CN113703451B - Self-adaptive fault-tolerant control method for formation of multiple mobile robots with preset performance - Google Patents

Self-adaptive fault-tolerant control method for formation of multiple mobile robots with preset performance Download PDF

Info

Publication number
CN113703451B
CN113703451B CN202110972856.5A CN202110972856A CN113703451B CN 113703451 B CN113703451 B CN 113703451B CN 202110972856 A CN202110972856 A CN 202110972856A CN 113703451 B CN113703451 B CN 113703451B
Authority
CN
China
Prior art keywords
formula
mobile robot
formation
control
robot
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202110972856.5A
Other languages
Chinese (zh)
Other versions
CN113703451A (en
Inventor
郭一军
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Huangshan University
Original Assignee
Huangshan University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Huangshan University filed Critical Huangshan University
Priority to CN202110972856.5A priority Critical patent/CN113703451B/en
Publication of CN113703451A publication Critical patent/CN113703451A/en
Application granted granted Critical
Publication of CN113703451B publication Critical patent/CN113703451B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process
    • 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
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0219—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory ensuring the processing of the whole working surface
    • 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
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0287—Control of position or course in two dimensions specially adapted to land vehicles involving a plurality of land vehicles, e.g. fleet or convoy travelling
    • G05D1/0291—Fleet control
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Landscapes

  • Engineering & Computer Science (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

The invention discloses a self-adaptive fault-tolerant control method for formation of multiple mobile robots with preset performance, which comprises the following specific steps of: establishing a mathematical model of a multi-mobile robot formation system considering the faults of an actuating mechanism; designing a preset performance multi-mobile robot formation speed control law; designing a self-adaptive fault-tolerant torque control law of the formation mobile robots; and (3) stability analysis of the self-adaptive fault-tolerant control method for the formation of the multiple mobile robots with preset performance. The multi-mobile-robot formation control method disclosed by the invention can realize the preset performance control of the formation error, effectively eliminate the adverse effects on the formation control caused by the system execution mechanism fault and the system external disturbance uncertainty, and realize stable and reliable formation control.

Description

Self-adaptive fault-tolerant control method for formation of multiple mobile robots with preset performance
Technical Field
The invention relates to the field of robot control methods, in particular to a self-adaptive fault-tolerant control method for multi-mobile robot formation with preset performance.
Background
With the complication of the work environment of the mobile robot and the more diversified work tasks, the single mobile robot is no longer suitable for bearing some special task requirements, and the multi-mobile robot system has many advantages compared with the single robot.
Faults, uncertain dynamics and external interference of an actuating mechanism generally bring great influence on transient performance and steady-state performance of a mobile robot formation system, and in severe cases, the formation system may be unstable, and even collision among robots may occur. However, current research on multi-mobile robot formation control mainly aims to improve the steady-state control accuracy of the robot formation system, and the transient response performance and output constraint problems of the formation system are rarely considered.
The method can ensure that the steady-state error of the formation closed-loop system is converged to a preset allowable range, and simultaneously ensure that the convergence speed and the overshoot are less than a certain preset value.
Disclosure of Invention
The invention aims to provide a self-adaptive fault-tolerant control method for multi-mobile-robot formation with preset performance, so as to solve the problem of unstable control of the mobile-robot formation in the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the self-adaptive fault-tolerant control method for the formation of the multiple mobile robots with preset performance, wherein the formation of the multiple mobile robots is formed by a plurality of mobile robots, comprises the following steps:
step 1, establishing a multi-mobile-robot formation system, wherein a kinematics and dynamics model of any mobile robot i is shown as a formula (1):
Figure BDA0003226521330000011
in the formula (1), q i ＝[x i ,y i ,θ i ] T ∈R 3 Represents a pose vector of the mobile robot i, where x i ，y i Respectively representing the coordinates theta of the mobile robot i in the X-axis direction and the Y-axis direction of the global coordinate system i Represents a direction angle of the mobile robot;
Figure BDA0003226521330000021
u i ＝[v i ,ω i ] T ∈R 2 a velocity vector representing the mobile robot i, consisting of the linear velocity and the angular velocity of the mobile robot i, v i Is the linear velocity, omega, of the mobile robot i i Is the angular velocity of the mobile robot i;
Figure BDA0003226521330000022
positive definite inertia matrix, m, representing mobile robot i i ，I i Respectively representing the mass and inertia of the mobile robot i; f i ∈R 2 Representing a ground friction force dynamic vector; tau is di ∈R 2 Representing an external time-varying bounded perturbation;
Figure BDA0003226521330000023
inputting a moment transformation array for the mobile robot i, wherein r i Radius of the driving wheel, b i For moving robots
Figure BDA0003226521330000024
The width of (d); tau is i ＝[τ 1i ,τ 2i ] T ∈R 2 Representing input torque vectors of two driving wheels of the mobile robot i;
step 2, considering the problem of the fault of the executing mechanism, the dynamic model of the mobile robot i can be modeled as shown in a formula (2):
Figure BDA0003226521330000025
in the formula (2), τ 1i ＝Δ 1i τ 11i +σ 1i ，τ 2i ＝Δ 2i τ 22i +σ 2i Wherein, τ 11i 、τ 22i Control torque signal output by controller, 0 < delta 1i ≤1，0＜Δ 2i A coefficient of unknown ≦ 1 for indicating the degree of failure, σ, of the ith mobile robot actuator 1i ，σ 2i Indicating an unknown additive fault of the i-th mobile robot actuator. Delta of 1i ，Δ 2i ，σ 1i And sigma 2i The magnitude of the value is determined by the degree of malfunction of the mobile robot actuator, e.g. when Δ 1i ＝Δ 2i 1 and σ 1i ＝σ 2i If =0, it indicates that the actuator of the i-th mobile robot has no fault;
multiplying both sides of equation (2) by
Figure BDA0003226521330000026
The formula (3) can be derived:
Figure BDA0003226521330000027
in the formula (3), the first and second groups,
Figure BDA0003226521330000028
suppose G i Bounded and satisfies the relation G i ||≤c i Wherein c is i Is an unknown normal number;
Figure BDA0003226521330000031
wherein, tau 11i 、τ 22i A control torque signal output for the controller;
step 3, determining a pilot robot in the multi-mobile-robot formation system, wherein an expected track generated by the pilot robot is determined by the following formula (4):
Figure BDA0003226521330000032
in the formula (4), q 0 ＝[x 0 ,y 0 ,θ 0 ] T ∈R 3 To pilot the movement track, x, of the mobile robot 0 ，y 0 Respectively representing the coordinates theta of the piloted robot in the X-axis direction and the Y-axis direction of the global coordinate system 0 Representing a direction angle of the piloted robot; v. of 0 The linear velocity of the piloted mobile robot; omega 0 Is the angular velocity of the piloted mobile robot.
To obtain the desired formation, first, the formation parameters are defined in the local coordinate system of the piloted mobile robot: expected relative distance to formation l id And relative direction angle theta id (ii) a Then, obtaining the desired trajectory of the reference point of any one of the following mobile robots i through coordinate transformation is shown in formula (5):
Figure BDA0003226521330000033
in the formula (5), [ x ] id ,y id ] T ∈R 2 I =1,2,3, …, N, representing a desired trajectory to follow mobile robot i, where x id As X-axis coordinate, y, of the desired trajectory id Is the Y-axis coordinate of the desired trajectory. Sending the expected track to a following mobile robot i which forms a formation with the expected track by a pilot robot; l id A desired formation relative distance; theta id A desired formation relative azimuth;
step 4, selecting a local coordinate system x of the following mobile robot i bi A point p in the forward direction of the axis i (p xi ,p yi ) As a reference point for the following mobile robot i, the coordinates of the following mobile robot i may be represented in the global coordinate system XOY as
Figure BDA0003226521330000034
Wherein p is xi To follow the coordinates of the i-reference point of the mobile robot in the X-axis direction, p yi For following the coordinates of i-reference point of mobile robot in Y-axis direction, L i The distance between the reference point and the origin of coordinates of the local coordinate system of the following mobile robot;
thus, the multi-mobile robot formation system control error equation can be defined as shown in equation (6):
Figure BDA0003226521330000041
in the formula (6), e xi The control error of the formation system in the X axial direction is obtained; e.g. of the type yi The control error of the Y-axis of the formation system is shown.
The time derivative is calculated for the formula (6), and the formula (1) and the formula (5) are combined, so that the dynamic equation of the formation control error of the multiple mobile robots can be obtained as shown in the formulas (7) and (8):
Figure BDA0003226521330000042
Figure BDA0003226521330000043
wherein,
Figure BDA0003226521330000044
the invention also comprises a step 5: designing a preset performance multi-mobile robot formation speed control law, wherein the process comprises the following steps:
step 5.1, the design of the preset performance function is shown as a formula (9):
μ ji (t)＝(μ ji,0 -μ ji,∞ )exp(-k ji t)+μ ji,∞ ，j＝x,y (9)，
in the formula (9), μ ji,0 0 is the initial value of the predetermined performance function, mu ji,∞ > 0 is the steady state value of the preset performance function when t → ∞ k ji Setting parameters for the convergence speed of the preset performance function if the convergence speed is more than 0;
to achieve the preset performance control requirement, the formation controller is designed to make the formation control error meet the requirement of the formula (10):
-μ ji (t)＜e ji ＜μ ji (t), j = x, y (10), and in equation (10), parameter μ ji,0 Is set to satisfy-mu ji,0 ＜e ji (0)＜μ ji,0 ；
And 5.2, defining an error transformation function as shown in a formula (11):
Figure BDA0003226521330000051
in formula (11), j = x, y; psi (-) is a strictly increasing smoothing function;
Figure BDA0003226521330000052
derivation of equation (11) yields equation (12):
Figure BDA0003226521330000053
in the formula (12), the first and second groups,
Figure BDA0003226521330000054
Figure BDA0003226521330000055
by defining the error transformation function, only delta is ensured in the design of the queue controller ji Bounded, i.e. guaranteeing a formation control error e xi 、e yi Meet a predetermined performance requirement, i.e., -mu ji (t)＜e ji ＜μ ji (t)；
Step 5.3, designing the Lyapunov function as shown in formulas (13) and (14):
Figure BDA0003226521330000056
Figure BDA0003226521330000057
wherein, delta xi An error transformation function selected for X-axis error control; delta yi An error transformation function selected for Y-axis error control;
equations (15) and (16) can be obtained by deriving equations (13) and (14):
Figure BDA0003226521330000061
Figure BDA0003226521330000062
design u from equations (15), (16) vi ，u ωi As shown in equations (17) and (18):
Figure BDA0003226521330000063
Figure BDA0003226521330000064
wherein u is vi ，u ωi Design parameter k 1i ＞0，k 2i ＞0；
The formula (17) and the formula (18) may be substituted for the formula (15) and the formula (16), respectively:
Figure BDA0003226521330000065
Figure BDA0003226521330000066
combining the formula (8), the control law of the formation speed of the multi-mobile robot with preset performance can be obtained as shown in the formula (21):
Figure BDA0003226521330000071
in the formula (21), v ci A pre-set performance multi-mobile robot formation linear speed control law; omega ci And forming an angular speed control law for the multi-mobile robot with preset performance.
The invention also comprises a step 6: designing a self-adaptive fault-tolerant torque control law of the formation mobile robot, wherein the process is as follows:
step 6.1, after the design of the speed control law of the formation mobile robot is finished, the design of the self-adaptive fault-tolerant moment control law is required to be carried out by combining a dynamic model of the mobile robot so as to obtain the actual control moment input of the following mobile robot; first, a velocity tracking error vector is defined as shown in equation (22):
Figure BDA0003226521330000072
in the formula (22), e 1i Tracking error for the linear velocity following the mobile robot i; e.g. of the type 2i Tracking error for following the angular velocity of the mobile robot i;
step 6.2, in order to improve the control precision of the speed tracking error, the invention designs an integral sliding mode surface shown as a formula (23):
Figure BDA0003226521330000073
in the formula (23), the first and second groups,S i ＝[s 1i ,s 2i ] T wherein s is 1i ，s 2i Respectively represent the vectors S i The first and second components of (a); k vi ＝diag{k v1i ,k v2i The value is more than 0, which is the design parameter of the integral sliding mode surface;
the time derivative of equation (23) can be derived as equation (24):
Figure BDA0003226521330000074
in the formula (24), the first and second groups,
Figure BDA0003226521330000075
wherein
Figure BDA0003226521330000076
D i Satisfies the relationship:
Figure BDA0003226521330000077
wherein, b i ＝max{1,c i The (x) is an unknown constant which,
Figure BDA0003226521330000081
can be obtained by on-line calculation;
step 6.3 for unknown item b i The invention adopts a parameter self-adaptive method for processing, and designs a self-adaptive fault-tolerant moment control law following the mobile robot i by combining a formula (24) as shown in a formula (25):
Figure BDA0003226521330000082
in the formula (25), the first and second groups,
Figure BDA0003226521330000083
k 3i ＞0，k 4i ＞0，k 5i a control gain parameter that is positive > 0; design parameter beta i The conditions need to be satisfied: beta is more than 0 i ＜1；sign (·) is a sign function;
Figure BDA0003226521330000084
is an unknown constant b i Is determined by the estimated value of (c),
Figure BDA0003226521330000085
the adaptive update law of (2) is shown in equation (26):
Figure BDA0003226521330000086
in the formula, k 6i A constant greater than zero.
Compared with the prior art, the invention has the advantages that:
the invention has the advantages that: the multi-mobile-robot formation control method can realize the preset performance control of the formation error, effectively eliminate the adverse effects of system execution mechanism faults and system external disturbance uncertainty on formation control, and realize reliable and stable formation control.
Drawings
Fig. 1 is a schematic diagram of a formation structure of multiple mobile robots according to the present invention.
Fig. 2a is a schematic diagram of a queuing error of the adaptive fault-tolerant control method Follower 1 with preset performance according to the present invention.
Fig. 2b is a schematic diagram of a queuing error of the adaptive fault-tolerant control method Follower 1 with preset performance according to the present invention.
Fig. 3a is a schematic diagram of a Follower 2 formation error of the adaptive fault-tolerant control method with preset performance according to the present invention.
Fig. 3b is a schematic diagram of a Follower 2 queuing error of the adaptive fault-tolerant control method with preset performance according to the present invention.
Fig. 4a is a schematic diagram of a queuing error of the adaptive fault-tolerant control method Follower 1 without the preset performance according to the present invention.
Fig. 4b is a schematic diagram of a queuing error of the adaptive fault-tolerant control method Follower 1 without the preset performance according to the present invention.
Fig. 5a is a schematic diagram of a queuing error of the adaptive fault-tolerant control method Follower 2 without the preset performance according to the present invention.
Fig. 5b is a schematic diagram of a queuing error of the adaptive fault-tolerant control method Follower 2 without the preset performance according to the present invention.
Fig. 6a shows control signals of a method C1 according to Follower 1 of the present invention.
Fig. 6b shows the control signals of the method C2 used by the Follower 1 according to the present invention.
Fig. 7a shows control signals of a method C1 used by Follower 2 according to the present invention.
Fig. 7b shows control signals of Follower 2 according to the present invention using method C2.
Fig. 8 is a block diagram of the control system according to the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
As shown in fig. 1, the invention relates to a self-adaptive fault-tolerant control method for formation of multiple mobile robots with preset performance, wherein the formation of multiple mobile robots is composed of multiple mobile robots, and the method comprises the following steps:
step 1, establishing a kinematics and dynamics model of any one mobile robot i in a multi-mobile-robot formation system as shown in a formula (1):
Figure BDA0003226521330000091
in the formula (1), q i ＝[x i ,y i ,θ i ] T ∈R 3 Represents the pose vector of the mobile robot i, where x i ，y i Represents the coordinates of the mobile robot i in the X-axis direction and the Y-axis direction of the global coordinate system, respectively, and θ i Representing a directional angle of the mobile robot;
Figure BDA0003226521330000092
u i ＝[v i ,ω i ] T ∈R 2 a velocity vector representing the mobile robot i, consisting of the linear velocity and the angular velocity of the mobile robot i, v i Is the linear velocity, omega, of the mobile robot i i Is the angular velocity of the mobile robot i;
Figure BDA0003226521330000093
represents the positive definite inertia matrix, m, of the mobile robot i i ，I i Respectively representing the mass and inertia of the mobile robot i; f i ∈R 2 Representing a ground friction force dynamic vector; tau is di ∈R 2 Representing an external time-varying bounded perturbation;
Figure BDA0003226521330000101
inputting a moment transformation array for the mobile robot i, wherein r i Radius of the driving wheel, b i For moving robots
Figure BDA0003226521330000102
The width of (d); tau is i ＝[τ 1i ,τ 2i ] T ∈R 2 Representing input torque vectors of two driving wheels of the mobile robot i;
and 2, in the working process of the queuing mobile robot, the fault problem of an actuating mechanism is inevitable. Once an executing mechanism breaks down, a light person can have an adverse effect on the formation control effect, and a failure of the formation control task of the multiple mobile robots is caused. Therefore, the problem of the failure of the mobile robot actuator needs to be considered in the formation control.
Considering the problem of actuator failure, the dynamic model of the mobile robot i can be modeled as shown in formula (2):
Figure BDA0003226521330000103
in the formula (2), τ 1i ＝Δ 1i τ 11i +σ 1i ，τ 2i ＝Δ 2i τ 22i +σ 2i Wherein, τ 11i 、τ 22i Control force output for controllerMoment signal, 0 < delta 1i ≤1，0＜Δ 2i A coefficient of unknown ≦ 1 for indicating the degree of failure, σ, of the ith mobile robot actuator 1i ，σ 2i Indicating an unknown additive fault of the i-th mobile robot actuator. Delta 1i ，Δ 2i ，σ 1i And sigma 2i The magnitude of the value is determined by the degree of malfunction of the mobile robot actuator, e.g. when Δ 1i ＝Δ 2i 1 and σ 1i ＝σ 2i If =0, it indicates that the actuator of the i-th mobile robot has no fault;
multiplying both sides of the formula (2) by
Figure BDA0003226521330000104
Formula (3) can be obtained:
Figure BDA0003226521330000105
in the formula (3), the first and second groups,
Figure BDA0003226521330000106
suppose G i Bounded and satisfies the relation G i ||≤c i Wherein c is i Is an unknown normal number;
Figure BDA0003226521330000107
wherein, tau 11i 、τ 22i A control torque signal output for the controller;
step 3, as shown in fig. 1, in the formation of the multiple mobile robots, one mobile robot is used as a pilot robot leader, the pilot robot leader has the function of generating corresponding reference tracks according to different operation tasks of the formation mobile robots, and the other mobile robots move along with the pilot robot.
In the invention, firstly, a pilot robot in a multi-mobile-robot formation system is determined, and an expected track generated by the pilot robot is determined by the following formula (4):
Figure BDA0003226521330000111
in the formula (4), q 0 ＝[x 0 ,y 0 ,θ 0 ] T ∈R 3 To pilot the movement track, x, of the mobile robot 0 ，y 0 Respectively representing the coordinates theta of the piloted robot in the X-axis direction and the Y-axis direction of the global coordinate system 0 Representing a direction angle of the piloted robot; v. of 0 The linear velocity of the piloted mobile robot; omega 0 Is the angular velocity of the piloted mobile robot.
To obtain the desired formation form, first, the formation parameters are defined in the local coordinate system of the piloting mobile robot: expected relative distance to formation l id And relative direction angle theta id (ii) a Then, obtaining a desired trajectory of a reference point of any one following mobile robot i through coordinate transformation is as shown in formula (5):
Figure BDA0003226521330000112
in the formula (5), [ x ] id ,y id ] T ∈R 2 I =1,2,3, …, N, representing a desired trajectory to follow mobile robot i, where x id As X-axis coordinate, y, of the desired trajectory id Is the Y-axis coordinate of the desired trajectory. Sending the expected track to a following mobile robot i which forms a formation with the expected track by a pilot robot; l id A desired relative distance to formation; theta id A desired formation relative azimuth;
step 4, selecting a local coordinate system x of the following mobile robot i bi A point p in the forward direction of the axis i (p xi ,p yi ) As a reference point for the following mobile robot i, the coordinates of the following mobile robot i may be represented in the global coordinate system XOY as
Figure BDA0003226521330000113
Wherein p is xi To follow the coordinates of the mobile robot i reference point in the X axis direction, p yi For following the coordinates of i-reference point of mobile robot in Y-axis direction, L i The distance between the reference point and the origin of coordinates of the local coordinate system of the following mobile robot;
thus, the multi-mobile robot formation system control error equation can be defined as shown in equation (6):
Figure BDA0003226521330000121
in the formula (6), e xi The control error of the formation system in the X axial direction is obtained; e.g. of the type yi The control error of the Y-axis of the formation system is shown.
The time derivative is calculated for the formula (6), and the formula (1) and the formula (5) are combined, so that the dynamic equation of the formation control error of the multiple mobile robots can be obtained as shown in the formulas (7) and (8):
Figure BDA0003226521330000124
Figure BDA0003226521330000122
wherein,
Figure BDA0003226521330000123
step 5, designing a preset performance multi-mobile robot formation speed control law, wherein the process is as follows:
step 5.1, the design of the preset performance function is shown as a formula (9):
μ ji (t)＝(μ ji,0 -μ ji,∞ )exp(-k ji t)+μ ji,∞ ，j＝x,y (9)，
in the formula (9), μ ji,0 0 is the initial value of the predetermined performance function, mu ji,∞ > 0 is the steady state value of the preset performance function when t → ∞ k ji And > 0 is a parameter for setting the convergence speed of the preset performance function.
To achieve the preset performance control requirement, the formation controller is designed to make the formation control error meet the requirement of the formula (10):
-μ ji (t)＜e ji ＜μ ji (t)，j＝x,y (10)，
in the formula (10), the parameter μ ji,0 Is set to satisfy-mu ji,0 ＜e ji (0)＜μ ji,0 。
And 5.2, defining an error transformation function as shown in a formula (11):
Figure BDA0003226521330000131
in formula (11), j = x, y; psi (·) is a strictly increasing smoothing function;
Figure BDA0003226521330000132
derivation of equation (11) yields equation (12):
Figure BDA0003226521330000133
in the formula (12), the first and second groups,
Figure BDA0003226521330000134
Figure BDA0003226521330000135
by defining the error transformation function, only delta is ensured in the design of the queue controller ji Bounded, i.e. guaranteeing a formation control error e xi 、e yi Meet a predetermined performance requirement, i.e., -mu ji (t)＜e ji ＜μ ji (t)。
Step 5.3, designing the Lyapunov function as shown in formulas (13) and (14):
Figure BDA0003226521330000136
Figure BDA0003226521330000137
wherein, delta xi An error transformation function selected for X-axis error control; delta yi An error transfer function is selected for Y-axis error control.
Equations (15) and (16) can be obtained by deriving equations (13) and (14):
Figure BDA0003226521330000141
Figure BDA0003226521330000142
design u from equations (15), (16) vi ，u ωi As shown in equations (17) and (18):
Figure BDA0003226521330000143
Figure BDA0003226521330000144
wherein u is vi ，u ωi Design parameter k 1i ＞0，k 2i ＞0。
The formula (17) and the formula (18) may be substituted for the formula (15) and the formula (16), respectively:
Figure BDA0003226521330000145
Figure BDA0003226521330000146
combining the formula (8), the control law of the formation speed of the multi-mobile robot with the preset performance is shown as a formula (21):
Figure BDA0003226521330000151
in the formula (21), v ci A pre-set performance multi-mobile robot formation linear speed control law; omega ci And forming an angular speed control law for the multi-mobile robot with preset performance.
Step 6, designing a self-adaptive fault-tolerant moment control law of the formation mobile robot, wherein the process is as follows:
and 6.1, after the design of the speed control law of the formation mobile robot is finished, designing a self-adaptive fault-tolerant moment control law by combining a dynamic model of the mobile robot so as to obtain the actual control moment input of the following mobile robot. First, a velocity tracking error vector is defined as shown in equation (22):
Figure BDA0003226521330000152
in the formula (22), e 1i Tracking error for the linear velocity following the mobile robot i; e.g. of the type 2i To follow the angular velocity of the mobile robot i.
Step 6.2, in order to improve the control precision of the speed tracking error, the invention designs an integral sliding mode surface as shown in a formula (23):
Figure BDA0003226521330000153
in the formula (23), S i ＝[s 1i ,s 2i ] T Wherein s is 1i ，s 2i Respectively represent the vectors S i The first and second components of (a); k vi ＝diag{k v1i ,k v2i And 0 is a design parameter of an integral sliding mode surface.
The time derivative of equation (23) can be derived as equation (24):
Figure BDA0003226521330000154
in the formula (24), the first and second groups,
Figure BDA0003226521330000155
wherein
Figure BDA0003226521330000156
D i Satisfies the relationship:
Figure BDA0003226521330000157
wherein, b i ＝max{1,c i The (x) is an unknown constant which,
Figure BDA0003226521330000158
can be obtained by on-line calculation.
Step 6.3 for unknown item b i The invention adopts a parameter self-adaptive method for processing, and designs a self-adaptive fault-tolerant moment control law following the mobile robot i by combining a formula (24) as shown in a formula (25):
Figure BDA0003226521330000161
in the formula (25), the first and second groups,
Figure BDA0003226521330000162
k 3i ＞0，k 4i ＞0，k 5i a control gain parameter that is positive > 0; design parameter beta i The conditions need to be satisfied: beta is more than 0 i Less than 1; sign (·) is a sign function;
Figure BDA0003226521330000163
is an unknown constant b i Is determined by the estimated value of (c),
Figure BDA0003226521330000164
the adaptive update law of (2) is shown in equation (26):
Figure BDA0003226521330000165
in the formula, k 6i A constant greater than zero.
The stability analysis of the self-adaptive fault-tolerant control method for the formation of the multiple mobile robots with the preset performance is as follows:
(1) The Lyapunov function is designed as shown in formula (27):
Figure BDA0003226521330000166
in the formula (27), β min > 0 is a matrix
Figure BDA0003226521330000167
The minimum eigenvalue of (c);
Figure BDA0003226521330000168
as an unknown parameter b i The estimation error of (2).
(2) Formula (28) is obtained by obtaining a time derivative of formula (27) and substituting formula (19), formula (20), formula (24), and formula (26):
Figure BDA0003226521330000169
(3) Formula (29) can be obtained by substituting formula (25) for formula (28):
Figure BDA0003226521330000171
in equation (29):
η i ＝min{2β min k 3i ,2ζ xi k 1i ,2ζ yi k 2i ,k 6i }，
Figure BDA0003226521330000172
further, from equation (29), the following inequality can be obtained:
Figure BDA0003226521330000173
(4) From V i As shown in the definition of (1) and the formula (29), δ xi ，δ yi ，S i ，
Figure BDA0003226521330000174
Is consistently bounded, so the formation control error e xi ，e yi And the preset performance requirement is met.
Examples
This example presents the comparison results for two different control methods: self-adaptive fault-tolerant control method (C1), u, for formation of multiple mobile robots with preset performance vi ，u ωi Designing formulas (17) and (18), and designing control moment as formula (25); self-adaptive fault-tolerant control method (C2), u, for formation of multiple mobile robots without preset performance vi ，u ωi Is designed as u vi ＝-k 7i e xi -Γ 1i ，u ωi ＝-k 8i e yi -Γ 2i ，k 7i ＞0，k 8i And (4) if the fault-tolerant torque control law is greater than 0, the self-adaptive fault-tolerant torque control law is designed as shown in the formula (25). In this embodiment there are three mobile robots, leader Robot, follower 1, follower 2.
Linear velocity v of Leader Robot 0 Is set as v 0 =0.5m/s, angular velocity ω 0 Set to ω 0 =0.1rad/s, initial pose coordinate set to q 0 ＝[0,0,0] T . Follower 1 has physical parameter set to m 1 ＝10.5kg，I 1 ＝3.11kg·m 2 ，r 1 ＝0.25m，b 1 ＝0.4m，L 1 =1.6m; the initial pose coordinate is set to [ -2-1 π/8 ]] T (ii) a Follower 2 has a physical parameter set to m 2 ＝10.5kg，I 2 ＝3.11kg·m 2 ，r 2 ＝0.25m，b 2 ＝0.4m，L 2 =1.6m; the initial pose coordinate is set to [ -3-2 π/9 [)] T 。
For better comparisonIn the study, the same controller parameter settings were the same in both control methods. The controller parameters for Follower 1 are set to: k is a radical of 11 ＝1.5，k 21 ＝1.6，k 31 ＝8，k 41 ＝1，k 51 ＝0.01，k 61 ＝0.03，K v1 ＝diag{0.4,0.5}；k 71 ＝1.5，k 81 ＝1.6；μ x1,0 ＝4，μ y1,0 ＝3，μ x1,∞ ＝μ y1,∞ ＝0.1，k x1 ＝k y1 And (5) =2. The controller parameters for Follower 2 are set to: k is a radical of 12 ＝1.5，k 22 ＝1.6，k 32 ＝8，k 42 ＝1，k 52 ＝0.01，k 62 ＝0.03，K v2 ＝diag{0.4,0.5}；k 72 ＝1.5，k 82 ＝1.6；μ x2,0 ＝4，μ y2,0 ＝3，μ x2,∞ ＝μ y2,∞ ＝0.1，k x2 ＝k y2 ＝2。
Suppose that the dynamic vector of the ground friction force borne by the 2 following mobile robots is F 1 ＝F 2 ＝[sin(t)+2.4,cos(t)+2.4] T (ii) a Exposed external time-bounded perturbation τ d1 ＝τ d2 ＝[0.1sin(t)+2,0.5cos(t)+0.4] T (ii) a The failure of the actuator is assumed to be
Figure BDA0003226521330000181
The simulation experiment results of the two control methods are shown in fig. 2a, fig. 2b, fig. 3a, fig. 3b, fig. 4a, fig. 4b, fig. 5a, fig. 5b, fig. 6a, fig. 6b, fig. 7a, fig. 7b, and fig. 8-and fig. 2a, fig. 2b, fig. 3a, and fig. 3b are schematic diagram of the formation errors of the adaptive fault-tolerant control methods Follower 1 and Follower 2 with preset performance according to the present invention, respectively; fig. 4a, 4b, 5a, and 5b are schematic diagrams of the formation errors of adaptive fault-tolerant control methods Follower 1 and Follower 2, respectively, without preset performance according to the present invention; fig. 6a, 6b and fig. 7a, 7b are control signals of Follower 1 and Follower 2, respectively, according to two control methods of the present invention. As can be seen from fig. 2a, 2b, 3a, and 3b, the adaptive fault-tolerant control method with the preset performance can effectively handle the adverse effects of system execution mechanism faults and system external disturbance uncertainty on formation control, the variation of formation errors is limited within a preset performance boundary, the convergence rate of the formation errors is not less than a preset convergence rate, and the steady-state errors of the formation are not greater than a preset steady-state value. As can be seen from fig. 4a, 4b, 5a, and 5b, under the condition of using the same controller parameters, the formation error of the adaptive fault-tolerant control method without the preset performance has a large fluctuation, and the change process breaks through the preset performance boundary, so that the formation control effect is obviously inferior to the adaptive fault-tolerant control method with the preset performance. Fig. 6a, 6b, 7a, and 7b show the control signals of Follower 1 and Follower 2, respectively, for the two control methods of the present invention, and it can be seen from the figure that the smoothness of the control signal with the preset performance control method is not as good as that without the preset performance control method, but remains substantially smooth and does not affect the practical application of the control method.
The described embodiments of the present invention are only for describing the preferred embodiments of the present invention, and do not limit the concept and scope of the present invention, and the technical solutions of the present invention should be modified and improved by those skilled in the art without departing from the design concept of the present invention, and the technical contents of the present invention which are claimed are all described in the claims.

Claims (1)

1. The self-adaptive fault-tolerant control method for the formation of the multiple mobile robots with preset performance is characterized by comprising the following steps of:
step 1, establishing a multi-mobile-robot formation system, wherein a kinematics and dynamics model of any mobile robot i is shown as a formula (1):
Figure FDA0003940642970000011
in the formula (1), q i ＝[x i ,y i ,θ i ] T ∈R 3 Represents a pose vector of the mobile robot i, where x i ，y i Respectively representing the coordinates theta of the mobile robot i in the X-axis direction and the Y-axis direction of the global coordinate system i Represents a direction angle of the mobile robot;
Figure FDA0003940642970000012
u i ＝[v i ,ω i ] T ∈R 2 a velocity vector representing the mobile robot i, consisting of the linear velocity and the angular velocity of the mobile robot i, v i Is the linear velocity, omega, of the mobile robot i i Is the angular velocity of the mobile robot i;
Figure FDA0003940642970000013
positive definite inertia matrix, m, representing mobile robot i i ，I i Respectively representing the mass and inertia of the mobile robot i; f i ∈R 2 Representing a ground friction force dynamic vector; tau is di ∈R 2 Representing an external time-varying bounded perturbation;
Figure FDA0003940642970000014
inputting a moment transformation array for the mobile robot i, wherein r i Radius of the driving wheel, b i For moving robots
Figure FDA0003940642970000015
The width of (d); tau is i ＝[τ 1i ,τ 2i ] T ∈R 2 Representing input torque vectors of two driving wheels of the mobile robot i;
step 2, considering the problem of the fault of the executing mechanism, the dynamic model of the mobile robot i can be modeled as shown in a formula (2):
Figure FDA0003940642970000016
in the formula (2), τ 1i ＝Δ 1i τ 11i +σ 1i ，τ 2i ＝Δ 2i τ 22i +σ 2i Wherein, τ 11i 、τ 22i Control torque signal output by controller, 0 < delta 1i ≤1，0＜Δ 2i A coefficient not more than 1 is unknown and is used for expressing the failure degree of the actuator of the ith mobile robot, sigma 1i ，σ 2i Indicating an unknown additive fault of an ith mobile robot actuator; delta 1i ，Δ 2i ，σ 1i And sigma 2i The magnitude of the value is determined by the degree of malfunction of the mobile robot actuator, e.g. when Δ 1i ＝Δ 2i 1 and σ 1i ＝σ 2i If =0, it means that the actuator of the i-th mobile robot is not in failure;
multiplying both sides of the formula (2) by
Figure FDA0003940642970000026
Formula (3) can be obtained:
Figure FDA0003940642970000021
in the formula (3), the first and second groups,
Figure FDA0003940642970000022
suppose G i Bounded and satisfies the relation G i ||≤c i Wherein c is i Is an unknown normal number;
Figure FDA0003940642970000023
wherein, tau 11i 、τ 22i A control torque signal output by the controller;
step 3, determining a pilot robot in the multi-mobile-robot formation system, wherein an expected track generated by the pilot robot is determined by the following formula (4):
Figure FDA0003940642970000024
in the formula (4), q 0 ＝[x 0 ,y 0 ,θ 0 ] T ∈R 3 To pilot the movement track, x, of the mobile robot 0 ，y 0 Respectively representing the coordinates theta of the piloted robot in the X-axis direction and the Y-axis direction of the global coordinate system 0 Representing a direction angle of the piloted robot; v. of 0 The linear velocity of the piloted mobile robot; omega 0 Is the angular velocity of the piloted mobile robot;
to obtain the desired formation form, first, the formation parameters are defined in the local coordinate system of the piloting mobile robot: expected relative distance to formation l id And relative direction angle theta id (ii) a Then, obtaining the desired trajectory of the reference point of any one of the following mobile robots i through coordinate transformation is shown in formula (5):
Figure FDA0003940642970000025
in the formula (5), [ x ] id ,y id ] T ∈R 2 I =1,2,3, …, N, representing a desired trajectory to follow mobile robot i, where x id As X-axis coordinate, y, of the desired trajectory id Sending the expected track to a following mobile robot i which forms a formation with the expected track by a pilot robot for the Y-axis coordinate of the expected track; l id A desired relative distance to formation; theta.theta. id A desired formation relative azimuth;
step 4, selecting a local coordinate system x of the following mobile robot i bi A point p in the forward direction of the axis i (p xi ,p yi ) As a reference point for the following mobile robot i, the coordinates of the following mobile robot i may be represented in the global coordinate system XOY as
Figure FDA0003940642970000031
Wherein p is xi To follow the coordinates of the i-reference point of the mobile robot in the X-axis direction, p yi For following the i reference point of the mobile robot in the Y axial directionCoordinate of (a), L i The distance between the reference point and the origin of coordinates of the local coordinate system of the following mobile robot;
thus, the multi-mobile robot formation system control error equation can be defined as shown in equation (6):
Figure FDA0003940642970000032
in the formula (6), e xi The control error of the formation system in the X axial direction is obtained; e.g. of the type yi The control error of the formation system in the Y-axis direction is obtained;
the time derivative is calculated for the formula (6), and the formula (1) and the formula (5) are combined, so that a dynamic equation of the formation control error of the multiple mobile robots can be obtained as shown in the formulas (7) and (8):
Figure FDA0003940642970000033
Figure FDA0003940642970000034
wherein,
Figure FDA0003940642970000035
and 5: designing a preset performance multi-mobile robot formation speed control law, wherein the process comprises the following steps:
step 5.1, the design of the preset performance function is shown as a formula (9):
μ ji (t)＝(μ ji,0 -μ ji,∞ )exp(-k ji t)+μ ji,∞ ，j＝x,y (9)，
in the formula (9), μ ji,0 0 is the initial value of the predetermined performance function, mu ji,∞ > 0 is the steady state value of the preset performance function when t → ∞ k ji Setting parameters for the convergence speed of the preset performance function if the convergence speed is more than 0;
to achieve the preset performance control requirement, the formation controller is designed to make the formation control error meet the requirement of the formula (10):
-μ ji (t)＜e ji ＜μ ji (t)，j＝x,y (10)，
in the formula (10), the parameter μ ji,0 Is set to satisfy-mu ji,0 ＜e ji (0)＜μ ji,0 ；
And 5.2, defining an error transformation function as shown in a formula (11):
Figure FDA0003940642970000041
in formula (11), j = x, y; psi (·) is a strictly increasing smoothing function;
Figure FDA0003940642970000042
derivation of equation (11) yields equation (12):
Figure FDA0003940642970000043
in the formula (12), the first and second groups,
Figure FDA0003940642970000044
j＝x,y；
by defining the error transformation function, only delta is ensured in the design of the queue controller ji Bounded, i.e. guaranteeing a formation control error e xi 、e yi Meet a predetermined performance requirement, i.e., -mu ji (t)＜e ji ＜μ ji (t)；
Step 5.3, designing the Lyapunov function as shown in formulas (13) and (14):
Figure FDA0003940642970000045
Figure FDA0003940642970000046
wherein, delta xi An error transformation function selected for X-axis error control; delta yi An error transformation function selected for Y-axis error control;
derivation of equations (13) and (14) yields equations (15) and (16):
Figure FDA0003940642970000051
Figure FDA0003940642970000052
design u from equations (15), (16) vi ，u ωi As shown in equations (17) and (18):
Figure FDA0003940642970000053
Figure FDA0003940642970000054
wherein u is vi ，u ωi Design parameter k 1i ＞0，k 2i ＞0；
The formula (17) and the formula (18) may be substituted for the formula (15) and the formula (16), respectively:
Figure FDA0003940642970000055
Figure FDA0003940642970000056
combining the formula (8), the control law of the formation speed of the multi-mobile robot with the preset performance is shown as a formula (21):
Figure FDA0003940642970000061
in the formula (21), v ci A pre-set performance multi-mobile robot formation linear speed control law; omega ci Forming an angular speed control law for the multi-mobile robot with preset performance;
step 6: designing a self-adaptive fault-tolerant torque control law of the formation mobile robot, wherein the process is as follows:
step 6.1, after the design of the speed control law of the formation mobile robot is finished, the design of the self-adaptive fault-tolerant moment control law is required to be carried out by combining a dynamic model of the mobile robot so as to obtain the actual control moment input of the following mobile robot; first, a velocity tracking error vector is defined as shown in equation (22):
Figure FDA0003940642970000062
in the formula (22), e 1i Tracking error for the linear velocity following the mobile robot i; e.g. of the type 2i Tracking error for following the angular velocity of the mobile robot i;
step 6.2, in order to improve the control precision of the speed tracking error, designing an integral sliding mode surface as shown in a formula (23):
Figure FDA0003940642970000063
in the formula (23), S i ＝[s 1i ,s 2i ] T Wherein s is 1i ，s 2i Respectively represent the vectors S i The first and second components of (a); k vi ＝diag{k v1i ,k v2i The value is more than 0, which is the design parameter of the integral sliding mode surface;
the time derivative of equation (23) can be derived from equation (24):
Figure FDA0003940642970000064
in the formula (24), the first and second groups,
Figure FDA0003940642970000065
wherein
Figure FDA0003940642970000066
D i Satisfies the relationship:
Figure FDA0003940642970000067
wherein, b i ＝max{1,c i The (x) is an unknown constant which,
Figure FDA0003940642970000068
can be obtained by on-line calculation;
step 6.3 for unknown item b i The self-adaptive method of parameters is adopted for processing, and the self-adaptive fault-tolerant moment control law of the following mobile robot i is designed by combining a formula (24) and is shown as a formula (25):
Figure FDA0003940642970000071
in the formula (25), the first and second groups,
Figure FDA0003940642970000072
k 3i ＞0，k 4i ＞0，k 5i a control gain parameter which is more than 0 and positive; design parameter beta i The conditions need to be satisfied: beta is more than 0 i Is less than 1; sign (·) is a sign function;
Figure FDA0003940642970000073
is an unknown constant b i Is determined by the estimated value of (c),
Figure FDA0003940642970000074
the adaptive update law of (2) is shown in equation (26):
Figure FDA0003940642970000075
in the formula, k 6i Is a constant greater than zero.
CN202110972856.5A 2021-08-24 2021-08-24 Self-adaptive fault-tolerant control method for formation of multiple mobile robots with preset performance Active CN113703451B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110972856.5A CN113703451B (en) 2021-08-24 2021-08-24 Self-adaptive fault-tolerant control method for formation of multiple mobile robots with preset performance

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110972856.5A CN113703451B (en) 2021-08-24 2021-08-24 Self-adaptive fault-tolerant control method for formation of multiple mobile robots with preset performance

Publications (2)

Publication Number Publication Date
CN113703451A CN113703451A (en) 2021-11-26
CN113703451B true CN113703451B (en) 2023-03-07

Family

ID=78654311

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110972856.5A Active CN113703451B (en) 2021-08-24 2021-08-24 Self-adaptive fault-tolerant control method for formation of multiple mobile robots with preset performance

Country Status (1)

Country Link
CN (1) CN113703451B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115202349B (en) * 2022-07-14 2024-07-05 广州大学 Multi-mobile robot collaborative formation control method, device, equipment and storage medium based on communication interference

Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8346391B1 (en) * 2006-12-28 2013-01-01 Science Applications International Corporation Methods and systems for an autonomous robotic platform
KR20170095583A (en) * 2016-02-15 2017-08-23 한국전자통신연구원 Apparatus and method for adaptive task planning of robot
CN108183645A (en) * 2018-01-29 2018-06-19 黄山学院 The double power sliding-mode controls of permanent magnet synchronous motor based on extended state observer
CN108614426A (en) * 2018-06-06 2018-10-02 黄山学院 A kind of Multi Mobile Robots Formation's robust control method based on interference observer
CN108983612A (en) * 2018-08-08 2018-12-11 华南理工大学 A kind of underwater robot formation control method kept with default capabilities and connection
CN109116736A (en) * 2018-09-19 2019-01-01 南京航空航天大学 The fault tolerant control method of linear multi-agent system actuator failures based on sliding formwork
CN109143859A (en) * 2018-08-29 2019-01-04 首都师范大学 A kind of adaptive consistency control method based on nonlinear object feedback system
CN110398975A (en) * 2019-09-04 2019-11-01 西北工业大学 A kind of navigator's follower type multiple aircraft formation fault tolerant control method based on broadcast operation framework

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8346391B1 (en) * 2006-12-28 2013-01-01 Science Applications International Corporation Methods and systems for an autonomous robotic platform
KR20170095583A (en) * 2016-02-15 2017-08-23 한국전자통신연구원 Apparatus and method for adaptive task planning of robot
CN108183645A (en) * 2018-01-29 2018-06-19 黄山学院 The double power sliding-mode controls of permanent magnet synchronous motor based on extended state observer
CN108614426A (en) * 2018-06-06 2018-10-02 黄山学院 A kind of Multi Mobile Robots Formation's robust control method based on interference observer
CN108983612A (en) * 2018-08-08 2018-12-11 华南理工大学 A kind of underwater robot formation control method kept with default capabilities and connection
CN109143859A (en) * 2018-08-29 2019-01-04 首都师范大学 A kind of adaptive consistency control method based on nonlinear object feedback system
CN109116736A (en) * 2018-09-19 2019-01-01 南京航空航天大学 The fault tolerant control method of linear multi-agent system actuator failures based on sliding formwork
CN110398975A (en) * 2019-09-04 2019-11-01 西北工业大学 A kind of navigator's follower type multiple aircraft formation fault tolerant control method based on broadcast operation framework

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
考虑执行器饱和补偿的移动机器人自适应积分滑模控制;郭一军;《重庆邮电大学学报( 自然科学版)》;20181231;第30卷(第6期);第854-860页 *

Also Published As

Publication number Publication date
CN113703451A (en) 2021-11-26

Similar Documents

Publication Publication Date Title
Xu et al. Robust adaptive neural control of nonminimum phase hypersonic vehicle model
Li et al. Neuro-controller design for nonlinear fighter aircraft maneuver using fully tuned RBF networks
Wen et al. Elman fuzzy adaptive control for obstacle avoidance of mobile robots using hybrid force/position incorporation
Su et al. A neural-network-based controller for a single-link flexible manipulator using the inverse dynamics approach
Pashilkar et al. A fault-tolerant neural aided controller for aircraft auto-landing
CN107703753B (en) Fault-tolerant control method for space manipulator
CN113268064B (en) Multi-mobile-robot cooperative formation control method considering communication time delay
Li et al. Finite-time control for quadrotor based on composite barrier Lyapunov function with system state constraints and actuator faults
CN114047773A (en) Underwater ore collection robot backstepping sliding mode self-adaptive attitude control method based on extended state observer
Do et al. Neural integral backstepping hierarchical sliding mode control for a ridable ballbot under uncertainties and input saturation
CN113703451B (en) Self-adaptive fault-tolerant control method for formation of multiple mobile robots with preset performance
Liu et al. Robust control of dual-linear-motor-driven gantry stage for coordinated contouring tasks based on feed velocity
Zhou et al. Spatial path following control of an autonomous underactuated airship
Long et al. Hierarchical trajectory tracking control for ROVs subject to disturbances and parametric uncertainties
Di et al. Low-level control with actuator dynamics for multirotor UAVs
CN115453888B (en) Multi-mobile robot formation control method based on equivalent input disturbance observer
CN110647161A (en) Under-actuated UUV horizontal plane trajectory tracking control method based on state prediction compensation
CN116360258A (en) Hypersonic deformed aircraft anti-interference control method based on fixed time convergence
Koropouli et al. ESC-MRAC of MIMO systems for constrained robotic motion tasks in deformable environments
Ali et al. Control system analysis and design of quadcopter in the presence of unmodelled dynamics and disturbances
Yang et al. Multi-degree-of-freedom joint nonlinear motion control with considering the friction effect
Wapenhans et al. Optimal trajectory planning with application to industrial robots
Chen et al. Adaptive Stiffness Visual Servoing for Unmanned Aerial Manipulators With Prescribed Performance
Koubaa et al. Intelligent control for nonholonomic mobile robot including actuator dynamics
Fang et al. Compliant Contact Force Control for Aerial Manipulator of Adaptive Neural Network-Based Robust Control

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant