CN112379590A - Mobile robot path tracking control method based on improved approach law - Google Patents
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Abstract
The invention discloses a mobile robot path tracking control method based on an improved approach law, which is specifically carried out according to the following steps; step 1: defining distance deviation and angle deviation, and establishing a path tracking error model; acquiring a reference path image with a camera; then, carrying out threshold segmentation and refinement on the acquired image; finally, calculating distance deviation and angle deviation under a mobile robot coordinate system through coordinate conversion and fitting; step 2: designing a switching function based on an inversion method, and improving a double-power approximation law to obtain an inversion sliding mode control law; and step 3: and (3) according to the inversion sliding mode control law obtained in the step (2), enabling the mobile robot to move along an expected path, and further realizing accurate and rapid path tracking. The invention solves the problem that the quick response characteristic and the steady-state performance are difficult to be considered in the path tracking process, realizes the quick tracking of the reference path and has smooth and buffeting-free tracking process.
Description
Technical Field
The invention belongs to the technical field of motion control of mobile robots, and particularly relates to a mobile robot path tracking control method based on an improved approach law.
Background
The mobile robot is widely applied to the fields of industry, agriculture, military and the like, so that the motion control problem of the mobile robot is widely concerned by academic circles at home and abroad. The path tracking means that the mobile robot follows an expected geometric path at a given speed under the action of a control law, and the fast and accurate tracking of a reference path is the key for realizing the high-performance motion control of the mobile robot.
At present, researchers propose various path tracking control methods, which mainly include two types of methods, namely fuzzy control and sliding mode variable structure control. Fuzzy control does not depend on an accurate mathematical model and has strong robustness, but simple fuzzy processing of information can cause reduction of control precision and deterioration of dynamic quality. The sliding mode variable structure control has the advantages of simple design, insensitivity to parameter change and external interference and the like, but the buffeting ratio is large when the system state approaches the sliding mode, and the speed is too small when the system state is far away from the sliding mode.
The double power approach law enables the system state to approach the sliding mode surface at a higher speed when the system state is far away from the sliding mode; on the contrary, when the system state approaches to the sliding mode, the sliding mode surface is reached at a slower speed, so that good steady-state performance is ensured, and buffeting is weakened. However, the approach speed does not have adaptive power, and thus the fast response characteristic is not significantly improved. In summary, the fast response characteristic and the steady-state performance of the current mobile robot in the path tracking process are difficult to be considered.
Disclosure of Invention
The invention aims to provide a mobile robot path tracking control method based on an improved approach law, and solves the problem that the rapid response characteristic and the steady-state performance of a mobile robot are difficult to be considered in the path tracking process.
The technical scheme adopted by the invention is that,
a mobile robot path tracking control method based on an improved approach law is specifically carried out according to the following steps;
step 1: acquiring a path parameter;
defining distance deviation and angle deviation, and establishing a path tracking error model; collecting a reference path image by a camera; then, carrying out threshold segmentation and refinement on the acquired image; finally, calculating distance deviation and angle deviation under a mobile robot coordinate system through coordinate conversion and fitting;
step 2: designing a controller:
designing a switching function based on an inversion method, and improving a double-power approximation law to obtain an inversion sliding mode control law based on the improved double-power approximation law;
and step 3: and (3) according to the inversion sliding mode control law obtained in the step (2), enabling the mobile robot to move along an expected path, and further realizing accurate and rapid path tracking.
The present invention is also characterized in that,
in step1, the path tracking error model can be described as the following formula (1):
wherein, x is defined1＝xe，x2＝θe，u＝w，xeIs the distance deviation between the mobile robot and the reference path, thetaeThe angular deviation is, v is the moving speed of the mobile robot, and u is the control law.
In step1, the camera is a Kinect camera.
In the step1, the refining specifically comprises: and (3) adopting a Zhang rapid parallel refinement function voidmimiding in an OpenCV visual library to obtain a single pixel point set corresponding to the reference path, then obtaining a pixel coordinate of the reference path, and converting the pixel point coordinate from a camera coordinate system to a mobile robot coordinate system.
In step1, the coordinate fitting specifically comprises: and calculating the mean value, calculating a correlation coefficient, and calculating a regression coefficient and a regression constant to obtain a reference path equation.
In step2, the switching function s is expressed by the following formula (13):
s＝θe+arctan(vxe) (13)，
an inversion sliding mode control law u based on the improved double power approximation law is as follows (19):
wherein k is1K ', α and α' are control law coefficients.
The invention has the beneficial effects that the mobile robot path tracking control method based on the improved approach law is based on the feature extraction research results of the AKAZE algorithm and the FREAK algorithm in recent years, combines the advantages of affine invariant features, and provides an IA-FAIF-based Qing Dynasty roban pattern extraction and matching method. The experimental results of a large number of images of complex patterns of clothes show that the method can give consideration to rapidity of characteristic detection and matching links, has strong visual angle change resistance, and realizes that the correct matching rate is not lower than 90% when the visual angle changes to 85 degrees, the average time consumption of characteristic detection is 0.315ms, the average time consumption of characteristic description is 0.207ms, and the average time consumption of characteristic matching is 0.189 ms.
Drawings
Fig. 1 is a schematic diagram of an inversion sliding mode path tracking control framework based on an improved double-power approximation law in the mobile robot path tracking control method based on the improved approximation law;
FIG. 2 is a schematic diagram of the path tracking of the mobile robot in the method for controlling the path tracking of the mobile robot based on the improved approximation rule;
FIG. 3 is a schematic diagram of a coordinate system in a method for controlling path tracking of a mobile robot based on an improved approximation rule according to the present invention;
FIG. 4 is a schematic diagram of an emulation result in the mobile robot path tracking control method based on the improved approximation rule;
FIG. 5 is a schematic diagram of an overall framework of a mobile robot path tracking remote control platform in the mobile robot path tracking control method based on the improved approximation rule;
fig. 6 is a schematic diagram comparing motion trajectories of a mobile robot in a mobile robot path tracking control method based on an improved approximation rule.
Detailed Description
The following describes a mobile robot path tracking control method based on the improved approach law in detail with reference to the accompanying drawings and the detailed description.
A mobile robot path tracking control method based on an improved approach law is specifically carried out according to the following steps;
step 1: acquiring a path parameter;
defining distance deviation and angle deviation, and establishing a path tracking error model; collecting a reference path image by a camera; then, carrying out threshold segmentation and refinement on the acquired image; finally, calculating distance deviation and angle deviation under a mobile robot coordinate system through coordinate conversion and fitting;
step 2: designing a controller:
designing a switching function based on an inversion method, and improving a double-power approximation law to obtain an inversion sliding mode control law based on the improved double-power approximation law;
and step 3: and (3) according to the inversion sliding mode control law obtained in the step (2), enabling the mobile robot to move along an expected path, and further realizing accurate and rapid path tracking.
The following describes a mobile robot path tracking control method based on the improved approach law according to a specific embodiment of the present invention in further detail.
(1) Acquiring a path parameter;
firstly, defining distance deviation and angle deviation, and establishing a path tracking error model; then, a Kinect camera is used for collecting a reference path image; next, performing threshold segmentation and refinement on the acquired image; and finally, calculating the distance deviation and the angle deviation under the coordinate system of the mobile robot through coordinate conversion and fitting.
1) A path tracking error model;
the path tracking problem is researched by adopting a two-wheel differential mobile robot, and a tracking schematic diagram is shown in fig. 2 on the assumption that a reference path is a straight line. Defining a global coordinate system XOY, making the barycenter of the mobile robot and the center of two wheel axes coincide with a point C, and carrying out physical analysis on the barycenter C of the mobile robot to make the speed v [ v, omega ] be ═ v]TThe dotted line frame is the field of view of the mobile robot, and the distance deviation between the mobile robot and the reference path is xeAngular deviation of thetae. Suppose that the mobile robot moves at a constant velocity v and defines x1＝xe，x2＝θeAnd u is w, the motion process satisfies the pure rolling no-slip condition, and the path tracking error model can be described as follows:
wherein, x is defined1＝xe，x2＝θe，u＝w，xeIs the distance deviation between the mobile robot and the reference path, thetaeThe angular deviation is, v is the moving speed of the mobile robot, and u is the control law.
The path tracking targets in the invention are as follows: under the action of the control law u, the robot can realize accurate and quick tracking of the reference path when t → ∞.
2) Dividing a threshold value;
the threshold segmentation is an image segmentation method with simple calculation and high operation efficiency, and aims to extract a target region from a background. The method adopts a pyramid segmentation function cvPrySegmentation provided in an OpenCV visual library to roughly segment an original image, and then adopts a threshold segmentation function cvThreshold to carry out accurate segmentation, so as to obtain a segmentation result graph (shown in figure 1) consisting of a black reference path and a white background area.
3) Thinning;
the reference path with a certain width is not beneficial to subsequent fitting, so that image thinning processing is required to reduce the processing amount of data. The Zhang fast parallel thinning algorithm has the advantage of fast calculation speed, and can ensure the connectivity of the thinned curves. According to the method, a Zhang fast parallel thinning function voidmimidining in an OpenCV visual library is adopted, so that a single pixel point set corresponding to a reference path is obtained (as shown in FIG. 1).
4) Converting coordinates;
after the pixel coordinates of the reference path are obtained, the pixel coordinates need to be converted from the camera coordinate system to the mobile robot coordinate system. The coordinate system position relationship between the mobile robot and the camera is shown in fig. 3. In fig. 3, the mobile robot coordinate system is OrXrYrZrThe default coordinate system of the Kinect camera is OcXcYcZcActual Kinect camera coordinate system is O'cX′cY′cZ′c，d1、d2And α are the amount of translation and the angular difference between the actual Kinect camera coordinate system and the default Kinect camera coordinate system, respectively. The method comprises the following specific steps:
step 1: assuming that the refined path pixel point coordinates are (a, b), the coordinates (a, b) are converted to the actual Kinect camera coordinate system according to the formula (1) to obtain coordinates (x'c,y'c,z'c)：
Wherein (u)0,v0) As principal point coordinates, (d)x,dy) These five parameters can be obtained by camera calibration as unit pixel size and f as camera focal length.
Step 2: coordinates (x ') according to formula (3)'c,y'c,z'c) Converting the coordinate into a default Kinect camera coordinate system to obtain a coordinate (x)c,yc,zc)：
Wherein d is1、d2And α is a parameter obtained by manual measurement.
Step 3: according to a rotation matrix R and a translation matrix T between a default Kinect camera coordinate system and a mobile robot coordinate system, coordinates (x) can be obtainedc,yc,zc) Converting the coordinate system of the mobile robot to obtain a coordinate (x)r,yr,zr)。
5) Fitting;
from the above steps, n path coordinate points, denoted as (x), can be obtainedi,yi) (i ═ 1,2, 3.., n), then the fitting procedure is as follows:
step 1: calculating an average value:
step 2: calculating a correlation coefficient:
step 3: calculating a regression coefficient k and a regression constant b:
step 4: obtaining a reference path equation:
y＝kx+b (7)，
the distance deviation xeAnd the angular deviation thetaeCan be calculated from equation (8):
xe＝-(b/k)cosθe θe＝arctan(1/k) (8)，
(2) designing a controller;
the invention designs an inversion sliding mode path tracking controller based on an improved double power approach law, and the design of a controller comprises two steps: (1) designing a switching function based on an inversion method to ensure that the sliding mode has good dynamic quality and is asymptotically stable; (2) by using the self-adaptive capacity of the variable exponential power approximation law for reference, the double power approximation law is improved, and the quick response characteristic and the steady-state performance of the system tracking process are improved. The specific process is as follows:
1) designing a switching function;
introduction 1: for any x ∈ R and | x | < ∞, there are
The word "═ holds if and only if x is 0.
The following are demonstrated and discussed:
1) when x is equal to 0, the number of x,
2) when x ∈ (0, + ∞), there is arctanx ∈ (0, π/2), then sin (arctanx) > 0, i.e.
3) When x ∈ (- ∞,0), there is arctanx ∈ (- π/2,0), then sin (arctanx) < 0, i.e.
From the theorem 1, a sliding mode switching function is designed by adopting an inversion method. The specific design process is as follows:
choosing a Lyapunov function shown in equation (9):
because of x1＝xe，x2＝θe，
The following can be obtained:
according to theorem 1, let θe＝-arctan(vxe) Then, there are:
because:
vxesin(arctan(vxe) Is equal to or more than 0 (if and only if vx)eWhen the result is 0 ═ true)
Then there are:
the conclusion can be drawn: when theta iseConverge to-arctan (vx)e) Time, system state xeConverging to zero. The switching function s is designed according to the theory as follows:
s＝θe+arctan(vxe) (13)，
by designing a suitable control law such that s → 0, i.e. θ is achievedeConverge to-arctan (vx)e) Thereby realizing xe→ 0 and thetae→0。
2) Designing a control law;
the invention introduces the self-adaptive power adjustment term into the double power approximation law, and provides an improved double power approximation law as shown in formula (14):
the values of α' are:
in the formula, k1Is more than 0, k' is more than 0, alpha is more than 1, beta is more than 0 and less than 1. Since the exponent alpha' of the double power term is variable, the approaching speed of the system at different stages can be adaptively followed by the systemThe system state. When the system state is far away from the sliding mode (| s | ≧ 1), k in the formula1|s|αsgn(s)-k′|s||s|sgn(s) plays a dominant role in enabling the system state to approach the sliding mode surface at a faster speed; otherwise-k' | sβsgn(s) dominates and reaches the slip-form face at a slower speed, ensuring good steady-state performance and attenuating buffeting. Therefore, the combination of the two terms can make the system have faster convergence speed and better motion quality. According to formula (13):
equation (14) and equation (17) are equal to each other, and thus:
therefore, an inverse sliding mode control law u based on the improved double power approximation law can be obtained as follows:
wherein k is1K ', α and α' are control law coefficients. The obtained inversion sliding mode control law enables the mobile robot to move along an expected path, and therefore accurate and rapid path tracking is achieved. .
The following describes a method for tracking and controlling a path of a mobile robot based on an improved approach law in further detail through simulation experiments.
The inversion sliding mode control law based on the improved double-power approximation law designed by the invention is recorded as a text method, the sliding mode control law based on the double-power approximation law is recorded as a method 1, and the error of the initial pose is givenThe linear velocity v of the mobile robot is 1m/s, and the simulation time is 8 seconds. The parameters of the two control laws are set as control law parameter k1＝0.8，k'＝1.4，α＝1.5，β＝0.8。
The simulation results are shown in fig. 3. It can be seen that the tracking error under the control law "text method" designed by the present invention can converge more quickly, for example, the distance/angle deviation converges to zero in about 1.4 seconds in the control law "text method" in fig. 4a, and the distance/angle deviation under the control law "method 1" reaches convergence after 4.5 seconds. As can be seen from fig. 4b, the buffeting is present in the control law "method 1" during the stabilization phase, whereas the control law "method herein" is smooth and buffeting-free. The control law "method herein" in fig. 4c converges to steady state faster than "method 1". The result shows that the control law designed by the invention not only can improve the rapidity of the convergence of the tracking error, but also has better steady-state performance.
2) Remote control experiment based on real scene;
in the invention, an iRobotCreate mobile robot is used as a controlled object, a path tracking remote control platform based on a mobile robot operating system is constructed, and the whole structure is shown in figure 5. The hardware part comprises: a Kinect camera, a client notebook, an iRobotCreate mobile robot, and a work-end desktop. The software part comprises: a mobile robot operating system ROS, a computer vision library OpenCV and a motion capture system.
The black adhesive tape (10 mm) on the ground is used as a reference path, and a path tracking experiment is carried out by adopting the path tracking control law designed by the invention. Setting pyramid segmentation thresholds as 270 and 50, and setting the maximum pyramid layer number as 9; the threshold in the threshold segmentation is 100; the iteration number in the image thinning is 300. Kinect camera parameters u0＝315.2(pixel)，v0＝261.6(pixel)，dx＝dy＝2.8(μm/pixel)，f＝1470(μm)，d1＝0.051m，d20.245m, rotation angle α 27 °; control law parameter k1＝0.8，k'＝1.4，α＝1.5，β＝0.8。
The real motion path of the mobile robot is obtained by using the motion capture system, and the position coordinates of the real motion path are compared with the reference path pasted on the ground, so as to obtain the comparison result between the reference path value and the real value, as shown in fig. 6. The starting coordinate of the mobile robot is (-0.4, 0.4). The root mean square error between the reference path and the actual path was calculated to be 0.012 meters. The experimental result shows that based on the constructed remote control experimental platform, under the control law designed by the invention, the tracking error of the mobile robot is converged faster and has better motion quality.
The invention relates to a mobile robot path tracking control method based on an improved approximation law.
Claims (7)
1. A mobile robot path tracking control method based on an improved approach law is characterized by comprising the following steps of;
step 1: acquiring a path parameter;
defining distance deviation and angle deviation, and establishing a path tracking error model; acquiring a reference path image with a camera; then, carrying out threshold segmentation and refinement on the acquired image; finally, calculating distance deviation and angle deviation under a mobile robot coordinate system through coordinate conversion and fitting;
step 2: designing a controller:
designing a switching function based on an inversion method, and improving a double-power approximation law to obtain an inversion sliding mode control law based on the improved double-power approximation law;
and step 3: and (3) according to the inversion sliding mode control law obtained in the step (2), enabling the mobile robot to move along an expected path, and further realizing accurate and rapid path tracking.
2. The method for controlling path tracking of mobile robot based on improved approach law according to claim 1, wherein in step1, the path tracking error model can be described as the following formula (1):
wherein, x is defined1＝xe，x2＝θe，u＝w，xeIs the distance deviation between the mobile robot and the reference path, thetaeThe angular deviation is, v is the moving speed of the mobile robot, and u is the control law.
3. The method as claimed in claim 1, wherein in step1, the camera is a Kinect camera.
4. The method according to claim 1, wherein in step1, the refining specifically comprises: and (3) adopting a Zhang rapid parallel thinning function voidmimiding in an OpenCV visual library to obtain a single pixel point set corresponding to the reference path, then obtaining a pixel coordinate of the reference path, and converting the pixel point coordinate from a camera coordinate system to a mobile robot coordinate system.
5. The method for controlling path tracking of a mobile robot based on improved approach law according to claim 1, wherein in step1, the coordinate fitting specifically comprises: and calculating the mean value, calculating a correlation coefficient, and calculating a regression coefficient and a regression constant to obtain a reference path equation.
6. The method for controlling path tracking of a mobile robot based on improved approach law according to claim 1, wherein in step2, the switching function s is represented by the following formula (13):
s＝θe+arctan(vxe) (13)。
7. the method for controlling path tracking of a mobile robot based on the improved approximation law according to claim 1, wherein the inverse sliding mode control law u based on the improved double power approximation law is represented by the following formula (19):
wherein k is1K ', α and α' are control law coefficients.
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