CN112034706A - Mobile robot fault-tolerant control method and equipment based on multi-mode switching - Google Patents

Mobile robot fault-tolerant control method and equipment based on multi-mode switching Download PDF

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CN112034706A
CN112034706A CN202010828057.6A CN202010828057A CN112034706A CN 112034706 A CN112034706 A CN 112034706A CN 202010828057 A CN202010828057 A CN 202010828057A CN 112034706 A CN112034706 A CN 112034706A
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mobile robot
mode
fault
switching
control method
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CN112034706B (en
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王书亭
谢远龙
蒋立泉
章小龙
孟杰
李鹏程
孙浩东
吴天豪
罗年猛
吴昊
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Huazhong University of Science and Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B11/00—Automatic controllers
    • G05B11/01—Automatic controllers electric
    • G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
    • G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P.I., P.I.D.
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B9/00—Safety arrangements
    • G05B9/02—Safety arrangements electric
    • G05B9/03—Safety arrangements electric with multiple-channel loop, i.e. redundant control systems
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/0055—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot with safety arrangements
    • G05D1/0077—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot with safety arrangements using redundant signals or controls
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/0088—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot characterized by the autonomous decision making process, e.g. artificial intelligence, predefined behaviours
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • 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
    • G05D1/0214—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory in accordance with safety or protection criteria, e.g. avoiding hazardous areas

Abstract

The invention belongs to the technical field related to mobile robot control, and discloses a mobile robot fault-tolerant control method and equipment based on multi-mode switching. The invention comprehensively considers the differential operation modes of the mobile robot, carries out unified modeling on the mobile robot, realizes the self-adaptive switching operation of various operation modes through the logic switching criterion of multi-target evaluation, and simultaneously considers the average residence time of the switching, thereby ensuring the operation efficiency and the control precision of the system.

Description

Mobile robot fault-tolerant control method and equipment based on multi-mode switching
Technical Field
The invention belongs to the technical field related to mobile robot control, and particularly relates to a mobile robot fault-tolerant control method and mobile robot fault-tolerant control equipment based on multi-mode switching.
Background
The trackless autonomous mobile robot can reduce the production cost and improve the production efficiency, is successfully applied to the fields of assembly, logistics, public health and epidemic prevention, national defense science and technology and the like, is an important pillar of intelligent manufacturing industry, has an important mark of national industrial intelligence level in the technical development level, and has important strategic significance.
The conventional trackless autonomous mobile robot generally adopts driving modes such as a double-drive differential wheel, a four-drive wheat wheel and a single steering wheel, wherein the double-drive differential wheel cannot translate, and needs to turn around repeatedly in a scene with dense logistics stop stations, so that the efficiency is low, the movement speed is low in a large-load application scene, the requirement on the flatness of the bottom surface of the wheat wheel is high, and the cost of the steering wheel is high. Compared with the driving mode, the driving mode of the four-wheel independent driving and independent full steering wheel hub motor has obvious advantages in the aspects of operation stability, flexibility, bearing capacity, ground adaptability and the like. From four-wheel corner distribution analysis, the full-steering mobile robot can be configured in modes such as origin rotation (accurate pose adjustment), diagonal movement (point-to-point rapid movement) and adjustable ackermann (movement and turning), so that singular configurations and obstacles can be avoided, and the rigidity of a Cartesian space is enhanced. Differential maneuvering mode motion characteristics such as ackman, double ackman, diagonal, etc. of a redundantly driven mobile robot are generally described in the documents "Ni J, Hu J, xing C l.an AWID and AWIS X-by-wire UGV: design and systematic mechanics dynamics control [ J ]. IEEE Transactions on Intelligent Transportation Systems,2018,20(2):654 666".
Although the existing literature describes the multi-mode motion characteristics of the mobile robot, the following two defects exist in the trajectory tracking control of the mobile robot: 1) adaptive switching control research of multiple modes (Ackerman, double Ackerman, diagonal and other modes) is not carried out, so that the control precision and the operation efficiency are limited; 2) the failure of the actuator is not considered, the multi-mode mobility of the mobile robot is improved, the complexity of the system and the number of drivers are increased, and the failure probability is increased. For example, the motor (actuator) may be involved in unpowered free rolling, such as a band-type brake in a fixed position, resulting in friction between the locked wheel and the ground; motor failure can result in loss of handling and steering performance and even system rollover.
Disclosure of Invention
Aiming at the defects or improvement requirements in the prior art, the invention provides a mobile robot fault-tolerant control method and equipment based on multi-mode switching, which utilize the redundant driving characteristics of a mobile robot to establish multi-mode supervision criteria and switching criteria, realize the autonomous switching operation of differentiated operation modes (including ackermann, double ackermann, diagonal movement and in-situ rotation), and simultaneously ensure the stability of a closed-loop system under the condition of driving wheel faults through fault-tolerant torque distribution, thereby realizing the accurate track tracking control of the mobile robot.
To achieve the above object, according to an aspect of the present invention, there is provided a fault-tolerant control method for a mobile robot based on multi-mode switching, the method including the steps of:
(1) designing a multi-mode switching supervision criterion based on a multi-mode operation dynamic model and following errors of a redundancy driving mobile platform;
(2) constructing a control target evaluation function based on a mode switching supervision variable xi (t) in the multi-mode switching supervision criterion;
(3) determining a logical switching criterion based on the control target evaluation function, the logical switching criterion being:
a if the system reference track angle of the next stage is less than or equal to 90 degrees, setting the switching signal sigma to be 1 and configuring the parameter k to be-1, and simultaneously, setting the virtual front wheel steering anglef(t) set to 90 degrees for quick pose adjustment;
b, if the system reference track angle in the next stage is larger than 90 degrees, performing multi-mode switching control through the following formula:
Figure BDA0002636949690000031
wherein t represents the current time; (t +1) represents the next time; σ (t) is a switching signal at time t;
Figure BDA0002636949690000037
so as to make
Figure BDA0002636949690000038
A Lyapunov function constructed for the variables;
Figure BDA0002636949690000039
a sliding mode matrix constructed by following errors;
Figure BDA00026369496900000310
is a control objective evaluation function; tau isadRepresenting the average residence time of the system mode.
Further, the step (3) is followed by a step of performing optimal torque distribution on the redundant driving mobile platform.
Further, a torque distribution optimizing objective function is adopted to realize the torque distribution to the driving wheels, and the torque distribution optimizing objective function is as follows:
Figure BDA0002636949690000032
in the formula (I), the compound is shown in the specification,
Figure BDA0002636949690000033
representing the moment increment at two moments; fi x(t) is the drive torque at time t for the ith wheel;
Figure BDA0002636949690000034
the expected value of the yaw moment is taken;
Figure BDA0002636949690000035
distributing the generated yaw moment for the moment of the current optimization time; mu.s1，μ2，μ3As a weight factor, satisfy mu1+μ2+μ3＝1。
Further, an optimization algorithm is adopted to optimize the torque distribution optimization objective function so as to obtain an optimal driving wheel torque distribution sequence under the fault condition.
Further, σ ═ 1, which indicates that the mobile robot switches to the pivot mode; σ ═ 2, indicating that the mobile robot switched to ackermann mode; σ ═ 3, indicating that the mobile robot switched to conventional dual ackermann mode; σ ═ 4, indicating that the mobile robot switched to the crab mode.
Further, the formula for the calculation of the mode switching supervision variable ξ (t) in the multi-mode switching supervision criterion based on the following error determination is:
Figure BDA0002636949690000036
in the formula (I), the compound is shown in the specification,
Figure BDA0002636949690000041
is the derivative of ξ (t); gamma rayσThe system energy attenuation coefficient; is a preset positive number.
Wherein, the following error is calculated by the following formula:
βe(t)＝βf(t)-βd(t)，γe(t)＝γf(t)-γd(t)
wherein, betae(t) and γe(t) respectively representing a sideslip angle following error and a yaw angle following error; beta is ad(t) is a sideslip angle reference command; gamma rayd(t) is a yaw rate reference command; beta is af(t) is a sideslip angle feedback value; gamma rayfAnd (t) is a yaw rate feedback value.
Further, the following error beta is utilizede(t) and γe(t) designing a fractional order PID controller to implement direct yaw moment control of the mobile robot system to obtain a corresponding side slip angle feedback value βf(t) and yaw rate feedback value γf(t), the fractional order PID controller is:
Figure BDA0002636949690000042
Figure BDA0002636949690000043
wherein s represents a complex field; cβAnd CγRespectively for controlling the sideslip angle and yaw rate,
Figure BDA0002636949690000044
and
Figure BDA0002636949690000045
respectively representing the proportionality coefficients of the controllers;
Figure BDA0002636949690000046
and
Figure BDA0002636949690000047
respectively, represent the integral parameters of the controller,
Figure BDA0002636949690000048
and
Figure BDA0002636949690000049
a differential parameter indicative of a controller;βandγis the fractional order of the controller.
Further, the sideslip angle reference command and the yaw rate reference command are determined by the following equations:
Figure BDA00026369496900000410
Figure BDA00026369496900000411
Figure BDA00026369496900000412
wherein s represents a complex field; omegaγAnd ωβRepresents the cut-off frequency; l is the length of the vehicle body; cfAnd CrRepresenting the cornering stiffness coefficients of the front and rear wheels, respectively; upsilon isx(t) longitudinal velocity at the center of gravity; m represents a vehicle body mass; lfAnd lrRespectively, the distances from the center of gravity of the vehicle body to the front and rear axles.
Further, a four-wheel drive model and a virtual front-rear wheel model are considered at the same time, and the mathematical expression of the multi-mode operation dynamic model is as follows:
Figure BDA0002636949690000051
Figure BDA0002636949690000052
Figure BDA0002636949690000053
wherein m represents a vehicle body mass; upsilon isx(t) longitudinal velocity at the center of gravity;
Figure BDA0002636949690000054
and
Figure BDA0002636949690000055
respectively representing the longitudinal and lateral tire forces at the nth drive wheel; β (t) and γ (t) represent the sideslip angle and yaw angular velocity, respectively;
Figure BDA0002636949690000056
and
Figure BDA0002636949690000057
respectively representing the derivative of the sideslip angle and the derivative of the yaw rate; i iszIs the moment of inertia; lfAnd lrRespectively showing the distances from the gravity center of the vehicle body to the front axle and the rear axle;r(t) represents a virtual rear wheel steering angle; mz(t) yaw moment generated by four-wheel traction moment; d is the width of the vehicle body;
Figure BDA0002636949690000058
Figure BDA0002636949690000059
and
Figure BDA00026369496900000510
respectively representing longitudinal driving forces acting on a rear right tire, a rear left tire, a front right tire and a front left tire;
wherein a virtual rear wheel steering angle is taken into accountr(t) is represented byr(t)＝kf(t), where k is a configuration parameter representing different operating modes:
Figure BDA00026369496900000511
according to another aspect of the present invention, there is provided an apparatus employing the fault-tolerant control method of a mobile robot based on multi-mode switching as described above.
Generally, compared with the prior art, the mobile robot fault-tolerant control method and device based on multi-mode switching provided by the invention mainly have the following beneficial effects:
1. the logic switching criterion is determined based on the multi-fault-tolerant control target evaluation function, and then the self-adaptive switching operation of multiple operation modes is realized according to the comparison result of the system reference track angle and 90 degrees at the next stage, so that the dynamic tracking performance of the system is ensured, and the operation efficiency and the control precision of the system are improved.
2. The invention considers the angle information of the reference track, thereby ensuring the running stability of the system through the pivot rotation mode when the system encounters acute and sharp turns and inhibiting the overshoot of the system.
3. The invention provides a multi-fault-tolerant control target evaluation function, and the mode switching average residence time is used as one of the weighing factors of the switching decision, thereby improving the switching speed and the switching efficiency of the system.
4. The torque distribution optimizing objective function is adopted to realize the torque distribution to the driving wheel, and the torque distribution optimizing objective function is optimized by utilizing an optimizing algorithm, so that the optimal driving wheel torque distribution sequence under the fault condition can be obtained, and the operation stability and the control precision are improved.
Drawings
FIG. 1 is a flow chart of a mobile robot fault-tolerant control method based on multi-mode switching provided by the invention;
fig. 2 (a) and (b) are schematic diagrams of a four-wheel drive model and a virtual front-rear wheel model of a mobile robot, respectively.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Referring to fig. 1 and fig. 2, the fault-tolerant control method for a mobile robot based on multi-mode switching provided by the present invention mainly includes the following steps:
step one, establishing a multi-mode operation dynamic model of a redundancy driving mobile platform.
Specifically, a four-wheel drive model and a virtual front-rear wheel model are considered at the same time, and the mathematical expression of the multi-mode operation dynamic model is as follows:
Figure BDA0002636949690000071
Figure BDA0002636949690000072
Figure BDA0002636949690000073
wherein m represents a vehicle body mass;
Figure BDA0002636949690000074
and
Figure BDA0002636949690000075
respectively representing a longitudinal tire force and a lateral tire force at the nth drive wheel; β (t) and γ (t) represent the sideslip angle and yaw angular velocity, respectively;
Figure BDA0002636949690000076
and
Figure BDA0002636949690000077
respectively representing the derivative of the sideslip angle and the derivative of the yaw rate; i iszIs the moment of inertia; lfAnd lrRespectively showing the distances from the gravity center of the vehicle body to the front axle and the rear axle;f(t) andr(t) representing virtual front and rear wheel steering angles, respectively; mz(t) yaw moment generated by four-wheel traction moment; d is the width of the vehicle body;
Figure BDA0002636949690000078
Figure BDA0002636949690000079
and
Figure BDA00026369496900000710
respectively representing longitudinal driving forces acting on a rear right tire, a rear left tire, a front right tire and a front left tire;
wherein a virtual rear wheel steering angle is taken into accountr(t) is represented byr(t)＝kf(t), where k is a configuration parameter representing different operating modes: where k is a configuration parameter representing different operating modes:
Figure BDA00026369496900000711
and step two, acquiring a data signal at the current moment and calculating a following error at the current moment. The data signals are state variable feedback values, including sideslip angle and yaw rate.
Specifically, the following error is calculated by the following formula:
βe(t)＝βf(t)-βd(t)，γe(t)＝γf(t)-γd(t)
wherein, betae(t) and γe(t) respectively representing a sideslip angle following error and a yaw angle following error; beta is ad(t) is a sideslip angle reference command; gamma rayd(t) is a yaw rate reference command; beta is af(t) is a slip angleA feedback value; gamma rayfAnd (t) is a yaw rate feedback value.
In order to realize the control of the mobile robot, a sideslip angle reference instruction and a yaw rate reference instruction are determined by the following formulas:
Figure BDA0002636949690000081
Figure BDA0002636949690000082
Figure BDA0002636949690000083
wherein s represents a complex field; omegaγAnd ωβRepresents the cut-off frequency; l is the length of the vehicle body; cfAnd CrRespectively representing cornering coefficients, upsilon, of front and rear wheelsx(t) longitudinal velocity at the center of gravity; upsilon isx(t) is the longitudinal velocity at the center of gravity.
The present embodiment employs a fractional order PID controller to obtain the corresponding feedback sideslip angle βf(t) and yaw rate γf(t), the fractional order PID controller is:
Figure BDA0002636949690000084
Figure BDA0002636949690000085
in the formula, CβAnd CγRespectively used for controlling the sideslip angle and the yaw angle speed;
Figure BDA0002636949690000086
and
Figure BDA0002636949690000087
a scaling factor representing the controller;
Figure BDA0002636949690000088
and
Figure BDA0002636949690000089
represents an integration parameter of the controller;
Figure BDA00026369496900000810
and
Figure BDA00026369496900000811
a differential parameter indicative of a controller;βandγis the fractional order of the controller. Preferably, the setting in this embodiment is such that,
Figure BDA0002636949690000091
Figure BDA0002636949690000092
β＝0.5，γ＝0.9。
and step three, determining multimode switching supervision criterion based on multimode switching based on the obtained following error.
Specifically, the calculation formula of the multimode-switching-based mode switching supervision variable ξ (t) based on the following error determination is:
Figure BDA0002636949690000093
in the formula (I), the compound is shown in the specification,
Figure BDA0002636949690000094
is the derivative of ξ (t); gamma rayσThe system energy attenuation coefficient; is a preset positive number, which is set to 0.01;
Figure BDA0002636949690000095
so as to make
Figure BDA0002636949690000096
A Lyapunov function constructed for the variables;
Figure BDA0002636949690000097
is a sliding-mode matrix constructed with a following error, wherein,
Figure BDA0002636949690000098
and
Figure BDA0002636949690000099
respectively represents betae(t) and γe(t) derivative of (t). Wherein the Lyapunov function
Figure BDA00026369496900000910
The expression is as follows:
Figure BDA00026369496900000911
in the formula (I), the compound is shown in the specification,Ta transpose calculation representing a matrix; k is a radical of1And k2Is a variable with a positive value, where k is the value1＝0.1，k2＝0.2。
And step four, constructing a control target evaluation function based on the mode switching supervision variable zeta (t) in the mode switching supervision criterion.
Specifically, the expression of the control target evaluation function is:
Figure BDA00026369496900000912
in the formula, τad＝ln((1+)μ)/γσRepresenting the system mode switching time, wherein ln is a logarithmic function with a natural number e as a base; μ represents a system stability coefficient; omega1And ω2Is a weight factor with the value of (0,1) and satisfies omega1+ω2Where 1 takes the value ω1＝0.1，ω20.9; xi is the angle of the reference track; sign is a sign function.
And step five, determining a logic switching criterion based on the control target evaluation function.
Specifically, in consideration of a sharp turning situation, if a special double ackermann mode with a steering angle of 90 degrees is used, namely the mobile robot pose can be rapidly adjusted in an in-place rotation mode, and the following error caused by the turning failure is prevented from being too large, the adopted logic switching criterion is as follows:
(1) if the reference track angle of the system at the next stage is less than or equal to 90 degrees, namely xi is less than or equal to 90 degrees,
Figure BDA0002636949690000101
indicating that the mobile robot is about to make a sharp turn, the switching signal σ is set to 1 and k is set to-1 while the front wheel steering angle is setfThe setting is 90 degrees, so that the pose can be adjusted quickly;
(2) if the system reference track angle estimation of the next stage is more than 90 degrees, namely xi is more than 90 degrees, J (tau)ad,Vσ(s (t)), ξ (t)) > 0, the multimode switching control is performed by the following formula:
Figure BDA0002636949690000102
wherein t represents the current time, and (t +1) represents the next time; σ (t) is a switching signal at time t;
Figure BDA00026369496900001010
so as to make
Figure BDA0002636949690000104
A Lyapunov function constructed for the variables;
Figure BDA0002636949690000105
a sliding mode matrix constructed by following errors;
Figure BDA0002636949690000106
is a control objective evaluation function.
In the present embodiment, σ is a switching signal representing the operation mode; sigma is 1, which indicates that the mobile robot is switched to the in-place rotation mode; σ ═ 2, indicating that the mobile robot switched to ackermann mode; σ ═ 3, indicating that the mobile robot switched to conventional dual ackermann mode; σ ═ 4, indicating that the mobile robot switched to the crab mode.
And step six, performing optimal torque distribution on the redundant driving mobile platform.
Specifically, driving torques of four tires are performed in consideration of the problem of failure of the driving wheels
Figure BDA0002636949690000107
Figure BDA0002636949690000108
And
Figure BDA0002636949690000109
the distribution of (a), characterizing the wheel torque under fault conditions, is:
Ti(t)＝ηi(t)Fi x(t)+(1-ηi(t))ui(t)
wherein i ═ rr, rl, fr, fl respectively denote right rear wheel, left rear wheel, right front wheel, left front wheel, uiRepresenting the friction with the ground, etai(t) is the failure coefficient:
Figure BDA0002636949690000111
in the formula etai(t)＝0,uiWhen the (t) is 0, the wheel has no driving force, but the motor has no internal contracting brake, so the contact force with the ground is rolling friction force; etai(t)＝0,
Figure BDA0002636949690000112
When a certain driving wheel fails, the wheel has no driving force, and thus the contact force with the ground is sliding friction.
The moment distribution optimizing objective function is adopted to realize the moment distribution to the wheel without faults under the condition of faults, and the moment distribution optimizing objective function is as follows:
Figure BDA0002636949690000113
in the formula,. DELTA.Fi x(t)＝Fi x(t+1)-Fi x(t) represents the torque increment at two moments; fi x(t) is the drive torque at time t for the ith wheel;
Figure BDA0002636949690000114
the expected value of the yaw moment is taken;
Figure BDA0002636949690000115
distributing the generated yaw moment for the moment of the current optimization time; mu.s1，μ2，μ3As a weight factor, satisfy mu1+μ2+μ3Where the value μ is given1＝0.8，μ1＝0.1，μ1＝0.1。
And optimizing the torque distribution optimizing objective function by utilizing an optimizing algorithm to obtain an optimal driving wheel torque distribution sequence under the fault condition, and preferably, optimizing and solving by adopting a particle swarm algorithm.
The particle swarm algorithm is adopted as follows:
Figure BDA0002636949690000116
Figure BDA0002636949690000117
Figure BDA0002636949690000118
in the formula, k' represents the current iteration number; q is 1, 2, 3 … is the number of the particle; a represents a system parameter to be identified;
Figure BDA0002636949690000119
and
Figure BDA00026369496900001110
respectively representing the solution space positions with iteration periods of k 'and k' + 1;
Figure BDA00026369496900001111
and
Figure BDA00026369496900001112
representing the moving speeds of the iteration periods k 'and k' +1, respectively; c. C1,c2Is the acceleration constant; r is1,r2A random number from 0 to 1; pbestqjAnd gbestqjRespectively representing a local optimal solution and a global optimal solution;
Figure BDA00026369496900001113
is a weight coefficient, set here as
Figure BDA00026369496900001114
And step seven, judging whether a termination condition is met, if so, terminating the program operation, otherwise, turning to the step two. Specifically, the termination condition is preset, and may be, for example, a running time.
The invention also provides equipment adopting the mobile robot fault-tolerant control method based on multimode switching.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A mobile robot fault-tolerant control method based on multi-mode switching is characterized by comprising the following steps:
(1) designing a multi-mode switching supervision criterion based on a multi-mode operation dynamic model and following errors of a redundancy driving mobile platform;
(2) constructing a control target evaluation function based on a mode switching supervision variable xi (t) in the multi-mode switching supervision criterion;
(3) determining a logical switching criterion based on the control target evaluation function, the logical switching criterion being:
a if the system reference track angle of the next stage is less than or equal to 90 degrees, setting the switching signal sigma to be 1 and configuring the parameter k to be-1, and simultaneously, setting the virtual front wheel steering anglef(t) set to 90 degrees for quick pose adjustment;
b, if the system reference track angle in the next stage is larger than 90 degrees, performing multi-mode switching control through the following formula:
Figure FDA0002636949680000011
wherein t represents the current time; (t +1) represents the next time; σ (t) is a switching signal at time t;
Figure FDA0002636949680000012
so as to make
Figure FDA0002636949680000013
A Lyapunov function constructed for the variables;
Figure FDA0002636949680000014
a sliding mode matrix constructed by following errors;
Figure FDA0002636949680000015
is a control objective evaluation function; tau isadRepresenting the average residence time of the system mode.
2. The fault-tolerant control method for the mobile robot based on the multi-mode switching as claimed in claim 1, characterized in that: and (4) after the step (3), performing optimal torque distribution on the redundant driving mobile platform.
3. The fault-tolerant control method for the mobile robot based on the multi-mode switching as claimed in claim 2, characterized in that: the torque distribution of the driving wheels is realized by adopting a torque distribution optimizing objective function, wherein the torque distribution optimizing objective function is as follows:
Figure FDA0002636949680000021
in the formula,. DELTA.Fi x(t)＝Fi x(t+1)-Fi x(t) represents the torque increment at two moments; fi x(t) is the drive torque at time t for the ith wheel;
Figure FDA0002636949680000022
the expected value of the yaw moment is taken;
Figure FDA0002636949680000023
distributing the generated yaw moment for the moment of the current optimization time; mu.s1，μ2，μ3As a weight factor, satisfy mu1+μ2+μ3＝1。
4. The fault-tolerant control method for the mobile robot based on the multi-mode switching as claimed in claim 3, characterized in that: and optimizing the torque distribution optimizing objective function by adopting an optimizing algorithm to obtain an optimal driving wheel torque distribution sequence under the fault condition.
5. The fault-tolerant control method for a mobile robot based on multimode switching according to any one of claims 1 to 4, characterized in that: sigma is 1, which indicates that the mobile robot is switched to the in-place rotation mode; σ ═ 2, indicating that the mobile robot switched to ackermann mode; σ ═ 3, indicating that the mobile robot switched to conventional dual ackermann mode; σ ═ 4, indicating that the mobile robot switched to the crab mode.
6. The fault-tolerant control method for a mobile robot based on multimode switching according to any one of claims 1 to 4, characterized in that: the formula for the calculation of the mode switching supervision variable ξ (t) in the multi-mode switching supervision criterion based on the following error determination is:
Figure FDA0002636949680000024
in the formula (I), the compound is shown in the specification,
Figure FDA0002636949680000025
is the derivative of ξ (t); gamma rayσThe system energy attenuation coefficient; is a preset positive number.
Wherein, the following error is calculated by the following formula:
βe(t)＝βf(t)-βd(t)，γe(t)＝γf(t)-γd(t)
wherein, betae(t) and γe(t) respectively representing a sideslip angle following error and a yaw angle following error; beta is ad(t) is a sideslip angle reference command; gamma rayd(t) is a yaw rate reference command; beta is af(t) is a sideslip angle feedback value; gamma rayfAnd (t) is a yaw rate feedback value.
7. The fault-tolerant control method for mobile robots based on multimode switching according to claim 6, characterized in that: using the following error betae(t) and γe(t) designing a fractional order PID controller to implement direct yaw moment control of the mobile robot system to obtain a corresponding side slip angle feedback value βf(t) and yaw rate feedback value γf(t), the fractional order PID controller is:
Figure FDA0002636949680000031
Figure FDA0002636949680000032
wherein s represents a complex field; cβAnd CγRespectively for controlling the sideslip angle and yaw rate,
Figure FDA0002636949680000033
and
Figure FDA0002636949680000034
respectively representing the proportionality coefficients of the controllers;
Figure FDA0002636949680000035
and
Figure FDA0002636949680000036
respectively, represent the integral parameters of the controller,
Figure FDA0002636949680000037
and
Figure FDA0002636949680000038
a differential parameter indicative of a controller;βandγis the fractional order of the controller.
8. The fault-tolerant control method for mobile robots based on multimode switching according to claim 6, characterized in that: the sideslip angle reference command and the yaw rate reference command are determined by the following formulas:
Figure FDA0002636949680000039
Figure FDA00026369496800000310
Figure FDA00026369496800000311
wherein s represents a complex field; omegaγAnd ωβRepresents the cut-off frequency; l is the length of the vehicle body; cfAnd CrRepresenting the cornering stiffness coefficients of the front and rear wheels, respectively; upsilon isx(t) longitudinal velocity at the center of gravity; m represents a vehicle body mass; lfAnd lrRespectively, the distances from the center of gravity of the vehicle body to the front and rear axles.
9. The fault-tolerant control method for a mobile robot based on multimode switching according to any one of claims 1 to 4, characterized in that: simultaneously considering a four-wheel drive model and a virtual front and rear wheel model, the mathematical expression of the multi-mode operation dynamic model is as follows:
Figure FDA0002636949680000041
Figure FDA0002636949680000042
Figure FDA0002636949680000043
wherein m represents a vehicle body mass; upsilon isx(t) longitudinal velocity at the center of gravity;
Figure FDA0002636949680000044
and
Figure FDA0002636949680000045
respectively representing the longitudinal and lateral tire forces at the nth drive wheel; beta (t) and gamma (t) represent the sideslip angle and yaw rate, respectivelyDegree;
Figure FDA0002636949680000046
and
Figure FDA0002636949680000047
respectively representing the derivative of the sideslip angle and the derivative of the yaw rate; i iszIs the moment of inertia; lfAnd lrRespectively showing the distances from the gravity center of the vehicle body to the front axle and the rear axle;r(t) represents a virtual rear wheel steering angle; mz(t) yaw moment generated by four-wheel traction moment; d is the width of the vehicle body;
Figure FDA0002636949680000048
Figure FDA0002636949680000049
and
Figure FDA00026369496800000410
respectively representing longitudinal driving forces acting on a rear right tire, a rear left tire, a front right tire and a front left tire;
wherein a virtual rear wheel steering angle is taken into accountr(t) is represented byr(t)＝kf(t), where k is a configuration parameter representing different operating modes:
Figure FDA00026369496800000411
10. an apparatus employing the multimode switch-based mobile robot fault-tolerant control method of any one of claims 1-9.
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