CN113253747A - Nonlinear trajectory tracking control method for four-rotor suspended transportation system based on segmented energy - Google Patents

Nonlinear trajectory tracking control method for four-rotor suspended transportation system based on segmented energy Download PDF

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CN113253747A
CN113253747A CN202110634702.5A CN202110634702A CN113253747A CN 113253747 A CN113253747 A CN 113253747A CN 202110634702 A CN202110634702 A CN 202110634702A CN 113253747 A CN113253747 A CN 113253747A
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aerial vehicle
unmanned aerial
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hanging
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平原
王明明
辛冀
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Tianjin University
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Tianjin University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • 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
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Abstract

The invention discloses a nonlinear trajectory tracking control method for a four-rotor-wing hanging transportation system based on segmented energy, and relates to the technical field of aircraft attitude control. A four-rotor hanging transportation system dynamic model in a two-dimensional plane is established based on a Lagrange method; selecting an S-curve expected track as an unmanned aerial vehicle hanging flight expected track based on the model; based on the viewpoint of segmentation capability, analyzing the energy of the load relative to the unmanned aerial vehicle, the common motion of the unmanned aerial vehicle body and the load and the generalized potential energy representing the position error, and designing and completing a nonlinear trajectory tracking controller; analyzing stability and convergence; and (5) simulation verification. In order to drive the unmanned aerial vehicle to stably fly to a desired position, an S-shaped curve with smooth speed is selected as an unmanned aerial vehicle target track. And then, an energy storage function of the system is constructed by adopting a segmented energy method, a nonlinear trajectory tracking controller is designed, and the tracking error of the quad-rotor unmanned aerial vehicle in the flight process is ensured to be always within a controllable range.

Description

Nonlinear trajectory tracking control method for four-rotor suspended transportation system based on segmented energy
Technical Field
The invention relates to the technical field of aircraft attitude control, in particular to a nonlinear trajectory tracking control method of a four-rotor hanging transportation system based on segmented energy.
Background
The four-rotor unmanned aerial vehicle serves as an ideal operation platform, and cargo transportation is carried out by hanging the cargo through flexible cables. The system has flexible maneuverability, and can quickly and efficiently finish cargo transportation tasks in places where other transportation tools are difficult to reach; the method is not limited by traffic and transportation limitations and geographical conditions, has low requirements on infrastructure and is convenient to operate; and is not limited by the shape of the hanging object. Thus, the application of the method is more and more extensive in the fields of military and civil use.
However, the hanging quad-rotor unmanned aerial vehicle is a multivariable, nonlinear, strongly-coupled, time-varying and underactuated high-order system and is a complex controlled object. Four rotor unmanned aerial vehicle flight stability and transportation security can receive to come from hanging the influence of object swing, especially when reacing the target point, hangs the thing and can produce comparatively violent swing, very easily takes place the incident, also can reduce conveying efficiency simultaneously. Therefore, research into the control problem of quad-rotor unmanned aerial vehicle overhead transport systems is necessary and important.
At present, the control algorithm of a suspended load unmanned aerial vehicle is relatively researched a few, and the method can be mainly divided into two research directions: one is to make the load reach the target position as quickly as possible with as little swing as possible by a trajectory generation and tracking method. Another technical route is to use various control strategies to try to eliminate the swinging of the load sling.
The problems of the method are as follows: the former is mostly open loop control and is very sensitive to external interference. The latter control method tends to generate a large attitude at the initial moment, increasing energy consumption, and the role of trajectory planning in the method is often neglected. Most of the methods for solving the problem of trajectory tracking have the defect that core indexes such as the maximum speed, the acceleration, the load swing angle, the transportation efficiency and the like of the unmanned aerial vehicle flight cannot be theoretically guaranteed.
Therefore, a trajectory tracking control method of a four-rotor hanging transportation system, which can enable the four rotors to quickly reach a desired position, can inhibit and eliminate the violent load swing and has application value, is required.
Disclosure of Invention
In order to overcome the problems in the related art, the disclosed embodiment of the invention provides a nonlinear trajectory tracking control method for a four-rotor suspended transportation system based on segmented energy. The technical scheme is as follows:
the nonlinear trajectory tracking control method of the four-rotor hanging transportation system based on the segmented energy comprises the following steps:
the method comprises the following steps: a four-rotor hanging transportation system dynamic model in a two-dimensional plane is established based on a Lagrange method;
step two: selecting a smooth and continuous S-curve expected trajectory as an unmanned aerial vehicle hanging flight expected trajectory based on the model;
step three: analyzing the energy of the load relative to the unmanned aerial vehicle, the common motion of the unmanned aerial vehicle body and the load and the generalized potential energy representing the position error based on the viewpoint of segmentation capability to obtain a system energy storage function, and designing and finishing the nonlinear trajectory tracking controller;
step four: stability and convergence analysis are carried out, the system stability is proved based on the Lyapunov technology and the Lassel invariance principle, and the controller can ensure that four system state quantities of the position error, the moving speed, the load swing angle and the angular speed of the quad-rotor unmanned aerial vehicle gradually converge to zero;
step five: and (5) simulation verification.
In one embodiment, in the first step, a four-rotor suspension system dynamics model in an X-Z plane is built, M and M respectively represent the mass of an unmanned aerial vehicle body and a load, L is the length of a lifting rope, g is the gravity acceleration, theta is a four-rotor attitude angle, gamma is an included angle between the lifting rope and a Z axis in an XOZ plane, and the dynamic modeling of the four-rotor suspension system is as follows:
Figure BDA0003105047580000031
wherein
Figure BDA0003105047580000032
As observable state variables, (F, τ) are input quantities, JyTo moment of inertia, MAnd m and L are known constants of the controlled object.
In one embodiment, in step two, to realize stable and safe transportation of the four-rotor unmanned aerial vehicle suspended load, the following smooth and continuous S-curve expected trajectory of speed is set:
Figure BDA0003105047580000033
wherein r isdIs the target distance in the horizontal direction, sv、saThe maximum speed and the acceleration allowed by the four-rotor unmanned aerial vehicle hanging, transporting and flying are respectively, and sigma belongs to R+Is an adjustable initial acceleration.
In one embodiment, to ensure that the drone starts smoothly and can reach the target location quickly, the selected desired trajectory needs to have the following properties:
properties 1: the expected horizontal displacement of the selected track converges asymptotically to rdFurthermore, the velocity and acceleration asymptotically converge to zero, i.e.:
Figure BDA0003105047580000034
properties 2: the speed, the acceleration and the jerk of the unmanned aerial vehicle are bounded, and the following constraint conditions are met:
Figure BDA0003105047580000035
wherein the content of the first and second substances,
Figure BDA0003105047580000036
jerk for a desired trajectory;
property 3 the horizontal initial displacement and velocity of the drone are zero, i.e.:
Figure BDA0003105047580000037
in one embodiment, in step three, first, the drone position error is defined as follows:
Figure BDA0003105047580000041
then there is
Figure BDA0003105047580000042
In order to ensure the stability of the system under the Lyapunov meaning, the acceleration of the unmanned aerial vehicle body is designed as follows:
Figure BDA0003105047580000043
then, the lift force F of the unmanned aerial vehicle is decomposed into F perpendicular to the direction of the lifting ropexAnd f in the direction of the lifting ropezSpecifically, the following are shown:
Figure BDA0003105047580000044
after substitution of formula (1) to give
Figure BDA0003105047580000045
The above formula is solved simultaneously with (8):
Figure BDA0003105047580000046
and then the controller output is obtained through (9) inverse solution:
Figure BDA0003105047580000047
in one embodiment, the initial state and system parameters are as follows:
the mass M of the quad-rotor unmanned aerial vehicle is 0.5kg, the load mass M is set to be 0.1kg, the rope length is 1M, the arm length of the rotor is 0.25M, and the inertia moment J isyIs 5 e-3;
the parameters of the nonlinear controller are defined as:
kp＝15,ke＝0.1,kdx＝0.15,kdz＝1。
in one embodiment, in step four, the controller based on the segmented energy view can ensure that the four system state quantities of the position error, the moving speed, the load swing angle and the angular speed of the quad-rotor unmanned aerial vehicle gradually converge to zero, that is:
Figure BDA0003105047580000051
in one embodiment, in step four, the signals in the closed loop system are all bounded, i.e.:
Figure BDA0003105047580000052
in one embodiment, the simulation verification specifically comprises the following steps:
firstly, testing the track tracking control performance of the method;
secondly, comparing the method with a passive PD control method, verifying the good control performance of the control algorithm;
then, the control performance of the method for the uncertainty of system parameters and for different target positions is further tested.
In one embodiment, the simulation verification includes trajectory tracking performance verification, contrast verification and robust performance verification.
The technical scheme provided by the embodiment of the invention has the following beneficial effects:
the invention provides a nonlinear trajectory tracking control method of a four-rotor suspended transportation system based on segmented energy, which selects an S-shaped curve with smooth speed as an unmanned aerial vehicle target trajectory for driving an unmanned aerial vehicle to stably fly to a desired position. And then, an energy storage function of the system is constructed by adopting a segmented energy method, and a nonlinear trajectory tracking controller is designed. Meanwhile, an error item is introduced into the controller, so that the tracking error of the quad-rotor unmanned aerial vehicle in the flight process is always within a controllable range, the effect of quickly reaching an expected position and inhibiting and eliminating the residual swing of a hanging object is achieved.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and together with the description, serve to explain the principles of the disclosure.
Figure 1 is a diagram of a four rotor pylon system in the X-Z plane provided by the present invention.
FIG. 2 is a diagram of simulation results of the nonlinear trajectory tracking control method of the present invention;
wherein a is an actual speed/expected speed diagram, b is an actual acceleration/expected acceleration diagram, c is a speed tracking error diagram, and d is an acceleration tracking error diagram.
FIG. 3 is a diagram of simulation results of the nonlinear trajectory tracking control method of the present invention;
wherein a is an actual track/expected track diagram, b is an actual track/expected track diagram, c is a hanging load swing angle diagram, and d is a driving force diagram.
FIG. 4 is a diagram of simulation results of a PD-based control method provided by the present invention;
wherein a is an actual track/expected track diagram, b is an actual track/expected track diagram, c is a hanging load swing angle diagram, and d is a driving force diagram.
FIG. 5 is a diagram of simulation results of the nonlinear trajectory tracking control method according to the present invention for different target positions;
wherein a is an actual track/expected track diagram, b is an actual track/expected track diagram, c is a hanging load swing angle diagram, and d is a driving force diagram.
FIG. 6 is a diagram of simulation results of the nonlinear trajectory tracking control method according to the present invention for different rope length variations;
wherein a is an actual track/expected track diagram, b is an actual track/expected track diagram, c is a hanging load swing angle diagram, and d is a driving force diagram.
FIG. 7 is a flow chart of a nonlinear trajectory tracking control method for a four-rotor hanging transportation system based on segmented energy provided by the invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein, but rather should be construed as broadly as the present invention is capable of modification in various respects, all without departing from the spirit and scope of the present invention.
It will be understood that when an element is referred to as being "secured to" another element, it can be directly on the other element or intervening elements may also be present. When an element is referred to as being "connected" to another element, it can be directly connected to the other element or intervening elements may also be present. As used herein, the terms "vertical," "horizontal," "left," "right," and the like are for purposes of illustration only and are not intended to represent the only embodiments.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
The invention aims to provide a nonlinear trajectory tracking control method of a four-rotor suspended transportation system based on segmented energy, and solves the problem that core indexes such as the maximum speed, the acceleration, the load swing angle, the transportation efficiency and the like of unmanned aerial vehicle flight can not be theoretically guaranteed in trajectory tracking control.
The nonlinear trajectory tracking control method of the four-rotor hanging transportation system based on the segmented energy comprises the following steps: firstly, a four-rotor hanging transportation system dynamic model in a two-dimensional plane is established based on a Lagrange method. And then, selecting a smooth and continuous S-curve expected track of the speed based on the model, analyzing the energy of the load relative to the unmanned aerial vehicle, the common motion of the unmanned aerial vehicle body and the load and the generalized potential energy representing the position error based on the view point of the segmentation capability, and finally obtaining a system energy storage function, thereby designing and completing the nonlinear track tracking controller. Subsequently, the stability of the system is proved based on the Lyapunov technology and the Lassel invariance principle, and the controller can ensure that the four system state quantities of the position error, the moving speed, the load swing angle and the angular speed of the quad-rotor unmanned aerial vehicle gradually converge to zero. Finally, simulation experiments verify that the method can achieve good track tracking control effect.
The method comprises the following specific steps:
the method comprises the following steps: lagrange method based dynamic model for four-rotor suspended transportation system in two-dimensional plane
As shown in FIG. 1, a four-rotor hanging system dynamic model in an X-Z plane is built. The coordinates follow the right hand rule, and the origin of the machine body coordinate system is the center of mass of the machine body.
M and M respectively represent the mass of the unmanned aerial vehicle body and load, L is the length of a lifting rope, g is the gravity acceleration, theta is the attitude angle of a four-rotor wing, gamma is the included angle between the lifting rope and the Z axis in the XOZ plane in the negative direction, and the condition that-pi/2 is more than gamma and less than pi/2 is met. The four-rotor hanging system dynamics modeling is as follows:
Figure BDA0003105047580000081
wherein
Figure BDA0003105047580000082
As observable state variables, (F, τ) are input quantities, JyM, L are known constants of the controlled object itself.
Step two: unmanned aerial vehicle hanging flight expected trajectory selection
For realizing stable safe transportation of four rotor unmanned aerial vehicle suspended load, set for following smooth continuous S curve expectation orbit of speed:
Figure BDA0003105047580000083
wherein r isdIs the target distance in the horizontal direction, sv、saThe maximum speed and the acceleration allowed by the four-rotor unmanned aerial vehicle hanging, transporting and flying are respectively, and sigma belongs to R+Is an adjustable initial acceleration. Meanwhile, in order to ensure that the unmanned aerial vehicle starts smoothly and can reach the target position quickly, the selected expected track has the following properties:
the trajectory selected by property 1 is expected to converge asymptotically to rdFurthermore, the velocity and acceleration asymptotically converge to zero, i.e.:
Figure BDA0003105047580000091
property 2 the drone speed, acceleration and jerk are bounded and satisfy the following constraints:
Figure BDA0003105047580000092
wherein the content of the first and second substances,
Figure BDA0003105047580000093
jerk of the desired trajectory.
Property 3 the horizontal initial displacement and velocity of the drone are zero, i.e.:
Figure BDA0003105047580000094
step three: nonlinear trajectory tracking controller design based on segmented energy
First, the drone position error is defined as follows:
Figure BDA0003105047580000095
then there is
Figure BDA0003105047580000096
In order to ensure the stability of the system in the Lyapunov meaning, the acceleration of the unmanned aerial vehicle body is designed to be
Figure BDA0003105047580000097
Then, the lift force F of the unmanned aerial vehicle is decomposed into F perpendicular to the direction of the lifting ropexAnd f in the direction of the lifting ropezSpecifically, the following are shown:
Figure BDA0003105047580000098
after substitution of formula (1) to give
Figure BDA0003105047580000101
The above formula is solved simultaneously with (8):
Figure BDA0003105047580000102
and then the controller output is obtained through (9) inverse solution:
Figure BDA0003105047580000103
in fact, from the energy storage function V3Can see that kpAnd k iseThe two control gains respectively influence the proportion of information of two aspects of the positioning error of the unmanned aerial vehicle body and the load swing angle in an energy storage function, so that the side weight degree of the controller for the two control tasks of the positioning of the body and the load swing reduction is influenced. When k ispA constant, keThe larger the controller, the more heavily the controller is to resist load swing, and vice versa the more heavily the positioning of the unmanned aerial vehicle fuselage.
The initial state and system parameters are as follows:
the mass M of the quad-rotor unmanned aerial vehicle is 0.5kg, the load mass M is set to be 0.1kg, the rope length is 1M, the arm length of the rotor is 0.25M, and the inertia moment J isyIs 5 e-3.
Considering the influence of the control gain on the weight of two control targets, namely the aircraft positioning and the load swing reduction, and the limitation of the system on the input amplitude, after repeated debugging, the parameters of the nonlinear controller are determined as follows:
kp＝15,ke＝0.1,kdx＝0.15,kdz＝1
step four: stability and Convergence analysis
Theorem 1 controller that obtains based on the view of segmentation energy can guarantee that four rotor unmanned aerial vehicle's position error, travel speed, load pivot angle and four system state variables of angular velocity all converge to zero gradually, promptly:
Figure BDA0003105047580000111
proof of selection V3As a Lyapunov candidate function, the following can be obtained after arrangement:
Figure BDA0003105047580000112
in this way, it can be seen that,
Figure BDA0003105047580000113
is semi-negatively set, V3The closed loop system is stable in Lyapunov meaning because of monotonous decreasing.
Theorem 2 the signals in closed-loop systems are all bounded, i.e.:
Figure BDA0003105047580000114
the proof is defined as the invariant set M:
Figure BDA0003105047580000115
according to the principle of Lassel invariance, the invariant set M only contains one balance point:
Figure BDA0003105047580000116
thus, theorem 2 proves.
Step five: simulation verification
The effectiveness of the method is verified through three groups of simulation. Specifically, the method comprises the following steps: firstly, testing the track tracking control performance of the method; then, comparing the method with a passive PD control method, verifying the good control performance of the control algorithm; next, the method was further tested for system parameter uncertainty and control performance for different target locations.
a. Trajectory tracking performance verification
In order to verify the tracking performance of the method provided by the invention on the planned track speed and the planned acceleration, an expected target position p is selecteddThe initial load swing angle is set to 0 ° (2.5 ). And because the target distances in the X direction and the Z direction in the plane are consistent, one set of data is used for analysis. The maximum speed is set to be 0.6m/s and the maximum acceleration is set to be 0.2m/s ^2 in the trajectory planning, and the method has good tracking effect (the maximum tracking of the speed and the acceleration)Error 0.05). The speed and the acceleration of the four-rotor transport system in the flight process are guaranteed to be within a reasonable range, and finally, the stable state can be achieved.
b. Contrast verification
The invention selects a PD control method based on passivity as a comparison method. The simulation results are shown in fig. 3 and fig. 4, the related quantification results are shown in table 1, and the comparison results mainly comprise the following five performance indexes:
(1) a quad-rotor drone final position;
(2) transit time (time for the drone to reach the target point);
(3) hanging the maximum swing angle of the load in the whole transportation process;
(4) after the unmanned aerial vehicle reaches a target point, hanging a residual swing angle of a load;
(5) the energy consumption is driven during the whole transportation process.
TABLE 1 quantification of the results of the comparative tests
Figure BDA0003105047580000121
Based on the above quantitative test results and data analysis, fig. 3 and 4 show that the final transportation time of the method is 7.0s, the transportation time based on the passive control method is 11.2s, and a positioning error of 2cm occurs. According to simulation results, the nonlinear trajectory tracking control method effectively avoids large attitude change during flying before starting, so that stable starting is realized, and larger initial swing of a suspended load is avoided. The method maintains the hanging load swing angle within a smaller range (maximum load swing angle up to 2.8) than the method based on passive control (maximum load swing angle up to 12.0). Meanwhile, the residual swing angle (the residual swing angle reaches 0.3 degrees) of the method is smaller than that of a passive control method (the residual swing angle reaches 1.2 degrees). Therefore, the method can better restrain and eliminate load swing. In addition, in the two control methods, the maximum driving force of the method is smaller, and energy consumption can be saved. These simulation results clearly demonstrate the excellent control performance of the proposed control method.
C. Robust performance verification
(1) Control performance testing for different target locations
In order to further verify the control performance of the method for different target positions under the condition of not changing the parameters of the controller, the following three conditions are considered:
case 1: p is a radical ofd＝(2.5,2.5)
Case 2: p is a radical ofd＝(5,2.5)
Case 3: p is a radical ofd＝(6,2.5)
In these three cases, an initial load swing angle of 0 ° is set. The simulation results obtained are shown in fig. 5. It can be seen that in these three cases, the method can still maintain good control performance. It should be noted that no matter what the target position is set, the trolley can achieve smooth start with good speed and acceleration constraints.
Control performance test for different hanging rope lengths
There is a hoist rope length L in the controller expression, so in principle the rope length should be known and entered as a parameter into the controller for optimal control. In practical applications, however, it may happen that the rope length is unknown or does not correspond to the set value in the controller.
L actually takes values of 0.4m, 1m and 1.2m respectively. The initial values of the system state variables x and z are 0, and the initial value of gamma is 0.
As can be seen from the simulation results of fig. 6, the proposed nonlinear trajectory tracking control method can accurately drive the carriage to the target position even when the rope length is unknown. In the whole transportation process, when the length of the rope is 0.4m, the maximum hanging swing angle reaches 1.35 degrees; when the length of the rope is 1m, the maximum hanging swing angle reaches 1.45 degrees; when the length of the rope is 1.5m, the maximum hanging swing angle reaches 1.56 degrees, the hanging swing angles are all in a small controllable range, and when the four rotors reach a target point, almost no residual swing exists. Therefore, the control performance of the proposed control method is not much affected by the variation of system parameters. The above results show that the method has strong robustness against system parameter changes.
Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This application is intended to cover any variations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.
It will be understood that the present disclosure is not limited to the precise arrangements described above and shown in the drawings and that various modifications and changes may be made without departing from the scope thereof. The scope of the present disclosure should be limited only by the attached claims.

Claims (10)

1. A nonlinear trajectory tracking control method of a four-rotor hanging transportation system based on segmented energy is characterized by comprising the following steps of:
the method comprises the following steps: a four-rotor hanging transportation system dynamic model in a two-dimensional plane is established based on a Lagrange method;
step two: selecting a smooth and continuous S-curve expected trajectory as an unmanned aerial vehicle hanging flight expected trajectory based on the model;
step three: analyzing the energy of the load relative to the unmanned aerial vehicle, the common motion of the unmanned aerial vehicle body and the load and the generalized potential energy representing the position error based on the viewpoint of segmentation capability to obtain a system energy storage function, and designing and finishing the nonlinear trajectory tracking controller;
step four: stability and convergence analysis are carried out, the system stability is proved based on the Lyapunov technology and the Lassel invariance principle, and the controller can ensure that four system state quantities of the position error, the moving speed, the load swing angle and the angular speed of the quad-rotor unmanned aerial vehicle gradually converge to zero;
step five: and (5) simulation verification.
2. The nonlinear trajectory tracking control method for the four-rotor hanging transportation system based on the segmented energy according to claim 1, characterized in that in step one, a dynamics model of the four-rotor hanging system in an X-Z plane is built, M and M respectively represent the mass of an unmanned aerial vehicle body and a load, L is the length of a lifting rope, g is the gravity acceleration, theta is a four-rotor attitude angle, gamma is an included angle between the lifting rope and a Z axis in an XOZ plane, and the dynamics modeling of the four-rotor hanging system is as follows, wherein-pi/2 < gamma < pi/2:
Figure FDA0003105047570000011
wherein
Figure FDA0003105047570000021
As observable state variables, (F, τ) are input quantities, JyM, L are known constants of the controlled object itself.
3. The nonlinear trajectory tracking control method for the four-rotor hanging transportation system based on the segmented energy according to claim 1, wherein in the second step, in order to realize stable and safe transportation of hanging loads of the four-rotor unmanned aerial vehicle, the following smooth and continuous S-curve expected trajectory with the speed is set:
Figure FDA0003105047570000022
wherein r isdIs the target distance in the horizontal direction, sv、saThe maximum speed and the acceleration allowed by the four-rotor unmanned aerial vehicle hanging, transporting and flying are respectively, and sigma belongs to R+Is an adjustable initial acceleration.
4. The method of claim 3, wherein the desired trajectory is selected to ensure smooth starting and rapid arrival at the target location of the drone:
properties 1: the expected horizontal displacement of the selected track converges asymptotically to rdFurthermore, the velocity and acceleration asymptotically converge to zero, i.e.:
Figure FDA0003105047570000023
properties 2: the speed, the acceleration and the jerk of the unmanned aerial vehicle are bounded, and the following constraint conditions are met:
Figure FDA0003105047570000024
wherein the content of the first and second substances,
Figure FDA0003105047570000025
jerk for a desired trajectory;
property 3 the horizontal initial displacement and velocity of the drone are zero, i.e.:
Figure FDA0003105047570000026
5. the method according to claim 3, wherein in step three, the drone position error is first defined as follows:
Figure FDA0003105047570000027
then there is
Figure FDA0003105047570000031
In order to ensure the stability of the system under the Lyapunov meaning, the acceleration of the unmanned aerial vehicle body is designed as follows:
Figure FDA0003105047570000032
then, the lift force F of the unmanned aerial vehicle is decomposed into F perpendicular to the direction of the lifting ropexAnd f in the direction of the lifting ropezSpecifically, the following are shown:
Figure FDA0003105047570000033
after substitution of formula (1) to give
Figure FDA0003105047570000034
The above formula is solved simultaneously with (8):
Figure FDA0003105047570000035
and then the controller output is obtained through (9) inverse solution:
Figure FDA0003105047570000036
6. the method of claim 5, wherein the initial conditions and system parameters are as follows:
the mass M of the quad-rotor unmanned aerial vehicle is 0.5kg, the load mass M is set to be 0.1kg, the rope length is 1M, the arm length of the rotor is 0.25M, and the inertia moment J isyIs 5 e-3;
the parameters of the nonlinear controller are defined as:
kp＝15,ke＝0.1,kdx＝0.15,kdz＝1。
7. the nonlinear trajectory tracking control method for a quadrirotor hanging transportation system based on segmented energy as claimed in claim 1, wherein in step four, the controller obtained based on the segmented energy view can ensure that four system state quantities of the quadrirotor unmanned aerial vehicle, such as position error, moving speed, load yaw angle and angular speed, gradually converge to zero, namely:
Figure FDA0003105047570000041
8. the nonlinear trajectory tracking control method for a four-rotor hanging transportation system based on segmented energy according to claim 1, wherein in step four, signals in a closed-loop system are all bounded, namely:
Figure FDA0003105047570000042
9. the nonlinear trajectory tracking control method for the segmented energy-based quad-rotor hanging transportation system according to claim 1, wherein the simulation verification specifically comprises the following steps:
firstly, testing the track tracking control performance of the method;
secondly, comparing the method with a passive PD control method, verifying the good control performance of the control algorithm;
then, the control performance of the method for the uncertainty of system parameters and for different target positions is further tested.
10. The method of claim 1, wherein the simulation verification comprises trajectory tracking performance verification, contrast verification and robustness performance verification.
CN202110634702.5A 2021-06-08 2021-06-08 Nonlinear trajectory tracking control method for four-rotor suspended transportation system based on segmented energy Pending CN113253747A (en)

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Cited By (1)

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CN115167145A (en) * 2022-08-08 2022-10-11 南开大学 Method and system for controlling landing of flying, lifting and loading mobile platform

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* Cited by examiner, † Cited by third party
Title
JUNTONG QI;YUAN PING;MINGMING WANG;CHONG WU: "A segmented energy-based nonlinear tracking control method for quadrotor transport system", ASIAN JOURNAL OF CONTROL, pages 1351 - 1362 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115167145A (en) * 2022-08-08 2022-10-11 南开大学 Method and system for controlling landing of flying, lifting and loading mobile platform
CN115167145B (en) * 2022-08-08 2024-05-10 南开大学 Landing control method and system for mobile platform of flying lifting load

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