CN111813140A - High-precision trajectory tracking control method for quad-rotor unmanned aerial vehicle - Google Patents

High-precision trajectory tracking control method for quad-rotor unmanned aerial vehicle Download PDF

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CN111813140A
CN111813140A CN202010763322.7A CN202010763322A CN111813140A CN 111813140 A CN111813140 A CN 111813140A CN 202010763322 A CN202010763322 A CN 202010763322A CN 111813140 A CN111813140 A CN 111813140A
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unmanned aerial
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CN111813140B (en
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王应洋
胡剑波
张鹏
郭基联
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Air Force Engineering University of PLA
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    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
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Abstract

The invention discloses a high-precision trajectory tracking control method for a quad-rotor unmanned aerial vehicle, which comprises the following steps: inputting the position reference instruction signal, the speed reference instruction signal, the position and the speed of the unmanned aerial vehicle into a translational subsystem control law, and calculating to obtain a virtual control law; performing coordinate transformation on the virtual control rate to obtain a resultant lift force generated by the rotor wing and an Euler angle reference instruction signal of the unmanned aerial vehicle; inputting the Euler angle reference command signal and the Euler angle of the unmanned aerial vehicle into an Euler angle control law, and calculating an angular velocity reference command signal of the unmanned aerial vehicle; inputting the angular speed reference command signal and the angular speed of the unmanned aerial vehicle into an angular speed control law, and calculating the torque of the rotor wing acting on the unmanned aerial vehicle; and inputting the resultant lift force and the torque into the unmanned aerial vehicle model to perform unmanned aerial vehicle trajectory tracking control. The invention realizes high-precision track tracking control by bringing the preset performance function into the design process of the control law; since no accurate model parameters and any estimator are relied on, the robustness and real-time of the control are ensured.

Description

High-precision trajectory tracking control method for quad-rotor unmanned aerial vehicle
Technical Field
The invention relates to the technical field of unmanned aerial vehicle control, in particular to a four-rotor unmanned aerial vehicle trajectory tracking control method with high precision.
Background
The quad-rotor unmanned aerial vehicle has important military and civil values, so that the quad-rotor unmanned aerial vehicle is always a research hotspot in the field of flight control. In recent years, quad-rotor drones are widely used in military patrol, package transportation, aerial photography and the like. However, the quad-rotor unmanned aerial vehicle is a typical multivariable, nonlinear, under-actuated and strong coupling system, so that it is very difficult to identify accurate pneumatic parameters and model parameters, and therefore, it is very difficult to perform high-precision trajectory tracking control.
Due to the underactuated dynamic characteristic of the quad-rotor unmanned aerial vehicle, the quad-rotor unmanned aerial vehicle is generally divided into two subsystems of translation and rotation, and control laws are designed respectively. In view of this, by fully considering model nonlinearity and flight state boundaries, control schemes such as sliding mode control, finite time convergence control, and adaptive control are applied to trajectory tracking control of the quadrotor aircraft. However, the above control schemes all rely on a quad-rotor drone affine model. In fact, the quad-rotor drone attitude angular velocity subsystem is a typical non-affine system due to strong coupling and non-linearity. Non-affine control methods have been under considerable investigation over the last decade. The non-affine function can be subjected to pseudo-affine transformation by assuming that the non-affine function is continuously derivable and based on a Taylor formula or a Lagrange median theorem, so that various control methods based on the control law can be conveniently designed. However, in practical applications, it is difficult to ensure that non-affine functions exist and are bounded in the control laws, so that ideal trajectory tracking control accuracy cannot be achieved.
Disclosure of Invention
The embodiment of the invention provides a trajectory tracking control method of a quad-rotor unmanned aerial vehicle with high precision, which can solve the problems in the prior art.
The invention provides a high-precision trajectory tracking control method for a quad-rotor unmanned aerial vehicle, which comprises the following steps of:
inputting the position reference instruction signal, the speed reference instruction signal and the unmanned aerial vehicle position and speed fed back by the unmanned aerial vehicle model into a translational subsystem control law, and calculating to obtain a virtual control law;
carrying out coordinate transformation on the virtual control rate to obtain a resultant lift force generated by the rotor wing and an Euler angle reference instruction signal of the unmanned aerial vehicle in a ground coordinate system;
inputting the Euler angle reference command signal and the Euler angle of the unmanned aerial vehicle in the ground coordinate system fed back by the unmanned aerial vehicle model into an Euler angle control law, and calculating to obtain an angular velocity reference command signal of the unmanned aerial vehicle in a body coordinate system;
inputting the angular speed reference command signal and the angular speed of the unmanned aerial vehicle fed back by the unmanned aerial vehicle model into an angular speed control law under a body coordinate system, and calculating to obtain a torque of a rotor wing acting on the unmanned aerial vehicle;
inputting the resultant lift force generated by the rotor and the torque of the rotor acting on the unmanned aerial vehicle into the unmanned aerial vehicle model, and performing trajectory tracking control on the unmanned aerial vehicle;
the control law of the translation subsystem introduces a performance function with small overshoot in the design to realize high-precision track tracking control, and the control law of the Euler angle introduces a performance function with a specific initial value in the design to ensure the stability of a closed-loop system.
Compared with the existing research result, the control method provided by the invention does not depend on accurate model parameters. In order to enhance the applicability of the control law, a non-affine model is established for the angular velocity subsystem, and a corresponding controllability assumption is adopted. In addition, the tracking control of small overshoot is realized by adopting an asymmetric performance function. The control method adopted by the invention does not need any estimator, greatly simplifies the control law structure and reduces the calculation complexity.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic model diagram of a quad-rotor drone;
FIG. 2 is a schematic diagram of small overshoot preset performance;
fig. 3 is a flowchart of a trajectory tracking control method for an unmanned aerial vehicle according to the present invention;
FIG. 4 is a graph illustrating the comparison of trajectory tracking control performance between the method of the present invention and a prior art method in the presence of a sudden trajectory change;
FIG. 5 is a schematic diagram of a comparison of the error surface of the translational subsystem and the position tracking error of the present invention and the prior art method in the presence of abrupt track changes;
FIG. 6 is a schematic diagram of comparing attitude angle and tracking error of the method of the present invention with a prior art method in the presence of a sudden change in trajectory;
FIG. 7 is a schematic comparison of control inputs for the method of the present invention and a prior art method in the presence of a sudden change in trajectory;
FIG. 8 is a schematic diagram of the attitude angular velocity and tracking error thereof of the method of the present invention in the presence of a sudden change in trajectory;
FIG. 9 is a graph illustrating a comparison of trajectory tracking control performance between the method of the present invention and a prior art method in the presence of a mass discontinuity;
FIG. 10 is a schematic illustration of a translation subsystem error surface versus position tracking error comparison for the method of the present invention and the prior art method in the presence of a mass discontinuity;
FIG. 11 is a schematic diagram comparing attitude angle and tracking error of the method of the present invention and a prior art method in the presence of a mass discontinuity;
FIG. 12 is a schematic comparison of control inputs for the method of the present invention and a prior art method in the presence of a mass discontinuity;
FIG. 13 is a schematic diagram of the attitude angular velocity and the tracking error thereof in the presence of a mass jump.
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 derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Before introducing the method of the present invention, the technology related to the unmanned aerial vehicle is explained.
Figure 1 is a quad-rotor drone structural schematic.
Figure BDA0002613687260000041
Is a ground coordinate system, meets the right-hand criterion, and has the z-axis vertically upward.
Figure BDA0002613687260000042
For unmanned aerial vehicle body coordinate system, the origin of coordinates sets up at the unmanned aerial vehicle barycenter. Xi ═ x, y, z]TAnd η ═ phi, theta, psi]TRespectively representing quadrotor unmanned aerial vehicle in ground coordinate system
Figure BDA0002613687260000043
The spatial position and the euler angle.
Quad-rotor unmanned aerial vehicle contains four engines altogether, wherein No. 1 and No. 3 rotor anticlockwise rotation, No. 2 and 4 rotor clockwise rotation. The force generated by each rotor can be expressed as fτ＝[f1,f2,f3,f4]TThe torque acting on the drone is tauw＝[τp,τq,τr]TThe combined lift force generated by all the rotor wings is U1According to the above definition, the following equation holds:
Figure BDA0002613687260000044
wherein: omegaiThe rotation speed of the ith engine; l is the arm length; a and b are pneumatic parameters. Equation (1) indicates that if f is knowniValue, i.e. to obtain ωiI is a value of 1,2,3,4, and fiCan be given a value ofp,τq,τrAnd U1The value of (2) is obtained.
The mathematical model of the quad-rotor unmanned aerial vehicle can be divided into a translation part and a rotation part, wherein a translation equation is established based on a ground coordinate system, and a rotation equation is established based on a body coordinate system. The specific mathematical model is as follows:
Figure BDA0002613687260000045
wherein:
Figure BDA0002613687260000046
for four rotor unmanned aerial vehicle in ground coordinate system
Figure BDA0002613687260000047
A lower velocity vector; w ═ p, q, r]TIs an in-vivo coordinate system of a quad-rotor unmanned plane
Figure BDA0002613687260000048
A lower angular velocity vector; m is the total mass of the quad-rotor unmanned aerial vehicle; g represents the gravitational acceleration; e.g. of the type3＝[0,0,1]TAs a ground coordinate system
Figure BDA0002613687260000049
A unit vector in the z-axis direction; dξ＝[dx,dy,dz]TAnd dw＝[dp,dq,dr]TRespectively, a bounded spatial position and an angular velocity disturbance signal. J ═ diag (J)x,Jy,Jz) As a coordinate system of the body
Figure BDA0002613687260000051
A lower inertia matrix;
Figure BDA0002613687260000052
is composed of a coordinate system of a machine body
Figure BDA0002613687260000053
Coordinate system to ground
Figure BDA0002613687260000054
The transformed rotation matrix is specifically formed as follows:
Figure BDA0002613687260000055
wherein s. sin (·), c. cos (·). W (η) is defined as:
Figure BDA0002613687260000056
wherein t. ═ tan (·).
The unmanned aerial vehicle model represented by the formula (2) has an under-actuated characteristic, and all states are difficult to be controlled independently through a design control law. Therefore, the control targets of the present invention are: calculating to obtain U through proper control law1And τwSo that xi and psi can stably track respective reference command signals xidAnd psidAnd the tracking error satisfies the preset performance. In order to achieve the above object, the present invention adopts the following reasonable assumptions for the unmanned aerial vehicle model represented by formula (2).
Assume that 1: reference command signal xid,ψdAnd its first and second time derivatives are continuous and bounded; the states xi, v, η and w of equation (2) are all measurable.
Assume 2: di(t) a Lipschitz continuous function that is bounded for time t; presence of unknown positive numbersm,
Figure BDA0002613687260000057
And
Figure BDA0002613687260000058
so that
Figure BDA0002613687260000059
And
Figure BDA00026136872600000510
(i ═ x, y, z, p, q, r) holds.
Preset performance with small overshoot
The preset performance means that the tracking error e (t) is converged into an adjustable residual set at a preset convergence rate and overshoot by a proper control law. The invention designs a preset performance method capable of realizing small overshoot aiming at a second-order system. The following error is first defined:
Figure BDA00026136872600000511
wherein c >0 is a parameter to be designed. To achieve preset performance control with small overshoot, assume that time s (t) satisfies the following inequality constraint:
Figure BDA0002613687260000061
Figure BDA0002613687260000062
and
Figure BDA0002613687260000063
the specific form of the asymmetric performance function is as follows:
Figure BDA0002613687260000064
wherein c is>l≥0,>0 and
Figure BDA0002613687260000065
for the parameter to be designed, exp (-) represents an exponential function. The above-mentioned preset performance can be explained by means of fig. 2.
Equation (7) shows
Figure BDA0002613687260000066
And
Figure BDA0002613687260000067
are bounded. (s (0) +, s (0) -) limits the overshoot of the error plane s (t) in transients. Interval(s)
Figure BDA0002613687260000068
Represents the allowable variation range of the error plane s (t) at steady state.
Theorem 1: if condition (6) is satisfied, then the tracking error e (t) is bounded, and for
Figure BDA0002613687260000069
e (t) satisfies an exponential convergence constraint.
To achieve the predetermined performance (6), a conversion error z (t) can be defined as:
Figure BDA00026136872600000610
wherein the normalized error
Figure BDA00026136872600000611
To simplify the presentation, the transformation function T is usedr(ζ(t))＝ζ(t)/(1-ζ2(T)) is defined as Tr(. cndot.) - (1, 1) → R. The first derivative of time is taken for z (t) to obtain:
Figure BDA00026136872600000612
wherein:
Figure BDA00026136872600000613
and:
Figure BDA00026136872600000614
theorem 2: for the
Figure BDA00026136872600000615
If there is an unknown positive number zMSo that | z (t) | is less than or equal to zMIf it is true, then
Figure BDA00026136872600000616
All have | ζ (t) & gt<1 is true.
Combining theorem 1 and theorem 2, if it can be controlled by designLaw making sure of
Figure BDA0002613687260000071
All have | z (t) | less than or equal to zMIf true, the tracking error e (t) is bounded and satisfies the exponential convergence constraints (9) and (10).
The asymmetric performance function (7) contains the system initial error. This not only avoids the potential singular problems, but also achieves a preset performance with little overshoot.
Fig. 3 is a flowchart of a trajectory tracking control method of a quad-rotor unmanned aerial vehicle with high precision according to the present invention. From the graph it can be seen that the control law used in the method does not depend on the exact model parameters. In addition, compared with the adaptive control law adopted for the quad-rotor unmanned aerial vehicle in the prior art, the control law adopted by the invention does not need any estimator, so that the computation complexity is lower.
The method of the invention comprises the following steps:
inputting the position reference instruction signal, the speed reference instruction signal and the actual position and speed of the unmanned aerial vehicle fed back by the quadrotor unmanned aerial vehicle model into a translational subsystem control law, and calculating to obtain a virtual control law;
carrying out coordinate transformation on the virtual control rate to obtain a resultant lift force generated by the rotor wing and an Euler angle reference instruction signal of the unmanned aerial vehicle in a ground coordinate system;
inputting an Euler angle reference command signal of the unmanned aerial vehicle in a ground coordinate system and an Euler angle of the unmanned aerial vehicle in the ground coordinate system fed back by a quadrotor unmanned aerial vehicle model into an Euler angle control law, and calculating to obtain an angular velocity reference command signal of the quadrotor unmanned aerial vehicle in a body coordinate system;
inputting an angular velocity reference command signal of the unmanned aerial vehicle in a body coordinate system and an angular velocity vector of the quad-rotor unmanned aerial vehicle fed back by a quad-rotor unmanned aerial vehicle model in the body coordinate system into an angular velocity control law, and calculating to obtain a torque of a rotor wing acting on the unmanned aerial vehicle;
the combined lift force generated by the rotor and the torque of the rotor acting on the unmanned aerial vehicle are input into a four-rotor unmanned aerial vehicle model, and trajectory tracking control is carried out on the four-rotor unmanned aerial vehicle.
In the above method, the translational subsystem control law is shown in formula (25), the coordinate transformation calculation is performed according to formula (26), the euler angle control law is shown in formula (31), the angular rate control law is shown in formula (33), and the quadrotor unmanned aerial vehicle model is shown in formula (2).
The specific design process of each control law is described in detail below.
Translational subsystem control law design
Defining position tracking error
Figure BDA0002613687260000081
To pair
Figure BDA0002613687260000082
The first derivative of time is obtained and combined with the model (2) to obtain the following error dynamics equation of the translation subsystem:
Figure BDA0002613687260000083
wherein
Figure BDA0002613687260000084
Rewritable is the equivalent of:
Figure BDA0002613687260000085
to analyze attitude angle tracking error
Figure BDA0002613687260000086
The effect on the speed subsystem control gain is achieved by the following algebraic transformation:
Figure BDA0002613687260000087
wherein
Figure BDA0002613687260000088
To simplify the presentation, define:
Figure BDA0002613687260000089
Figure BDA00026136872600000810
by analysis of matrices
Figure BDA00026136872600000811
Each step sequence main sub-type D1，D2And D3The following can be obtained:
Figure BDA0002613687260000091
Figure BDA0002613687260000092
Figure BDA0002613687260000093
thus in the collection
Figure BDA0002613687260000094
Within the range of (A) and (B),
Figure BDA0002613687260000095
is a positive definite symmetric matrix. In the present invention, the following tight set is specifically chosen
Figure BDA0002613687260000096
Ensure that
Figure BDA0002613687260000097
The positive nature of (1).
Figure BDA0002613687260000098
Assume that 3: attitude angle initial condition of quad-rotor unmanned aerial vehicle satisfies | phi (0) | ═φ0<π/2，|θ(0)|＝θ0<π/2，
Figure BDA0002613687260000099
And is
Figure BDA00026136872600000910
Wherein
Figure BDA00026136872600000911
Figure BDA0002613687260000101
θdAnd phidGenerated by a translation subsystem control law.
Hypothesis 3 guarantees that in the initial phase of control
Figure BDA0002613687260000102
The positive nature of (1). In practical applications, the requirements of assumption 3 can be met by placing the quad-rotor drone in a direction that points approximately to the tracking trajectory; in the process of designing the control law of the rotating subsystem, the attitude angle tracking error is caused by designing a performance function
Figure BDA0002613687260000103
And
Figure BDA0002613687260000104
the time instants being in the set omegasIn (1). The above arrangement can make
Figure BDA0002613687260000105
The time is positive, and the controllability of the translational subsystem (12) is ensured.
Defining a virtual control law u for a translational subsystem (12)ξ＝[ux,uy,uz]TThe following were used:
Figure BDA0002613687260000106
defining a virtual control law Deltauξ＝uξ-m0ge3Wherein m is0Is the approximate mass of a quad-rotor drone in practice. Will be (15), (16) and delta uξThe substitution in (2) yields:
Figure BDA0002613687260000107
wherein:
Figure BDA0002613687260000108
to handle a second order dynamic system (21), a time-varying error surface s is definedξ＝[sx,sy,sz]TThe following were used:
Figure BDA0002613687260000109
wherein c isξ＝diag(cx,cy,cz) Is a positive definite symmetric matrix and ci>liAnd i is x, y, z. Designing a performance function
Figure BDA00026136872600001010
And
Figure BDA00026136872600001011
the following were used:
Figure BDA00026136872600001012
wherein c isi>li≥0,i>0,
Figure BDA00026136872600001013
And is
Figure BDA00026136872600001014
i＝x,y,z。
Defining a normalized error
Figure BDA0002613687260000111
i-x, y, z and the virtual sub-control law Δ uξThe translation subsystem control law is as follows:
Figure BDA0002613687260000112
whereinξ＝diag(x,y,z) Is a positive definite diagonal matrix, rξ＝diag(rx,Υy,Υz)，
Figure BDA0002613687260000113
i＝x,y,z，zξIs a time varying error surface sξAssociated conversion errors. An ideal euler angle command can be obtained according to equation (20), that is, the coordinate transformation formula is:
Figure BDA0002613687260000114
with reference command psi to be designeddTogether, thetadAnd phidWill be the command signal for the rotational subsystem.
In the present invention, the virtual control law u is not directly designedξBut first by designing the virtual control law auξThen transformed to obtain uξ. Otherwise, when ζx(t)＝ζy(t)＝ζzWhen (t) ═ 0, | | uξThe singular problem of equation (26) arises from | 0.
Control law design for rotary subsystem
In order to make the control law more applicable, the rotation subsystem in the system (2) is expressed as the following non-affine model:
Figure BDA0002613687260000115
wherein f isk(w,τk) Is a continuous unknown non-affine function, d'kIs a bounded external disturbance.
Assume 4: presence of continuous functiong k(w,τk)，
Figure BDA0002613687260000116
h k(w) and
Figure BDA0002613687260000117
satisfies the following conditions:
Figure BDA0002613687260000118
whereinkAnd
Figure BDA0002613687260000119
k is p, q, r is an unknown constant. For the
Figure BDA00026136872600001110
Presence of unknown positive number gk,mSatisfy the requirement of
Figure BDA00026136872600001111
Because four rotor unmanned aerial vehicle inertia matrix J is unknown positive definite matrix. Combined differential equation
Figure BDA00026136872600001112
In the form of (a), it is easy to know that hypothesis 4 is reasonable. Meanwhile, assume 4 guarantees controllability of the angular velocity subsystem. In the interval
Figure BDA0002613687260000121
Upper, fk(w,τk) With taukThe law of change of (c) remains unknown. Non-affine function in interval τk≥kUpper bound and interval of
Figure BDA0002613687260000122
Is cancelled. The condition of assumption 4 is more relaxed than the assumption adopted in the prior art that the non-affine function must be partializable.
Defining angular velocity tracking error
Figure BDA0002613687260000123
To pair
Figure BDA0002613687260000124
The first derivative of time is taken in conjunction with equation (27) to obtain:
Figure BDA0002613687260000125
hereinafter, a preset performance control law capable of realizing small overshoot is designed for the rotating subsystem based on a reverse control technology. The design process is divided into the following two steps.
Step 1: according to assumption 3, a performance function is selected:
Figure BDA0002613687260000126
wherein
Figure BDA0002613687260000127
The Euler angle control law w is designed as followsd：
Figure BDA0002613687260000128
Wherein
Figure BDA0002613687260000129
And isη＝diag(φ,θ,ψ) Is a positive definite diagonal matrix, zηThe euler angle conversion error.
Step 2: similar to the above steps, a performance function is selected:
Figure BDA00026136872600001210
wherein by selecting suitable parameters it can be ensured
Figure BDA00026136872600001211
This is true. Design ofAs the lower corner rate control law:
Figure BDA00026136872600001212
wherein
Figure BDA00026136872600001213
w＝diag(p,q,r) Is a positive diagonal matrix.
The invention adopts two sets of simulation researches to verify the effectiveness of the control method. The model parameters of the quad-rotor unmanned aerial vehicle are as follows: l is 0.5m, m0＝2kg，g＝9.81m/s2，Jx＝Jy＝0.004kgm2，Jz＝0.0084kgm2. To verify the robustness of the control law, C ═ C is defined0[1+0.3sin(0.1t)]Wherein C and C0Representing the actual and ideal values of the moment of inertia, respectively. The external interference signal is taken as:
Figure BDA0002613687260000131
the control parameters of the preset performance control law are selected as follows: c. Cξ＝diag(3,3,3)，ξ＝diag(0.2,0.2,0.2)，ηBiag (2,2,2) andwbiag (4,4, 4). All the preset performance control laws adopt the same error conversion mode Tr(ζ(t))＝ζ(t)/(1-ζ2(t)) and different performance function boundaries:
Figure BDA0002613687260000132
in both simulations, the sliding mode control law SMC proposed in the document JabbariAss H, Yoon J.robust image-based control of the quadrat irregular temporal [ J ]. Nonlinear Dyn.2016,85(3): 2035-.
Quad-rotor unmanned aerial vehicle tracking control with track mutation
Assume that quad-rotor drone is from an initial statePoint xi (0) ═ 2,4,0]T,
Figure BDA0002613687260000133
Along the xi trace at a speed of 0.55m/sdAnd (5) flying. As shown in fig. 4(a), to ensure smooth target trajectory, the corners of the rectangle are each replaced by a quarter of a circular arc with a radius of 0.5 m.
Fig. 4-8 are simulation results. As can be seen from fig. 4 and 5, the proposed location tracking of the preset performance control law (PPC) has a smaller overshoot and shorter response time than SMC. FIGS. 6 and 7 show that both the pose angle and the control input for PPC and SMC are bounded, and that the pose angle tracking error for PPC is bounded
Figure BDA0002613687260000134
Satisfies a predetermined property, and thus
Figure BDA0002613687260000135
The time is kept positive, i.e. the controllability of the speed subsystem is guaranteed. FIG. 8 shows the angular velocity tracking error of PPC
Figure BDA0002613687260000136
The preset envelope is satisfied. In summary, compared with SMC, the PPC provided by the present invention does not require accurate model parameters and can achieve higher control accuracy.
Quad-rotor unmanned aerial vehicle tracking control with mass mutation
To verify the ability of the control law to handle the quad-rotor drone trajectory tracking problem with model uncertainty, assume quad-rotor drone is in initial state ξd(0)＝[0,0,0]T,
Figure BDA0002613687260000141
Along a reference track xid＝[xd,yd,zd]TFlying, wherein:
Figure BDA0002613687260000142
quad-rotor drones may have a parcel release or pick up process while performing parcel transport tasks. Therefore, suppose that there are the following mass jumps in the flight of the drone:
Figure BDA0002613687260000143
fig. 9-13 are simulation results. As can be seen from fig. 9 and 10, compared to SMC, PPC can achieve better transient and steady state performance, and the error plane of the translational sub-system satisfies the preset performance envelope. Although the quality of the quad-rotor unmanned aerial vehicle changes suddenly, the PPC can still realize high-precision tracking control. Fig. 11 and 13 show: in the PPC example, error
Figure BDA0002613687260000144
And
Figure BDA0002613687260000145
all satisfy the preset performance. Fig. 12 shows that there is no high-frequency chatter in the control input curves in both the SMC and PPC examples.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (6)

1. A trajectory tracking control method for a quad-rotor unmanned aerial vehicle with high precision is characterized by comprising the following steps:
inputting the position reference instruction signal, the speed reference instruction signal and the unmanned aerial vehicle position and speed fed back by the unmanned aerial vehicle model into a translational subsystem control law, and calculating to obtain a virtual control law;
carrying out coordinate transformation on the virtual control rate to obtain a resultant lift force generated by the rotor wing and an Euler angle reference instruction signal of the unmanned aerial vehicle in a ground coordinate system;
inputting the Euler angle reference command signal and the Euler angle of the unmanned aerial vehicle in the ground coordinate system fed back by the unmanned aerial vehicle model into an Euler angle control law, and calculating to obtain an angular velocity reference command signal of the unmanned aerial vehicle in a body coordinate system;
inputting the angular speed reference command signal and the angular speed of the unmanned aerial vehicle fed back by the unmanned aerial vehicle model into an angular speed control law under a body coordinate system, and calculating to obtain a torque of a rotor wing acting on the unmanned aerial vehicle;
inputting the resultant lift force generated by the rotor and the torque of the rotor acting on the unmanned aerial vehicle into the unmanned aerial vehicle model, and performing trajectory tracking control on the unmanned aerial vehicle;
the control law of the translation subsystem introduces a performance function with small overshoot in the design to realize high-precision track tracking control, and the control law of the Euler angle introduces a performance function with a specific initial value in the design to ensure the stability of a closed-loop system.
2. A method of trajectory tracking control for a quad-rotor drone with high precision according to claim 1, wherein said drone model is represented as:
Figure FDA0002613687250000011
wherein
Figure FDA0002613687250000012
The velocity vector of the unmanned plane in the ground coordinate system is xi ═ x, y, z]TAnd η ═ phi, theta, psi]TRespectively representing the space position and Euler angle of the unmanned aerial vehicle in a ground coordinate system, wherein m is the total mass of the unmanned aerial vehicle, U1For the combined lift generated by all the rotors,
Figure FDA0002613687250000013
is a rotation matrix transformed from a body coordinate system to a ground coordinate system, e3＝[0,0,1]TIs a unit vector in the z-axis direction in the ground coordinate system, g represents the gravity acceleration, dξ＝[dx,dy,dz]TAnd dw＝[dp,dq,dr]TA bounded spatial position and angular velocity interference signal, w ═ p, q, r]TThe angular velocity vector of the unmanned plane in the body coordinate system is J ═ diag (J)x,Jy,Jz) Is an inertia matrix in a body coordinate system, tauw＝[τp,τq,τr]TFor the torque of the rotor acting on the drone, W (η) is defined as:
Figure FDA0002613687250000021
wherein s. sin (·), c. cos (·), and t. tan (·).
3. The trajectory tracking control method for the quad-rotor unmanned aerial vehicle with high precision according to claim 2, wherein the method for calculating the virtual control law comprises the following steps:
defining position tracking error
Figure FDA0002613687250000022
In which ξdFor position reference command signals, pair
Figure FDA0002613687250000023
And (3) solving a first derivative of time, and combining an unmanned aerial vehicle model to obtain the following error kinetic equation of the translation subsystem:
Figure FDA0002613687250000024
wherein
Figure FDA0002613687250000025
Rewritten as the equivalent of:
Figure FDA0002613687250000026
in order to analyze the influence of the attitude angle tracking error on the control gain of the speed subsystem, the following algebraic transformation is adopted:
Figure FDA0002613687250000027
wherein
Figure FDA0002613687250000028
For simplicity of presentation, define:
Figure FDA0002613687250000029
Figure FDA0002613687250000031
defining a virtual control law u aiming at an error dynamics equation of a translation subsystemξ＝[ux,uy,uz]TThe following were used:
Figure FDA0002613687250000032
defining a virtual sub-control law Deltauξ＝uξ-m0ge3Wherein m is0For approximate mass of a quad-rotor drone in practice, Rz(ψ)、
Figure FDA0002613687250000033
And Δ uξTaken into the unmanned aerial vehicle model to yield:
Figure FDA0002613687250000034
wherein:
Figure FDA0002613687250000035
to process the above equation, a time-varying error surface s is definedξ＝[sx,sy,sz]TThe following were used:
Figure FDA0002613687250000036
wherein c isξ＝diag(cx,cy,cz) Is a positive definite symmetric matrix; designing a performance function
Figure FDA0002613687250000037
And
Figure FDA0002613687250000038
the following were used:
Figure FDA0002613687250000039
wherein c isi>li≥0,
Figure FDA00026136872500000310
And is
Figure FDA00026136872500000311
Defining a normalized error
Figure FDA00026136872500000312
z and the virtual sub-control law DeltauξThe translation subsystem control law is as follows:
Figure FDA00026136872500000313
whereinξ＝diag(x,y,z) Is positive definite diagonal array, upsilonξ＝diag(Υx,Υy,Υz)，
Figure FDA0002613687250000041
zξIs a time varying error surface sξThe associated errors in the conversion are such that,
Figure FDA0002613687250000042
4. a method for trajectory tracking control of a quad-rotor drone with high precision according to claim 3, characterized in that said virtual control rate is transformed in coordinates according to the following equation:
Figure FDA0002613687250000043
wherein phi isd、θdAre all euler angle reference command signals.
5. A trajectory tracking control method for a quad-rotor unmanned aerial vehicle with high precision according to claim 2, wherein the method for calculating the angular velocity reference command signal of the unmanned aerial vehicle in the body coordinate system comprises the following steps:
the rotation subsystem in the unmanned aerial vehicle model is expressed as the following non-affine model:
Figure FDA0002613687250000044
wherein f isk(w,τk) Is a continuous unknown non-affine function, d'kExternal disturbances that are bounded;
defining angular velocity tracking error
Figure FDA0002613687250000045
To pair
Figure FDA0002613687250000046
The first derivative of time is obtained by combining the following formula:
Figure FDA0002613687250000047
based on a reverse control technique, a performance function is selected:
Figure FDA0002613687250000048
wherein
Figure FDA0002613687250000049
Euler angle control law wdComprises the following steps:
Figure FDA00026136872500000410
wherein p isd、qd、rdAn angular velocity reference command signal of the unmanned aerial vehicle under a body coordinate system,
Figure FDA00026136872500000411
and isη＝diag(φ,θ,ψ) Is a positive definite diagonal matrix, zηThe euler angle conversion error.
6. A method for trajectory tracking control of a quad-rotor drone with high precision according to claim 5, characterized in that the method of calculating the torque exerted by the rotor on the drone is:
selecting a performance function:
Figure FDA0002613687250000051
by passingSelecting appropriate parameters to ensure
Figure FDA0002613687250000052
The angular rate control law is:
Figure FDA0002613687250000053
wherein, taup、τq、τrFor the torque of the rotor acting on the drone,
Figure FDA0002613687250000054
w＝diag(p,q,r) Is a positive diagonal matrix.
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