CN112034842A - Service robot speed constraint tracking control method suitable for different users - Google Patents

Service robot speed constraint tracking control method suitable for different users Download PDF

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CN112034842A
CN112034842A CN202010794629.3A CN202010794629A CN112034842A CN 112034842 A CN112034842 A CN 112034842A CN 202010794629 A CN202010794629 A CN 202010794629A CN 112034842 A CN112034842 A CN 112034842A
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speed
random
robot
service robot
different users
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CN112034842B (en
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孙平
孙桐
薛皖东
李树江
刘明硕
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Shenyang University of Technology
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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
    • G05D1/0214—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory in accordance with safety or protection criteria, e.g. avoiding hazardous areas
    • 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 speed constraint tracking control method of the service robot suitable for different users comprises the following steps: 1) establishing a random differential equation describing the mass change of different users; 2) restricting the movement speed of the robot in the axial axis and rotation angle directions; 3) establishing a tracking error system by utilizing the constrained motion speed in the step 2) and combining the random differential equation in the step 1), and establishing an exponential stability condition of the tracking error system based on a random stability theory to realize a speed constraint tracking control method suitable for different users. The controller of the invention has simple design and easy realization, and the controller has no quality information of users, thereby enabling the service robot to be applied to different users and improving the track tracking precision; meanwhile, a method for restricting the movement speed is provided for the service robot system described by the random differential equation, the robot speed is prevented from sudden change, and the safety of a user is guaranteed.

Description

Service robot speed constraint tracking control method suitable for different users
The technical field is as follows:
the invention relates to the field of control of service robots, in particular to a control method of a wheeled life service robot.
Background art:
traffic accidents and aging population increase the number of the patients with dysbasia year by year, and the patients with dysbasia cannot get timely and effective exercise training due to the lack of professional rehabilitation personnel in China, so that the walking function is gradually lost, and the daily independent life cannot be realized. With the application of the service robot in places such as homes, nursing homes and the like, the problem of self-standing life of walking disorder patients is effectively solved. However, in practical applications, users with different masses may cause the robot to deviate from the indoor motion trajectory, which seriously affects the tracking accuracy of the robot, and even causes the robot to collide with surrounding obstacles. In addition, the uncertain external environment in the robot motion process inevitably leads to the sudden change of the speed of the robot and threatens the safety of a user. Therefore, it is important to research a control method of the service robot to be adaptable to users of different qualities and to help the walking disorder patients to realize daily independent life at a restricted movement speed.
In recent years, there have been many research results on tracking control of a service robot, but none of the results can solve the problem of random variation of quality of different users. If the robot cannot adapt to users with different qualities, not only is the tracking precision affected, but also excessive tracking errors can cause the robot to collide with surrounding objects, thereby threatening the safety of the users. Meanwhile, the service robot dynamics system described by the random differential equation cannot directly restrict the movement speed of the service robot dynamics system. Therefore, no tracking control method with randomly changing quality and constrained speed for different users exists so far, and the method for improving the tracking precision of the service robot is researched based on a new visual angle, so that the method has important significance for ensuring that asynchronous dysbasia patients can safely realize daily independent life.
The invention content is as follows:
the purpose of the invention is as follows:
in order to solve the problems, the invention provides a service robot speed constraint tracking control method suitable for different users, aiming at improving the tracking precision of the robot and ensuring the safety of the users.
The technical scheme is as follows:
a service robot speed constraint tracking control method suitable for different users,
the method comprises the following steps:
1) according to the dynamic model of the service robot, the coefficient matrix M is calculated0Decomposing the mass m of the middle trainer into a constant value and a random variable, and establishing a random differential equation describing the mass change of different users;
2) based on a kinematic model of the service robot, a model prediction control method for controlling the movement speed of each wheel is provided, and the robot is further constrained on an x axis,ySpeed of movement of axes and rotation angles
Figure BDA0002625102450000021
3) Establishing a tracking error system by utilizing the constrained motion speed in the step 2) and combining the random differential equation in the step 1), and establishing an exponential stability condition of the tracking error system based on a random Lyapunov stability theory to realize a speed constraint tracking control method suitable for different users.
In step 1): the kinetic model is described as follows:
Figure BDA0002625102450000022
wherein
Figure BDA0002625102450000023
Figure BDA0002625102450000024
X (t) represents an actual walking track of the service robot, u (t) represents a control input force, fi(I ═ 1,2,3) denotes the input force per wheel, M denotes the mass of the robot, M denotes the mass of the user, I denotes the mass of the robot0Representing moment of inertia, M0B (theta) is a coefficient matrix; theta denotes the angle between the horizontal axis and the line connecting the center of the robot and the center of the first wheel, l denotes the distance from the center of the system to the center of each wheel,
Figure BDA00026251024500000212
representing the moment of inertia of the user;
coefficient matrix M0Mass m of the middle user is decomposed into m ═ mr+ Δ m, where mrRepresenting a set constant value of mass, Δ m representing a random variation value of mass, and converting Δ m into random noise η (t), the following equation is obtained:
Figure BDA0002625102450000025
wherein
Figure BDA0002625102450000026
Is MRAn inverse matrix of
Figure BDA0002625102450000027
Figure BDA0002625102450000028
The random noise η (t) is expressed as
Figure BDA0002625102450000029
Wherein upsilon represents a 3-dimensional independent random process, and
Figure BDA00026251024500000210
order to
Figure BDA00026251024500000211
(v ═ 1,2, 3; σ ═ 1,2,3), and calculated
Figure BDA0002625102450000031
Further, the formula (3) is represented by
Figure BDA0002625102450000032
Setting the spectral density of the random noise eta (t) as
Figure BDA0002625102450000033
Namely, it is
Figure BDA0002625102450000034
Where Λ represents the spectral density matrix,
Figure BDA0002625102450000035
representing a random process with a spectral density distribution, thus obtaining a random differential equation for the service robot
Figure BDA0002625102450000036
In step 2): the kinematic model of the system is described as follows:
Figure BDA0002625102450000037
wherein B isG(t) represents a coefficient matrix, and
Figure BDA0002625102450000038
V(t)＝[v1(t) v2(t) v3(t)]T，vi(t) (i ═ 1,2,3) represents the speed of movement of each wheel;
as further shown in equation (7),
Figure BDA0002625102450000039
discretizing equation (8), and making y (t) ═ x (t) represent system output, and writing speed input v (t) into incremental expression form to obtain the prediction model as follows
Figure BDA00026251024500000310
Wherein k is 0,1, …, N-1, N represents the prediction time domain; x (k) and X (k +1) respectively represent the motion trail of the robot at the current moment and the later moment; y (k) represents the robot motion position output at the current moment; Δ V (k) represents the current time speed increment, V (k-1) represents the previous time speed input; a ═ I3，
Figure BDA00026251024500000311
T represents the sampling time, I3An identity matrix representing a suitable dimension;
next, the x-axis is constructed,yPredicted speed of shaft and rotation angle direction
Figure BDA00026251024500000312
And predicted input for each wheel speed
Figure BDA00026251024500000313
The constraints of (2) are as follows:
Figure BDA00026251024500000314
wherein
Figure BDA0002625102450000041
Predictive input representing speed, NCIn order to control the time domain,
Figure BDA0002625102450000042
upper and lower predicted input bounds representing speeds, respectively;
Figure BDA0002625102450000043
which represents the predicted actual speed of movement,
Figure BDA0002625102450000044
an upper bound and a lower bound representing the actual movement speed, respectively;
from equation (9), the predicted speed model is obtained as follows:
Figure BDA0002625102450000045
wherein
Figure BDA0002625102450000046
Φ＝BpL0，G＝BpL1，
Figure BDA0002625102450000047
B (k +), 0,1 … N-1 represents the values of the coefficient matrix B at different sampling instants in equation (9);
substituting equation (11) into constraint (10) and conditioning the constraint as a speed input increment
Figure BDA0002625102450000048
In the form of
Figure BDA0002625102450000049
Wherein
Figure BDA00026251024500000410
Figure BDA00026251024500000411
Figure BDA00026251024500000412
Figure BDA00026251024500000413
b1minAnd b1maxRespectively represent
Figure BDA00026251024500000414
Lower and upper limits of constraints; b2minAnd b2maxRespectively represent
Figure BDA00026251024500000415
Lower and upper limits of constraints;
and then have
Figure BDA00026251024500000416
Wherein
Figure BDA00026251024500000417
The objective function J is established as follows:
Figure BDA00026251024500000418
wherein
Figure BDA00026251024500000419
Indicating a specified speed of movement, Q1And Q2Respectively positive definite regulating matrixes; by substituting formula (11) into formula (14), the objective function is expressed as
Figure BDA00026251024500000420
Wherein
Figure BDA00026251024500000421
Thus, by solving the quadratic programming optimization problem equations (15) and (13), the velocity input increments are obtained
Figure BDA00026251024500000422
Will be provided with
Figure BDA00026251024500000423
First speed increment of
Figure BDA00026251024500000424
The speed input V (k) of each wheel of the robot is obtained by substituting the speed input V (k) into a prediction model (9), and the V (k) is used for controlling a motion speed system (8) of the service robot so as to restrict the motion speed system in an x axis,yActual speed of shaft, rotation angle direction
Figure BDA0002625102450000051
In step 3): constrained speed of motion
Figure BDA0002625102450000052
And combining a random differential equation, establishing a tracking error system, and constructing an index of the tracking error system based on a random Lyapunov stabilization theoryStabilizing the condition, obtaining a speed constraint tracking controller suitable for different users, serving the actual walking track X (t) of the robot, and designating the training track X by the doctord(t), restricted speed of motion
Figure BDA0002625102450000053
Specified speed of movement
Figure BDA0002625102450000054
Setting the tracking error e1(t) and velocity tracking error e2(t) are each independently
e1(t)＝X(t)-Xd(t) (16)
Figure BDA0002625102450000055
Wherein alpha represents a parameter to be designed, and a tracking error system is obtained according to a random differential equation of the rehabilitation walking robot as follows:
de1(t)＝[e2(t)+αe1(t)]dt (18)
Figure BDA0002625102450000056
the Lyapunov function is designed as
Figure BDA0002625102450000057
Based on the random stabilization theory to obtain
Figure BDA0002625102450000058
Wherein I represents an identity matrix of appropriate dimensions; according to Young's inequality, for a given constant ρ1＞0,ρ2Greater than 0, has
Figure BDA0002625102450000059
Figure BDA00026251024500000510
Wherein the content of the first and second substances,
Figure BDA00026251024500000511
representing the F norm of the matrix, and the upper bound of which is h;
further, the controller u (t) is designed as follows:
Figure BDA00026251024500000512
wherein the parameter to be designed
Figure BDA00026251024500000513
λ1＞0,ρ1＞0,λ2> 0 represents a controller parameter;
thus, the random exponential settling of the tracking error system (16) (17) is achieved by the controller (24) and in accordance with equation (21). The advantages and effects are as follows:
a service robot speed constraint tracking control method suitable for different users,
1) according to the dynamic model of the service robot, the coefficient matrix M is calculated0Decomposing the mass m of the middle trainer into a constant value and a random variable, and establishing a random differential equation describing the mass change of different users;
2) based on a kinematic model of the service robot, a model prediction control method for controlling the movement speed of each wheel is provided, so that the robot is restrained on an x axis,ySpeed of movement of shaft in rotation angle direction
Figure BDA0002625102450000061
3) And establishing a tracking error system by utilizing the constrained motion speed and combining a random differential equation, establishing an exponential stability condition of the tracking error system based on a random Lyapunov stability theory, and obtaining the speed constrained tracking controller suitable for different users.
The method comprises the following steps:
step 1) decomposing the quality m of a trainer into a constant value and a random variable based on a dynamic model of a service robot, and establishing a random differential equation describing the quality change of different users, wherein the random differential equation is characterized in that: the dynamic model of the system is described below
Figure BDA0002625102450000062
Wherein
Figure BDA0002625102450000063
Figure BDA0002625102450000064
X (t) represents an actual walking track of the service robot, u (t) represents a control input force, fiRepresenting the input force per wheel, M representing the mass of the robot, M representing the mass of the user, I0Representing moment of inertia, M0And B (theta) is a coefficient matrix. Theta denotes the angle between the horizontal axis and the line connecting the center of the robot and the center of the first wheel, l denotes the distance from the center of the system to the center of each wheel,
Figure BDA0002625102450000065
representing the moment of inertia of the user;
coefficient matrix M0Mass m of the middle user is decomposed into m ═ mr+ Δ m, where mrRepresenting a given mass constant, Δ m represents a random variation of mass, and converting Δ m into random noise η (t), yielding the following equation:
Figure BDA0002625102450000066
wherein
Figure BDA0002625102450000067
Figure BDA0002625102450000071
The random noise η (t) is expressed as
Figure BDA0002625102450000072
Where upsilon represents a 3-dimensional independent random process, which can be derived
Figure BDA0002625102450000073
Order to
Figure BDA0002625102450000074
(v ═ 1,2, 3; σ ═ 1,2,3), and calculated
Figure BDA0002625102450000075
Further, the formula (3) can be changed into
Figure BDA0002625102450000076
Setting the spectral density of the random noise eta (t) as
Figure BDA0002625102450000077
Namely, it is
Figure BDA0002625102450000078
Where Λ represents the spectral density matrix,
Figure BDA0002625102450000079
representing random processes with spectral density distribution, so random differential equations for the service robot are available
Figure BDA00026251024500000710
Step 2) based on the kinematic model of the service robot, a model prediction control method for controlling the movement speed of each wheel is provided, and then the robot is restrained on an x axis,yThe motion speed of axle, rotation angle direction, its characterized in that: the kinematic model of the system is described below
Figure BDA00026251024500000711
Wherein
Figure BDA00026251024500000712
V(t)＝[v1(t) v2(t) v3(t)]T，vi(t) (i ═ 1,2,3) represents the speed of movement of each wheel.
As further shown in equation (7),
Figure BDA00026251024500000713
discretizing equation (8) and letting y (t) ═ x (t) represent the system output and writing the velocity input v (t) into an incremental representation, a predictive model is obtained as follows
Figure BDA0002625102450000081
Wherein k is 0,1, …, N-1, N represents the prediction time domain; x (k) and X (k +1) respectively represent the motion trail of the robot at the current moment and the later moment; y (k) represents the robot motion position output at the current moment; Δ V (k) represents the current timeThe moment speed increment, V (k-1) represents the speed input of the previous moment; a ═ I3，
Figure BDA0002625102450000082
T represents the sampling time, I3An identity matrix of appropriate dimensions is represented.
Next, the x-axis is constructed,yPredicted speed of shaft and rotation angle direction
Figure BDA0002625102450000083
And predicted input for each wheel speed
Figure BDA0002625102450000084
The constraints of (2) are as follows:
Figure BDA0002625102450000085
wherein
Figure BDA0002625102450000086
Predictive input representing speed, NCIn order to control the time domain,
Figure BDA0002625102450000087
upper and lower predicted input bounds representing speeds, respectively;
Figure BDA0002625102450000088
which represents the predicted actual speed of movement,
Figure BDA0002625102450000089
representing the upper and lower bounds of the actual speed of movement, respectively.
From equation (9), the predicted speed model can be obtained as follows
Figure BDA00026251024500000810
Wherein
Figure BDA00026251024500000811
Φ＝BpL0，G＝BpL1，
Figure BDA00026251024500000812
B (k +), 0,1 … N-1 represents the values of the coefficient matrix B at different sampling instants in equation (9).
Substituting equation (11) into constraint (10) and conditioning the constraint as a speed input increment
Figure BDA00026251024500000813
In the form of
Figure BDA00026251024500000814
Wherein
Figure BDA00026251024500000815
Figure BDA00026251024500000816
Figure BDA00026251024500000817
Figure BDA00026251024500000818
And then have
Figure BDA00026251024500000819
Wherein
Figure BDA00026251024500000820
The objective function J is established as follows
Figure BDA00026251024500000821
Wherein
Figure BDA0002625102450000091
Indicating a specified speed of movement, Q1And Q2Respectively positive definite adjustment matrices. By substituting equation (11) into equation (14), the objective function can be expressed as
Figure BDA0002625102450000092
Wherein
Figure BDA0002625102450000093
Thus, by solving the quadratic programming optimization problem equations (15) and (13), the velocity input increments are obtained
Figure BDA0002625102450000094
Will be provided with
Figure BDA0002625102450000095
First speed increment of
Figure BDA0002625102450000096
The speed input V (k) of each wheel of the robot can be obtained by substituting the speed input V (k) into a prediction model (9), and the motion speed system (8) of the service robot can be controlled by utilizing V (k), so that the robot can be restrained on an x axis,yActual speed of shaft, rotation angle direction
Figure BDA0002625102450000097
Step 3) utilizing the restricted movement speed
Figure BDA0002625102450000098
Combined with random differentiationAn equation is established, a tracking error system is established, an exponential stability condition of the tracking error system is established based on a random Lyapunov stability theory, and a speed constraint tracking controller suitable for different users is obtained, and the method is characterized in that: the actual walking track X (t) of the service robot, the training track X appointed by the doctord(t), restricted speed of motion
Figure BDA0002625102450000099
Specified speed of movement
Figure BDA00026251024500000910
Setting the tracking error e1(t) and velocity tracking error e2(t) are each independently
e1(t)＝X(t)-Xd(t) (16)
Figure BDA00026251024500000911
Wherein alpha represents a parameter to be designed, and a tracking error system is obtained according to a random differential equation of the rehabilitation walking robot as follows:
de1(t)＝[e2(t)+αe1(t)]dt (18)
Figure BDA00026251024500000912
the Lyapunov function is designed as
Figure BDA00026251024500000913
Based on the random stabilization theory to obtain
Figure BDA00026251024500000914
Where I represents an identity matrix of appropriate dimensions. According to Young's inequality, for a given constant ρ1＞0,ρ2Greater than 0, has
Figure BDA00026251024500000915
Figure BDA0002625102450000101
Wherein the content of the first and second substances,
Figure BDA0002625102450000102
represents the F-norm of the matrix and has its upper bound h.
Further, the controller u (t) is designed as follows:
Figure BDA0002625102450000103
wherein the parameter to be designed
Figure BDA0002625102450000104
λ1＞0,ρ1＞0,λ2> 0 denotes the controller parameter.
Thus, the random exponential settling of the tracking error system (16) (17) can be achieved by the controller (24) and according to equation (21). Since there is no user quality information in the controller u (t), and e2(t) the service robot can track the indoor motion trail at the constrained motion speed for different users with randomly changing masses.
And 4) providing the output PWM signals to a motor driving module based on the MSP430 series single-chip microcomputer, so that the service robot can help different people and track indoor motion tracks at a constrained motion speed, and is characterized in that: the MSP430 series single-chip microcomputer is used as a main controller, and an input of the main controller is connected with a motor speed measuring module and an 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 each electrical device. The control method of the main controller comprises reading feedback signals of the motor encoder and the main controllerGiven control command signal Xd(t) and
Figure BDA0002625102450000105
an error signal is calculated. According to the error signal, the main controller calculates the control quantity of the motor according to a preset control algorithm, the control quantity is sent to the motor driving module, and the motor rotates to drive the wheels to maintain self balance and move according to a specified mode.
In summary, the present invention is a service robot speed constraint tracking control method suitable for different users, and has the following advantages:
the invention combines a dynamics model to decompose the user mass m into a steady value and a random variable, and establishes a random differential equation which describes the mass change of different users; based on a kinematic model of the service robot, a model prediction control method for restricting the movement speed of the robot is provided; a controller design method suitable for random variation of different users is provided by using constrained motion speed and combining random differential equations, an exponential stability condition of a tracking error system is constructed by adopting a random Lyapunov stability theory, and a speed constraint tracking controller suitable for different users is obtained. The controller of the invention has simple design and easy realization, and the controller has no quality information of users, thereby enabling the service robot to be applied to different users and improving the track tracking precision; meanwhile, a method for restricting the movement speed is provided for the service robot system described by the random differential equation, the robot speed is prevented from sudden change, and the safety of a user is guaranteed.
Description of the drawings:
FIG. 1 is a block diagram of the operation of the controller of the present invention;
FIG. 2 is a system diagram of the present invention;
FIG. 3 is a minimum MSP430 single-chip microcomputer system according to the present invention;
FIG. 4 is a peripheral expansion circuit of the host controller according to the present invention;
fig. 5 is a hardware first principle circuit of the present invention.
The specific implementation mode is as follows:
a service robot speed constraint tracking control method suitable for different users,
the method comprises the following steps:
1) according to the dynamic model of the service robot, the coefficient matrix M is calculated0Decomposing the mass m of the middle trainer into a constant value and a random variable, and establishing a random differential equation describing the mass change of different users;
2) based on a kinematic model of the service robot, a model prediction control method for controlling the movement speed of each wheel is provided, and the robot is further constrained on an x axis,ySpeed of movement of axes and rotation angles
Figure BDA0002625102450000111
3) Establishing a tracking error system by utilizing the constrained motion speed in the step 2) and combining the random differential equation in the step 1), and establishing an exponential stability condition of the tracking error system based on a random Lyapunov stability theory to realize a speed constraint tracking control method suitable for different users.
In step 1): the kinetic model is described as follows:
Figure BDA0002625102450000112
wherein
Figure BDA0002625102450000113
Figure BDA0002625102450000114
X (t) represents an actual walking track of the service robot, u (t) represents a control input force, fi(I ═ 1,2,3) denotes the input force per wheel, M denotes the mass of the robot, M denotes the mass of the user, I denotes the mass of the robot0Representing moment of inertia, M0And B (theta) is a coefficient matrix. Theta denotes the horizontal axis and the robot center and the first wheelThe angle between the center lines, l represents the distance from the center of the system to the center of each wheel,
Figure BDA0002625102450000115
representing the moment of inertia of the user;
coefficient matrix M0Mass m of the middle user is decomposed into m ═ mr+ Δ m, where mrRepresenting a set constant value of mass, Δ m representing a random variation value of mass, and converting Δ m into random noise η (t), the following equation is obtained:
Figure BDA0002625102450000121
wherein
Figure BDA0002625102450000122
Is MRAn inverse matrix of
Figure BDA0002625102450000123
Figure BDA0002625102450000124
The random noise η (t) is expressed as
Figure BDA0002625102450000125
Where upsilon represents a 3-dimensional independent random process, which can be derived
Figure BDA0002625102450000126
Order to
Figure BDA0002625102450000127
(v ═ 1,2, 3; σ ═ 1,2,3), β represents an element in the inverse matrix, and is calculated
Figure BDA0002625102450000128
Further, the formula (3) can be changed into
Figure BDA0002625102450000129
Setting the spectral density of the random noise eta (t) as
Figure BDA00026251024500001210
Namely, it is
Figure BDA00026251024500001211
Where Λ represents the spectral density matrix,
Figure BDA00026251024500001212
representing random processes with spectral density distribution, so random differential equations for the service robot are available
Figure BDA00026251024500001213
In step 2): the kinematic model of the system is described as follows:
Figure BDA00026251024500001214
wherein B isG(t) represents a coefficient matrix, and
Figure BDA00026251024500001215
V(t)＝[v1(t) v2(t) v3(t)]T，vi(t) (i ═ 1,2,3) represents the speed of movement of each wheel.
As further shown in equation (7),
Figure BDA00026251024500001216
discretizing equation (8) and letting y (t) ═ x (t) represent the system output and writing the velocity input v (t) into an incremental representation, a predictive model is obtained as follows
Figure BDA0002625102450000131
Wherein k is 0,1, …, N-1, N represents the prediction time domain; x (k) and X (k +1) respectively represent the motion trail of the robot at the current moment and the later moment; y (k) represents the robot motion position output at the current moment; Δ V (k) represents the current time speed increment, V (k-1) represents the previous time speed input; a ═ I3，
Figure BDA0002625102450000132
T represents the sampling time, I3An identity matrix of appropriate dimensions is represented.
Next, the x-axis is constructed,yPredicted speed of shaft and rotation angle direction
Figure BDA0002625102450000133
And predicted input for each wheel speed
Figure BDA0002625102450000134
The constraints of (2) are as follows:
Figure BDA0002625102450000135
wherein
Figure BDA0002625102450000136
Predictive input representing speed, NCIn order to control the time domain,
Figure BDA0002625102450000137
upper and lower predicted input bounds representing speeds, respectively;
Figure BDA0002625102450000138
which represents the predicted actual speed of movement,
Figure BDA0002625102450000139
representing the upper and lower bounds of the actual speed of movement, respectively.
From equation (9), the predicted speed model can be derived as follows:
Figure BDA00026251024500001310
wherein
Figure BDA00026251024500001311
Φ＝BpL0，G＝BpL1，
Figure BDA00026251024500001312
B (k +), 0,1 … N-1 represents the values of the coefficient matrix B at different sampling instants in equation (9).
Substituting equation (11) into constraint (10) and conditioning the constraint as a speed input increment
Figure BDA00026251024500001313
In the form of
Figure BDA00026251024500001314
Wherein
Figure BDA00026251024500001315
Figure BDA00026251024500001316
Figure BDA00026251024500001317
Figure BDA00026251024500001318
b1minAnd b1maxRespectively represent
Figure BDA00026251024500001319
Lower and upper limits of constraints; b2minAnd b2maxRespectively represent
Figure BDA00026251024500001320
Lower and upper bounds of the constraint.
And then have
Figure BDA00026251024500001321
Wherein
Figure BDA00026251024500001322
GL、bmCoefficient matrix of (13)
The objective function J is established as follows:
Figure BDA0002625102450000141
wherein
Figure BDA0002625102450000142
Indicating a specified speed of movement, Q1And Q2Respectively positive definite adjustment matrices. By substituting equation (11) into equation (14), the objective function can be expressed as
Figure BDA0002625102450000143
Wherein
Figure BDA0002625102450000144
Thus, by solving the quadratic programming optimization problem equations (15) and (13), the velocity input increments are obtained
Figure BDA0002625102450000145
Will be provided with
Figure BDA0002625102450000146
First speed increment of
Figure BDA0002625102450000147
The speed input V (k) of each wheel of the robot can be obtained by substituting the speed input V (k) into a prediction model (9), and the motion speed system (8) of the service robot can be controlled by utilizing V (k), so that the robot can be restrained on an x axis,yActual speed of shaft, rotation angle direction
Figure BDA0002625102450000148
In step 3): constrained speed of motion
Figure BDA00026251024500001416
And combining a random differential equation, establishing a tracking error system, establishing an exponential stability condition of the tracking error system based on a random Lyapunov stability theory, obtaining speed constraint tracking controllers suitable for different users, serving the actual walking track X (t) of the robot, and designating a training track X by a doctord(t), restricted speed of motion
Figure BDA0002625102450000149
Specified speed of movement
Figure BDA00026251024500001410
Setting the tracking error e1(t) and velocity tracking error e2(t) are each independently
e1(t)＝X(t)-Xd(t) (16)
Figure BDA00026251024500001411
Wherein alpha represents a parameter to be designed, and a tracking error system is obtained according to a random differential equation of the rehabilitation walking robot as follows:
de1(t)＝[e2(t)+αe1(t)]dt (18)
Figure BDA00026251024500001412
the Lyapunov function is designed as
Figure BDA00026251024500001413
Based on the random stabilization theory to obtain
Figure BDA00026251024500001414
Where I represents an identity matrix of appropriate dimensions. According to Young's inequality, for a given constant ρ1＞0,ρ2Greater than 0, has
Figure BDA00026251024500001415
Figure BDA0002625102450000151
Wherein the content of the first and second substances,
Figure BDA0002625102450000152
represents the F-norm of the matrix and has its upper bound h.
Further, the controller u (t) is designed as follows:
Figure BDA0002625102450000153
wherein the parameter to be designed
Figure BDA0002625102450000154
λ1＞0,ρ1＞0,λ2> 0 denotes the controller parameter.
Thus, the random exponential settling of the tracking error system (16) (17) can be achieved by the controller (24) and according to equation (21).
Since there is no user quality information in the controller u (t), and e2(t) the service robot can track the indoor motion trail at the constrained motion speed for different users with randomly changing masses.
The invention uses the coefficient matrix M according to the dynamic model of the service robot0The quality m of the middle trainer is decomposed into a constant value and a random variable, and a random differential equation of the service robot is established; based on a kinematic model of the service robot, a model prediction control method for restricting the movement speed of the robot by controlling the speed of each wheel is provided; furthermore, a tracking error system is established by utilizing the constrained motion speed and combining a random differential equation, a controller design method suitable for random variation of different user qualities is provided, an exponential stability condition of the tracking error system is established by adopting a random Lyapunov stability theory, speed constraint tracking controllers suitable for different users are obtained, the tracking precision of the service robot system is improved, and the safety of the users is guaranteed.
The MSP430 series single-chip microcomputer based intelligent service robot provides output PWM signals to the motor driving module, so that the service robot can help different people and track indoor movement tracks at a restricted movement speed, the MSP430 series single-chip microcomputer serves as a main controller, and an input motor speed measuring module and an output motor driving module of the main controller are connected; the motor driving module is connected with the direct current motor; the power supply system supplies power to each electrical device. The control method of the main controller is to read the feedback signal of the motor encoder and the control command signal X given by the main controllerd(t) And
Figure BDA0002625102450000155
an error signal is calculated. According to the error signal, the main controller calculates the control quantity of the motor according to a preset control algorithm, the control quantity is sent to the motor driving module, and the motor rotates to drive the wheels to maintain self balance and move according to a specified mode.
The invention is further described with reference to the accompanying drawings, but the scope of the invention is not limited by the embodiments.
A service robot speed constraint tracking control method suitable for different users is characterized in that:
1) according to the dynamic model of the service robot, the coefficient matrix M is calculated0Decomposing the mass m of the middle trainer into a constant value and a random variable, and establishing a random differential equation describing the mass change of different users;
2) based on a kinematic model of the service robot, a model prediction control method for controlling the motion speed of each wheel is provided, so that the motion speeds of the robot in the directions of an x axis, a y axis and a rotation angle are restrained
Figure BDA00026251024500001610
3) And establishing a tracking error system by utilizing the constrained motion speed and combining a random differential equation, establishing an exponential stability condition of the tracking error system based on a random Lyapunov stability theory, and obtaining the speed constrained tracking controller suitable for different users.
The method comprises the following steps:
step 1) decomposing the quality m of a trainer into a constant value and a random variable based on a dynamic model of a service robot, and establishing a random differential equation describing the quality change of different users, wherein the random differential equation is characterized in that: the dynamic model of the system is described below
Figure BDA0002625102450000161
Wherein
Figure BDA0002625102450000162
Figure BDA0002625102450000163
X (t) represents an actual walking track of the service robot, u (t) represents a control input force, fiRepresenting the input force per wheel, M representing the mass of the robot, M representing the mass of the user, I0Representing moment of inertia, M0And B (theta) is a coefficient matrix. Theta denotes the angle between the horizontal axis and the line connecting the center of the robot and the center of the first wheel, l denotes the distance from the center of the system to the center of each wheel,
Figure BDA0002625102450000164
representing the moment of inertia of the user.
Coefficient matrix M0Mass m of the middle user is decomposed into m ═ mr+ Δ m, where mrRepresenting a given mass constant, Δ m represents a random variation of mass, and converting Δ m into random noise η (t), yielding the following equation:
Figure BDA0002625102450000165
wherein
Figure BDA0002625102450000166
Figure BDA0002625102450000167
The random noise η (t) is expressed as
Figure BDA0002625102450000168
Where upsilon represents 3-dimensional independenceA random process, can obtain
Figure BDA0002625102450000169
Order to
Figure BDA0002625102450000171
(v ═ 1,2, 3; σ ═ 1,2,3), and calculated
Figure BDA0002625102450000172
Further, the formula (3) can be changed into
Figure BDA0002625102450000173
Setting the spectral density of the random noise eta (t) as
Figure BDA0002625102450000174
Namely, it is
Figure BDA0002625102450000175
Where Λ represents the spectral density matrix,
Figure BDA0002625102450000176
representing random processes with spectral density distribution, so random differential equations for the service robot are available
Figure BDA0002625102450000177
Step 2) based on the kinematic model of the service robot, a model prediction control method for controlling the movement speed of each wheel is provided, and then the robot is restrained on an x axis,yThe motion speed of axle, rotation angle direction, its characterized in that: the kinematic model of the system is described below
Figure BDA0002625102450000178
Wherein
Figure BDA0002625102450000179
V(t)＝[v1(t) v2(t) v3(t)]T，vi(t) (i ═ 1,2,3) represents the speed of movement of each wheel.
As further shown in equation (7),
discretizing equation (8) and letting y (t) ═ x (t) represent the system output and writing the velocity input v (t) into an incremental representation, a predictive model is obtained as follows
Figure BDA00026251024500001711
Wherein k is 0,1, …, N-1, N represents the prediction time domain; Δ V (k) represents the current time speed increment, V (k-1) represents the previous time speed input; a ═ I3，
Figure BDA00026251024500001714
T represents the sampling time, I3An identity matrix of appropriate dimensions is represented.
Next, the x-axis is constructed,yPredicted speed of shaft and rotation angle direction
Figure BDA00026251024500001712
And predicted input for each wheel speed
Figure BDA00026251024500001713
The constraints of (2) are as follows:
Figure BDA0002625102450000181
wherein
Figure BDA0002625102450000182
Predictive input representing speed, NCIn order to control the time domain,
Figure BDA0002625102450000183
upper and lower predicted input bounds representing speeds, respectively;
Figure BDA0002625102450000184
which represents the predicted actual speed of movement,
Figure BDA0002625102450000185
representing the upper and lower bounds of the actual speed of movement, respectively.
From equation (9), the predicted speed model can be obtained as follows
Figure BDA0002625102450000186
Wherein
Figure BDA0002625102450000187
Φ＝BpL0，G＝BpL1，
Figure BDA0002625102450000188
B (k +), 0,1 … N-1 represents the values of the coefficient matrix B at different sampling instants in equation (9).
Substituting equation (11) into constraint (10) and conditioning the constraint as a speed input increment
Figure BDA0002625102450000189
In the form of
Figure BDA00026251024500001810
Wherein
Figure BDA00026251024500001811
Figure BDA00026251024500001812
Figure BDA00026251024500001813
Figure BDA00026251024500001814
And then have
Figure BDA00026251024500001815
Wherein
Figure BDA00026251024500001816
The objective function J is established as follows
Figure BDA00026251024500001817
Wherein
Figure BDA00026251024500001818
Indicating a specified speed of movement, Q1And Q2Respectively positive definite adjustment matrices. By substituting equation (11) into equation (14), the objective function can be expressed as
Figure BDA00026251024500001819
Wherein
Figure BDA00026251024500001820
Thus, by solving the quadratic programming optimization problem equations (15) and (13), the velocity input increments are obtained
Figure BDA00026251024500001821
Will be provided with
Figure BDA00026251024500001822
First speed increment of
Figure BDA00026251024500001823
The speed input V (k) of each wheel of the robot can be obtained by substituting the speed input V (k) into a prediction model (9), and the motion speed system (8) of the service robot can be controlled by utilizing V (k), so that the robot can be restrained on an x axis,yActual speed of shaft, rotation angle direction
Figure BDA0002625102450000191
Step 3) utilizing the restricted movement speed
Figure BDA00026251024500001913
And combines random differential equation to establish a tracking error system, constructs an exponential stability condition of the tracking error system based on random Lyapunov stability theory, and obtains speed constraint tracking controllers suitable for different users, which is characterized in that: the actual walking track X (t) of the service robot, the training track X appointed by the doctord(t), restricted speed of motion
Figure BDA0002625102450000192
Specified speed of movement
Figure BDA0002625102450000193
Setting the tracking error e1(t) and velocity tracking error e2(t) are each independently
e1(t)＝X(t)-Xd(t) (16)
Figure BDA0002625102450000194
Wherein alpha represents a parameter to be designed, and a tracking error system is obtained according to a random differential equation of the rehabilitation walking robot as follows:
de1(t)＝[e2(t)+αe1(t)]dt (18)
Figure BDA0002625102450000195
the Lyapunov function is designed as
Figure BDA0002625102450000196
Based on the random stabilization theory to obtain
Figure BDA0002625102450000197
Where I represents an identity matrix of appropriate dimensions. According to Young's inequality, for a given constant ρ1＞0,ρ2Greater than 0, has
Figure BDA0002625102450000198
Figure BDA0002625102450000199
Wherein the content of the first and second substances,
Figure BDA00026251024500001910
represents the F-norm of the matrix and has its upper bound h.
Further, the controller u (t) is designed as follows:
Figure BDA00026251024500001911
wherein the parameter to be designed
Figure BDA00026251024500001912
λ1＞0,ρ1＞0,λ2> 0 denotes the controller parameter.
Thus, the random exponential settling of the tracking error system (16) (17) can be achieved by the controller (24) and according to equation (21). Since there is no user quality information in the controller u (t), and e2(t) the service robot can track the indoor motion trail at the constrained motion speed for different users with randomly changing masses.
And 4) providing the output PWM signal to a motor drive module based on the MSP430 series single-chip microcomputer, so that the service robot can help different users and track indoor motion tracks at a constrained motion speed, and is characterized in that: the MSP430 series single-chip microcomputer is used as a main controller, and an input of the main controller is connected with a motor speed measuring module and an 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 each electrical device. The control method of the main controller is to read the feedback signal of the motor encoder and the control command signal X given by the main controllerd(t) and
Figure BDA0002625102450000201
an error signal is calculated. According to the error signal, the main controller calculates the control quantity of the motor according to a preset control algorithm, the control quantity is sent to the motor driving module, and the motor rotates to drive the wheels to maintain self balance and move according to a specified mode.
And (4) conclusion:
the invention solves the problem of speed constraint tracking control of the service robot with randomly changed quality of different users, and establishes a random differential equation describing the quality change of different users based on a dynamic model of the service robot; a model prediction control method for restricting the movement speed of the robot is provided; a controller design method suitable for random variation of different users is provided by utilizing constrained motion speed and combining random differential equations, an exponential stability condition of a tracking error system is constructed based on a random Lyapunov stability theory, and a speed constraint tracking controller suitable for different users is obtained. The method effectively inhibits the influence of quality changes of different users on the tracking performance of the system, avoids sudden change of the speed of the robot, improves the tracking precision of the service robot and ensures the safety of the users.

Claims (4)

1. A service robot speed constraint tracking control method suitable for different users is characterized in that:
the method comprises the following steps:
1) according to the dynamic model of the service robot, the coefficient matrix M is calculated0Decomposing the mass m of the middle trainer into a constant value and a random variable, and establishing a random differential equation describing the mass change of different users;
2) based on the kinematic model of the service robot, a model prediction control method for controlling the motion speed of each wheel is provided, and then the motion speeds of the robot in the directions of an x axis, a y axis and a rotation angle are restrained
Figure FDA0002625102440000016
3) Establishing a tracking error system by utilizing the constrained motion speed in the step 2) and combining the random differential equation in the step 1), and establishing an exponential stability condition of the tracking error system based on a random Lyapunov stability theory to realize a speed constraint tracking control method suitable for different users.
2. The method as claimed in claim 1, wherein the service robot speed constraint tracking control method is applied to different users, and comprises:
in step 1): the kinetic model is described as follows:
Figure FDA0002625102440000011
wherein
Figure FDA0002625102440000012
Figure FDA0002625102440000013
X (t) represents an actual walking track of the service robot, u (t) represents a control input force, fi(I ═ 1,2,3) denotes the input force per wheel, M denotes the mass of the robot, M denotes the mass of the user, I denotes the mass of the robot0Representing moment of inertia, M0B (theta) is a coefficient matrix; theta denotes the angle between the horizontal axis and the line connecting the center of the robot and the center of the first wheel, l denotes the distance from the center of the system to the center of each wheel,
Figure FDA0002625102440000014
representing the moment of inertia of the user;
coefficient matrix M0Mass m of the middle user is decomposed into m ═ mr+ Δ m, where mrRepresenting a set constant value of mass, Δ m representing a random variation value of mass, and converting Δ m into random noise η (t), the following equation is obtained:
Figure FDA0002625102440000015
wherein
Figure FDA0002625102440000021
Is MRAn inverse matrix of
Figure FDA0002625102440000022
Figure FDA0002625102440000023
The random noise η (t) is expressed as
Figure FDA0002625102440000024
Wherein upsilon represents a 3-dimensional independent random process, and
Figure FDA0002625102440000025
order to
Figure FDA0002625102440000026
And calculate
Figure FDA0002625102440000027
Further, the formula (3) is represented by
Figure FDA0002625102440000028
Setting the spectral density of the random noise eta (t) as
Figure FDA0002625102440000029
Namely, it is
Figure FDA00026251024400000214
Where Λ represents the spectral density matrix,
Figure FDA00026251024400000215
representing a random process with a spectral density distribution, thus obtaining a random differential equation for the service robot
Figure FDA00026251024400000210
3. The method as claimed in claim 1, wherein the service robot speed constraint tracking control method is applied to different users, and comprises: in step 2): the kinematic model of the system is described as follows:
Figure FDA00026251024400000211
wherein B isG(t) represents a coefficient matrix, and
Figure FDA00026251024400000212
V(t)＝[v1(t) v2(t) v3(t)]T，vi(t) (i ═ 1,2,3) represents the speed of movement of each wheel;
as further shown in equation (7),
Figure FDA00026251024400000213
discretizing equation (8), and making y (t) ═ x (t) represent system output, and writing speed input v (t) into incremental expression form to obtain the prediction model as follows
Figure FDA0002625102440000031
Wherein k is 0,1, …, N-1, N represents the prediction time domain; x (k) and X (k +1) respectively represent the motion trail of the robot at the current moment and the later moment; y (k) represents the robot motion position output at the current moment; Δ V (k) represents the current time speed increment, V (k-1) represents the previous time speed input; a ═ I3，
Figure FDA0002625102440000032
T represents the sampling time, I3An identity matrix representing a suitable dimension;
next, the predicted velocities for the x-axis, y-axis, and rotation angle directions are constructed
Figure FDA0002625102440000033
And predicted input for each wheel speed
Figure FDA0002625102440000034
The constraints of (2) are as follows:
Figure FDA0002625102440000035
wherein
Figure FDA0002625102440000036
Predictive input representing speed, NCIn order to control the time domain,
Figure FDA0002625102440000037
upper and lower predicted input bounds representing speeds, respectively;
Figure FDA0002625102440000038
which represents the predicted actual speed of movement,
Figure FDA0002625102440000039
an upper bound and a lower bound representing the actual movement speed, respectively;
from equation (9), the predicted speed model is obtained as follows:
Figure FDA00026251024400000310
wherein
Figure FDA00026251024400000311
Φ＝BpL0，G＝BpL1，
Figure FDA00026251024400000312
B (k +), 0,1 … N-1 represents the values of the coefficient matrix B at different sampling instants in equation (9);
substituting equation (11) into constraint (10) and conditioning the constraint as a speed input increment
Figure FDA00026251024400000313
In the form of
Figure FDA00026251024400000314
Wherein
Figure FDA00026251024400000315
Figure FDA00026251024400000316
Figure FDA00026251024400000317
Figure FDA00026251024400000318
b1minAnd b1maxRespectively represent
Figure FDA00026251024400000319
Lower and upper limits of constraints; b2minAnd b2maxRespectively represent
Figure FDA00026251024400000320
Lower and upper limits of constraints;
and then have
Figure FDA00026251024400000321
Wherein
Figure FDA00026251024400000322
The objective function J is established as follows:
Figure FDA0002625102440000041
wherein
Figure FDA0002625102440000042
Indicating a specified speed of movement, Q1And Q2Respectively positive definite regulating matrixes; by substituting formula (11) into formula (14), the objective function is expressed as
Figure FDA0002625102440000043
Wherein Θ is 2 (G)TQ1G+Q2),
Figure FDA0002625102440000044
Thus, by solving the quadratic programming optimization problem equations (15) and (13), the velocity input increments are obtained
Figure FDA0002625102440000045
Will be provided with
Figure FDA0002625102440000046
First inIncrement of speed
Figure FDA0002625102440000047
Substituting into a prediction model (9) to obtain speed input V (k) of each wheel of the robot, and controlling a motion speed system (8) of the service robot by utilizing V (k) so as to restrict the actual speed of the service robot in the directions of an x axis, a y axis and a rotation angle
Figure FDA0002625102440000048
4. The method as claimed in claim 1, wherein the service robot speed constraint tracking control method is applied to different users, and comprises:
in step 3): constrained speed of motion
Figure FDA0002625102440000049
And combining a random differential equation, establishing a tracking error system, establishing an exponential stability condition of the tracking error system based on a random Lyapunov stability theory, obtaining speed constraint tracking controllers suitable for different users, serving the actual walking track X (t) of the robot, and designating a training track X by a doctord(t), restricted speed of motion
Figure FDA00026251024400000410
Specified speed of movement
Figure FDA00026251024400000411
Setting the tracking error e1(t) and velocity tracking error e2(t) are each independently
e1(t)＝X(t)-Xd(t) (16)
Figure FDA00026251024400000412
Wherein alpha represents a parameter to be designed, and a tracking error system is obtained according to a random differential equation of the rehabilitation walking robot as follows:
de1(t)＝[e2(t)+αe1(t)]dt (18)
Figure FDA00026251024400000413
the Lyapunov function is designed as
Figure FDA00026251024400000414
Based on the random stabilization theory to obtain
Figure FDA00026251024400000415
Wherein I represents an identity matrix of appropriate dimensions; according to Young's inequality, for a given constant ρ1＞0,ρ2Greater than 0, has
Figure FDA00026251024400000416
Figure FDA0002625102440000051
Wherein the content of the first and second substances,
Figure FDA0002625102440000052
representing the F norm of the matrix, and the upper bound of which is h;
further, the controller u (t) is designed as follows:
Figure FDA0002625102440000053
wherein the parameter to be designed
Figure FDA0002625102440000054
λ1＞0,ρ1＞0,λ2> 0 represents a controller parameter;
thus, the random exponential settling of the tracking error system (16) (17) is achieved by the controller (24) and in accordance with equation (21).
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CN113377115B (en) * 2021-07-05 2023-10-20 沈阳工业大学 Stable control method for service robot to autonomously learn transient movement time
WO2023103553A1 (en) * 2021-12-09 2023-06-15 灵动科技（北京）有限公司 Trajectory planning method for plurality of robots, and computer program product

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