CN117850246A - Tracking control method for single-wheel mobile robot - Google Patents
Tracking control method for single-wheel mobile robot Download PDFInfo
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- CN117850246A CN117850246A CN202410258253.2A CN202410258253A CN117850246A CN 117850246 A CN117850246 A CN 117850246A CN 202410258253 A CN202410258253 A CN 202410258253A CN 117850246 A CN117850246 A CN 117850246A
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- 229920006395 saturated elastomer Polymers 0.000 claims abstract description 16
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Abstract
The invention discloses a single-wheel mobile robot tracking control method, which comprises the steps of providing a state feedback tracking control law according to a single-wheel mobile robot tracking control error equation; designing a high-gain predictor according to an error equation to obtain an estimated state of the high-gain predictor; obtaining an output feedback tracking control law according to the estimation state of the high-gain predictor; determining the saturation of the saturated output feedback tracking control law according to the maximum value of the state feedback tracking control law; obtaining a saturated output feedback tracking control law according to the output feedback tracking control law; and designing the gain and parameters of the high-gain observer meeting the stability condition to obtain the output feedback tracking control law meeting the requirement. According to the invention, all data of the displacement of the single-wheel mobile robot are not required to be directly acquired, the practicability of the control method is improved, an accurate system model is not required to be established, and the application range of the control method is widened.
Description
Technical Field
The invention relates to the technical field of single-wheel mobile robot control, in particular to a single-wheel mobile robot tracking control method.
Background
In practical applications, sensors for measuring states such as displacement, speed, acceleration, etc. of the single-wheel mobile robot cannot be obtained effectively due to high price, etc., so that the state feedback control of the single-wheel mobile robot cannot be realized, and therefore, research on output feedback tracking control of the single-wheel mobile robot for the reasons that all states cannot be obtained by using the sensors is important.
Currently, for the single-wheel mobile robot tracking control method, state feedback tracking control is generally designed, namely, the method is designed under an ideal condition that all states of the single-wheel mobile robot can be measured through sensors.
However, in practical application, because the actual conditions of expensive sensors, limited sensors, damage and the like often occur, the state of the single-wheel mobile robot cannot be measured completely, so that the state feedback tracking control method is difficult to realize, and for the difficulty that the displacement data of the single-wheel mobile robot in a certain direction cannot be measured through the sensors, the prior art has the case of designing a common observer to perform output feedback control.
Meanwhile, the single-wheel mobile robot in operation is also influenced by factors such as external environment interference, modeling errors and the like, and a common observer can only perform state estimation on an accurate model and output feedback, and cannot overcome the influence of imprecise factors of the model on a system, so that the effectiveness of a control effect is reduced.
Disclosure of Invention
The invention aims to provide a single-wheel mobile robot tracking control method which can solve the problem that displacement data of a single-wheel mobile robot in a certain direction cannot be obtained through measurement of a sensor and can also solve the influence of modeling errors on a system.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: a tracking control method of a single-wheel mobile robot comprises the following steps:
s1, obtaining a state feedback tracking control law according to a tracking control error equation of the single-wheel mobile robot;
s2, designing a high-gain predictor according to an error equation to obtain an estimated state of the high-gain predictor;
s3, obtaining an output feedback tracking control law according to the estimation state of the high-gain predictor;
s4, determining the saturation of the saturated output feedback tracking control law according to the maximum value of the state feedback tracking control law;
s5, obtaining a saturated output feedback tracking control law according to the output feedback tracking control law,
；
wherein,representing saturation function->Is saturation;
s6, designing the gain of the high-gain observer meeting the stability conditionAnd parameters->And obtaining an output feedback tracking control law meeting the requirements.
Preferably, in the step S1, the tracking control error equation of the single-wheel mobile robot is:
；
wherein,is error state vector, +.>For virtual control force, ++>For target control->Respectively->Shaft displacement, & lt & gt>Shaft displacement and->The tracking error of the included angle of the axes,for outputting the vector +.>Is a coefficient matrix.
Preferably, in the step S1, the state feedback tracking control law is:
；
wherein,for controller gain, a closed loop system matrix is formed by a pole allocation methodIs Hurwitz.
Preferably, in the step S2, according to a single-wheel mobile robot tracking control error equation, the high-gain observer equation is designed as follows:
；
wherein,for high gain observer gain, +.>For high gain observer parameters,/->Is the state vector of the high gain observer, +.>Is the output vector of the high gain observer, +.>As a function of
Nominal function of (2), i.e. function in the original system +.>Modeling errors are allowed.
Preferably, in the step S3, the state generated by the high-gain observer is substituted for the state in the state feedback vibration damping control law, and the output feedback tracking control law is obtained as follows:
。
preferably, in the step S4, the saturation of the saturated output feedback tracking control law is determined according to the maximum value of the state feedback tracking control law, that is:
。
preferably, in the step S5, the output feedback tracking control law is saturated according to the saturation obtained in the feedback tracking control law, that is, a saturated output feedback tracking control law is obtained:
。
preferably, in the step S6, the gain of the high gain observer satisfying the stability condition is designedAnd parameters->The specific process is as follows:
A1. designing gain of high gain observer using pole allocation methodSo thatAll roots of (2) have negative real parts;
A2. adjusting parameters of a high gain observerSo that the state of the closed loop system under the high gain observer is asymptotically stable.
Compared with the prior art, the invention has the advantages that:
1. according to the invention, all data of the displacement of the single-wheel mobile robot are not required to be directly acquired, and the practicability of the control method is improved. Compared with the existing control method requiring all displacement data of the single-wheel mobile robot, the method can be used for only measuring and obtaining displacement data of the single-wheel mobile robot in a certain direction, and zero-error tracking of the single-wheel mobile robot on a target track is effectively controlled.
2. The invention does not need to establish an accurate system model, and widens the application range of the control method. Compared with the existing control algorithm requiring an accurate system model, the gain of the high-gain observer in the control overcomes the influence of external interference, modeling errors of the system and other factors, and ensures the accuracy and adaptability of the target track zero error tracking of the single-wheel mobile robot.
3. The form of the tracking control law covers linear tracking control and nonlinear tracking control, can be applied to other tracking control scenes except the tracking control law, and has good expansibility for wider application models and stricter control requirements.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a diagram of a dynamic model of a single-wheel mobile robot;
FIG. 2 is a graph of a simulation of the tracking error response of the displacement of the x-axis of the single wheel mobile robot according to the present invention;
FIG. 3 is a graph showing a tracking error response value simulation of the y-axis displacement of the single-wheel mobile robot according to the present invention;
FIG. 4 is a graph showing a tracking error response value simulation of the included angle between the single-wheel mobile robot and the x-axis;
FIG. 5 is a numerical simulation diagram of the single-wheel mobile robot tracking the 8-shaped target track under the condition that all states of the single-wheel mobile robot can be measured by a sensor;
FIG. 6 is a simulation diagram of a single-wheel mobile robot tracking 8-shaped target track when the parameter is 0.2 under the condition that the state is estimated by the high-gain observer;
fig. 7 is a simulation diagram of a single-wheel mobile robot tracking 8-shaped target track when the parameter is 0.1 under the condition that the high-gain observer estimates the obtained state.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making clear and defining the scope of the present invention.
The state feedback tracking control law of the common single-wheel mobile robot is as follows:
wherein,control force applied to the single-wheel mobile robot, respectively,>target control force for the tracked target track, < >>For virtual control force, ++>Respectively->Shaft displacement, & lt & gt>Shaft displacement and->Tracking error of the axis angle.
Therefore, the realization of the tracking control law requires that the sensor measures the displacement, the speed and the acceleration data of the single-wheel mobile robot in real time, and once a certain sensor cannot measure certain state data, the state feedback tracking control cannot be realized.
Therefore, the invention provides a single-wheel mobile robot tracking control method, which comprises the following steps:
s1, obtaining a state feedback tracking control law according to a tracking control error equation of the single-wheel mobile robot；
S2, designing a high-gain predictor according to an error equation to obtain an estimated state of the high-gain predictor；
S3, obtaining an output feedback tracking control law according to the estimation state of the high-gain predictor；
S4, determining the saturation of the saturated output feedback tracking control law according to the maximum value of the state feedback tracking control law；
S5, obtaining a saturated output feedback vibration damping control law according to the output feedback vibration damping control law；
S6, designing the gain of the high-gain observer meeting the stability conditionAnd parameters->And obtaining an output feedback tracking control law meeting the requirements.
Specifically, a destrack error equation is obtained according to the one-wheel mobile robot dynamics model as shown in fig. 1.
The tracking control error equation of the single-wheel mobile robot is as follows:
（1）
wherein,is error state vector, +.>The control forces are respectively virtual control forces,for target control->Respectively->Shaft displacement, & lt & gt>Shaft displacement and->Tracking error of axis angle, ">For outputting the vector +.>Respectively coefficient matrices.
A state feedback tracking control law is designed for a single-wheel mobile robot tracking system (1):
（2）
wherein,for controller gain, a closed loop system matrix is formed by a pole allocation methodIs Hurwitz.
According to the system equation (1), a high gain observer is designed:
（3）
wherein,for high gain observer gain, +.>For high gain observer parameters,/->Is the state vector of the high gain observer, +.>Is the output vector of the high gain observer, +.>Is a function->Nominal function of (2), i.e. function in the original system +.>Modeling errors are allowed.
Will be highState of gain observer (3)Instead of state feedback tracking the state in control law (2)>Obtaining an output feedback tracking control law:
（4）
determining the saturation of the saturated output feedback tracking control law according to the maximum value of the state feedback tracking control law (2):
（5）
saturating the output feedback tracking control law (4) by the saturation obtained in the step (5) to obtain a saturated output feedback tracking control law:
（6）
designing the gain of a high gain observer that satisfies stability conditionsAnd parameters->The process of (2) is as follows:
A1. design of high gain observer gain using pole allocation methodSo that the equationAll roots of (2) have negative real parts;
A2. adjusting parameters of a high gain observerSo thatThe closed loop system state under the high gain observer is asymptotically stable.
Such as the one-wheel mobile robot shown in fig. 1. As shown in fig. 2 and 3, the state feedback tracking control law (2) and the output feedback tracking control law (6) are used as tracking controllers of the single-wheel mobile robot, respectively, and the MATLAB is used for performing numerical simulation.
At this time, the gain of the controller is obtained by using a pole allocation methodApplying a state feedback tracking controller (2) to the single-wheel mobile robot, resulting in +.f. indicated by the solid lines in FIGS. 2-4>Shaft displacement, & lt & gt>Shaft displacement and->The tracking error response of the axis angle. However, in consideration of the fact that the whole displacement of the single-wheel mobile robot is difficult to obtain through the measurement of the sensor in practical application, and modeling errors possibly exist in the system model (1), the state feedback tracking control law (2) is invalid in the cases. In these cases, a high gain observer (3) and its output feedback tracking control law (4) are designed. Obtain +.>Thereby obtaining a saturated output feedback tracking controller (6), selectingAnd the parameters of the high gain observer are selected respectively +.>Applying a tracking controller to the single-wheel mobile robot to obtain a tracking 8-shaped displacement error response shown by two dotted lines in fig. 2 to 4, and black is a single-wheel mobile robot tracking rail shown in fig. 5The trace, gray, is the target trace. As shown in fig. 6 and 7, it can be seen that: under the condition that the initial state is the same, the single-wheel mobile robot can track the 8-shaped target track more quickly and without errors than the single-wheel mobile robot with the parameter of 0.1.
It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
Claims (8)
1. The single-wheel mobile robot tracking control method is characterized by comprising the following steps of:
s1, obtaining a state feedback tracking control law according to a tracking control error equation of the single-wheel mobile robot;
s2, designing a high-gain predictor according to an error equation to obtain an estimated state of the high-gain predictor;
s3, obtaining an output feedback tracking control law according to the estimation state of the high-gain predictor;
s4, determining the saturation of the saturated output feedback tracking control law according to the maximum value of the state feedback tracking control law;
s5, obtaining a saturated output feedback tracking control law according to the output feedback tracking control law,
；
wherein,representing saturation function->Is saturation;
s6, designing the gain of the high-gain observer meeting the stability conditionAnd parameters->And obtaining an output feedback tracking control law meeting the requirements.
2. The method according to claim 1, wherein in the step S1, the single-wheel mobile robot tracking control error equation is:
；
wherein,is error state vector, +.>For the purpose of a virtual control force,for target control->Respectively->Shaft displacement, & lt & gt>Shaft displacement and->Tracking error of axis angle, ">For outputting the vector +.>Is the coefficientA matrix.
3. The method for tracking and controlling the single-wheel mobile robot according to claim 2, wherein: in the step S1, the state feedback tracking control law is:
；
wherein,for controller gain, a closed loop system matrix is formed by a pole allocation methodIs Hurwitz.
4. The method according to claim 3, wherein in the step S2, according to a single-wheel mobile robot tracking control error equation, a high-gain observer equation is designed as follows:
；
wherein,for high gain observer gain, +.>For high gain observer parameters,/->Is the state vector of the high gain observer, +.>Is the output vector of the high gain observer, +.>As a function of
Nominal function of (2), i.e. function in the original system +.>Modeling errors are allowed.
5. The method according to claim 4, wherein in the step S3, the state generated by the high gain observer is used to replace the state in the state feedback vibration damping control law, and the output feedback tracking control law is obtained as follows:
。
6. the method according to claim 5, wherein in the step S4, the saturation of the saturation output feedback tracking control law is determined according to the maximum value of the state feedback tracking control law, that is:
。
7. the method according to claim 6, wherein in step S5, the output feedback tracking control law is saturated according to the saturation obtained in the feedback tracking control law, that is, a saturated output feedback tracking control law is obtained:
。
8. the method according to claim 4, wherein in step S6, the gain of the high gain observer satisfying the stability condition is designedAnd parameters->The specific process is as follows:
A1. designing gain of high gain observer using pole allocation methodSo thatAll roots of (2) have negative real parts;
A2. adjusting parameters of a high gain observerSo that the state of the closed loop system under the high gain observer is asymptotically stable.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103592847A (en) * | 2013-10-30 | 2014-02-19 | 天津大学 | Hypersonic aerocraft nonlinear control method based on high-gain observer |
| CN108508750A (en) * | 2018-05-08 | 2018-09-07 | 重庆大学 | A kind of output feedback ontrol method of TORA systems |
| CN111596679A (en) * | 2020-06-03 | 2020-08-28 | 青岛大学 | Finite time output feedback attitude tracking control method for aircraft |
| CN114035588A (en) * | 2021-11-30 | 2022-02-11 | 黄山学院 | Mobile robot trajectory tracking event trigger control method |
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103592847A (en) * | 2013-10-30 | 2014-02-19 | 天津大学 | Hypersonic aerocraft nonlinear control method based on high-gain observer |
| CN108508750A (en) * | 2018-05-08 | 2018-09-07 | 重庆大学 | A kind of output feedback ontrol method of TORA systems |
| CN111596679A (en) * | 2020-06-03 | 2020-08-28 | 青岛大学 | Finite time output feedback attitude tracking control method for aircraft |
| CN114035588A (en) * | 2021-11-30 | 2022-02-11 | 黄山学院 | Mobile robot trajectory tracking event trigger control method |
Non-Patent Citations (4)
| Title |
|---|
| MUHAMMAD ASIF, ET AL: "Output feedback control for trajectory tracking of wheeled mobile robot", 《INTELLIGENT AUTOMATION AND SOFT COMPUTING》, vol. 22, no. 1, 22 May 2015 (2015-05-22) * |
| YU-MEI HUANG&JING LEI: "Predictive Feedback Linearization Tracking Control for WMR Systems with Control Delay", 《INTEGRATED FERROELECTRICS》, vol. 217, no. 1, 21 July 2021 (2021-07-21) * |
| 鄢立夏;马保离;: "轮式移动机器人的位置量测输出反馈轨迹跟踪控制", 控制理论与应用, no. 06, 15 June 2016 (2016-06-15) * |
| 雷婧，等: "《机器人系统输出反馈控制》", vol. 1, 30 November 2023, 清华大学出版社, pages: 37 - 62 * |
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