CN107992069B - Guidance law design method for unmanned aerial vehicle path tracking control - Google Patents

Guidance law design method for unmanned aerial vehicle path tracking control Download PDF

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CN107992069B
CN107992069B CN201711230202.5A CN201711230202A CN107992069B CN 107992069 B CN107992069 B CN 107992069B CN 201711230202 A CN201711230202 A CN 201711230202A CN 107992069 B CN107992069 B CN 107992069B
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郑黎明
周启航
赵桂军
夏峥
黄海涛
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Shanghai Radio Equipment Research Institute
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    • G—PHYSICS
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    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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Abstract

The invention discloses a guidance law design method for unmanned aerial vehicle path tracking control, which comprises the following steps: s1, projecting the unmanned aerial vehicle from the initial position A of the unmanned aerial vehicle to a preset track with the flying speed of the unmanned aerial vehicle being V, taking the projection point as O, and recording the distance between the flying track of the unmanned aerial vehicle and the preset track as an eccentric distance d; s2, obtaining a circle with radius r by taking the projection point as the center of the circle, taking the intersection point of the circle and the preset track along the front of the unmanned aerial vehicle in the speed direction as B, and recording the length of AB as L1*Design L1 with B as reference point*The law of guidance is that in the case of guidance,
Figure DDA0001488051610000011
s3, selecting the radius as R*Reference circle of1 *Calculating to obtain a lateral acceleration command a of the unmanned aerial vehicle by using centripetal acceleration and motion geometry relations*. The advantages are that: the problem that the tracking speed is too slow in tracking control in the prior art can be solved.

Description

Guidance law design method for unmanned aerial vehicle path tracking control
Technical Field
The invention relates to the technical field of unmanned aerial vehicles, in particular to a guidance law design method for unmanned aerial vehicle path tracking control.
Background
The unmanned aerial vehicle can carry various electronic equipment loads to replace a traditional piloting plane to execute various complex and dangerous tasks, and the wide application prospect and the adaptability to the complex tasks enable the unmanned aerial vehicle to become the key field of domestic and foreign research in recent years. The unmanned plane path tracking control is one of important technologies for unmanned plane flight control, and means that an unmanned plane tracks an expected flight path meeting flight requirements and performance constraints to complete a predetermined flight task, and the performance of the tracking control directly influences the stability, safety and economy of flight.
In the problem of unmanned aerial vehicle path tracking control, guidance law design is needed, namely, an expected speed and an expected turning rate are designed, so that the unmanned aerial vehicle can fly along a preset track, and the tracking error between the flight track and the preset track is as small as possible. When the flight track of the unmanned aerial vehicle deviates from the preset track, a reasonable lateral acceleration instruction needs to be designed to reduce the tracking error.
One of the existing tracking guidance laws is an L1 nonlinear guidance algorithm: and calculating a virtual target point on a preset track according to the forward-looking distance, and calculating a lateral acceleration instruction according to a circular transfer strategy. Although the algorithm is simple in calculation, the algorithm is limited by the selection of the forward looking distance, the forward looking distance is required to be larger than an initial error, and the tracking speed is too slow due to the larger forward looking distance, so that the flight performance of the unmanned aerial vehicle is affected.
Disclosure of Invention
The invention aims to provide a guidance law design method for unmanned aerial vehicle path tracking control, which can solve the problem that the tracking rate is too slow in tracking control in the prior art.
In order to achieve the purpose, the invention is realized by the following technical scheme:
a guidance law design method for unmanned aerial vehicle path tracking control is characterized by comprising the following steps:
s1, projecting the unmanned aerial vehicle from the initial position A of the unmanned aerial vehicle to a preset track with the flying speed of the unmanned aerial vehicle being V, taking the projection point as O, and recording the distance between the flying track of the unmanned aerial vehicle and the preset track as an eccentric distance d;
s2, obtaining a circle with radius r by taking the projection point as the center of the circle, taking the intersection point of the circle and the preset track along the front of the unmanned aerial vehicle in the speed direction as B, and recording the length of AB as L1*Design L1 with point B as reference point*The law of guidance is that in the case of guidance,
Figure GDA0002782379920000021
s3, selecting the radius as R*Reference circle of1 *Calculating to obtain a lateral acceleration command a of the unmanned aerial vehicle by using centripetal acceleration and motion geometry relations*。
In the guidance law designing method for unmanned aerial vehicle path tracking control described above, in step S3:
center of circle O1 *Is the intersection point of the perpendicular bisector of the line segment AB and the projection line AO;
radius R*Is a line segment AO1 *Length.
In the guidance law design method for unmanned aerial vehicle path tracking control, step S3 specifically includes:
recording the included angle between the speed of the unmanned aerial vehicle and the reference connecting line between the position of the unmanned aerial vehicle and the reference point as eta*Selecting a radius R*Reference circle of1 *The lateral acceleration command a of the unmanned planes *Is denoted by as *＝V2/R*Meanwhile, the kinematic geometrical relationship can be used to obtain L1*＝2R*sinη*Finally, a is obtaineds *＝2V2sinη*/L1*。
The guidance law design method for unmanned aerial vehicle path tracking control further comprises the following steps:
and S4, under the condition that the tracked preset track is a straight line, carrying out linearization processing on the nonlinear guidance law, and enabling the path tracking problem to be equivalent to a second-order damping system problem of the eccentricity d.
In the guidance law design method for unmanned aerial vehicle path tracking control, the step S4 specifically includes:
under the condition that the tracked preset track is a straight line, when the unmanned aerial vehicle starts to track the preset track, the speed V deflects by a certain angle under the action of a lateral acceleration instruction, and an included angle eta is recorded*＝η1+η2，η1Is the angle between the speed V of the unmanned aerial vehicle and the horizontal line, eta2The first derivative and the second derivative of the eccentricity d are recorded as the included angle between the horizontal line and the reference line AB
Figure GDA0002782379920000022
And
Figure GDA0002782379920000023
obtaining:
Figure GDA0002782379920000024
at the same time, the kinematic geometry relationship yields:
Figure GDA0002782379920000031
two-order damping system equation for obtaining eccentricity d by combining the two equations
Figure GDA0002782379920000032
Wherein ζ is damping, wnFor the frequency of the second order damping system:
Figure GDA0002782379920000033
Figure GDA0002782379920000034
Figure GDA0002782379920000035
compared with the prior art, the invention has the following advantages: the original L1 nonlinear guidance method must require that the forward looking distance is larger than the initial error, but once a larger forward looking distance is selected, the lateral acceleration value is too small, and the tracking speed is too slow; meanwhile, as the tracking error is continuously reduced, the lateral acceleration is continuously calculated by adopting a larger forward sight distance, and the forward sight distance is limited to be larger than the initial error.
Drawings
Fig. 1 is a schematic diagram of the design of the guidance law at L1 in the tracking control process of the unmanned aerial vehicle in the invention;
FIG. 2 is a schematic view of the decomposition calculation of the angle in the tracking control process of the unmanned aerial vehicle in the invention;
FIG. 3 is a numerical diagram of horizontal distance and vertical distance in the tracking control process of the unmanned aerial vehicle according to the present invention;
FIG. 4 shows an included angle eta in the tracking control process of the unmanned aerial vehicle according to the invention*A time-varying numerical map;
fig. 5 is a flowchart of the design method of the L1 guidance law for unmanned aerial vehicle tracking control according to the present invention.
Detailed Description
The present invention will now be further described by way of the following detailed description of a preferred embodiment thereof, taken in conjunction with the accompanying drawings.
As shown in fig. 5, the present invention provides a guidance law design method for unmanned aerial vehicle path tracking control, which includes the following steps:
s1, projecting the unmanned aerial vehicle from the initial position A of the unmanned aerial vehicle to a preset track with the flying speed of the unmanned aerial vehicle being V, taking the projection point as O, and recording the distance between the flying track of the unmanned aerial vehicle and the preset track as an eccentric distance d;
in this embodiment, as shown in fig. 1, the unmanned aerial vehicle flies rightwards at a constant speed V of 10m/s, an initial position is denoted as a, the predetermined track is a straight line path, a projection point from the point a to the predetermined track is denoted as O, a distance between the flight track of the unmanned aerial vehicle and the predetermined track is an eccentricity d, and an initial value d is050 m. The unmanned aerial vehicle is required to fly along a preset track according to a tracking instruction, namely the value of the eccentricity d is finally constant to be 0;
s2, obtaining a circle with radius r by taking the projection point as the center of the circle, taking the intersection point of the circle and the preset track along the front of the unmanned aerial vehicle in the speed direction as B, and recording the length of AB as L1*Design L1 with point B as reference point*The law of guidance is that in the case of guidance,
Figure GDA0002782379920000041
in this embodiment, the radius r of the circle is 10m, the intersection point of the circle and the front of the predetermined track (along the direction of the unmanned aerial vehicle speed V) is B, and the connection AB is recorded as the length L1*(ii) a Meanwhile, considering the design of the original L1 guidance law as a comparison reference, a reference circle O with the radius R is selected1Taking the AC length as L1 ═ 60m>d is 50 m. New guidance law at this timeIn the design
Figure GDA0002782379920000042
And C is a reference point directly in front of the projection point directly selected in the original L1 guidance law, namely the C point in the original L1 guidance law corresponds to the B point in the improved guidance law.
S3, selecting the radius as R*Reference circle of1 *Calculating to obtain a lateral acceleration command a of the unmanned aerial vehicle by using centripetal acceleration and motion geometry relationsA first step of; specifically, the center of circle O1 *Is the intersection point of the perpendicular bisector of the line segment AB and the projection line AO; radius R*Is O1 *As a circle center, a line segment AO1 *The length is a radius.
In order to verify the convergence of the guidance law, in the present embodiment, step S4 is further included after step S3, and for example, when the predetermined track to be tracked is a straight line, the nonlinear guidance law is linearized, and the path tracking problem is equivalent to a second-order damping system problem of the eccentricity d.
The step S3 specifically includes:
as shown in FIG. 2, let us note that the angle between the speed of the drone and the reference line between the position of the drone and the reference point is η*Selecting a radius R*Reference circle of1 *The lateral acceleration command a of the unmanned planes *Is denoted by as *＝V2/R*Meanwhile, the kinematic geometrical relationship can be used to obtain L1*＝2R*sinη*Finally, a is obtaineds *＝2V2sinη*/L1*. The included angle between the speed V of the unmanned aerial vehicle in the original L1 guidance law and the reference connecting line AC is eta, namely eta in the original L1 guidance law corresponds to eta in the improved guidance law*。
The step S4 specifically includes:
as shown in fig. 2, when the tracked predetermined track is a straight line, that is, when the unmanned aerial vehicle starts to track the predetermined track, and when the unmanned aerial vehicle starts to track the predetermined track, the speed V will deflect by a certain angle under the action of the lateral acceleration command, and the included angle η is recorded*＝η1+η2，η1Is the angle between the speed V of the unmanned aerial vehicle and the horizontal line, eta2The first derivative and the second derivative of the eccentricity d are recorded as the included angle between the horizontal line and the reference line AB
Figure GDA0002782379920000051
And
Figure GDA0002782379920000052
obtaining:
Figure GDA0002782379920000053
at the same time, the kinematic geometry relationship yields:
Figure GDA0002782379920000054
two-order damping system equation for obtaining eccentricity d by combining the two equations
Figure GDA0002782379920000055
Wherein ζ is damping, wnFor the frequency of the second order damping system:
Figure GDA0002782379920000056
Figure GDA0002782379920000057
Figure GDA0002782379920000058
it can be seen that the problem is equivalent to a second-order damping system by adopting the idea of feedback linearization, thereby proving the stability and convergence of the eccentricity d, i.e. theoretically proving L1*Guidance law design methodThe drone will eventually necessarily fly along the predetermined flight path under the conditions.
As shown in FIG. 3, the present invention L1*Compared with the original L1 guidance law, the nonlinear improved guidance law design method has the advantages that the convergence rate is higher, the overshoot is smaller, the unmanned aerial vehicle quickly completes the tracking process, and the eccentricity d is reduced to 0 from 50m under the action of a lateral acceleration instruction; as shown in fig. 4, L1*Included angle eta in nonlinear improved guidance law design method*Convergence is faster, and in the case of a larger initial value, it converges to 0 degrees quickly. The root cause is the lateral acceleration command as *＝2V2sinη*/L1*For dynamic variation, the lateral acceleration a decreases with the eccentricity ds *The value is increased, speeding up the tracking process.
In summary, the present invention provides an L1*The nonlinear guidance law improved design method can solve the problem that the tracking rate is too slow in tracking control in the existing method.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.

Claims (3)

1. A guidance law design method for unmanned aerial vehicle path tracking control is characterized by comprising the following steps:
s1, projecting the unmanned aerial vehicle from the initial position A of the unmanned aerial vehicle to a preset track with the flying speed of the unmanned aerial vehicle being V, taking the projection point as O, and recording the distance between the flying track of the unmanned aerial vehicle and the preset track as an eccentric distance d;
s2, obtaining a circle with radius r by taking the projection point as the center of the circle, taking the intersection point of the circle and the preset track along the front of the unmanned aerial vehicle in the speed direction as B, and recording the length of AB as L1*Design L1 with point B as reference point*The law of guidance is that in the case of guidance,
Figure FDA0002782379910000011
s3, selecting the radius as R*Reference circle of1 *Calculating to obtain a lateral acceleration command a of the unmanned aerial vehicle by using centripetal acceleration and motion geometry relations*；
In the step S3: center of circle O1 *Is the intersection point of the perpendicular bisector of the line segment AB and the projection line AO; radius R*Is line segment A O1 *A length;
the step S3 specifically includes: recording the included angle between the speed of the unmanned aerial vehicle and the reference connecting line between the position of the unmanned aerial vehicle and the reference point as eta*Selecting a radius R*Reference circle of1 *The lateral acceleration command a of the unmanned planes *Is denoted by as *＝V2/R*Meanwhile, the kinematic geometrical relationship can be used to obtain L1*＝2R*sinη*Finally, a is obtaineds *＝2V2sinη*/L1*。
2. The guidance law design method for unmanned aerial vehicle path tracking control according to claim 1, further comprising:
and S4, under the condition that the tracked preset track is a straight line, carrying out linearization processing on the nonlinear guidance law, and enabling the path tracking problem to be equivalent to a second-order damping system problem of the eccentricity d.
3. The guidance law design method for unmanned aerial vehicle path tracking control according to claim 2, wherein the step S4 specifically includes:
under the condition that the tracked preset track is a straight line, when the unmanned aerial vehicle starts to track the preset track, the speed V deflects by a certain angle under the action of a lateral acceleration instruction, and an included angle eta is recorded*＝η1+η2，η1Is the angle between the speed V of the unmanned aerial vehicle and the horizontal line, eta2The first derivative and the second derivative of the eccentricity d are recorded as the included angle between the horizontal line and the reference line AB
Figure FDA0002782379910000012
And
Figure FDA0002782379910000013
obtaining:
Figure FDA0002782379910000014
at the same time, the kinematic geometry relationship yields:
Figure FDA0002782379910000021
two-order damping system equation for obtaining eccentricity d by combining the two equations
Figure FDA0002782379910000022
Wherein ζ is damping, wnFor the frequency of the second order damping system:
Figure FDA0002782379910000023
Figure FDA0002782379910000024
Figure FDA0002782379910000025
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CN109708639B (en) * 2018-12-07 2022-11-22 湖北航天飞行器研究所 Method for generating lateral guidance instruction of aircraft for tracking straight line and circular arc path in flat flight
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CN111857185B (en) * 2020-08-10 2022-11-04 南京航空航天大学 Unmanned aerial vehicle track forming guidance law design method based on dynamic reference points
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