CN113885499B - Robot track fault-tolerant control method for detection in cavity - Google Patents
Robot track fault-tolerant control method for detection in cavity Download PDFInfo
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Abstract
The invention belongs to the field of track tracking fault-tolerant control of a detection robot in a cavity, and provides a track fault-tolerant control method of the detection robot in the cavity, which comprises the following steps: firstly, overcoming the influence of gravity on the movement of the detection robot in the cavity in an adsorption mode; secondly, establishing a coordinate conversion equation of the detection robot, converting a three-dimensional coordinate system of a cavity in the cavity into a plane inertial coordinate system through the coordinate conversion equation, and establishing a plane kinematics model and a dynamics model of the detection robot; then, based on the planar kinematic model and the dynamic model, establishing a state space equation for detecting the failure of the actuator of the robot; then, observing a fault signal of the actuator by designing a fault observer, and compensating in a subsequent controller; and finally, utilizing the observation result of the observer, adopting a fractional order sliding mode control method, and designing a controller to carry out track tracking fault-tolerant control on the robot for detection.
Description
Technical Field
The invention relates to the field of track tracking fault-tolerant control of a detection robot in a cavity, in particular to a track fault-tolerant control method of a detection robot in a cavity.
Background
In the modern manufacturing industry, a cylindrical design scheme is adopted for a plurality of devices, and the devices are difficult to ensure not to be damaged in the production, manufacture and transportation processes, so that the device has great significance for internal detection and later maintenance of the devices. Because the space inside the partial cavity is narrow, the manual work is difficult to enter, and the mobile robot is adopted to replace the manual work to enter the cavity for maintenance, so that the scheme is safe, convenient and reliable. The Mecanum wheel omnidirectional mobile robot (Mecanum Wheel Omnidirectional Robot, MWOR) can move in all directions under the condition that the posture of the wheels is not changed, and the Mecanum wheel omnidirectional mobile robot reaches any reachable position of the cavity equipment, so that the detection of the equipment in the cavity is more comprehensive, and the MWOR is used for entering the cavity for maintenance, so that the detection effect rate can be greatly improved, and the method has great significance in the research on the control method of the MWOR in the cavity.
PID control (Proportion Integration Differentiation Control), backstepping control (Back Stepping Control) neural network control (Neural Networks Control), sliding mode control (Sliding Mode Control) and the like are control methods commonly used for mobile robots today. PID control is only suitable for simple control, is sensitive to environmental parameter change and is troublesome to set and optimize; the backstepping control depends on an accurate mathematical model, but the accurate model of various mobile robots is difficult to obtain in the actual control process; the neural network control has strong nonlinear approximation capability, but the number of network layers and the number of nodes in each layer are difficult to determine; the sliding mode variable structure control is insensitive to external interference and disturbance, has certain robustness, but is easy to cause buffeting.
Disclosure of Invention
The invention aims to provide a robot track fault-tolerant control method for detection in a cavity, which realizes track control of an omnidirectional mobile robot in the cavity, considers strong robustness of sliding mode variable structure control, improves traditional sliding mode variable structure control, realizes the purpose of weakening buffeting, and obtains better track control effect.
The invention solves the technical problems and adopts the following technical scheme:
the invention provides a robot track fault-tolerant control method for detection in a cavity, which comprises the following steps:
and 5, utilizing an observation result of the observer, adopting a fractional order sliding mode control method, and designing a controller to carry out track tracking fault-tolerant control on the robot for detection.
Further, step 1 specifically refers to: the adsorption force of the detection robot is equal to the forward pressure to be compensated, so that ideal conditions of a planar kinematic model and a dynamic model of the detection robot in the cavity are achieved.
Further, the robot needs the forward pressure F compensated by adsorption mode at the angle gamma c The size is as follows:
F c ＝mg(1-cosγ+f r sinγ)
wherein m is the mass of the detection robot, g is the gravitational acceleration, f r The friction coefficient between the detection robot and the inner wall surface of the cavity is the friction coefficient between the detection robot and the inner wall surface of the cavity;
the adsorption force is calculated by adopting the attachment mode of the negative pressure air chamber, and the calculation formula is as follows:
F x ＝0.01(P 0 -P a )·S
wherein ,P0 Is the ambient pressure, P a The pressure in the negative pressure air chamber is S, and the area of the upper surface of the negative pressure air chamber is S.
Further, in step 2, the conversion relationship between the three-dimensional coordinate system and the planar inertial coordinate system in the cavity is:
wherein [ γdρ ]] T For the detection of the three-dimensional coordinate system coordinates of the robot in the cavity, R GIS Is the radius of the cross section of the cavity body, [ x ] p y p φ] T To detect the attitude of a robot in a planar world coordinate system.
The conversion relation between the plane inertial coordinate system and the robot body coordinate system for detection is as follows:
wherein [xm y m ] T In order to detect the coordinates of the body of the robot,
a transformation matrix of robot plane coordinates with phi as an argument with respect to body coordinates is represented.
The planar kinematic model and the dynamic model of the robot for detection are as follows:
wherein R is a real number, is the radius of the Mecanum wheel of the robot,
for detecting the rotational angular velocity of each wheel of the robot, τ= [ τ ] 1 τ 2 τ 3 τ 4 ] T D for detecting driving moment output by four driving motors of robot θ ∈R 4×4 Represents a viscous friction matrix, matrix->
For converting the matrix, the conversion relation between the rotation angular speed of the robot wheel and the movement speed of the robot is represented, the matrix +.>
Representing the transformation relationship between the angular acceleration of the robot wheel rotation and the driving moment +.>
Are all constant, a is half of the body width of the robot for detection, b is half of the body length, J ω For moment of inertia of the wheel about the centre of rotation, J Z To detect the moment of inertia of the robot about the center of rotation.
Further, in step 3, the state space equation of the detection robot in the plane inertial coordinate system is:
wherein ：
f(x 1 ,x 2 ) Is state x 1 ,x 2 Is a non-linear function of (c) and (d),
and />
Deriving a matrix variable defined for the simplified expression in the engineering for the formula;
when the detection robot actuator fails, the desired control torque does not coincide with the actual output torque, and therefore the detection robot actuator failure equation is expressed as:
τ F ＝(1-η)τ+στ s
wherein ,τF Representing the actual output of the actuator in the event of a failure, τ being the desired actuator output of the design, η being a positive number greater than zero and less than 1, τ s Representing a time-varying actuator bias fault, σ=1 when the actuator bias fault exists, otherwise, σ=0;
when the detecting robot fails, substituting a detecting robot actuator failure formula into a state space equation of the detecting robot in a plane inertial coordinate system, wherein tau is tau F Instead of this.
Further, the state space equation for detecting the failure of the robot actuator is expressed simply as:
wherein F is a composite fault signal.
Further, in step 4, when the fault observer is designed to observe the fault signal of the actuator, the simplified expression of the state space equation of the fault of the robot actuator for detection is rewritten as:
let z= [ x ] T 1 x T 2 F] T And assuming that the fault signal F is differentiable, an expansion state equation is obtained:
wherein ：
therefore, the designed fault observer is as follows:
wherein ,
respectively represent x 1 、x 2 And an estimated value of F->
For observer gain, beta 0 Is real, represents the observer bandwidth, the value of which is determined by the change frequency of faults, the faster the faults change, beta 0 The larger the value that needs to be taken, the a 1 ,a 2 ,a 3 The positive number is a parameter to be designed and needs to be given according to actual conditions;
further, the step 5 specifically includes the following steps:
step 501, defining a track tracking error as:
e＝x 1 -x d
wherein ,x1 To detect the actual position of the robot, x d Is the target position;
step 502, selecting a fractional order switching plane:
where ε is a constant to be designed that is greater than 0.
Step 503, selecting a supercoiled approach algorithm:
wherein ：
λ＝diag(λ 1 ,λ 2 ,λ 3 )，K 1 ＝[k 11 ,0，0；0,k 12 ，0；0 0k 13 ]，K 2 ＝[k 21 ,0,0；0,k 22 ,0；0,0,k 23 ]
|s| 1/2 ＝diag(|s 1 | 1/2 ,|s 2 | 1/2 ,|s 3 | 1/2 )，sign(s)＝[sign(s 1 ),sign(s 2 ),sign(s 3 )] T
wherein ,λ1 ，λ 2 ，λ 3 ，k ij All are positive numbers greater than 0, sign (·) is a sign function, D α For fractional differential operators, α is a positive number greater than 0 and less than 1, K 1 ,K 2 Is a gain matrix;
step 504, the fractional differential calculation method is as follows:
D α [f(e)]represents an alpha-order derivative of the function f (e), where f (e) is the function of step 502 with respect to the tracking error e, Γ (n-t) represents a gamma function, 0<n-α<1, n is an integer less than 1+alpha, t isAn integration starting point, here 0, when α is greater than-1 and less than 0, the fractional differential is converted into fractional integration;
the fractional order integral calculation method comprises the following steps:
I μ [f(e)]representing mu-order integration of the function f (e);
the derivative of the fractional order switching plane can be obtained:
simplified expression formula and fractional order switching plane formula of state space equation for detecting robot actuator fault, and observing the obtained fault signal by using fault observer
Instead of F, it is possible to obtain:
the method has the beneficial effects that through the method for controlling the track fault tolerance of the robot for detecting in the cavity, the traditional sliding mode structure control is improved, the fractional order theory is introduced into the sliding mode control, the buffeting of the SMC controller is reduced under the condition of ensuring the robustness of the system, the control effect is improved, the faster convergence time, the smaller overshoot and the smaller steady-state tracking error are obtained.
Drawings
FIG. 1 is a flow chart of a method for fault-tolerant control of a robot trajectory for detection in a chamber according to an embodiment of the present invention;
FIG. 2 is a working schematic diagram of a track control method of an in-cavity maintenance robot according to an embodiment of the invention;
FIG. 3 is a front view of a three-dimensional coordinate system of the cavity interior of the cavity according to an embodiment of the present invention;
FIG. 4 is a top view of a three-dimensional coordinate system of the cavity interior of the cavity according to an embodiment of the present invention;
FIG. 5 is a world coordinate system and a body coordinate system of a robot for inspection according to an embodiment of the present invention;
fig. 6 is a diagram of simulation results according to an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is described in detail below with reference to the accompanying drawings and the embodiments.
Examples
The embodiment of the invention provides a fault-tolerant control method for a robot track for detection in a cavity, which is shown in a flowchart of figure 1, wherein the method comprises the following steps:
s1, overcoming the influence of gravity on the motion of the detection robot in the cavity in an adsorption mode;
s2, establishing a coordinate conversion equation of the detection robot, converting a three-dimensional coordinate system of a cavity in the cavity into a plane inertial coordinate system through the coordinate conversion equation, and establishing a plane kinematics model and a dynamics model of the detection robot;
s3, establishing a state space equation for detecting the fault of the actuator of the robot based on the planar kinematic model and the dynamic model;
s4, observing fault signals of the actuator through a designed fault observer, and compensating in a subsequent controller;
s5, utilizing an observation result of the observer, adopting a fractional order sliding mode control method, and designing a controller to carry out track tracking fault-tolerant control on the robot for detection.
In this embodiment, the detection robot is a mecanum wheel omnidirectional mobile robot, and the cavity is a cylindrical cavity. Referring to fig. 3-5, three coordinate systems are adopted in the space motion coordinate system of the omnidirectional mobile robot in the cavity, namely a three-dimensional coordinate system in the cavity, a plane inertial coordinate system and a robot body coordinate system. The three-dimensional coordinate system in the cavity is used for describing the three-dimensional space motion of the omni-directional mobile robot in the cavity; the plane inertial coordinate system is used for describing the motion track and the gesture of the omnidirectional mobile robot on a plane; the robot body coordinate system is fixed on the robot and moves together with the robot, and is used for describing the dynamic characteristic of the movement of the omnidirectional mobile robot.
Cavity three-dimensional coordinate system γdρ: gamma is the included angle between the connecting line of the gravity center of the robot and the cross section of the cavity and the vertical direction, d is the distance between the robot and the inlet of the cavity, and ρ is the included angle between the moving direction of the robot and the symmetrical axis of the cavity.
Inertial coordinate system XOY: also called fixed coordinate system or ground coordinate system, any point in the cavity is selected as origin, where the position of the cavity inlet is selected, X axis coincides with the tangent line of the cavity and horizontal plane, and the position sensor arranged on the robot body is used for measuring the position [ X ] of the robot in the inertial coordinate system p y p φ] T The inertial sensor arranged on the robot body is used for measuring the linear speed and the angular speed of the robot body
Carrier coordinate system x m o m y m : also called motion coordinate system or non-inertial coordinate system, origin o m Coincides with the center of gravity of the omnidirectional mobile robot, o m y m The axis is parallel to the motion direction of the mobile robot, o m x m The axis is parallel to the symmetry axis of the robot.
Referring to fig. 2, in this embodiment, a state space model of the inspection robot is finally obtained through a series of mathematical transformations by establishing a kinematic model and a dynamic model of the inspection robot, and the trajectory control of the inspection robot in the cavity is realized by using a control method based on a fractional order sliding mode.
In the practical application process, the implementation process of the method for performing track tracking control on the cavity maintenance robot in the cavity is specifically as follows:
step 1: overcoming the influence of gravity.
Unlike ground movement, the movement of the Mecanum wheel omni-directional mobile robot in the cavity is affected by gravity throughThe adsorption pattern overcomes this effect. Forward pressure F required to be compensated by adsorption mode when angle gamma is reached by Mecanum wheel omnidirectional mobile robot c The size is as follows:
F c ＝mg(1-cosγ+f r sinγ) (1)
wherein m is the mass of the Mecanum wheel omnidirectional mobile robot, g is the gravitational acceleration, f r The friction coefficient between the Mecanum wheel omnidirectional mobile robot and the inner wall surface of the cavity is the friction coefficient between the Mecanum wheel omnidirectional mobile robot and the inner wall surface of the cavity;
the adsorption force is calculated by adopting the attachment mode of the negative pressure air chamber, and the calculation formula is as follows:
F x ＝0.01(P 0 -P a )·S (2)
wherein ,P0 Is the ambient pressure, P a The pressure in the negative pressure air chamber is S, and the area of the upper surface of the negative pressure air chamber is S.
Here, the adsorption force is equal to the forward pressure to be compensated, and ideal conditions of the mechanical model and the dynamic model of the Mecanum wheel omnidirectional mobile robot in the cavity are achieved.
Step 2: after the influence of gravity is overcome by an adsorption mode, the movement of the Mecanum wheel omnidirectional mobile robot in the cavity can be approximately in plane movement, so that coordinate conversion is performed, a coordinate conversion equation, a plane kinematics model and a dynamics model of the Mecanum wheel omnidirectional mobile robot are established, and then the controller is designed according to the Mecanum wheel omnidirectional mobile robot model.
It should be noted that the conversion relationship between the three-dimensional coordinate system and the planar inertial coordinate system in the cavity is:
wherein [ γdρ ]] T For the detection of the three-dimensional coordinate system coordinates of the robot in the cavity, R GIS Is the radius of the cross section of the cavity body, [ x ] p y p φ] T To detect the attitude of a robot in a planar world coordinate system.
The conversion relation between the plane inertial coordinate system and the Mecanum wheel omnidirectional mobile robot body coordinate system is as follows:
wherein [xm y m ] T In order to detect the coordinates of the body of the robot,
a transformation matrix of robot plane coordinates with phi as an argument with respect to body coordinates is represented.
The coordinate conversion equation and the kinematic model and the kinetic model of the Mecanum wheel omnidirectional mobile robot are as follows:
wherein R is a real number, is the radius of the Mecanum wheel of the robot,
for detecting the rotational angular velocity of each wheel of the robot, τ= [ τ ] 1 τ 2 τ 3 τ 4 ] T D for detecting driving moment output by four driving motors of robot θ ∈R 4×4 Representing a viscous friction matrix, the specific values of which need to be determined experimentally, the matrix
For converting the matrix, the conversion relation between the rotation angular speed of the robot wheel and the movement speed of the robot is represented, the matrix +.>
Representing the transformation relationship between the angular acceleration of the robot wheel rotation and the driving moment +.>
Are all constant, a is half of the width of the machine body of the Mecanum wheel omnidirectional mobile robot, b is half of the length of the machine body, J ω For moment of inertia of the wheel about the centre of rotation, J Z Is the moment of inertia of the Mecanum wheel omni-directional mobile robot around the rotation center.
Step 3: in the motion process of the robot, the robot actuator may malfunction, and the state space equation of the MWOR actuator malfunction is established by combining the kinematics model and the dynamics model in consideration of the condition of the robot malfunction, so that the subsequent observer and controller design is facilitated.
Here, the three-dimensional coordinates required to be reached by the Mecanum wheel omnidirectional mobile robot are converted into plane coordinates through the conversion relation of the three-dimensional coordinate system of the cavity in the cavity and the plane coordinate system, and the three-dimensional posture can be indirectly controlled by controlling the posture of the robot on the plane. Therefore, the state space equation of the Mecanum wheel omnidirectional mobile robot in the plane inertial coordinate system is as follows:
f(x 1 ,x 2 ) Is state x 1 ,x 2 Is a non-linear function of (c) and (d),
and />
Matrix variables defined for the simplified expression in the engineering of formula derivation have no actual physical meaning.
When the Mecanum wheel omni-directional mobile robot actuator fails, the desired control torque is inconsistent with the actual output torque, and in general, the Mecanum wheel omni-directional mobile robot actuator failure can be expressed as:
τ F ＝(1-η)τ+στ s (7)
wherein ,τF Representing the actual output at the time of actuator failure, τ is the desired actuator output for the design. η is a positive number greater than zero and less than 1.τ s Representing a time-varying actuator bias fault, σ=1 when the actuator bias fault exists, otherwise, σ=0.
When the Mecanum wheel omnidirectional mobile robot fails, substituting the formula (7) into the formula (6), wherein tau is tau F Instead of this. To facilitate the design of the controller, the state space equation for the failure of the robotic actuator is expressed as
Wherein F is a composite fault signal.
Step 4: when the Mecanum wheel omnidirectional mobile robot breaks down, a fault observer is designed to observe fault signals and compensate in a subsequent controller in order to reduce control performance attenuation caused by the faults.
Therefore, the above state space equation can be rewritten as:
here, z= [ x T 1 x T 2 F] T And assuming that the fault signal F is differentiable, the expansion state equation can be obtained:
wherein ,
therefore, the design fault observer is as follows:
wherein 
Respectively represent x 1 、x 2 And an estimated value of F->
For observer gain, beta 0 Is real, represents the observer bandwidth, the value of which is determined by the change frequency of faults, the faster the faults change, beta 0 The larger the value that needs to be taken, the a 1 ,a 2 ,a 3 The positive number is a parameter to be designed and needs to be given according to actual conditions.
Step 5: and (3) integrating the results of the steps, adopting a fractional order sliding mode variable structure control method, and utilizing the observation result of an observer to design a controller to perform track tracking fault-tolerant control on the MWOR so as to achieve the aim of track tracking fault-tolerant control of the robot in the cavity.
In this embodiment, first, the track tracking error is defined as:
wherein ,x1 Is the actual position of the MWOR, x d Is the target position;
secondly, selecting a fractional order switching surface:
where ε is a constant to be designed that is greater than 0.
Then, selecting a supercoiled approach algorithm:
wherein ：
λ＝diag(λ 1 ,λ 2 ,λ 3 )，K 1 ＝[k 11 ,0，0；0,k 12 ，0；0 0 k 13 ]，K 2 ＝[k 21 ,0,0；0,k 22 ,0；0,0,k 23 ]
|s| 1/2 ＝diag(|s 1 | 1/2 ,|s 2 | 1/2 ,|s 3 | 1/2 )，sign(s)＝[sign(s 1 ),sign(s 2 ),sign(s 3 )] T
wherein ,λ1 ，λ 2 ，λ 3 ，k ij All are positive numbers greater than 0, sign (·) is a sign function, D α For fractional differential operators, α is a positive number greater than 0 and less than 1, K 1 ,K 2 Is a gain matrix;
here, the fractional differential calculation method is:
D α [f(e)]represents an alpha-order differentiation of the function f (e), where f (e) is the function of step 502 with respect to tracking error e, f (e) = |e| ε sign (e), Γ (n-t) represents a gamma function, 0<n-α<1, n is an integer less than 1+α, t is the start of integration, typically 0;
when alpha is more than-1 and less than 0, the fractional order differential conversion is converted into fractional order integral, and the fractional order integral calculation method is as follows:
I μ [f(e)]representing mu-order integration of the function f (e);
the derivative of (11) is obtained:
from (8), (11), (12) by observing the resulting fault signal
Instead of the unknown fault F, it is possible to obtain:
it should be noted that, the trace tracking fault-tolerant effect of the method in the embodiment of the present invention is verified by the following digital simulation:
in this embodiment, in order to verify the effectiveness of the method of the present invention, there is provided
The initial value of each variable is 0, the tracking radius is 2m, the tracking effect is shown in fig. 6, and the following conclusion is obtained through digital simulation analysis: the control precision of the track control of the cavity Mecanum wheel omnidirectional mobile robot in the cavity can be improved, buffeting is effectively weakened, and the practicability of the track tracking control algorithm of the cavity Mecanum wheel omnidirectional mobile robot in the cavity is improved. />
Claims (7)
1. The fault-tolerant control method of the robot track for the detection in the cavity is characterized by comprising the following steps:
step 1, overcoming the influence of gravity on the movement of the detection robot in the cavity in an adsorption mode;
step 2, establishing a coordinate conversion equation of the robot for detection, converting a three-dimensional coordinate system of a cavity in the cavity into a plane inertial coordinate system through the coordinate conversion equation, and establishing a plane kinematics model and a dynamics model of the robot for detection;
step 3, based on the plane kinematics model and the dynamics model, establishing a state space equation for detecting the fault of the actuator of the robot;
step 4, observing fault signals of the actuator through a designed fault observer, and compensating in a subsequent controller;
step 5, utilizing the observation result of the observer, adopting a fractional order sliding mode control method, and designing a controller to carry out track tracking fault-tolerant control on the robot for detection; the method specifically comprises the following steps:
step 501, defining a track tracking error as:
e＝x 1 -x d
wherein ,x1 To detect the actual position of the robot, x d Is the target position;
step 502, selecting a fractional order switching plane:
wherein epsilon is a constant to be designed that is greater than 0;
step 503, selecting a supercoiled approach algorithm:
wherein ：
λ＝diag(λ 1 ,λ 2 ,λ 3 )，K 1 ＝[k 11 ,0，0；0,k 12 ，0；0 0 k 13 ]，K 2 ＝[k 21 ,0,0；0,k 22 ,0；0,0,k 23 ]|s| 1/2 ＝diag(|s 1 | 1/2 ,|s 2 | 1/2 ,|s 3 | 1/2 )，sign(s)＝[sign(s 1 ),sign(s 2 ),sign(s 3 )] T
wherein ,λ1 ，λ 2 ，λ 3 ，k ij All are positive numbers greater than 0, sign (·) is a sign function, D α For fractional differential operators, α is a positive number greater than 0 and less than 1, K 1 ,K 2 Is a gain matrix;
step 504, the fractional differential calculation method is as follows:
D α [f(e)]representing an alpha-order derivative of the function f (e), where f (e) is a function of the tracking error e, Γ (n-t) represents a gamma function, 0 < n-alpha < 1, n is an integer less than 1+ alpha, t is the start of integration, where 0, and when alpha is greater than-1 and less than 0, the fractional-order derivative is converted into a fractional-order integral;
the fractional order integral calculation method comprises the following steps:
I μ [f(e)]representing mu-order integration of the function f (e);
the derivative of the fractional order switching plane can be obtained:
the simplified expression formula of state space equation of the fault of the robot executor for detection, fractional order switching surface formula and supercoiled approaching algorithm are used to observe the obtained fault signal
Instead of the unknown fault F, it is possible to obtain:
wherein M represents the conversion relation between the angular acceleration of the robot wheel rotation and the driving moment, f (x) 1 ,x 2 ) Is state x 1 ,x 2 Is a non-linear function of (c) and (d),
(phi) is a matrix variable defined for the simplified expression in the formula derivation engineering, ++>
And respectively representing the estimated values of F, wherein F is a composite fault signal.
2. The method for fault-tolerant control of a robot trajectory for in-cavity detection according to claim 1, wherein step 1 specifically means: the adsorption force of the detection robot is equal to the forward pressure to be compensated, so that ideal conditions of a planar kinematic model and a dynamic model of the detection robot in the cavity are achieved.
3. The fault-tolerant control method for robot trajectory for in-chamber detection according to claim 2, wherein the robot requires a positive pressure F compensated by adsorption at an angle γ c The size is as follows:
F c ＝mg(1-cosγ+f r sinγ)
wherein gamma is the included angle between the connecting line of the gravity center of the robot and the cross section of the cavity and the vertical direction, m is the mass of the robot for detection, g is the gravitational acceleration, f r The friction coefficient between the detection robot and the inner wall surface of the cavity is the friction coefficient between the detection robot and the inner wall surface of the cavity;
the adsorption force is calculated by adopting the attachment mode of the negative pressure air chamber, and the calculation formula is as follows:
F x ＝0.01(P 0 -P a )·S
wherein ,P0 Is the ambient pressure, P a The pressure in the negative pressure air chamber is S, and the area of the upper surface of the negative pressure air chamber is S.
4. The method for fault-tolerant control of a robot trajectory for in-cavity detection according to claim 1, wherein in step 2, the conversion relationship between the three-dimensional coordinate system and the planar inertial coordinate system in the cavity is:
wherein [ γdρ ]] T For the detection of the three-dimensional coordinate system coordinates of the robot in the cavity, R GIS Is the radius of the cross section of the cavity body, [ x ] p y p φ] T To detect the attitude of the robot in a planar world coordinate system;
the conversion relation between the plane inertial coordinate system and the robot body coordinate system for detection is as follows:
wherein [xm y m ] T In order to detect the coordinates of the body of the robot,
a transformation matrix representing robot plane coordinates with phi as an independent variable relative to body coordinates;
the planar kinematic model and the dynamic model of the robot for detection are as follows:
wherein R is a real number, is the radius of the Mecanum wheel of the robot,
for detecting the rotational angular velocity of each wheel of the robot, τ= [ τ ] 1 τ 2 τ 3 τ 4 ] T D for detecting driving moment output by four driving motors of robot θ ∈R 4 ×4 Represents a viscous friction matrix, matrix->
To transform the matrix, the transformation relation between the rotation angular speed of the robot wheel and the movement speed of the robot is represented, and the matrix
Representing the transformation relationship between the angular acceleration of the robot wheel rotation and the driving moment +.>
Are all constant, a is half of the body width of the robot for detection, b is half of the body length, J ω For moment of inertia of the wheel about the centre of rotation, J Z To detect the moment of inertia of the robot about the center of rotation.
5. The fault-tolerant control method of a robot trajectory for detection in a chamber according to any one of claims 1 to 4, wherein in step 3, a state space equation of the robot for detection in a planar inertial coordinate system is:
wherein ：
x 1 ＝[x p y p φ] T ，
r is a real number and is the radius of a Mecanum wheel of the robot; τ= [ τ ] 1 τ 2 τ 3 τ 4 ] T The driving moment is output by four driving motors of the robot for detection; matrix array
Representing the transformation relation between the angular acceleration of the rotation of the robot wheel and the driving moment; [ x ] p y p φ] T To detect the attitude of the robot in a planar world coordinate system; f (x) 1 ,x 2 ) Is state x 1 ,x 2 Is a nonlinear function of (2); d (D) θ ∈R 4×4 Representing a viscous friction matrix; />
(φ) and />
And (phi) is defined for simplifying expression in formula derivation engineeringA sense matrix variable; a is half of the width of the body of the robot for detection, and b is half of the length of the body;
when the detection robot actuator fails, the desired control torque does not coincide with the actual output torque, and therefore the detection robot actuator failure equation is expressed as:
τ F ＝(1-η)τ+στ s
wherein ,τF Representing the actual output of the actuator in the event of a fault, eta being a positive number greater than zero and less than 1, tau s Representing a time-varying actuator bias fault, σ=1 when the actuator bias fault exists, otherwise, σ=0;
when the detecting robot fails, substituting a detecting robot actuator failure formula into a state space equation of the detecting robot in a plane inertial coordinate system, wherein tau is tau F Instead of this.
6. The method for fault-tolerant control of robot trajectory for detection in a chamber according to claim 5, wherein the state space equation for the failure of the robot actuator for detection is expressed simply as:
wherein F is a composite fault signal.
7. The method according to claim 6, wherein in step 4, when the fault observer is designed to observe the fault signal of the actuator, the simplified expression of the state space equation of the fault of the robot actuator for detection is rewritten as:
let z= [ x ] T 1 x T 2 F] T And assuming that the fault signal F is differentiable, an expansion state equation is obtained:
wherein ：
therefore, the designed fault observer is as follows:
wherein ,
for observer gain, beta 0 Is real, represents the observer bandwidth, the value of which is determined by the change frequency of faults, the faster the faults change, beta 0 The larger the value that needs to be taken, the a 1 ,a 2 ,a 3 Is a positive number. />
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