CN117406710A - Mobile robot track tracking control method based on dynamic terminal sliding mode control - Google Patents
Mobile robot track tracking control method based on dynamic terminal sliding mode control Download PDFInfo
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Abstract
A mobile robot track tracking control method based on dynamic terminal sliding mode control comprises the following steps: 1) Analyzing a differential mobile robot, establishing a kinematic and dynamic model of the mobile robot under the condition of disturbance, and establishing a discretized track tracking error model based on the vehicle dynamic model; 2) Designing a kinematic trajectory tracking controller; 3) The method comprises the steps of designing an extended state observer to observe undetermined disturbance d in a dynamic model of the mobile robot; 4) And designing a mobile robot track tracking dynamic sliding mode controller based on the disturbance compensation of the extended state observer. The method and the device improve the robustness and the track tracking precision of the mobile robot control system.
Description
Technical Field
The invention belongs to the field of robot tracking control, relates to a track tracking control method of a wheel type differential mobile robot, and particularly relates to a mobile robot track tracking control method based on dynamic terminal sliding mode control.
Background
With the continuous development and perfection of robotics, mobile robots are now being applied in various fields such as industry, military, etc., and remain a hot spot for current robot field research. The mobile robot can be disturbed differently under different environments, such as dynamic parameter perturbation during road surface jolt, and the rain and snow head sheave skids sideways, so that a larger error occurs in the track tracking of the mobile robot. The sliding mode control is widely studied and applied in the field of mobile robots by virtue of the good anti-interference capability.
Disclosure of Invention
In order to further improve the robustness and track tracking precision of a mobile robot control system, the invention provides a mobile robot track tracking control method based on dynamic terminal sliding mode control, and designs a dynamic terminal sliding mode controller combined with an extended state observer, wherein the extended state observer is used for observing unmodeled dynamic and external interference and eliminating the shake phenomenon in sliding mode control, and the sliding mode dynamics controller ensures that tracking errors of a robot can be converged in a limited time.
In order to solve the technical problems, the invention provides the following technical scheme:
a mobile robot track tracking control method based on dynamic terminal sliding mode control comprises the following steps:
1) The method comprises the following steps of establishing a kinematic model of the mobile robot:
taking the center point o of the axis of the driving wheel of the mobile robot as a reference point, the kinematic model of the mobile robot is generally expressed as:
wherein q= [ xy θ ]] T The pose of the mobile robot under the global coordinate system at the moment k, x and y are the abscissa and the ordinate of the mobile robot under the global coordinate system, and θ is the yaw angle; u= [ vω ]] T The velocity matrix is the velocity matrix of the mobile robot, v is the linear velocity of the mobile robot, and omega is the angular velocity of the mobile robot; the transformation matrix S (q) is:
2) The kinematic trajectory tracking controller is designed as follows:
in order to enable the mobile robot to quickly track the expected track, the kinematic control rate of the robot is required to be designed to calculate the proper speed; the track tracking error model at the moment k of the mobile robot is as follows:
in the formula, v r ，ω r The expected linear speed and angular speed of the mobile robot; e, e x ，e y ，e θ Tracking errors of the mobile robot under a local coordinate system; in order to ensure that the track tracking error of the mobile robot can be converged to 0 more quickly and stably, designing a kinematic control rate by adopting an inversion method;
taking a new virtual feedback control rate:
z＝e x -k 1 arctan(ω)e y (4)
wherein k is 1 >0; the virtual feedback control rate can enable the mobile robot to track an expected track faster, and the lyapunov function is taken as follows:
for the derivation of the above, the following kinematic control rate is designed by the lyapunov stability theorem:
wherein k is 1 >0，k 2 >0，k 3 >0；v c ，ω c Is the expected k+1 moment calculated by the pose information of the mobile robot at the current k momentSpeed and angular speed;
3) The dynamic model of the mobile robot under the condition of disturbance is established, and the process is as follows:
the speed matrix of the mobile robot is controlled by the output torque of the left wheel motor and the right wheel motor of the robot, and external factors such as friction can influence the control precision of the robot, so that the dynamic model of the mobile robot is required to be established for further improving the performance of a robot control system, and the dynamic model of the mobile robot after being simplified is usually as follows:
wherein M is 0 ＝S T (q)MS(q)-ΔM，M 0 M (q) is a positive inertia matrix of the robot, and DeltaM is an uncertain part of the system; d= [ d ] 1 d 2 ] T Is the sum of the disturbances to which the system is subjected; b (q) is a driving moment transformation matrix; τ= [ τ ] 1 τ 2 ] T Moment output for left and right driving wheels of the robot; further comprises the following steps:
3) The extended state observer observes the undetermined disturbance d in the dynamic model of the mobile robot, and the process is as follows:
the existence of unknown disturbances d in the dynamic model pattern (8) is typically observed using an extended state observer as follows:
wherein z is 1 ＝[z 11 z 12 ] T ，z 2 ＝[z 21 z 22 ] T The observed value of the sum error d and u is output for the system;is a sensor measurement; k (K) 1 ＝diag{k 11 k 12 }>0,K 2 ＝diag{k 21 k 22 }>0 is an observation gain parameter matrix; e, e s ＝[e s1 e s2 ] T Is an observation error; the fal (·) function is a switching function, whose expression is:
wherein i=1, 2; sigma is the linear segment interval width;
4) The sliding mode dynamics controller is designed, and the process is as follows:
introducing an extended state observer observation value into a designed sliding mode dynamics controller so as to enable a mobile robot track tracking error to quickly converge, and defining a speed tracking error:
e＝u-u c (11)
wherein e= [ e 1 e 2 ] T The integral slip plane is designed as follows:
s＝e+c∫e dt (12)
where c=diag { c 1 c 2 }>0, for the parameters of the sliding mode surface to be designed, in order to ensure that the sliding mode surface can be converged in a limited time, eliminate control buffeting of a system and improve control performance, the sliding mode surface is combined with a terminal sliding mode idea, and the following new dynamic terminal sliding mode surface is designed:
wherein q and p are positive odd numbers and satisfy q<p<2q； Is a positive definite matrix to be designed. The dynamic sliding mode surface is derived:
the derivatives of the formula (8), the formula (15), and the formula (16) are substituted into the formula (18) and are:
taking the index approach rateWherein-> For the approach law parameters to be designed, the dynamic terminal dynamics control law of the system is designed as follows:
further, in the step 4), the dynamic terminal sliding mode track tracking control process is obtained as follows:
4.1: giving an expected track of the mobile robot, discretizing the expected track, and acquiring expected positions of the mobile robot at different points;
4.2: the process of (16) in the calculation formula is:
4.2.1 initializing parameters, namely initial pose, mass, moment of inertia, radius of a driving wheel and axial distance of the driving wheel of the mobile robot;
4.2.2, substituting the difference between the expected pose of the robot and the current pose into an outer ring kinematic control rate formula (11) of the mobile robot, and calculating the expected speed and the angular speed of the mobile robot;
4.2.3 substituting the expected speed and the angular speed of the mobile robot into an inner ring dynamics control rate formula (13) of the mobile robot, calculating the moment of the left wheel and the right wheel of the differential speed mobile robot, and observing a system total error d by using an extended state observer;
4.3: the moment calculated in 4.2 is sent to a driving motor, and the robot is controlled to track the expected track;
4.4: let k=k+1, jump to 4.2.
The beneficial effects of the invention are as follows: and the robustness and the track tracking precision of the mobile robot control system are improved.
Drawings
FIG. 1 is a schematic illustration of a mobile robot pose;
fig. 2 is a closed loop block diagram of a sliding mode trajectory tracking control.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1 and 2, a mobile robot trajectory tracking control method based on dynamic terminal sliding mode control, the method comprising the steps of:
1) The method comprises the following steps of establishing a mobile robot kinematic model:
taking the center point o of the axis of the driving wheel of the mobile robot as a reference point, the kinematic model of the mobile robot is generally expressed as:
wherein q= [ x y θ ]] T The pose of the mobile robot under the global coordinate system at the moment k, x and y are the abscissa and the ordinate of the mobile robot under the global coordinate system, and theta is the yaw angle; u= [ vω ]] T The velocity matrix is the velocity matrix of the mobile robot, v is the linear velocity of the mobile robot, and omega is the angular velocity of the mobile robot; variableThe matrix of the transform S (q) is:
2) The kinematic trajectory tracking controller is designed as follows:
in order to enable the mobile robot to quickly track the expected track, the kinematic control rate of the robot is required to be designed to calculate the proper speed; the track tracking error model at the moment k of the mobile robot is as follows:
in the formula, v k ，ω r The expected linear speed and angular speed of the mobile robot; e, e x ，e y ，e θ Tracking errors of the mobile robot under a local coordinate system; in order to ensure that the track tracking error of the mobile robot can be converged to 0 more quickly and stably, designing a kinematic control rate by adopting an inversion method;
taking a new virtual feedback control rate:
z＝e x -k 1 arctan(ω)e y (4)
wherein k is 1 >0; the virtual feedback control rate can enable the mobile robot to track an expected track faster, and the lyapunov function is taken as follows:
deriving the above, the following kinematic control rate can be designed by the lyapunov stability theorem:
wherein k is 1 >0，k 2 >0，k 3 >0；v c ，ω c Is moved byExpected speed and angular speed of k+1 moment calculated by pose information of the robot at the current k moment;
3) The dynamic model of the mobile robot under the condition of disturbance is established, and the process is as follows:
the speed matrix of the mobile robot is controlled by the output torque of the left wheel motor and the right wheel motor of the robot, and external factors such as friction can influence the control precision of the robot, so that the dynamic model of the mobile robot is required to be established for further improving the performance of a robot control system, and the dynamic model of the mobile robot after being simplified is usually as follows:
wherein M is 0 ＝S T (q)MS(q)-ΔM，M 0 M (q) is a positive inertia matrix of the robot, and DeltaM is an uncertain part of the system; d= [ d ] 1 d 2 ] T Is the sum of the disturbances to which the system is subjected;b (q) is a driving moment transformation matrix; τ= [ τ ] 1 τ 2 ] T Moment output for left and right driving wheels of the robot; further comprises the following steps:
3) The extended state observer observes the undetermined disturbance d in the dynamic model of the mobile robot, and the process is as follows:
the existence of unknown disturbances d in the dynamic model pattern (8) is typically observed using an extended state observer as follows:
wherein z is 1 ＝[z 11 z 12 ] T ，z 2 ＝[z 21 z 22 ] T The observed value of the sum error d and u is output for the system;is a sensor measurement; k (K) 1 ＝diag{k 11 k 12 }>0,K 2 ＝diag{k 21 k 22 }>0 is an observation gain parameter matrix; e, e s ＝[e s1 e s2 ] T Is an observation error; the fal (·) function is a switching function, whose expression is:
wherein i=1, 2; sigma is the linear segment interval width;
4) The sliding mode dynamics controller is designed, and the process is as follows:
introducing an extended state observer observation value into a designed sliding mode dynamics controller so as to enable a mobile robot track tracking error to quickly converge, and defining a speed tracking error:
e＝u-u c (11)
wherein e= [ e 1 e 2 ] T The integral slip plane is designed as follows:
s＝e+c∫e dt (12)
where c=diag { c 1 c 2 }>0, for the parameters of the sliding mode surface to be designed, in order to ensure that the sliding mode surface can be converged in a limited time, eliminate control buffeting of a system and improve control performance, the sliding mode surface is combined with a terminal sliding mode idea, and the following new dynamic terminal sliding mode surface is designed:
wherein q and p are positive odd numbers and satisfy q<p<2q； Is a positive definite matrix to be designed. The dynamic sliding mode surface is derived:
the derivatives of the formula (8), the formula (15), and the formula (16) are substituted into the formula (18) and are:
taking the index approach rateWherein-> For the approach law parameters to be designed, the dynamic terminal dynamics control law of the system is designed as follows:
the dynamic terminal sliding mode track tracking control process can be obtained according to the analysis:
4.1: giving an expected track of the mobile robot, discretizing the expected track, and acquiring expected positions of the mobile robot at different points;
4.2: the process of (16) in the calculation formula is:
4.2.1 initializing parameters, namely initial pose, mass, moment of inertia, radius of a driving wheel and axial distance of the driving wheel of the mobile robot;
4.2.2, substituting the difference between the expected pose of the robot and the current pose into an outer ring kinematic control rate formula (11) of the mobile robot, and calculating the expected speed and the angular speed of the mobile robot;
4.2.3 substituting the expected speed and the angular speed of the mobile robot into an inner ring dynamics control rate formula (13) of the mobile robot, calculating the moment of the left wheel and the right wheel of the differential speed mobile robot, and observing a system total error d by using an extended state observer;
4.3: the moment calculated in 4.2 is sent to a driving motor, and the robot is controlled to track the expected track;
4.4: let k=k+1, jump to 4.2.
According to the scheme of the embodiment, the dynamic terminal sliding mode controller combined with the extended state observer is designed, the extended state observer is used for observing unmodeled dynamic and external interference, meanwhile, the shake phenomenon in sliding mode control is eliminated, and the sliding mode dynamics controller ensures that tracking errors of a robot can be converged in a limited time. The robustness and the track tracking precision of the mobile robot control system are effectively improved.
The embodiments described in this specification are merely illustrative of the manner in which the inventive concepts may be implemented. The scope of the present invention should not be construed as being limited to the specific forms set forth in the embodiments, but the scope of the present invention and the equivalents thereof as would occur to one skilled in the art based on the inventive concept.
Claims (2)
1. The mobile robot track tracking control method based on dynamic terminal sliding mode control is characterized by comprising the following steps:
1) The method comprises the following steps of establishing a kinematic model of the mobile robot:
taking the center point o of the axis of the driving wheel of the mobile robot as a reference point, the kinematic model of the mobile robot is generally expressed as:
wherein q= [ x ] y θ] T The pose of the mobile robot under the global coordinate system at the moment k, x and y are the abscissa and the ordinate of the mobile robot under the global coordinate system, and θ is the yaw angle; u= [ vω ]] T The velocity matrix is the velocity matrix of the mobile robot, v is the linear velocity of the mobile robot, and omega is the angular velocity of the mobile robot; the transformation matrix S (q) is:
2) The kinematic trajectory tracking controller is designed as follows:
in order to enable the mobile robot to quickly track the expected track, the kinematic control rate of the robot is required to be designed to calculate the proper speed; the track tracking error model at the moment k of the mobile robot is as follows:
in the formula, v r ，ω r The expected linear speed and angular speed of the mobile robot; e, e x ，e y ，e θ Tracking errors of the mobile robot under a local coordinate system; in order to ensure that the track tracking error of the mobile robot can be converged to 0 more quickly and stably, designing a kinematic control rate by adopting an inversion method;
taking a new virtual feedback control rate:
z＝e x -k 1 arctan(ω)e y (4)
wherein k is 1 >0; the virtual feedback control rate can enable the mobile robot to track an expected track faster, and the lyapunov function is taken as follows:
for the derivation of the above, the following kinematic control rate is designed by the lyapunov stability theorem:
wherein k is 1 >0，k 2 >0，k 3 >0；v c ，ω c The expected speed and the angular speed of the k+1 moment are calculated by pose information of the mobile robot at the current k moment;
3) The dynamic model of the mobile robot under the condition of disturbance is established, and the process is as follows:
the speed matrix of the mobile robot is controlled by the output torque of the left wheel motor and the right wheel motor of the robot, and external factors such as friction can influence the control precision of the robot, so that the dynamic model of the mobile robot is required to be established for further improving the performance of a robot control system, and the dynamic model of the mobile robot after being simplified is usually as follows:
wherein M is 0 ＝S T (q)MS(q)-ΔM，M 0 M (q) is a positive inertia matrix of the robot, and DeltaM is an uncertain part of the system; d= [ d ] 1 d 2 ] T Is the sum of the disturbances to which the system is subjected; b (q) is a driving moment transformation matrix; τ= [ τ ] 1 τ 2 ] T Moment output for left and right driving wheels of the robot; further comprises the following steps:
3) The extended state observer observes the undetermined disturbance d in the dynamic model of the mobile robot, and the process is as follows: the existence of unknown disturbances d in the dynamic model pattern (8) is typically observed using an extended state observer as follows:
wherein z is 1 ＝[z 11 z 12 ] T ，z 2 ＝[z 21 z 22 ] T The observed value of the sum error d and u is output for the system;is a sensor measurement; k (K) 1 ＝diag{k 11 k 12 }>0,K 2 ＝diag{k 21 k 22 }>0 is an observation gain parameter matrix; e, e s ＝[e s1 e s2 ] T Is an observation error; the fal (·) function is a switching function, whose expression is:
wherein i=1, 2; sigma is the linear segment interval width;
4) The sliding mode dynamics controller is designed, and the process is as follows:
introducing an extended state observer observation value into a designed sliding mode dynamics controller so as to enable a mobile robot track tracking error to quickly converge, and defining a speed tracking error:
e＝u-u c (11)
wherein e= [ e 1 e 2 ] T The integral slip plane is designed as follows:
where c=diag { c 1 c 2 }>0, for the parameters of the sliding mode surface to be designed, in order to ensure that the sliding mode surface can be converged in a limited time, eliminate control buffeting of a system and improve control performance, the sliding mode surface is combined with a terminal sliding mode idea, and the following new dynamic terminal sliding mode surface is designed:
wherein q and p are positive odd numbers and satisfy q<p<2q； For the positive definite matrix to be designed, the derivation of the dynamic sliding mode surface is as follows:
the derivatives of the formula (8), the formula (15), and the formula (16) are substituted into the formula (18) and are:
taking the index approach rateWherein-> For the approach law parameters to be designed, the dynamic terminal dynamics control law of the system is designed as follows:
2. the mobile robot trajectory tracking control method based on dynamic terminal sliding mode control according to claim 1, wherein in the step 4), the dynamic terminal sliding mode trajectory tracking control process is obtained as follows:
4.1: giving an expected track of the mobile robot, discretizing the expected track, and acquiring expected positions of the mobile robot at different points;
4.2: the process of (16) in the calculation formula is:
4.2.1 initializing parameters, namely initial pose, mass, moment of inertia, radius of a driving wheel and axial distance of the driving wheel of the mobile robot;
4.2.2, substituting the difference between the expected pose of the robot and the current pose into an outer ring kinematic control rate formula (11) of the mobile robot, and calculating the expected speed and the angular speed of the mobile robot;
4.2.3 substituting the expected speed and the angular speed of the mobile robot into an inner ring dynamics control rate formula (13) of the mobile robot, calculating the moment of the left wheel and the right wheel of the differential speed mobile robot, and observing a system total error d by using an extended state observer;
4.3: the moment calculated in 4.2 is sent to a driving motor, and the robot is controlled to track the expected track;
4.4: let k=k+1, jump to 4.2.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117850215A (en) * | 2024-03-08 | 2024-04-09 | 华东交通大学 | Model-free self-adaptive sliding mode control method and system for high-speed motor train unit and electronic equipment |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117850215A (en) * | 2024-03-08 | 2024-04-09 | 华东交通大学 | Model-free self-adaptive sliding mode control method and system for high-speed motor train unit and electronic equipment |
| CN117850215B (en) * | 2024-03-08 | 2024-05-17 | 华东交通大学 | Model-free self-adaptive sliding mode control method and system for high-speed motor train unit and electronic equipment |
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