage cost

Is as shown in equation (30):

wherein Q is the weight occupied by the control input, and a larger term indicates a smaller desired control energy; r represents the weight occupied by the state variable, and the larger the term is, the smoother the state variable is expected to be. Since the perch maneuver needs to achieve the purpose of rapid deceleration through large change of the state quantity, the stage cost does not limit the state quantity, and Q is set to diag [0,0,0,0 ]; in order to minimize the input energy of the entire process, R is set to diag [1,1 ].

Setting initial time t of each perch maneuver iteration in simulation ₀ 0s, initial state x ₀ ＝[13；0；0.1770；0]End point state

Equal to the end of the initial feasible trajectory. The sampling time of the unmanned aerial vehicle continuous system discretization is set to be delta t 0.01s, the prediction time domain N is 7, and the number of data points of each iteration in the convex local security set is 21. Time T to reach the end point for each iteration ^j Not fixed, defined as:

the conditions for the end of the iterative algorithm are:

i.e. the maximum deviation between the state quantity of the ith iteration and the state quantity of the (i-1) th iteration is less than the tolerance y 10 ^-8 The trajectory of the ith iteration is referred to as the optimal trajectory at this time.

The simulation results are shown in fig. 5, 6a, 6b, 6c, 6d, 6e, 6f, 7a, and 7 b. The blue curve in fig. 5 represents the cost of each iteration, and the red dotted line represents the optimal cost, and it can be seen that as the number of iterations increases, the cost gradually decreases until a stable value is converged, and at the number of iterations j equal to 35, the cost function converges to the optimal value.

Fig. 6a, 6b, 6c, 6d, 6e, and 6f show state quantity change curves for different numbers of iterations. Wherein the blue dotted line is the initial feasible trajectory of the perch maneuver, and the red solid line is the optimal trajectory of the perch maneuver at the iteration number j of 35. It can be seen that under the action of the LMPC, as the number of iterations increases, the trajectory of the perch maneuver gradually deviates from the initial feasible trajectory and approaches the optimal trajectory. In addition, as can be seen from fig. 6a, 6b, 6c, 6d, 6e, and 6f, the state quantities of each iteration can satisfy the constraint condition, and the trajectory of each iteration can reach the end point of the initial trajectory.

Fig. 7a and 7b show control amount change curves for different numbers of iterations. Wherein the blue dotted line is the control quantity corresponding to the initial feasible trajectory of the perch maneuver, and the red solid line is the control quantity corresponding to the optimal trajectory. As can be seen from the figure, the control amount is generally gradually reduced as the number of iterations increases, which also intuitively shows that the cost is gradually reduced as the number of iterations increases (since the drawing of the specification can only be a gray scale, the colors in the drawing cannot be seen, and thus the description is given).

The invention establishes an aerodynamic model and a nonlinear dynamic model of a perching and landing maneuver system aiming at the longitudinal movement of the perching and landing maneuver of the fixed-wing unmanned aerial vehicle. In order to obtain an ILMPC strategy initial feasible track with the end point state quantity meeting expected requirements, a CILQR algorithm is used for optimizing the perch maneuver track. The simulation result shows that the end point values of the speed and the height gradually approach the set target end point value along with the increase of the iteration times, and all the state quantities and the control quantities meet the set constraint, so that the effectiveness of the CILQR algorithm is shown. The invention designs a data-driven ILMPC strategy aiming at the problem of track optimization and control of unmanned aerial vehicle perching maneuver with unknown reference track, and the controller can learn from previous iteration and improve the performance. The simulation result shows that the iteration cost is gradually reduced along with the increase of the iteration times, the perch maneuver trajectory is gradually converged to the optimal trajectory, and the effectiveness of the designed controller is shown.

The present invention provides an iterative optimization and control method for unmanned aerial vehicle perching maneuver, and a plurality of methods and ways for implementing the technical scheme, and the above description is only a preferred embodiment of the present invention, it should be noted that, for those skilled in the art, a plurality of improvements and embellishments can be made without departing from the principle of the present invention, and these improvements and embellishments should also be regarded as the protection scope of the present invention. All the components not specified in the present embodiment can be realized by the prior art.

Claims

1. An iterative optimization and control method for unmanned aerial vehicle perching maneuver is characterized by comprising the following steps:

step 2, planning state quantities such as position, speed, pitch angle and the like at the motor terminal point of the perch by adopting a constrained iterative linear quadratic regulator CILQR to obtain an optimal track;

and 3, taking the optimal track obtained in the step 2 as an initial feasible track of an iterative learning model predictive control ILMPC strategy, and designing an iterative learning model predictive controller.

2. The method of claim 1, wherein the perch maneuver dynamics model of step 1 is:

Represents the derivative of V; m is the mass of the aircraft, g is the gravitational acceleration, T is the engine thrust, I _y Is the pitching moment of inertia of the unmanned aerial vehicle; m is aerodynamicThe moments, L and D represent the lift and drag experienced by the drone, respectively.

3. The method of claim 2, wherein the expression equations of M, L and D are:

where ρ is the air density, S is the aerodynamic area of the drone, C _L 、C _D And C _M Respectively representing the lift, resistance and moment coefficients of the fixed-wing drone.

4. The method of claim 3, wherein C is _L 、C _D And C _M The expression equations are respectively:

5. The method of claim 4, wherein step 2 comprises the steps of:

s.t.x _k+1 ＝f(x _k ,u _k ),k＝0,1,…,N-1 (4b)

x ₀ ＝x _start (4c)

g _uk (u _k )<0,k＝0,1,…,N-1 (4d)

g _xk (x _k )<0,k＝0,1,…,N (4e)

wherein x in the formula (4a) _k And u _k Respectively is a perching maneuver state variable and a control input variable when the time step number is k, N is the time step number required by the unmanned aerial vehicle to complete one perching maneuver, x _N Is the end point quantity of state, phi (x) _N ) Is the end-of-line phase cost, L _k (x _k ,u _k ) Is the stage cost when the time step number is k, argmin represents the independent variable value when the function value is minimum, x ^* And u ^* The state quantity sequence and the control input sequence when the cost function obtains the minimum value;

f (·,) in formula (4b) represents the perch maneuver dynamics equation;

g in formula (4d) _uk (u _k ) Representing control input constraints;

g in formula (4e) _xk (x _k ) Representing a constraint on a state quantity;

step 2-2, introducing a logarithmic barrier function in order to process the constraint in the problem 1;

and 2-3, constructing a restricted iteration quadratic regulator CILQR algorithm of the perch maneuver based on the logarithm barrier function.

6. The method according to claim 5, wherein in step 2-2, the logarithmic barrier function b (x, u) is:

7. The method according to claim 6, characterized in that step 2-3 comprises in particular the steps of:

step 2-3-1: given a perch maneuver initial control sequence

step 2-3-3: solving the unconstrained optimization problem obtained in the step 2-3-2 by using an iteration LQR algorithm, and obtaining a control sequence u of the next iteration;

step 2-3-4: judging whether the current control sequence u can enable the perching track to meet the constraint condition by using straight line search, if so, performing the step 2-3-5, and if not, enabling u to be alpha u until the perching track meets the constraint condition;

step 2-3-5: forward simulation to obtain the current state sequence

q ═ μ q, and return to step 2-3-2.