CN116627138B - Control method for self-adaptive weight mass of mobile robot with speed interval constraint - Google Patents
Control method for self-adaptive weight mass of mobile robot with speed interval constraint Download PDFInfo
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Abstract
The invention discloses a tracking control method for self-adaptive weight mass of a wheeled mobile robot with motion speed interval constraint. The method is characterized in that: based on a kinematic model of the mobile robot, restricting the movement speed of the robot within a specified interval range by limiting the speed input of each wheel by using a model prediction method; establishing a tracking error system by using the interval constraint motion speed and the dynamic model, providing a tracking control method of the self-adaptive weight mass, and realizing the asymptotic stability of the tracking error system based on the Lyapunov theory; based on STM32H7 series singlechip provide output PWM signal to motor drive module, to the mobile robot who loads different mass heavy object, can both realize the safe tracking motion under interval speed constraint. The method utilizes a new technology to restrict the movement speed interval of the mobile robot and adapts to different weight masses to realize cargo handling.
Description
Technical field:
The present invention relates to the field of mobile robot control, and more particularly to a method for controlling a weight-loaded wheeled mobile robot.
The background technology is as follows:
In recent years, more and more mobile robots are born to assist and even replace human beings to finish the carrying of industrial automation, industrial manufacturing and other production and living. In practical application, because the working space of the mobile robot is limited by the environment or the mobile robot and human are in the same working space, in order to ensure the safety and the conveying efficiency of the working environment, the higher performance requirement is put forward on the movement speed of the mobile robot; in addition, in the process of moving the robot, the robot generally needs to move according to a designated track, and because the weight to be moved is generally different in quality, a large track tracking error is often generated, so that collision danger with surrounding objects or staff is caused. Therefore, the control method for researching the motion speed interval constraint and the self-adaptive weight quality of the mobile robot has important significance for improving the environmental safety and the working efficiency of the mobile robot.
Although the existing research improves the tracking performance of the mobile robot from different angles, the related research results are not available in the tracking control method which considers the motion speed interval constraint of the mobile robot and the self-adaptive weight quality at the same time. In order to improve the safety of the moving environment of the mobile robot and the working efficiency of transporting goods, the invention utilizes a new technology to restrict the moving speed interval of the mobile robot, and provides a control method of the self-adaptive weight quality of the mobile robot from a new view angle under the restriction of the speed interval, thereby providing a new safe tracking moving mode for the mobile robot.
The invention comprises the following steps:
The invention aims to:
in order to solve the problems, the invention provides a mobile robot self-adaptive weight quality control method constrained by a movement speed interval, and aims to improve the safety and the working efficiency of a robot movement environment.
The technical scheme is as follows:
the invention is realized by the following technical scheme:
the self-adaptive weight quality control method of the mobile robot constrained by the movement speed interval is characterized by comprising the following steps of:
1) Based on a kinematic model of the mobile robot, limiting the speed input of each wheel by using a model prediction method, and establishing a system performance optimization index to restrict the motion speed of the mobile robot within a specified interval range;
2) By utilizing the interval constraint motion speed and the dynamic model, a mobile robot tracking error system is established, the information of weight quality is depicted in a separation system, an estimation expression of the weight quality is designed, a self-adaptive weight quality tracking control method is provided, and the asymptotic stability of the tracking error system is realized based on the Lyapunov theory.
The method comprises the following steps:
step 1) based on a kinematic model of a mobile robot, limiting the speed input of each wheel by using a model prediction method, and establishing a system performance optimization index to restrict the motion speed of the mobile robot within a specified interval range, and the method is characterized in that: the kinematic model of the mobile robot is described as follows
Wherein,
Representing the movement speeds of the mobile robot in three directions of an x axis, a y axis and a rotation angle; k (θ) represents a coefficient matrix, and θ represents an included angle between the x-axis and the x' -axis; v i (t) denotes the movement speed of each wheel of the mobile robot, i=1, 2,3,4; a represents half of the distance between the left and right wheels.
Further, the mobile robot kinematic model (1) is written as follows
Wherein the method comprises the steps ofIs the generalized inverse matrix of K (θ). Let X (t) = [ X (t) y (t) θ (t) ] T denote the system motion trajectory state, V (t) denote the system input,Representing the system output, discretizing the kinematic model (2), and expressing the speed input as an increment form to obtain a robot prediction model as
Where V (k-1) represents the speed input at the previous time of the system, Δv (k) = [ Δv 1(k) Δv2(k) Δv3(k) Δv4(k)]T ] represents the speed input increment at the current time, a=i 3 is the identity matrix,And T is a sampling period for the coefficient matrix of the prediction model.
Let N be the prediction time domain and N C be the control time domain. In order to restrict the actual motion speed of the robot, the speed of the mobile robot in a prediction time domain is establishedThe constraint interval of (2) is as follows:
Wherein the method comprises the steps of Represents the movement speed of the robot from the time k to the time k+N-1 in the prediction time domain,Represents the minimum value of the robot speed constraint interval in the prediction time domain,The maximum value of the robot speed constraint interval in the prediction time domain is represented.
The predicted time-domain mobile robot motion speed model obtained by the formula (3) is as follows:
Wherein the method comprises the steps of Represents the robot speed input delta in the control time domain, and Λ=r qΞ0,Φ＝RqΞ1,
R (k+ρ), ρ=0, 1 … N-1 represents a coefficient matrix corresponding to the robot system from time k to time k+n-1 in the prediction time domain, and I 4 represents a 4×4 identity matrix. Substituting equation (5) into equation (4) yields a predicted increment of velocity input in the time domainConstraint conditions of (2)
Wherein the method comprises the steps of
Further, the formula (6) may be in the form of:
wherein, phi is ν＝[-ΦT ΦT]T, the total number of the components is two,
In order to obtain a movement speed constraint interval of the mobile robot and avoid a specified speedThe error is too large, and the following objective function is established:
where G represents a positive definite symmetric matrix of appropriate dimensions. Substituting equation (5) into equation (8) can function the system objective into the following form
Wherein h=2 phi is T G phi, the total number of the components is,The optimization problem of the constraint of the available robot movement speed interval by combining the formula (7) and the formula (9) is as follows
Thus, by solving the optimization problem equation (10), a constrained sequence of velocity input increments can be obtainedAnd will beThe first value of the speed increment delta V (k) is used as the speed increment delta V (k), the prediction model (3) is used for calculating the limited speed input V (k) of each wheel of the mobile robot, and the kinematic model (2) is further used for calculating the movement speed of the mobile robotThe robot is constrained in a specified interval range, so that the safety of the robot motion environment is realized.
And 2) establishing a mobile robot tracking error system by using the interval constraint motion speed and the kinetic model, separating the information of the weight mass in the system, designing an estimation expression of the weight mass, providing a self-adaptive weight mass tracking control method, and realizing the asymptotic stability of the tracking error system based on the Lyapunov theory. The method is characterized in that: the mobile robot dynamics model is described as follows
Wherein the method comprises the steps of
M represents the mass of the mobile robot, M represents the mass of different heavy objects loaded, I 0 represents the moment of inertia of the mobile robot, X (t) represents the motion track of the mobile robot in three directions of the X axis, the y axis and the rotation angle, and u (t) represents the control input force of four wheels of the mobile robot.
On the basis of the mobile robot dynamics model (11), let X 1 (t) =x (t),The system state equation is obtained as follows:
Let the appointed training track of robot be X d (t), the actual motion track be X (t), then obtain the track tracking error as:
e1(t)＝X(t)-Xd(t)＝x1(t)-Xd(t) (13)
Design variables α and utilizing constrained speed of motion The resulting velocity tracking error is:
wherein c 1 >0 is the tuning parameter for the variable α.
Based on the dynamic model (12), the error system is obtained by combining the formula (14):
For equation (15), the coefficient matrix M 0 contains information about the robot loading weight mass M, and is decomposed as follows:
M0＝A+mH (16)
Wherein the method comprises the steps of
The estimated expression for the weight mass is designed using equation (16) as follows:
Wherein the method comprises the steps of Is an estimated value of M 0, which,Is the estimated value of m, and the estimated error
In order to enable a mobile robot to carry out a tracking movement with constrained movement speeds in the case of loading different mass goods, a control input force and an adaptation law are designed based on an error system (15) as follows:
Wherein the method comprises the steps of The generalized inverse matrix of B (theta), c 2 >0 is the regulating parameter of the controller, and gamma is the regulating parameter of the self-adaptive law.
The lyapunov function for building the mobile robot tracking error system is as follows:
deriving the error system (15) along the edge of the error system (20) to obtain
Substituting the control input force (18) and the adaptive law (19) into the formula (21) to obtain
Then, as can be seen from the equation (22), the track tracking error e 1 (t) and the speed tracking error e 2 (t) can realize asymptotic stability, and the controller (18) can restrict the actual movement speed of the mobile robot within a certain interval range, and under the condition of loading weights with different weights, the robot can adapt to the weight change to realize safe tracking movement.
And 3) providing an output PWM signal for a motor driving module based on an STM32H7 serial singlechip, and realizing safe tracking motion under interval speed constraint for mobile robots loaded with weights of different masses. The method is characterized in that: STM32H7 series singlechips are used as a main controller, and the input of the main controller is connected with a motor speed measuring module, and the output of the main controller is connected with a motor driving module; the motor driving module is connected with the direct current motor; the power supply system supplies power to the respective electrical devices. The control method of the main controller is to read the feedback signal X (t) of the motor encoder and the command signal X d (t) given by the main controller, and calculate an error signal. According to the error signal, the main controller calculates the control quantity of the motor according to a preset control algorithm, and sends the control quantity to the motor driving module, and the motor drives the wheels to rotate and move according to a designed control mode.
The advantages and effects:
The invention relates to a self-adaptive weight quality control method of a mobile robot constrained by a movement speed interval. The method is characterized in that: based on a kinematic model of the mobile robot, restricting the movement speed of the robot within a specified interval range by limiting the speed input of each wheel by using a model prediction method; by utilizing the interval constraint motion speed and the dynamic model, a tracking error system is established, the weight mass information of the system is separated, the estimated expression form is designed, a tracking control method of the self-adaptive weight mass is provided, and the asymptotic stability of the tracking error system is realized based on the Lyapunov theory. The method utilizes a new technology to restrict the movement speed interval of the mobile robot, adapts to different weight masses, realizes cargo handling, and improves the safety and the working efficiency of the robot movement environment.
Description of the drawings:
FIG. 1 is a block diagram of the operation of a controller according to the present invention;
FIG. 2 is a graph of a system of the present invention;
FIG. 3 shows a STM32H7 single-chip microcomputer minimum system of the invention;
FIG. 4 is a circuit of the ICM20948 speed measurement module of the present invention;
FIG. 5 is a circuit of a TB6612 motor drive module of the invention;
Fig. 6 is a HX711 weight mass measurement circuit of the present invention;
fig. 7 is a circuit of the general principles of the hardware of the present invention.
The specific embodiment is as follows:
the present invention will be further described with reference to the accompanying drawings, but the scope of the present invention is not limited by the examples.
The self-adaptive weight quality control method of the mobile robot constrained by the movement speed interval is characterized by comprising the following steps of:
1) Based on a kinematic model of the mobile robot, limiting the speed input of each wheel by using a model prediction method, and establishing a system performance optimization index to restrict the motion speed of the mobile robot within a specified interval range;
2) By utilizing the interval constraint motion speed and the dynamic model, a mobile robot tracking error system is established, the information of weight quality is depicted in a separation system, an estimation expression of the weight quality is designed, a self-adaptive weight quality tracking control method is provided, and the asymptotic stability of the tracking error system is realized based on the Lyapunov theory.
The method comprises the following steps:
step 1) based on a kinematic model of a mobile robot, limiting the speed input of each wheel by using a model prediction method, and establishing a system performance optimization index to restrict the motion speed of the mobile robot within a specified interval range, and the method is characterized in that: the kinematic model of the mobile robot is described as follows
Wherein,
Representing the movement speeds of the mobile robot in three directions of an x axis, a y axis and a rotation angle; k (θ) represents a coefficient matrix, and θ represents an included angle between the x-axis and the x' -axis; v i (t) denotes the movement speed of each wheel of the mobile robot, i=1, 2,3,4; a represents half of the distance between the left and right wheels.
Further, the mobile robot kinematic model (1) is written as follows
Wherein the method comprises the steps ofIs the generalized inverse matrix of K (θ). Let X (t) = [ X (t) y (t) θ (t) ] T denote the system motion trajectory state, V (t) denote the system input,Representing the system output, discretizing the kinematic model (2), and expressing the speed input as an increment form to obtain a robot prediction model as
Where V (k-1) represents the speed input at the previous time of the system, Δv (k) = [ Δv 1(k) Δv2(k) Δv3(k) Δv4(k)]T ] represents the speed input increment at the current time, a=i 3 is the identity matrix,And T is a sampling period for the coefficient matrix of the prediction model.
Let N be the prediction time domain and N C be the control time domain. In order to restrict the actual motion speed of the robot, the speed of the mobile robot in a prediction time domain is establishedThe constraint interval of (2) is as follows:
Wherein the method comprises the steps of Represents the movement speed of the robot from the time k to the time k+N-1 in the prediction time domain,Represents the minimum value of the robot speed constraint interval in the prediction time domain,The maximum value of the robot speed constraint interval in the prediction time domain is represented.
The predicted time-domain mobile robot motion speed model obtained by the formula (3) is as follows:
Wherein the method comprises the steps of Represents the robot speed input delta in the control time domain, and Λ=r qΞ0,Φ＝RqΞ1,
R (k+ρ), ρ=0, 1 … N-1 represents a coefficient matrix corresponding to the robot system from time k to time k+n-1 in the prediction time domain, and I 4 represents a 4×4 identity matrix. Substituting equation (5) into equation (4) yields a predicted increment of velocity input in the time domainConstraint conditions of (2)
Wherein the method comprises the steps of
Further, the formula (6) may be in the form of:
wherein, phi is ν＝[-ΦT ΦT]T, the total number of the components is two,
In order to obtain a movement speed constraint interval of the mobile robot and avoid a specified speedThe error is too large, and the following objective function is established:
where G represents a positive definite symmetric matrix of appropriate dimensions. Substituting equation (5) into equation (8) can function the system objective into the following form
Wherein h=2 phi is T G phi, the total number of the components is,The optimization problem of the constraint of the available robot movement speed interval by combining the formula (7) and the formula (9) is as follows
Thus, by solving the optimization problem equation (10), a constrained sequence of velocity input increments can be obtainedAnd will beThe first value of the speed increment delta V (k) is used as the speed increment delta V (k), the prediction model (3) is used for calculating the limited speed input V (k) of each wheel of the mobile robot, and the kinematic model (2) is further used for calculating the movement speed of the mobile robotThe robot is constrained in a specified interval range, so that the safety of the robot motion environment is realized.
And 2) establishing a mobile robot tracking error system by using the interval constraint motion speed and the kinetic model, separating the information of the weight mass in the system, designing an estimation expression of the weight mass, providing a self-adaptive weight mass tracking control method, and realizing the asymptotic stability of the tracking error system based on the Lyapunov theory. The method is characterized in that: the mobile robot dynamics model is described as follows
Wherein the method comprises the steps of
M represents the mass of the mobile robot, M represents the mass of different heavy objects loaded, I 0 represents the moment of inertia of the mobile robot, X (t) represents the motion track of the mobile robot in three directions of the X axis, the y axis and the rotation angle, and u (t) represents the control input force of four wheels of the mobile robot.
On the basis of the mobile robot dynamics model (11), let X 1 (t) =x (t),The system state equation is obtained as follows:
Let the appointed training track of robot be X d (t), the actual motion track be X (t), then obtain the track tracking error as:
e1(t)＝X(t)-Xd(t)＝x1(t)-Xd(t) (13)
Design variables α and utilizing constrained speed of motion The resulting velocity tracking error is:
Where c 1 >0 is the tuning parameter for variable α.
Based on the dynamic model (12), the error system is obtained by combining the formula (14):
For equation (15), the coefficient matrix M 0 contains information about the robot loading weight mass M, and is decomposed as follows:
M0＝A+mH (16)
Wherein the method comprises the steps of
The estimated expression for the weight mass is designed using equation (16) as follows:
Wherein the method comprises the steps of Is an estimated value of M 0, which,Is the estimated value of m, and the estimated error
In order to enable a mobile robot to carry out a tracking movement with constrained movement speeds in the case of loading different mass goods, a control input force and an adaptation law are designed based on an error system (15) as follows:
Wherein the method comprises the steps of The generalized inverse matrix of B (theta), c 2 >0 is the regulating parameter of the controller, and gamma is the regulating parameter of the self-adaptive law.
The lyapunov function for building the mobile robot tracking error system is as follows:
deriving the error system (15) along the edge of the error system (20) to obtain
Substituting the control input force (18) and the adaptive law (19) into the formula (21) to obtain
Then, as can be seen from the equation (22), the track tracking error e 1 (t) and the speed tracking error e 2 (t) can realize asymptotic stability, and the controller (18) can restrict the actual movement speed of the mobile robot within a certain interval range, and under the condition of loading weights with different weights, the robot can adapt to the weight change to realize safe tracking movement.
And 3) providing an output PWM signal for a motor driving module based on an STM32H7 serial singlechip, and realizing safe tracking motion under interval speed constraint for mobile robots loaded with weights of different masses. The method is characterized in that: STM32H7 series singlechips are used as a main controller, and the input of the main controller is connected with a motor speed measuring module, and the output of the main controller is connected with a motor driving module; the motor driving module is connected with the direct current motor; the power supply system supplies power to the respective electrical devices. The control method of the main controller is to read the feedback signal X (t) of the motor encoder and the command signal X d (t) given by the main controller, and calculate an error signal. According to the error signal, the main controller calculates the control quantity of the motor according to a preset control algorithm, and sends the control quantity to the motor driving module, and the motor drives the wheels to rotate and move according to a designed control mode.
Claims (1)
1. The control method of the self-adaptive weight mass of the mobile robot with the speed interval constraint is characterized in that the motion speed of the robot is constrained in a specified interval range by limiting the speed input of each wheel by using a model prediction method based on a kinematic model of the mobile robot; establishing a tracking error system by using the interval constraint motion speed and the dynamic model, providing a tracking control method of the self-adaptive weight mass, and realizing the asymptotic stability of the tracking error system based on the Lyapunov theory; the method comprises the following steps:
1) Based on a kinematic model of the mobile robot, limiting the speed input of each wheel by using a model prediction method, and establishing a system performance optimization index to restrict the motion speed of the mobile robot within a specified interval range;
2) Establishing a mobile robot tracking error system by using a motion speed and a dynamic model of interval constraint, separating information of weight quality in the system, designing an estimation expression of the weight quality, providing a tracking control method of self-adaptive weight quality, and realizing asymptotic stability of the tracking error system based on a Lyapunov theory;
Based on the kinematic model of the mobile robot, the motion speed of the mobile robot is constrained in a specified interval range by limiting the speed input of each wheel and establishing a system performance optimization index by using a model prediction method, and the kinematic model of the mobile robot is described as follows
Wherein,
Representing the movement speeds of the mobile robot in three directions of an x axis, a y axis and a rotation angle; k (θ) represents a coefficient matrix, and θ represents an included angle between the x-axis and the x' -axis; v i (t) denotes the movement speed of each wheel of the mobile robot, i=1, 2,3,4; a represents half of the distance between the left wheel and the right wheel;
Further, the mobile robot kinematic model (1) is written as follows
Wherein the method comprises the steps ofA generalized inverse matrix of K (θ); let X (t) = [ X (t) y (t) θ (t) ] T denote the system motion trajectory state, V (t) denote the system input,Representing the system output, discretizing the kinematic model (2), and expressing the speed input as an increment form to obtain a robot prediction model as
Where V (k-1) represents the speed input at the previous time of the system, Δv (k) = [ Δv 1(k) Δv2(k) Δv3(k) Δv4(k)]T ] represents the speed input increment at the current time, a=i 3 is the identity matrix,The coefficient matrix is a coefficient matrix of a prediction model, and T is a sampling period;
Let N be the prediction time domain and N C be the control time domain; in order to restrict the actual motion speed of the robot, the speed of the mobile robot in a prediction time domain is established The constraint interval of (2) is as follows:
Wherein the method comprises the steps of Represents the movement speed of the robot from the time k to the time k+N-1 in the prediction time domain,Represents the minimum value of the robot speed constraint interval in the prediction time domain,Representing the maximum value of the robot speed constraint interval in the prediction time domain;
The predicted time-domain mobile robot motion speed model obtained by the formula (3) is as follows:
Wherein the method comprises the steps of Represents the robot speed input delta in the control time domain, and Λ=r qΞ0,Φ＝RqΞ1,
R (k+ρ), ρ=0, 1 … N-1 represents the coefficient matrix corresponding to the robot system from time k to time k+n-1 in the prediction domain, and I 4 represents the 4×4 identity matrix; substituting equation (5) into equation (4) yields a predicted increment of velocity input in the time domainConstraint conditions of (2)
Wherein the method comprises the steps of
Further, the formula (6) may be in the form of:
Wherein, phi is ν＝[-ΦTΦT]T, the total number of the components is two,
In order to obtain a movement speed constraint interval of the mobile robot and avoid a specified speedThe error is too large, and the following objective function is established:
wherein G represents a positive definite symmetric matrix of appropriate dimension; substituting equation (5) into equation (8) can function the system objective into the following form
Wherein h=2 phi is T G phi, the total number of the components is,The optimization problem of the constraint of the available robot movement speed interval by combining the formula (7) and the formula (9) is as follows
Thus, by solving the optimization problem equation (10), a constrained sequence of velocity input increments can be obtainedAnd will beThe first value of the speed increment delta V (k) is used as the speed increment delta V (k), the prediction model (3) is used for calculating the limited speed input V (k) of each wheel of the mobile robot, and the kinematic model (2) is further used for calculating the movement speed of the mobile robotThe robot is constrained in a specified interval range, so that the safety of the robot motion environment is realized;
The method comprises the steps of establishing a mobile robot tracking error system by utilizing a motion speed and a dynamic model of interval constraint, separating information of weight mass in the system, designing an estimation expression of the weight mass, providing a tracking control method of self-adaptive weight mass, realizing asymptotic stability of the tracking error system based on Lyapunov theory, and describing the mobile robot dynamic model as follows
Wherein the method comprises the steps of
M represents the mass of the mobile robot, M represents the mass of different heavy objects loaded, I 0 represents the moment of inertia of the mobile robot, X (t) represents the motion track of the mobile robot in three directions of an X axis, a y axis and a rotation angle, and u (t) represents the control input force of four wheels of the mobile robot;
On the basis of the mobile robot dynamics model (11), let X 1 (t) =x (t), The system state equation is obtained as follows:
Let the appointed training track of robot be X d (t), the actual motion track be X (t), then obtain the track tracking error as:
e1(t)＝X(t)-Xd(t)＝x1(t)-Xd(t) (13)
design variable alpha and utilize constrained speed of motion The resulting velocity tracking error is:
Wherein c 1 >0 is the tuning parameter for variable α;
based on the dynamic model (12), the error system is obtained by combining the formula (14):
For equation (15), the coefficient matrix M 0 contains information about the robot loading weight mass M, and is decomposed as follows:
M0＝A+mH (16)
Wherein the method comprises the steps of
The estimated expression for the weight mass is designed using equation (16) as follows:
Wherein the method comprises the steps of Is an estimated value of M 0, which,Is the estimated value of m, and the estimated error
In order to enable a mobile robot to carry out a tracking movement with constrained movement speeds in the case of loading different mass goods, a control input force and an adaptation law are designed based on an error system (15) as follows:
Wherein the method comprises the steps of A generalized inverse matrix of B (theta), c 2 >0 is an adjusting parameter of the controller, and gamma is an adjusting parameter of the self-adaptive law;
the lyapunov function for building the mobile robot tracking error system is as follows:
deriving the error system (15) along the edge of the error system (20) to obtain
Substituting the control input force (18) and the adaptive law (19) into the formula (21) to obtain
Then, as can be seen from the equation (22), the track tracking error e 1 (t) and the speed tracking error e 2 (t) can realize asymptotic stability, and the controller (18) can restrict the actual movement speed of the mobile robot within a certain interval range, and under the condition of loading weights with different weights, the robot can adapt to the weight change to realize safe tracking movement.
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