CN111694361B - Steel structure flexible flaw detection robot track tracking method based on improved approach law sliding mode control - Google Patents
Steel structure flexible flaw detection robot track tracking method based on improved approach law sliding mode control Download PDFInfo
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Abstract
A flexible flaw detection robot track tracking method based on improved approach law sliding mode control is characterized in that a kinematic model and an error model of front and rear vehicle bodies of a flexible flaw detection robot are built based on coordinate transformation and incomplete constraint, a constraint model of a flexible flaw detection robot steel belt is built based on an Euler's beam theory, linear speed and angular speed of an expected tracking track are obtained according to the constraint model, a sliding mode surface is introduced based on a sliding mode control theory, an approach law of the sliding mode surface is improved and designed to obtain a sliding mode controller of the linear speed and the angular speed of the robot, the linear speed and the angular speed of the expected tracking track are input as the sliding mode controller to obtain linear speed and angular speed control output of the front and rear vehicle bodies, then the output speed of each wheel is calculated, and track tracking motion control of the robot is completed. The invention can lead the flexible flaw detection robot to track the expected track in a limited time, has high tracking speed and high tracking precision and has strong robustness to external disturbance.
Description
Technical Field
The invention relates to a robot track tracking control method for plane steering kinematic modeling, front and rear vehicle body posture and speed constraint and sliding mode variable structure control theory of a rigid-flexible coupling flaw detection robot for steel structure detection.
Background
At present, a wired data acquisition method is widely adopted in steel structure health detection, but the defects of complicated wiring and great labor cost are overcome; a flexible robot with autonomous movement, data acquisition and wireless communication functions is used as an intelligent mobile detection unit, so that the problems of detection blind areas and incomplete detection existing in the current detection are solved.
Because of the complex structures such as various inner and outer corners, reinforcing ribs, different surfaces in space and the like in the steel structure building, the flexible robot needs to pass over or avoid various barriers. The steel structure flaw detection robot is provided with two vehicle bodies, each vehicle body is a two-wheel differential-drive mobile robot, and the flexible robot is connected with the front and rear vehicle bodies by adopting a deformable flexible steel belt so as to flexibly cross various obstacles. In order to avoid obstacles in the plane, it is first of all to be able to track the given trajectory by the robot. Consistent with a common mobile robot, a rigid-flexible coupled robot still belongs to a multi-input multi-output nonlinear system subject to incomplete constraint. However, the front and rear vehicle bodies of the robot are connected through the steel belts, so that additional constraint is brought, an additional driver is not needed, and great difficulty is brought to modeling and control of the robot.
The whole structure of the flexible flaw detection robot is different from that of a general mobile robot, and is mainly characterized in that a front car body and a rear car body are connected through flexible steel belts which can be deformed, so that additional motion constraint is brought. Therefore, the kinematic modeling of the whole robot needs to be solved, including the incomplete constraint of the wheeled mobile robot and the constraint of the steel belt, and a foundation is provided for realizing the control of the robot.
In order to solve the problem that the flexible robot realizes real-time tracking of a specified track on a steel structure, a motion control method suitable for the robot model is required to be provided. The flaw detection robot is provided with two mobile robot car bodies, and the existing mobile robot track tracking method can be referred to.
Disclosure of Invention
In order to overcome the defects of the prior art, and to realize the track tracking control of the novel steel structure flexible flaw detection robot and reduce the attitude error in the control process, the invention provides a robot kinematics modeling method combining the steel belt deformation constraint and a sliding mode variable structure control algorithm based on an improved approach law, and the model and the algorithm are applied to the track tracking control of the flaw detection robot with rigid-flexible coupling, and finally provides a track tracking method with small error and good robustness.
The technical scheme adopted for solving the technical problems is as follows:
a steel structure flexible flaw detection robot track tracking method based on improved approach law sliding mode control comprises the following steps:
step one: according to the defect detection robot, a front car body and a rear car body are two-wheel differential driving mobile robots, a single robot car body kinematic model is built according to non-integrity constraint, then a car body track tracking error model is built through coordinate transformation, and the robot obtains a pose tracking error through real-time resolving pose and expected pose comparison;
step two: the speed constraint of the front and rear car bodies is obtained by carrying out elasto-mechanical analysis on the steel strip, namely the beams of the front and rear car bodies and bending deformation of the beams. Selecting a motion reference point according to a motion model of the flaw detection robot, obtaining simplified kinematic speed constraint by combining the speed constraint, and calculating expected speeds required by front and rear vehicle bodies;
step three: according to the track tracking error model of each car body obtained in the step one, designing a sliding mode control algorithm for car body track tracking based on a sliding mode control theory, wherein the algorithm improves a sliding mode approach law in sliding mode control to obtain a control law with faster response and smaller sliding mode jitter;
step four: and (3) taking the expected speed required by the front and rear vehicle bodies obtained in the step two as input of sliding mode control to obtain speed control output of the front and rear vehicle bodies, and then calculating the speed output of each wheel to finish track tracking motion control of the robot.
In the first step, the surface of each wheel of the steel structure flaw detection robot is stuck with a powerful arc magnet, so that the friction between the wheel and the adsorption surface is enhanced, and only pure rolling but no sliding can be considered to occur between the wheel and the contact surface, and under the condition, each robot body meets the non-integrity constraint;
each vehicle body of the flexible robot is geometrically symmetrical about a central axis, and under the ideal condition, an independent robot vehicle body kinematic model is established by combining a general two-wheel differential mobile robot structure on the assumption that the geometric center of each vehicle body coincides with the mass center;
then, because the errors between the actual pose of the robot car body and the pose of the reference robot car body are described, the pose errors under the global coordinates need to be subjected to coordinate transformation, and then the pose errors of each car body are as follows:
and then differentiating the above formula to obtain a pose error differential equation:
the pose error in the model is q ie ＝[x ie y ie φ ie ] Τ In which the yaw angle error phi ie Measuring the current actual yaw angle phi by an inertial measurement unit IMU i Then subtracted from the desired yaw angle and then combined with the current attitude angle phi after the encoder data on the wheel is acquired i Obtaining the current coordinate (x) through dead reckoning i ，y i ) Then calculate the position error x ie And y ie 。
In the second step, if the front and rear bodies have certain pose at any moment, the front and rear boundaries of the steel strip are basically determined, the steel strip connecting the front and rear bodies of the robot is regarded as a beam, the width h of the steel strip, which accords with the largest dimension of the cross section, is far smaller than the length L (h < L) and the thickness is far smaller than the width (b < h), and the relationship between the deflection of the steel strip and the boundaries of the two ends is obtained by using an Euler-Bernoulli beam equation:
where u represents the deflection of the beam, x represents the position along the x-axis, p (x) represents the lateral uniform load applied to the beam, E represents the modulus of elasticity of the steel strip material, and I is the moment of inertia;
according to the deflection angle psi of the front and rear car bodies connected by the steel belt, the boundary relationship of the steel belt is obtained
And then bringing the boundary conditions of the obtained steel strip deformation into an Euler-Bernoulli equation, and solving the deflection of the steel strip:
wherein L is the length of the strip before deformation, ψ 1 The subscript 1 of (1) indicates the front body end, ψ 2 The subscript 2 of (2) denotes the rear body end;
the shortening in the longitudinal direction due to the deformation of the steel strip in the transverse direction is denoted dL:
substituting the equation of the length change of the steel belt into boundary conditions of the front and rear vehicle bodies to obtain speed constraints of the front and rear vehicle bodies:
to facilitate the simplification of the kinematic model, the reference point O is defined as the front and rear body centroid line
Is defined by a central point of the lens. During the movement, the front and rear vehicle body centers and the reference point O have the same rotation center and rotation angular velocity, defined as w o And assume ψ during motion 1 ＝-ψ 2 Always hold, define ψ= |ψ 1 |＝|ψ 2 I, then, the velocity relationship between the center point O and the front and rear vehicle bodies is obtained:
in the formula, v o For the speed of reference point O, v 1 、v 2 The speeds of the mass centers of the front and rear bodyworks respectively.
In the third step, firstly, according to the kinematic trajectory error equation established in the first step, a sliding mode controlled switching function is designed based on an inversion design method in combination with a Lyapunov function so that the trajectory error tends to zero;
selecting Lyapunov function
Deriving it:
then designing virtual control quantity phi ie ＝-arctan(v ir y ie ). Defining a sliding die surface as follows by utilizing the obtained virtual control quantity:
then, a power function approach law in sliding mode control is designed, and the basic form of the power function approach law is as follows:
where sgn (·) is a sign function defined as:
then, in order to increase the convergence rate in the control process, the power function approach law is improved as follows:
wherein p > 0 represents the speed gain of the system state approaching motion to the sliding mode surface, 0 < q < 1 is the power term coefficient, alpha > 0, and arsinih (·) is the inverse hyperbolic tangent function;
then combining the improved power function approach law of the sliding mode switching surface with an actual robot track error equation to obtain the following relation:
finally, the sliding mode control law of each vehicle body of the robot is obtained:
wherein v is i Is the linear velocity control quantity w of the corresponding car body i Is the angular velocity control quantity corresponding to the car body, v ir Indicating the desired linear velocity, w, of the corresponding vehicle body ir Indicates the desired angular velocity of the corresponding vehicle body, ζ=arctan (v ir y ie )。
In the fourth step, a reference track is designated for the reference point O, the expected speed and the angular speed are given, and the expected speed and the angular speed of the front and the rear vehicle bodies are obtained according to the speed constraint of the centroid of the front and the rear vehicle bodies and the reference point O obtained in the second step;
then, taking the expected speed and the angular speed of the front and rear vehicle bodies as the input of the sliding mode control law in the third step, solving the control output of the front and rear vehicle bodies, namely the speed and the angular speed control quantity of the front and rear vehicle bodies, and then solving the wheel speed control quantity corresponding to each vehicle body by utilizing the speed, the angular speed and the structural parameters of each vehicle body;
and finally, the track tracking control of the flexible steel structure flaw detection robot is completed by means of obtaining the rotation speed output of each wheel of the robot.
The technical conception of the invention is as follows: the overall kinematic model of the robot with the flexible steel belt is complex and difficult to directly describe and apply to a control link. On the one hand, the flexible steel belts enable the front and rear bodyworks to deflect, twist and even misplace, and on the other hand, the flexible steel belts also mean a more complex kinematic model, and the movement processes of the front and rear axles must be coordinated. Therefore, here I use the relative arrangement of the front and rear bodies and the length change of the steel strip to simplify the kinematic model.
Each individual body of the flexible robot can be considered a two-wheeled differentially driven mobile robot. Forward speed v of each vehicle body i And angular velocity w i The relationship with the wheel rotation speed can be expressed by the following formula:
wherein r is w Is the radius of the wheel, d is the distance between the left wheel and the right wheel, omega il And omega il Respectively representing the rotation angular speeds of left and right wheels, wherein i=1, 2 respectively represent the front and rear vehicle bodies of the flexible robot;
to correctly describe the overall kinematics of the robot with the steel strip connection, a kinematic model effective for robot control is obtained, which requires consideration of the front and rear vehicle body constraints due to the deformation of the steel strip. Assuming a defined pose for the front and rear bodies at any one time, the front and rear boundaries of the steel strip are substantially defined, and the role of the steel strip in this robot can be roughly regarded as a beam. This is because the strip substantially conforms to the maximum dimensional width h of the cross section, which is much smaller than the length L (h < L), which conforms to a basic assumption for beams in elastic mechanics. And because the material is elastic steel, the material is a typical isotropic material and is suitable for using elastomechanical analysis.
The beneficial effects of the invention are mainly shown in the following steps:
1. and (3) modeling the deformation of the steel belt of the robot based on the Euler Bernoulli beam equation, and obtaining the speed constraint of the front and rear vehicle bodies of the flexible flaw detection robot.
2. And the reference track planning based on the center reference point simplifies the kinematic model and the control flow of the whole flexible flaw detection robot.
3. The flexible flaw detection robot sliding mode control method based on the improved sliding mode approach law improves the robustness of the rigid-flexible coupling robot in the track tracking process.
4. The flexible flaw detection robot sliding mode control method based on the improved sliding mode approach law improves the accuracy and stability of the rigid-flexible coupling robot in the track tracking process.
Drawings
FIG. 1 is a schematic structural view of a flexible flaw detection robot
FIG. 2 is a control schematic block diagram of a flexible flaw detection robot
FIG. 3 is a graph of linear velocity and angular velocity for tracking a linear trajectory
FIG. 4 is a graph of a trace for a straight trace
FIG. 5 is a graph of error in tracking a straight line trajectory
FIG. 6 is a graph of linear and angular velocity for tracking a circular trajectory
FIG. 7 is a trace plot of a trace of a circular trace
FIG. 8 is a graph of error in tracking a circular trajectory
Detailed Description
The invention is further described below with reference to the accompanying drawings:
FIG. 1 is a schematic view of a flexible inspection robot, where x w O w y w Is the world coordinate system, x 1 y 1 Is a front car body moving coordinate system, x 2 y 2 Is a rear car body moving coordinate system, C 1 And C 2 The mass centers of the front and rear bodyworks are respectively, O is C 1 And C 2 D is half the length of two driving axles of the same vehicle body, r w Is the radius of the driving wheel, I is the steering center, r o The steering radius of the point O is the distance between two particles, and the angle theta is the included angle between the motion direction of the flexible flaw detection robot and the x direction of the world coordinate system. Wherein the driving wheel 1 and the driving wheel 3 are mounted on the front vehicle body 2, and the driving wheel 5 and the driving wheel 7 are mounted on the rear vehicle body 6. One end of the flexible steel belt 4 is fixed on the vehicle body 2, and the other end is fixed on the vehicle body 6, so that the vehicle body 2 and the vehicle body 6 are connected.
Referring to fig. 2 to 6, a track tracking method of a steel structure flexible flaw detection robot based on improved approach law sliding mode control comprises the following steps:
step one: establishing a kinematic model of the flexible flaw detection robot and an expected track model of the reference robot, and establishing a track tracking error model according to the kinematic model and the expected track model;
step two: analyzing mechanical and kinematic characteristics of the flexible steel belt, deducing the motion constraint of the steel belt on the front and rear vehicle bodies, and establishing a robot integral track tracking control model by combining the motion constraint and the track tracking error model obtained in the step one;
step three: combining the track tracking error model and the speed constraint in the first step and the second step, and designing a virtual control feedback quantity phi ie And slip form surface s i1 Sum s i2 Finally, the linear velocity v is designed by utilizing the improved approach law i And angular velocity w i Control law of (2);
in a specific embodiment, the specific steps of the invention are as follows:
step one: establishing a wheel type mobile robot kinematic model of a front and rear vehicle body of the flexible flaw detection robot:
the subscripts i=1 and 2 in the formula respectively represent the front and rear vehicle bodies of the flexible robot, and the constraint condition is that
Under the constraint condition, the instantaneous speed on the two wheel axes of the front and rear vehicle bodies is ensured to be 0, wherein (x i ，y i ) Representing the coordinates of the centroid of a two-wheeled vehicle model in a Cartesian coordinate system, phi i The heading angle of the car body, and the pose of each car body is represented by a generalized coordinate vector q i ＝[x i y i φ i ] Τ And (3) representing. The expected trajectory model of the reference robot is:
wherein (x) r y r φ r ) Is the desired trajectory pose, v r And w r The expected linear velocity and the expected angular velocity are respectively compared with an expected track model and a kinematic model, and the track gesture is obtained through coordinate transformationError equation of (2):
and deriving the differential equation to obtain a robot track tracking error differential equation:
step two: combining the Euler Bernoulli equation of the flexible steel belt and the constraint conditions of the front and rear vehicle bodies to obtain the disturbance deformation of the steel belt:
where L is the length of the strip before deformation, where E represents the modulus of elasticity of the strip material, I is the moment of inertia, replaced by k=ei,
representing bending deformation of two ends of the steel strip, psi 1 The subscript 1 of (1) indicates the front body end, ψ 2 The subscript 2 of (2) indicates the rear car body end, and the resulting lateral deformation of the steel strip is used to calculate the shortening dL of the straight line distance at both ends thereof:
the distance between the two ends of the shortened steel belt, namely the distance between the front and the rear vehicle bodies is L f To express:
L f ＝L-dL
will L f Deriving time, and combining the instantaneous geometric relationship of the front and rear vehicle bodies of the robot to obtain the speed constraint of the front and rear vehicle bodies:
further use of front and rear body centroid C 1 And C 2 The speed of the midpoint O of (c) is taken as an intermediate quantity to simplify the speed constraint. During the movement, the front and rear vehicle body centers and the reference point O have the same rotation center and rotation angular velocity, defined as w o And assume ψ during motion 1 ＝-ψ 2 Always hold, define ψ= |ψ 1 |＝|ψ 2 | a. The invention relates to a method for producing a fibre-reinforced plastic composite. Then, the velocity relationship between the center point O and the front and rear vehicle bodies is obtained:
in the formula, v o For the speed of reference point O, v 1 、v 2 The speeds of the mass centers of the front and rear vehicle bodies respectively;
step three: design an intermediate Lyapunov function V i Deriving an intermediate virtual control quantity phi using an inversion design method ie ：
φ ie ＝-arctan(v ir y ie )
Lyapunov function
And deriving the following steps:
wherein, because of the reference input variable v ir > 0, when x ie When converging to 0, the second term on the right side of the above equal sign also converges to 0; from the quotation 1, we know y ie v ir sin(arctan(v ir y ie ) Not less than 0, and also having the first term on the right side of the equation less than 0; thus (2)
Negative definite, and when y ie Converging to 0, phi ie Also converge to 0;
therefore, a sliding mode switching function is selected, and the specific form is as follows:
according to the above analysis, when s i1 When converging to 0, then there is x ie Converging to 0. When s is i2 When converging to 0, i.e. phi ie Convergence to-arctan (v) ir y ie ) When (1): due to the virtual control quantity phi ie ＝-arctan(v ir y ie ) Wherein the characteristic of the arctan (·) anti-hyperbolic tangent function results in y ie Phi when 0 ie Also 0, and the result is a systematic error x ie y ie φ ie ] Τ Converging to 0;
an improved sliding mode approach law is designed:
wherein p is i1 ＞0,p i2 And > 0 represents the approaching motion of the system state to the sliding mode surface s i Speed gain=0; argin (·) is an anti-hyperbolic sine function, sgn (·) is a sign function; q is 0 < q i1 ＜1,0＜q i2 The expression < 1 is an index of a power term in an approach law, and influences a specific numerical value of the term; alpha i1 ＞0,α i2 The value of more than 0 is positive gain of an anti-hyperbolic sine function term, and the approach speed of a moving point at a position far from a sliding mode surface can be adjusted;
finally, a track tracking sliding mode controller is designed:
wherein v is i Is the linear velocity control quantity w of the corresponding car body i Is the angular velocity control quantity corresponding to the car body, v ir Indicating the desired linear velocity, w, of the corresponding vehicle body ir Indicates the desired angular velocity of the corresponding vehicle body, ζ=arctan (v ir y ie )；
Selecting Lyapunov function as:
wherein k is 1 And k 2 Are positive numbers greater than zero;
and deriving the following steps:
V i (s)＝
-k i1 (p i1 |s i1 | qi1 sgn(s i1 )s i1 +a i1 arsinh(s i1 )s i1 )
-k i2 (p i2 |s i2 | qi2 sgn(s i2 )s i2 +a i2 arsinh(s i2 )s i2 )≤0
only when s i When the value of the sum is =0,
when s is i When not equal to 0, ++>
Thus->
The control system is lyapunov stable, and the track tracking error of the system converges to zero along with the sliding mode surface according to the previous analysis of the sliding mode surface, so that the flexible robot control system can be proved to be stable.
Step four: the linear speed and the angular speed control quantity of the front and rear vehicle bodies of the flexible flaw detection robot are obtained from the three steps, and the actual control wheel speed of each driving wheel can be calculated through the relation between the driving wheel speed of each vehicle body and the linear speed and the angular speed. Forward speed v of each vehicle body i And yaw rate w i The relationship with the wheel rotation speed can be expressed by the following formula:
wherein omega il Represents the left driving wheel rotation speed omega of each car body ir Representing the right drive wheel speed for each vehicle body. And finally, the track tracking control of the flexible flaw detection robot is finished by the specific implementation to the control of the driving wheel speed.
In summary, the invention can lead the track tracking error of the robot system to gradually converge to zero, thereby completing the tracking of the robot on the appointed track, and having good tracking effect and strong robustness.
In the embodiment of the invention, two models of straight line and circular tracking track are adopted:
(1) Straight line trajectory, where v r ＝1m/s，w r =0rad/s. The selected controller parameter is p 11 ＝p 21 ＝1.5,p 12 ＝p 22 ＝1.2，q 11 ＝q 21 ＝0.8,a 11 ＝a 21 ＝1.1，a 12 ＝a 22 ＝0.8q 12 ＝q 22 =0.8. Fig. 3 shows the linear velocity v in the linear trajectory tracking i And angular velocity w i Fig. 4 is a graph of an actual motion trajectory and an expected motion trajectory of the flexible flaw detection robot, and fig. 5 is a pose error map of trajectory tracking.
(2) Circular trajectory, where v r ＝1m/s,w r =1.5 rad/s. The selected controller parameter is p 11 ＝p 21 ＝1.5,p 12 ＝p 22 ＝1.2，q 11 ＝q 21 ＝0.8,a 11 ＝a 21 ＝1.5,a 12 ＝a 22 ＝1.2。q 12 ＝q 22 =0.8. Fig. 6 is a linear velocity v in circular trajectory tracking i And angular velocity w i Fig. 7 is a graph of an actual motion trajectory and an expected motion trajectory of the flexible flaw detection robot, and fig. 8 is a pose error map of trajectory tracking.
Claims (4)
1. The track tracking method of the steel structure flexible flaw detection robot based on the improved approach law sliding mode control is characterized by comprising the following steps of:
step one: according to the defect detection robot, a front car body and a rear car body are two-wheel differential driving mobile robots, a single robot car body kinematic model is built according to non-integrity constraint, then a car body track tracking error model is built through coordinate transformation, and the robot obtains a pose tracking error through real-time resolving pose and expected pose comparison;
step two: the method comprises the steps of carrying out elastohydrodynamic analysis on a beam of a front car body and a rear car body, obtaining speed constraint of the front car body and the rear car body through bending deformation of the beam, selecting a motion reference point according to a motion model of a flaw detection robot, obtaining simplified kinematic speed constraint by combining the speed constraint, and calculating expected speeds required by the front car body and the rear car body;
step three: according to the track tracking error model of each car body obtained in the step one, designing a sliding mode control algorithm for car body track tracking based on a sliding mode control theory, wherein the algorithm improves a sliding mode approach law in sliding mode control to obtain a control law with faster response and smaller sliding mode jitter;
step four: taking the expected speed required by the front and rear vehicle bodies obtained in the second step as input of sliding mode control to obtain speed control output of the front and rear vehicle bodies, and then calculating the speed output of each wheel to finish track tracking motion control of the robot;
in the second step, if the front and rear vehicle bodies have the determined pose at any moment, the front and rear boundaries of the steel belt are basically determined, the steel belt connecting the front and rear vehicle bodies of the robot is regarded as a beam, the maximum dimension of the steel belt conforming to the cross section is that the width h is far smaller than the length L, the thickness is far smaller than the width, and the relationship between the deflection of the steel belt and the boundaries of two ends is obtained by using an Euler-Bernoulli beam equation:
where u represents the deflection of the beam, x represents the position along the x-axis, p (x) represents the lateral uniform load applied to the beam, E represents the modulus of elasticity of the steel strip material, and I is the moment of inertia;
according to the deflection angle psi of the front and rear car bodies connected by the steel belt, the boundary relationship of the steel belt is obtained
And then bringing the boundary conditions of the obtained steel strip deformation into an Euler-Bernoulli equation, and solving the deflection of the steel strip:
wherein L is the length of the strip before deformation, ψ 1 The subscript 1 of (1) indicates the front body end, ψ 2 The subscript 2 of (2) denotes the rear body end;
the shortening in the longitudinal direction due to the deformation of the steel strip in the transverse direction is denoted dL:
substituting the equation of the length change of the steel belt into boundary conditions of the front and rear vehicle bodies to obtain speed constraints of the front and rear vehicle bodies:
to facilitate the simplification of the kinematic model, the reference point O is defined as the front and rear body centroid line
During the movement, the center of the front and rear vehicle bodies and the reference point O have the same rotation center and rotation angular velocity, which is defined as w o And assume ψ during motion 1 ＝-ψ 2 Always hold, define ψ= |ψ 1 |＝|ψ 2 I, then, the velocity relationship between the center point O and the front and rear vehicle bodies is obtained: />
In the formula, v o For the speed of reference point O, v 1 、v 2 The speeds of the mass centers of the front and rear bodyworks respectively.
2. The method for tracking the track of the steel structure flexible flaw detection robot based on the improved approach law sliding mode control according to claim 1, wherein in the third step, firstly, according to a kinematic track error equation established in the first step, a sliding mode control switching function is designed based on an inversion design method in combination with a Lyapunov function so that the track error is enabled to be zero;
selecting Lyapunov function
Deriving it:
y ie and x ie Is a position error;
then designing virtual control quantity phi ie ＝-arctan(v ir y ie ) Using the virtual control amount obtained above, a slip plane is defined as:
then, a power function approach law in sliding mode control is designed, and the basic form of the power function approach law is as follows:
where sgn (·) is a sign function defined as:
then, in order to increase the convergence rate in the control process, the power function approach law is improved as follows:
wherein p > 0 represents the speed gain of the system state approaching motion to the sliding mode surface, 0 < q < 1 is the power term coefficient, alpha > 0, and arsinih (·) is the inverse hyperbolic tangent function;
then combining the improved power function approach law of the sliding mode switching surface with an actual robot track error equation to obtain the following relation:
finally, the sliding mode control law of each vehicle body of the robot is obtained:
wherein v is i Is the linear velocity control quantity w of the corresponding car body i Is the angular velocity control quantity corresponding to the car body, v ir Indicating the desired linear velocity, w, of the corresponding vehicle body ir Indicates the desired angular velocity of the corresponding vehicle body, ζ=arctan (v ir y ie )。
3. The method for tracking the track of the steel structure flexible flaw detection robot based on the improved approach law sliding mode control according to claim 2, wherein in the first step, a powerful arc magnet is attached to the surface of each wheel of the steel structure flaw detection robot, friction between the wheel and an adsorption surface is enhanced, only pure rolling but no sliding between the wheel and a contact surface is defined, and each robot body meets the non-integrity constraint;
each vehicle body of the flexible robot is geometrically symmetrical about a central axis, and an independent robot vehicle body kinematic model is established by combining a two-wheel differential mobile robot structure under the assumption that the geometric center of each vehicle body coincides with the mass center;
then, because the errors between the actual pose of the robot car body and the pose of the reference robot car body are described, the pose errors under the global coordinates need to be subjected to coordinate transformation, and then the pose errors of each car body are as follows:
and then differentiating the above formula to obtain a pose error differential equation:
the pose error in the model is q ie ＝[x ie y ie φ ie ] Τ In which the yaw angle error phi ie Measuring the current actual yaw angle phi by an inertial measurement unit IMU i Then subtracted from the desired yaw angle and then combined with the current attitude angle phi after the encoder data on the wheel is acquired i Obtaining the current coordinate (x) through dead reckoning i ，y i ) Then calculate the position error x ie And y ie 。
4. The method for tracking the track of the steel structure flexible flaw detection robot based on the improved approach law sliding mode control according to claim 1, wherein in the fourth step, a reference track is designated for a reference point O and expected speed and angular speed are given, and the expected speed and the angular speed of the front and rear vehicle bodies are obtained according to the speed constraint of the mass centers of the front and rear vehicle bodies and the reference point O obtained in the second step;
then, taking the expected speed and the angular speed of the front and rear vehicle bodies as the input of the slip form control law in the third step, solving the speed and the angular speed control quantity of the front and rear vehicle bodies, and then solving the wheel speed control quantity corresponding to each vehicle body by utilizing the speed and the angular speed of each vehicle body and the structural parameters;
and finally, the track tracking control of the flexible steel structure flaw detection robot is completed by means of obtaining the rotation speed output of each wheel of the robot.
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