CN113342003A - Robot track tracking control method based on open-closed loop PID (proportion integration differentiation) type iterative learning - Google Patents

Robot track tracking control method based on open-closed loop PID (proportion integration differentiation) type iterative learning Download PDF

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CN113342003A
CN113342003A CN202110794279.5A CN202110794279A CN113342003A CN 113342003 A CN113342003 A CN 113342003A CN 202110794279 A CN202110794279 A CN 202110794279A CN 113342003 A CN113342003 A CN 113342003A
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mobile robot
open
iterative learning
robot
track
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刘晓平
黎星华
顾恺琦
田智予
张承耀
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Beijing University of Posts and Telecommunications
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Beijing University of Posts and Telecommunications
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0276—Control of position or course in two dimensions specially adapted to land vehicles using signals provided by a source external to the vehicle

Abstract

The invention discloses a robot track tracking control method based on open-closed loop PID type iterative learning, which comprises the following steps: s1, acquiring motion data of a mobile robot, acquiring the relation between time and a track of the mobile robot based on the motion data of the mobile robot, and constructing a discrete kinematics model based on the relation between the time and the track of the mobile robot; s2, formulating a target track, obtaining a motion state of the mobile robot based on the discrete kinematics model, and obtaining an error between the motion track of the mobile robot and the target track based on the motion state; and S3, iterating the error, and correcting the control input of the mobile robot. The invention can combine the open-loop iterative learning control law with the closed-loop iterative learning control law, quickly realize the output of the target track in the limited time, simultaneously meet the requirements of the robot system on the tracking precision and the anti-interference performance, and improve the system tracking control performance of the robot.

Description

Robot track tracking control method based on open-closed loop PID (proportion integration differentiation) type iterative learning
Technical Field
The invention relates to the field of mobile robot trajectory tracking control, in particular to a robot trajectory tracking control method based on open-closed loop PID (proportion integration differentiation) type iterative learning.
Background
The mobile robot has time-varying, strong coupling and nonlinear dynamic characteristics, and an accurate and complete mobile robot motion model cannot be obtained actually due to the inaccuracy of measurement and modeling and the influence of load change and external disturbance. The well-designed controller is an important premise for ensuring the robot to realize the track tracking, so that the controller has very important significance for further improving the control precision and the convergence speed of the track tracking of the mobile robot.
At present, many methods are used to solve the tracking problem of mobile robots, such as optimal control, backstepping control, sliding mode control, fuzzy control, neural network control, and combination of multiple control methods. Because an Iterative Learning Control (ILC) method is simple and does not need an accurate mathematical model of a dynamic system, the ILC is widely applied to an industrial robot with strong coupling, nonlinearity and multivariable to quickly and accurately execute a track tracking task. And the problems of the control method, such as the requirement of an accurate mathematical model for an optimal control method, the problem of dimension explosion in the design process of a backstepping method, the problem of system buffeting caused by discontinuity of sliding mode control, low control precision of a fuzzy control method, poor real-time performance of a neural network control method and the like, can be effectively solved.
The basic idea of ILC is to correct the current control input using the error information measured during the previous or several previous operations of the system, and to gradually reduce the tracking error of the system through multiple repeated operations until the output trajectory is tracked to the target trajectory over the entire time interval. Because the convergence condition based on the PID type iterative learning law is simple and is only related to a small number of system parameters, the method has good robustness on an uncertain system, is simple and effective in algorithm, small in calculated amount, needs a very small number of system priori knowledge, and is one of the most mature iterative learning control algorithms. Because the previous error information of the system is only utilized based on the open-loop PID type iterative learning control law, the error information of the current operation of the system is abandoned; the closed-loop PID type iterative learning control law only utilizes the error information of the current operation of the system and discards the error information of the previous operation of the system. Therefore, both of these methods have certain drawbacks from the control point of view.
Disclosure of Invention
Aiming at the problems, the invention provides a robot track tracking control method based on open-closed loop PID type iterative learning, which aims to solve the technical problems in the prior art, can combine an open-loop iterative learning control law with a closed-loop iterative learning control law, quickly realize the output of a target track on track tracking in limited time, simultaneously meet the requirements of a robot system on tracking precision and anti-interference performance, and improve the system tracking control performance of the robot.
In order to achieve the purpose, the invention provides the following scheme: the invention provides a robot track tracking control method based on open-closed loop PID type iterative learning, which comprises the following steps:
s1, acquiring motion data of a mobile robot, acquiring the relation between time and a track of the mobile robot based on the motion data of the mobile robot, and constructing a discrete kinematics model based on the relation between the time and the track of the mobile robot;
s2, formulating a target track, obtaining a motion state of the mobile robot based on the discrete kinematics model, and obtaining an error between the motion track of the mobile robot and the target track based on the motion state;
and S3, iterating the error, and correcting the control input of the mobile robot.
Preferably, the mobile robot type employs an incompletely constrained mobile robot.
Preferably, the specific process of S3 is: and correcting the current control input by utilizing a PID controller according to the error information output by the current iteration and the error information output by the previous iteration, and correspondingly adjusting the parameters of a learning gain matrix of proportion, integral and differential in the control input.
Preferably, the PID controller is an open-loop PID type iterative learning trajectory tracking controller.
Preferably, the discrete kinematic model is specifically:
Figure BDA0003162045810000031
q(k+1)＝q(k)+B(q(k)，k)up(k)
wherein:
Figure BDA0003162045810000032
where k is a discrete time sample, k is 1, …, n; delta T is the motion sampling time of the mobile robot; q (k) represents a mobile robot state vector, q (k) being [ x [ ]p(k)，yp(k)，θp(k)]T，xp(k) And yp(k) Is the coordinate of the center of mass of the mobile robot in a rectangular coordinate system, thetap(k) Is the azimuth angle of the mobile robot; u. ofp(k) Representing the control input velocity vector, up(k)＝[vp(k)，wp(k)]T，vp(k) And wp(k) Linear and angular velocities for the mobile robot motion; b (q), (k), k) is
Figure BDA0003162045810000041
The equivalent expression of (1).
Preferably, the error information iteration of the mobile robot is specifically:
qi(k+1)＝qi(k)+B(qi(k)，k)ui(k)+βi(k)
yi(k)＝qi(k)+γi(k)
in the formula, qi(k)，ui(k)，yi(k)，βi(k)，γi(k) Respectively the state, input, output, state disturbance and output noise of the ith iteration, Cqi(k) Is as follows.
Preferably, the trajectory tracking controller for open-closed loop PID type iterative learning specifically is:
Figure BDA0003162045810000042
LP(k)＝kpL(k)
LI(k)＝kiL(k)
LD(k)＝kdL(k)
where k is a discrete time sample, k is 1, …, n; l isP(k)、LI(k)、LD(k) Respectively, proportional, integral and differential learning gain matrices; k is a radical ofp、ki、kdProportional coefficient, integral coefficient and differential coefficient; e.g. of the typei(k)、ei(l) Learning errors for a previous iteration; e.g. of the typei+1(k)、ei+1(l) Learning an error for the current iteration; u. ofi(k) Is the input to the ith iteration.
Preferably, the track tracking controller of the open-closed loop PID type iterative learning controls the mobile robot to perform circular track and cosine track tracking motion.
The invention discloses the following technical effects:
1. the iterative learning control method is adopted in the invention, the control of the nonlinear coupling dynamic system with high uncertainty can be realized by a very simple algorithm in a given time range without depending on an accurate mathematical model of the system, and the given target track can be tracked with high precision.
2. The invention combines the open-loop iterative learning control law with the closed-loop iterative learning control law, can simultaneously utilize the error information of the previous operation and the error information of the current operation of the system to correct the current control input, and further improves the tracking control performance of the system.
3. By applying the open-loop PID type iterative learning control law, the accuracy of the track tracking control and the convergence speed of the algorithm are improved, and the differential type mobile robot tracking method is well suitable for external interference and noise influence, can quickly track the upper target track, and has a better tracking effect during track tracking.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a schematic diagram of a kinematics model and trajectory tracking problem of an incompletely constrained mobile robot according to an embodiment of the present invention;
FIG. 3 is a block diagram of a trajectory tracking control system of a mobile robot according to an embodiment of the present invention;
fig. 4(a) is a circular trajectory tracking motion picture of the mobile robot at 0 second under the open-close loop PID type iterative learning control law in the embodiment of the present invention;
fig. 4(b) is a circular trajectory tracking moving picture of the mobile robot at the 10 th second under the open-close loop PID type iterative learning control law in the embodiment of the present invention;
fig. 4(c) is a circular trajectory tracking moving picture of the mobile robot at 20 th second under the open-close loop PID type iterative learning control law in the embodiment of the present invention;
fig. 4(d) is a circular trajectory tracking moving picture of the mobile robot at 30 th second under the open-close loop PID type iterative learning control law in the embodiment of the present invention;
fig. 4(e) is a circular track tracking moving picture of the mobile robot at 40 th second under the open-close loop PID type iterative learning control law in the embodiment of the present invention;
fig. 4(f) is a circular trajectory tracking moving picture of the mobile robot at 50 th second under the open-close loop PID type iterative learning control law in the embodiment of the present invention;
FIG. 5 is a curve diagram of a circular trajectory tracking situation of the mobile robot under the PID type iterative learning control law in the embodiment of the present invention;
FIG. 6 is a schematic diagram of a curve of a circular trajectory tracking situation of the mobile robot under an open-close loop PID type iterative learning control law in the embodiment of the present invention;
FIG. 7 is a schematic diagram of an error curve in the x direction for a mobile robot to track a circular track under a PID type iterative learning control law and an open-close loop PID type iterative learning control law in the embodiment of the present invention;
FIG. 8 is a schematic diagram of a y-direction error curve of a mobile robot tracking a circular track under a PID type iterative learning control law and an open-close loop PID type iterative learning control law in the embodiment of the present invention;
FIG. 9 is a schematic diagram of an azimuth error curve for a mobile robot to track a circular track under a PID type iterative learning control law and an open-close loop PID type iterative learning control law according to an embodiment of the present invention;
fig. 10(a) is a 0 th cosine trajectory tracking motion picture of the mobile robot under the open-close loop PID type iterative learning control law in the embodiment of the present invention;
fig. 10(b) is a cosine trajectory tracking moving picture of the mobile robot at 10 th second under the open-close loop PID type iterative learning control law in the embodiment of the present invention;
fig. 10(c) is a 20 th cosine trajectory tracking motion picture of the mobile robot under the open-close loop PID type iterative learning control law in the embodiment of the present invention;
fig. 10(d) is a cosine trajectory tracking moving picture of the mobile robot at 30 seconds under the open-close loop PID type iterative learning control law in the embodiment of the present invention;
fig. 10(e) is a cosine trajectory tracking moving picture of the mobile robot at 40 th second under the open-close loop PID type iterative learning control law in the embodiment of the present invention;
fig. 10(f) is a cosine trajectory tracking moving picture of the mobile robot at 50 th second under the open-close loop PID type iterative learning control law in the embodiment of the present invention;
FIG. 11 is a curve diagram illustrating a cosine trajectory tracking situation of a mobile robot under a PID type iterative learning control law according to an embodiment of the present invention;
FIG. 12 is a curve diagram illustrating a cosine trajectory tracking situation of a mobile robot under an open-close loop PID type iterative learning control law according to an embodiment of the present invention;
fig. 13 is a schematic diagram of an error curve in the x direction of the mobile robot tracking the cosine trajectory under the PID iterative learning control law and the open-close loop PID iterative learning control law in the embodiment of the present invention;
FIG. 14 is a schematic diagram of an error curve in the y direction for tracking a cosine trajectory by a mobile robot under a PID type iterative learning control law and an open-close loop PID type iterative learning control law according to an embodiment of the present invention;
fig. 15 is a schematic view of an azimuth error curve of a mobile robot tracking a cosine trajectory under a PID iterative learning control law and an open-close loop PID iterative learning control law according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Referring to fig. 1 to 3, the present embodiment provides a robot trajectory tracking control method based on open-closed loop PID type iterative learning, including the following steps:
s1, collecting motion data of the mobile robot, obtaining a relation between time and a track of the mobile robot based on the motion data of the mobile robot, and constructing a discrete kinematics model based on the relation between the time and the track of the mobile robot, wherein the influence of external interference and noise on the state and output of a robot control system in an iteration process is considered.
Constructing a discrete kinematics model, wherein the motion state of the mobile robot in discrete time is specifically as follows:
Figure BDA0003162045810000091
q(k+1)＝q(k)+B(q(k)，k)up(k)
wherein:
Figure BDA0003162045810000092
where k is a discrete time sample, k is 1, …, n; delta T is the motion sampling time of the mobile robot; q (k) represents a mobile robot state vector, q (k) being [ x [ ]p(k)，yp(k)，θp(k)]T，xp(k) And yp(k) Is the coordinate of the center of mass of the mobile robot in a rectangular coordinate system, thetap(k) Is the azimuth angle of the mobile robot; u. ofp(k) Representing the control input velocity vector, up(k)＝[vp(k)，wp(k)]T，vp(k) And wp(k) Linear and angular velocities for the mobile robot motion; b (q), (k), k) is
Figure BDA0003162045810000093
The equivalent expression of (1).
The control problem of the robot motion trail tracking is to determine the control input up(k)＝[vp(k)，wp(k)]TSo that the actual pose state P (k) of the robot can be tracked to the expected pose state Pd(k) I.e. xp(k)→xd(k)，yp(k)→yd(k)，θp(k)→θd(k)。
S2, formulating a target track, obtaining the motion state of the mobile robot based on the discrete kinematics model, and obtaining the error between the motion track of the mobile robot and the target track based on the motion state.
And S3, iterating the error, and correcting the control input of the mobile robot. The method specifically comprises the following steps: and correcting the current control input by using a PID controller according to the error information output by the current iteration and the error information output by the previous iteration, and correspondingly adjusting the parameters of a learning gain matrix of proportion, integral and differentiation in the control input.
The mobile robot type adopts an incomplete constraint mobile robot, and the PID controller is an open-close loop PID type iterative learning trajectory tracking controller.
The error information iteration of the mobile robot is specifically as follows:
qi(k+1)＝qi(k)+B(qi(k)，k)ui(k)+βi(k)
yi(k)＝qi(k)+γi(k)
in the formula, qi(k)，ui(k)，yi(k)，βi(k)，γi(k) Respectively the state, input, output, state disturbance and output noise of the ith iteration, Cqi(k) Is as follows.
The track tracking controller for the open-closed loop PID type iterative learning specifically comprises:
Figure BDA0003162045810000101
LP(k)＝kpL(k)
LI(k)＝kiL(k)
LD(k)＝kdL(k)
where k is a discrete time sample, k is 1, …, n; l isP(k)、LI(k)、LD(k) Respectively, proportional, integral and differential learning gain matrices; k is a radical ofp、ki、kdProportional coefficient, integral coefficient and differential coefficient; e.g. of the typei(k)、ei(l) Learning errors for a previous iteration; e.g. of the typei+1(k)、ei+1(l) Learning an error for the current iteration; u. ofi(k) Is the input to the ith iteration.
Note that: for example, if the robot needs to track the desired trajectory 100 times, i is 100, but each iteration needs 50s, for example, and the time is discretized by 0.1s, the number k of discrete points (sampling points) is 500.
The proportional coefficient is used for accelerating the response speed of the system, the integral coefficient is used for eliminating steady-state errors, and the differential coefficient is used for improving the dynamic characteristics of the system. And the track tracking controller of the open-closed loop PID type iterative learning controls the mobile robot to perform circular track and cosine track tracking motion.
Example 1
Referring to fig. 4-9, in order to verify the superiority of the open-close loop PID Type Iterative Learning Control law proposed by the present invention to track the trajectory of the Mobile Robot, experiments were performed with the Mobile Robot trajectory tracking controller designed by the PID Type Iterative Learning Control law proposed in the prior art (h.wang, j.dong, and y.wang, "Discrete PID-Type Iterative Learning Control for Mobile Robot," Journal of Control Science and Engineering, pp.1-7, 2016 "). The mobile robot changes the initial state coordinate P (0) to [1, 0, pi/2 ]]TTracking a circular track with the radius of 1m and the equation of the circular track is Pd＝[xd(t)，yd(t)，θd(t)]T＝[cos(0.05πt)，sin(0.05πt)，0.05πt+π/2]T. The selected PID parameter is kp＝0.02、ki＝0.02、kd0.01, the state interference term is betai(t)＝0.001[sin(40πt)+0.05random(0，8)，sin(40πt)+0.05random(0，8)，sin(40πt)+0.05random(0，4)]TThe output measurement noise is white Gaussian noise and satisfies N (t) to N (0, 1), gammai(t) 0.001n (t). In the formula, random is a random number returned between 0 and 4; n (t) N (0, 1) represents a normal distribution of the noise N (t) subject to the criterion.
A part of a moving picture of the mobile robot performing the circular trajectory tracking of the open-closed loop PID type iterative learning control law is shown in fig. 3, and it can be seen from fig. 3 that the moving trajectory of the robot is approximately a circle.
The results of the circular trajectory tracking experiment of the mobile robot based on the PID type iterative learning control law and the open-closed loop PID type iterative learning control law are shown in FIGS. 5-9. As can be seen from fig. 5 and 6, both control laws track the desired circular trajectory well under the influence of external disturbances and noise. However, it can be seen from fig. 7-9 that the trajectory tracking effect of the open-closed loop PID type iterative learning control law-based design proposed by the present invention is better than that of the PID type iterative learning control law-based design. The mobile robot based on the open-closed loop PID type iterative learning control law has the advantages of higher tracking control precision, smaller pose error and higher convergence speed of the algorithm, and can effectively improve the track tracking performance of the mobile robot.
Example 2
Referring to fig. 10-15, in order to further verify that the open-close loop PID type iterative learning control law provided by the present invention can be applied to a mobile robot to track other tracks, a cosine curve is selected as the tracking track of the robot. And the experimental comparison is carried out with a mobile robot track tracking controller designed by a PID type iterative learning control law. The mobile robot changes from the initial state P (0) to [0, 1, 0 ]]TThe cosine trajectory is tracked, and the cosine trajectory equation is expressed as follows:
Pd＝[xd(t)，yd(t)，θd(t)]T＝[0.125t，cos(0.125t)，-atan(sin(0.125t))]T
wherein t is the moving time of the robot, and the selected PID parameter is kp＝0.02、ki＝0.015、kd0.01. The values of the state disturbance term and the noise are the same as those in embodiment 1.
A part of a motion picture of the mobile robot performing cosine trajectory tracking of the open-closed loop PID type iterative learning control law is shown in fig. 10, and it can be seen from fig. 10 that the motion trajectory of the robot is approximate to the shape of a cosine curve.
The results of the cosine trajectory tracking experiment of the mobile robot based on the PID type iterative learning control law and the open-closed loop PID type iterative learning control law are shown in FIGS. 11-12. As can be seen from fig. 11-12, both control laws track the desired cosine trajectory well under the influence of external disturbances and noise. However, as can be seen from fig. 13 to 15, the trajectory tracking effect of the open-closed loop PID type iterative learning control law-based design proposed by the present invention is better than that of the PID type iterative learning control law-based design. The mobile robot based on the open-closed loop PID type iterative learning control law has the advantages of higher tracking control precision, smaller pose error and higher convergence speed of the algorithm, and can effectively improve the track tracking performance of the mobile robot.
The invention discloses the following technical effects:
1. the iterative learning control method is adopted in the invention, the control of the nonlinear coupling dynamic system with high uncertainty can be realized by a very simple algorithm in a given time range without depending on an accurate mathematical model of the system, and the given target track can be tracked with high precision.
2. The invention combines the open-loop iterative learning control law with the closed-loop iterative learning control law, can simultaneously utilize the error information of the previous operation and the error information of the current operation of the system to correct the current control input, and further improves the tracking control performance of the system.
3. By applying the open-loop PID type iterative learning control law, the accuracy of the track tracking control and the convergence speed of the algorithm are improved, and the differential type mobile robot tracking method is well suitable for external interference and noise influence, can quickly track the upper target track, and has a better tracking effect during track tracking.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the present invention in its spirit and scope. Are intended to be covered by the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (8)

1. The robot track tracking control method based on the open-closed loop PID type iterative learning is characterized by comprising the following steps of:
s1, acquiring motion data of a mobile robot, acquiring the relation between time and a track of the mobile robot based on the motion data of the mobile robot, and constructing a discrete kinematics model based on the relation between the time and the track of the mobile robot;
s2, formulating a target track, obtaining a motion state of the mobile robot based on the discrete kinematics model, and obtaining an error between the motion track of the mobile robot and the target track based on the motion state;
and S3, iterating the error, and correcting the control input of the mobile robot.
2. The method for robot trajectory tracking control based on open-closed loop PID type iterative learning of claim 1, wherein the mobile robot type employs an incomplete constraint mobile robot.
3. The robot trajectory tracking control method based on the open-closed loop PID type iterative learning of claim 1, wherein the specific process of S3 is as follows: and correcting the current control input by utilizing a PID controller according to the error information output by the current iteration and the error information output by the previous iteration, and correspondingly adjusting the parameters of a learning gain matrix of proportion, integral and differential in the control input.
4. The robot trajectory tracking control method based on open-closed loop PID-type iterative learning of claim 3, wherein the PID controller is an open-closed loop PID-type iterative learning trajectory tracking controller.
5. The robot trajectory tracking control method based on the open-closed loop PID type iterative learning of claim 1, wherein the discrete kinematics model is specifically:
Figure FDA0003162045800000021
q(k+1)＝q(k)+B(q(k)，k)up(k)
wherein:
Figure FDA0003162045800000022
where k is a discrete time sample, k is 1, …, n; delta T is the motion sampling time of the mobile robot; q (k) represents a mobile robot state vector, q (k) being [ x [ ]p(k)，yp(k)，θp(k)]T，xp(k) And yp (k) is the coordinate of the centroid of the mobile robot in a rectangular coordinate system, thetap(k) Is the azimuth angle of the mobile robot; u. ofp(k) Representing the control input velocity vector, up(k)＝[vp(k)，wp(k)]T，vp(k) And wp(k) Linear and angular velocities for the mobile robot motion; b (q), (k), k) is
Figure FDA0003162045800000023
The equivalent expression of (1).
6. The robot trajectory tracking control method based on the open-closed loop PID type iterative learning of claim 5, wherein the error information iteration of the mobile robot is specifically:
qi(k+1)＝qi(k)+B(qi(k)，k)ui(k)+βi(k)
yi(k)＝qi(k)+γi(k)
in the formula, qi(k)，ui(k)，yi(k)，βi(k)，γi(k) Respectively state, input, output, state interference and output noise of the ith iteration.
7. The robot trajectory tracking control method based on open-closed loop PID type iterative learning of claim 4, wherein the trajectory tracking controller of the open-closed loop PID type iterative learning is specifically:
Figure FDA0003162045800000031
LP(k)＝kpL(k)
LI(k)＝kiL(k)
LD(k)＝kdL(k)
where k is a discrete time sample, k is 1, …, n; l isP(k)、LI(k)、LD(k) Respectively, proportional, integral and differential learning gain matrices; k is a radical ofp、ki、kdProportional coefficient, integral coefficient and differential coefficient; e.g. of the typei(k)、ei(l) Learning errors for a previous iteration; e.g. of the typei+1(k)、ei+1(l) Learning an error for the current iteration; u. ofi(k) Is the input to the ith iteration.
8. The robot trajectory tracking control method based on open-closed loop PID type iterative learning of claim 4, wherein the trajectory tracking controller of open-closed loop PID type iterative learning controls the mobile robot to perform circular trajectory and cosine trajectory tracking motion.
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