CN112947073B - Model predictive control-based carrier-based aircraft sliding track tracking method - Google Patents
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Abstract
A carrier-based aircraft sliding track tracking method based on model predictive control belongs to the field of autonomous motion control of equipment. Firstly, an extended dicyclohexyl model is established on the basis of a classical dicyclohexyl model according to the size parameters and the mechanical parameters of the carrier-based aircraft, and the movement of the carrier-based aircraft is described. Second, a reference dispatch trajectory generated by the trajectory planning module is obtained. Thirdly, based on the established extended bicycle model and related constraints, a model predictive controller model is established, and related parameters in the controller, such as sampling intervals, tracking error weights, control weights and the like, are set. Fourth, the reference trajectory is tracked using a constructed model predictive controller. The invention can realize accurate and reliable tracking of the carrier-based aircraft on the reference dispatching track in the single-machine sliding dispatching mode under the disturbance environment, the relevant constraint of the state variable and the control input in the tracking link is strictly satisfied, the change curve of the state variable has no obvious oscillation, and the invention has good applicability.
Description
Technical Field
The invention belongs to the field of autonomous motion control of equipment, and relates to a ship-based aircraft sliding track tracking method based on model predictive control.
Background
The carrier-based aircraft is main combat equipment carried on the aircraft carrier, and the operational efficiency in the operation and recovery links determines the combat effectiveness of the aircraft carrier. The carrier-based aircraft mainly has two dispatching modes on the deck, namely a single-machine sliding mode and a traction mode of a hauled tractor with a rod. At present, after the dispatching instruction is generated, dispatching is realized in a mode that a carrier-based aircraft pilot steers an aircraft or a tractor driver steers a tractor. The potential fatigue factors, sight interference and other factors of pilots/drivers and the complex plate surface environment make the safety of the transportation process difficult to ensure.
At present, a large number of students have studied on automatic generation of ship-based aircraft deck maneuvering trajectories. If constraints such as a motion equation, obstacle avoidance, upper and lower limits of state/control variables and the like can be comprehensively considered in a track planning stage, after the track to be transferred is generated, the anti-disturbance track tracking method is further combined, so that safe and reliable autonomous transfer can be realized. Common trajectory tracking methods include model predictive control, sliding mode control, nonlinear control, and the like. The model predictive control method can process various constraints under a unified frame, and has great advantages for tracking the track of the carrier-borne aircraft with various constraints being considered.
The model predictive control method solves an open-loop optimal control problem at each sampling time, so that when the model predictive control method is used for track tracking, the tracking performance is affected by the following factors:
(1) If the constraint setting is too many in the open loop problem, a longer online calculation time is caused, a larger sampling interval is forced to be adopted, and the resistance of the controller to external disturbance is weakened;
(2) If the motion model is selected improperly in the open loop optimal control problem, serious oscillation is generated on state variables or control inputs of the carrier-based aircraft, so that the comfort level of a driver is greatly influenced or the service life of a controller is greatly shortened.
Disclosure of Invention
In order to solve the technical problems, the invention provides a ship-based aircraft sliding track tracking method based on model predictive control. The method realizes high-precision and high-robustness track tracking in the single-machine sliding and dispatching mode by reasonably setting constraint and motion equation in the open-loop optimal control problem, and has good applicability.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a ship-based aircraft sliding track tracking method based on model predictive control is realized based on an automatic control system and comprises a track planning module and a track tracking module, wherein the track planning module generates a reference dispatching track according to dispatching instructions, the track tracking module tracks the reference dispatching track, and the track tracking is realized by a model predictive control algorithm. Firstly, an extended dicyclohexyl model is established on the basis of a classical dicyclohexyl model according to the size parameters and the mechanical parameters of the carrier-based aircraft, and the movement of the carrier-based aircraft is described. Next, a reference dispatch trajectory generated by the trajectory planning module is obtained. And thirdly, based on the established extended bicycle model and related constraints, establishing a model predictive controller model, and setting related parameters in the controller, such as sampling intervals, tracking error weights, control weights and the like. And finally, tracking the reference track by using the constructed model predictive controller. The calculation flow chart of the invention is shown in fig. 1, and comprises the following steps:
step 1: establishing an extended dicyclohexyl model for describing the movement of the carrier-based aircraft in a single-machine sliding mode
In the single-vehicle coasting and dispatching mode shown in fig. 2, the position of the rear wheel is described by using the midpoint G (x, y) of the rear wheel, and the variable θ is used to represent the direction of the carrier-based aircraft, and the translational speed of the midpoint G is v. The position of the front wheel of the carrier-based aircraft is recorded as a point F, and the variable is recorded as a variableThe distance between the point F and the point G is denoted as L. If the state space of the carrier-based aircraft is +.>The sliding movement of the carrier-based aircraft can be controlled byThe following classical dicyclohexyl model is described:
where a represents the acceleration of the aircraft, ω represents the angular velocity of the steering angle of the front wheels of the aircraft, and t is a time variable.
If the classical bicycle model in formula (1) is directly used for track tracking, the control variables are a and ω, which will lead to severe oscillations of the control variables, which affect the pilot's handling comfort on the one hand and reduce the controller's service life on the other hand. For this purpose, the invention introduces the jerk j (i.e. the second derivative of the velocity v) of the aircraft and the angular acceleration α of the front steering angle on the basis of the classical dicyclohexyl model to build an extended dicyclohexyl model, which is used for the construction of the model predictive controller. In the extended dicyclohexyl model, the state space isThe control variable is noted u= (j, α) T The method is specifically expressed as follows:
where f is a function representing an extended dicyclohexyl model.
Step 2: obtaining a reference dispatch trajectory generated by a trajectory planning module
And obtaining a reference dispatching track by a track planning module. The reference allocation track comprises a series of discrete points of the carrier-based aircraftUpper corresponding position information->And orientation angle information-> wherein t1 and tM The start time and the end time of the reference dispatch trajectories are represented, respectively. In the reference dispatch track, the initial position is +.>The initial orientation angle is->The position of the terminal is +.>The initial orientation angle is->
Step 3: based on the established extended dicyclohexyl model and related constraint, a model predictive controller model is established
The model predictive controller solves an open-loop optimal control problem at each sampling time and records the set of sampling times as wherein />In order to construct a controller for tracking the sliding track of the carrier-based aircraft, the controller is provided with a control unit for controlling the sliding track of the carrier-based aircraft at the sampling time>Solving is defined in the control window as follows>Open loop optimal control problem on->
wherein ,for defined tracking error, x ref 、y ref And theta ref Respectively represent according to-> and />Constructing a spline interpolation function; p=diag { P 1 ,P 2 ,P 3 Sum r=diag { R 1 ,R 2 Weight values of tracking error and control input are represented respectively, sign diag {.cndot } represents diagonal matrix, weight parameter P 1 、P 2 、P 3 、R 1 and R2 The value of (2) is regulated according to the actual condition; t represents the control window length of the model control predictor and is generally set between 1s and 5s; />Representing the sampling time +.>The collected state of the carrier-based aircraft; v max Represents the upper limit of the coasting speed v, +.>Representing the front wheel angle +.>Upper limit of amplitude of a), a max Represents the upper limit of the amplitude, omega, of the acceleration a of the carrier-borne aircraft max An upper limit of amplitude, alpha, representing the angular velocity omega of the front wheel corner max Representing the upper limit of the amplitude of the angular acceleration alpha of the front wheel corner, j max Representing the upper limit of the amplitude of the jerk j of the carrier-based aircraft; these upper limits are generally determined based on the safety constraints of the carrier-based aircraft deployment process and the mechanical parameters of the carrier-based aircraft, particularly if in a trajectory planning moduleHaving considered the relevant constraints, these upper limits are typically relaxed slightly (e.g., 5% -10% relaxed) in the design of the model predictive controller to ensure tracking performance under disturbances.
Step 4: tracking a reference trajectory using a structured model predictive controller
Continuously solving problems using the model predictive controller constructed in step 3The starting time of the open-loop optimal control problem to be solved at the current sampling time is not less than the terminal operation time in the reference track (namely +.>)。
The beneficial effects of the invention are as follows: by means of an automation technology, the precise disturbance-resistant track tracking of the carrier-based aircraft on the reference track in the single-machine sliding and dispatching mode is realized, the potential influence of human factors such as fatigue and sight interference of pilots is eliminated, and the safety and reliability of the dispatching process are improved.
Drawings
FIG. 1 is a flow chart of the calculation of the present invention.
FIG. 2 is a description of the carrier-based mechanism in a stand-alone glide mode of the invention.
Fig. 3 is a reference dispatch trajectory given in an embodiment of the present invention.
FIG. 4 is a graph showing tracking error (in m/s) of the abscissa of the carrier-based aircraft in an embodiment of the present invention.
FIG. 5 is a graph showing tracking error (in m/s) of the ordinate of the carrier-based aircraft in an embodiment of the invention.
FIG. 6 is a graph showing tracking error (in deg/s) of the orientation angle of the carrier-based aircraft in an embodiment of the invention.
FIG. 7 shows actual planing speed (in m/s) of the carrier-based aircraft in an embodiment of the invention.
FIG. 8 is an actual front wheel corner (in deg) of a carrier-based aircraft in an embodiment of the invention.
FIG. 9 is an angular velocity (in deg/s) of the actual front wheel corner of the carrier-based aircraft in accordance with an embodiment of the present invention.
FIG. 10 is a graph showing actual acceleration (in m/s) of the carrier-based aircraft in an embodiment of the invention 2 )。
Detailed Description
The invention is further described below with reference to specific embodiments, taking the deck of the Nimitz-level aircraft carrier shown in fig. 3 as a simulation environment, and tracking the reference transportation tracks of four carrier-based aircraft carriers numbered 1,2, 3 and 4.
For each carrier aircraft in the figure, the relevant mechanical parameters and constraints are shown in table 1. The reference dispatch trajectories generated by the trajectory planning module are shown in fig. 3. In the reference dispatch track, the starting time and the terminal time are respectively t 1＝0s and tM The initial state and the terminal state of the four carrier-based aircraft used are shown in table 2, respectively.
Table 1 mechanical parameters and constraints of carrier-borne aircraft
Initial state and terminal state of four carrier-based aircraft in table 2 track planning module
In the constructed model predictive controller, a sampling interval δt=0.05s is set; setting the control window length to t=4s; setting the correlation weight coefficient as P 1 ＝10 5 、P 2 ＝10 5 、P 3 ＝10 4 、R 1＝1 and R2 =1. Setting the disturbance of jerk as delta for simulating the external disturbance in the actual tracking link j (subject to standard deviation of 0.01 m/s) 3 Zero mean gaussian distribution) of the front wheel angular acceleration is delta α (subject to standard deviation of 0.01 deg/s) 2 Is a zero-mean gaussian distribution). Setting an actual initial state table of the carrier-based aircraft for simulating initial state disturbance in an actual tracking link3。
Table 3 actual initial State of Carrier-based aircraft in track tracking Link
A ship-based aircraft sliding track tracking method based on model predictive control comprises the following steps:
step 1: establishing an extended dicyclohexyl model for describing the movement of the carrier-based aircraft in a single-machine sliding mode
According to the given relative mechanical parameters of the carrier-based aircraft, the extended bicycle model of the carrier-based aircraft in the single-machine sliding mode is as follows
Step 2: obtaining a reference dispatch trajectory generated by a trajectory planning module
The reference allocation and transportation tracks of the carrier-based aircraft No. 1-4 obtained by the track planning module respectively correspond to the curves (1) to (4) in the figure 3.
Step 3: based on the established extended dicyclohexyl model and related constraint, a model predictive controller model is established
The set of sampling moments is wherein />k=1, 2, …. At sampling instant +.>The acquired state of the carrier-based aircraft is recorded as +.>Open loop optimal control problem to be solved->The definition is as follows
wherein ,for defined tracking error, x ref 、y ref And theta ref Respectively represent according to-> and />Constructing a spline interpolation function; p=diag {10 ] 5 ,10 5 ,10 4 And r=diag {1,1} represent the weights of the tracking error and the control input, respectively.
Step 4: tracking a reference trajectory using a structured model predictive controller
Table 4 carrier-based aircraft terminal tracking error
Continuously solving problems using the model predictive controller constructed in step 3Until meeting->The tracking errors of the positions and the orientation angles of the carrier-based aircraft are shown in fig. 4-6, and the terminal tracking errors of four carrier-based aircraft are shown in table 4, so that the errors of three variables can be well suppressed, the terminal errors are extremely small, and the precision requirements in the actual dispatching link can be met; the actual state changes of the four carrier-based aircraft under the action of the controller are shown in fig. 7-10And the quantity can find that the 4-class state quantity meets the related constraint and has no obvious oscillation phenomenon.
The invention describes the movement of the carrier-based aircraft in the single-machine sliding and dispatching mode by adopting the extended dicyclohexyl model based on the classical dicyclohexyl model, and develops a track tracking method of the carrier-based aircraft sliding track based on the model predictive control method, thereby realizing the autonomous dispatching in the single-machine sliding and dispatching mode. Compared with the existing manual operation-based transportation mode, the invention overcomes the defect that the ship-based aircraft is easy to be subjected to factor impressions such as manual fatigue, sight line obstruction and the like, and greatly improves the safety and reliability of the ship-based aircraft deck transportation link, thereby ensuring the efficiency of the ship-based aircraft running/recycling link.
The examples described above represent only embodiments of the invention and are not to be understood as limiting the scope of the patent of the invention, it being pointed out that several variants and modifications may be made by those skilled in the art without departing from the concept of the invention, which fall within the scope of protection of the invention.
Claims (2)
1. The carrier-based aircraft sliding track tracking method based on model predictive control is characterized in that the carrier-based aircraft sliding track tracking method is realized based on a track planning module and a track tracking module, a track planning module generates a reference dispatching track according to dispatching instructions, the track tracking module tracks the reference dispatching track, and the track tracking is realized by a model predictive control algorithm; the method comprises the following steps:
step 1: establishing an extended dicyclohexyl model for describing the movement of the carrier-based aircraft in a single-machine sliding mode
In a single-machine sliding and dispatching mode, the position of the rear wheel is described by using the midpoint G (x, y) of the rear wheel, and the variable theta is used for expressing the orientation of the carrier-borne aircraft, and the translational speed of the midpoint G is v; the position of the front wheel of the carrier-based aircraft is recorded as a point F, and the variable is recorded as a variableThe distance between the point F and the point G is recorded as L; if the state space of the carrier-based aircraft is +.>The planing motion of the carrier aircraft can be described by the following classical dicyclohexyl model:
wherein a represents the acceleration of the aircraft, ω represents the angular velocity of the steering angle of the front wheels of the aircraft, and t is a time variable;
introducing jerk j of an airplane and angular acceleration alpha of a front steering angle on the basis of a classical dicycle model to establish an expanded dicycle model, and using the expanded dicycle model for constructing a model prediction controller, wherein the jerk j is a second derivative of the speed v; in the extended dicyclohexyl model, the state space isThe control variable is noted u= (j, α) T The method is specifically expressed as follows:
wherein f is a function representing an extended dicyclohexyl model;
step 2: obtaining a reference dispatch trajectory generated by a trajectory planning module
Obtaining a reference dispatching track by a track planning module; the reference allocation track comprises a series of discrete points of the carrier-based aircraftUpper corresponding position information->And orientation angle information-> wherein t1 and tM Respectively representing the starting time and the terminal time of the reference dispatch track; in the reference dispatch track, the initial position is +.>The initial orientation angle is->The position of the terminal is +.>The orientation angle of the terminal is->
Step 3: based on the established extended dicyclohexyl model and related constraint, a model predictive controller model is established
The model predictive controller solves an open-loop optimal control problem at each sampling time and records the set of sampling times as wherein ,/>In order to construct a controller for tracking the sliding track of the carrier-based aircraft, the controller is provided with a control unit for controlling the sliding track of the carrier-based aircraft at the sampling time>Solving is defined in the control window as follows>Open loop optimal control problem on->
wherein ,for defined tracking error, x ref 、y ref And theta ref Respectively represent according to and />Constructing a spline interpolation function; p=diag { P 1 ,P 2 ,P 3 Sum r=diag { R 1 ,R 2 Weight values of tracking error and control input are represented respectively, sign diag {.cndot } represents diagonal matrix, weight parameter P 1 、P 2 、P 3 、R 1 and R2 The value of (2) is regulated according to the actual condition; t represents the control window length of the model control predictor; />Representing the sampling time +.>The collected state of the carrier-based aircraft; v max Represents the upper limit of the coasting speed v, +.>Representing the front wheel angle +.>Upper limit of amplitude of a), a max Represents the upper limit of the amplitude, omega, of the acceleration a of the carrier-borne aircraft max An upper limit of amplitude, alpha, representing the angular velocity omega of the front wheel corner max Upper limit of amplitude representing front wheel corner angular acceleration alpha，j max Representing the upper limit of the amplitude of the jerk j of the carrier-based aircraft;
step 4: tracking a reference trajectory using a structured model predictive controller
Continuously solving problems using the model predictive controller constructed in step 3Until the starting time of the open-loop optimal control problem to be solved at the current sampling moment is not less than the terminal operation time in the reference track, namely +.>
2. The method for tracking the sliding track of the carrier-based aircraft based on model predictive control according to claim 1, wherein the control window length is set between 1s and 5 s.
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