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 PDFInfo
- Publication number
- 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
- Authority
- CN
- China
- Prior art keywords
- speed
- random
- robot
- service robot
- different users
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 61
- 239000011159 matrix material Substances 0.000 claims description 49
- 230000003595 spectral effect Effects 0.000 claims description 15
- 230000001276 controlling effect Effects 0.000 claims description 10
- 238000005070 sampling Methods 0.000 claims description 10
- 230000006641 stabilisation Effects 0.000 claims description 6
- 238000011105 stabilization Methods 0.000 claims description 6
- 230000003750 conditioning effect Effects 0.000 claims description 5
- 238000005457 optimization Methods 0.000 claims description 5
- 230000001105 regulatory effect Effects 0.000 claims description 2
- 206010017577 Gait disturbance Diseases 0.000 description 3
- 238000010586 diagram Methods 0.000 description 2
- 208000037265 diseases, disorders, signs and symptoms Diseases 0.000 description 2
- 208000035475 disorder Diseases 0.000 description 2
- 206010039203 Road traffic accident Diseases 0.000 description 1
- 230000032683 aging Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000000474 nursing effect Effects 0.000 description 1
- 230000002093 peripheral effect Effects 0.000 description 1
- 230000000007 visual effect Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- 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, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- 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, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- 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, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- 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
Landscapes
- Engineering & Computer Science (AREA)
- Aviation & Aerospace Engineering (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
- Numerical Control (AREA)
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
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
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:
wherein
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,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:
The random noise η (t) is expressed asWherein upsilon represents a 3-dimensional independent random process, and
Further, the formula (3) is represented by
Setting the spectral density of the random noise eta (t) asNamely, it isWhere Λ represents the spectral density matrix,representing a random process with a spectral density distribution, thus obtaining a random differential equation for the service robot
In step 2): the kinematic model of the system is described as follows:
wherein B isG(t) represents a coefficient matrix, and
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 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
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,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 directionAnd predicted input for each wheel speedThe constraints of (2) are as follows:
whereinPredictive input representing speed, NCIn order to control the time domain,upper and lower predicted input bounds representing speeds, respectively;which represents the predicted actual speed of movement,an upper bound and a lower bound representing the actual movement speed, respectively;
from equation (9), the predicted speed model is obtained as follows:
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 incrementIn the form of
Wherein
b1minAnd b1maxRespectively representLower and upper limits of constraints; b2minAnd b2maxRespectively representLower and upper limits of constraints;
and then have
The objective function J is established as follows:
whereinIndicating a specified speed of movement, Q1And Q2Respectively positive definite regulating matrixes; by substituting formula (11) into formula (14), the objective function is expressed as
Thus, by solving the quadratic programming optimization problem equations (15) and (13), the velocity input increments are obtainedWill be provided withFirst speed increment ofThe 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
In step 3): constrained speed of motionAnd 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 motionSpecified speed of movementSetting the tracking error e1(t) and velocity tracking error e2(t) are each independently
e1(t)=X(t)-Xd(t) (16)
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)
the Lyapunov function is designed as
Based on the random stabilization theory to obtain
Wherein I represents an identity matrix of appropriate dimensions; according to Young's inequality, for a given constant ρ1>0,ρ2Greater than 0, has
further, the controller u (t) is designed as follows:
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
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
Wherein
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,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:
wherein
The random noise η (t) is expressed asWhere upsilon represents a 3-dimensional independent random process, which can be derived
Further, the formula (3) can be changed into
Setting the spectral density of the random noise eta (t) asNamely, it isWhere Λ represents the spectral density matrix,representing random processes with spectral density distribution, so random differential equations for the service robot are available
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
Wherein
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
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,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 directionAnd predicted input for each wheel speedThe constraints of (2) are as follows:
whereinPredictive input representing speed, NCIn order to control the time domain,upper and lower predicted input bounds representing speeds, respectively;which represents the predicted actual speed of movement,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
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 incrementIn the form of
Wherein
And then have
The objective function J is established as follows
WhereinIndicating 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
Thus, by solving the quadratic programming optimization problem equations (15) and (13), the velocity input increments are obtainedWill be provided withFirst speed increment ofThe 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 directionStep 3) utilizing the restricted movement speedCombined 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 motionSpecified speed of movementSetting the tracking error e1(t) and velocity tracking error e2(t) are each independently
e1(t)=X(t)-Xd(t) (16)
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)
the Lyapunov function is designed as
Based on the random stabilization theory to obtain
Where I represents an identity matrix of appropriate dimensions. According to Young's inequality, for a given constant ρ1>0,ρ2Greater than 0, has
Further, the controller u (t) is designed as follows:
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) andan 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
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:
wherein
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,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:
The random noise η (t) is expressed asWhere upsilon represents a 3-dimensional independent random process, which can be derived
Further, the formula (3) can be changed into
Setting the spectral density of the random noise eta (t) asNamely, it isWhere Λ represents the spectral density matrix,representing random processes with spectral density distribution, so random differential equations for the service robot are available
In step 2): the kinematic model of the system is described as follows:
wherein B isG(t) represents a coefficient matrix, and
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
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,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 directionAnd predicted input for each wheel speedThe constraints of (2) are as follows:
whereinPredictive input representing speed, NCIn order to control the time domain,upper and lower predicted input bounds representing speeds, respectively;which represents the predicted actual speed of movement,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:
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 incrementIn the form of
Wherein
b1minAnd b1maxRespectively representLower and upper limits of constraints; b2minAnd b2maxRespectively representLower and upper bounds of the constraint.
And then have
The objective function J is established as follows:
whereinIndicating 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
Thus, by solving the quadratic programming optimization problem equations (15) and (13), the velocity input increments are obtainedWill be provided withFirst speed increment ofThe 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
In step 3): constrained speed of motionAnd 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 motionSpecified speed of movementSetting the tracking error e1(t) and velocity tracking error e2(t) are each independently
e1(t)=X(t)-Xd(t) (16)
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)
the Lyapunov function is designed as
Based on the random stabilization theory to obtain
Where I represents an identity matrix of appropriate dimensions. According to Young's inequality, for a given constant ρ1>0,ρ2Greater than 0, has
Further, the controller u (t) is designed as follows:
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) Andan 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
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
Wherein
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,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:
wherein
The random noise η (t) is expressed asWhere upsilon represents 3-dimensional independenceA random process, can obtain
Further, the formula (3) can be changed into
Setting the spectral density of the random noise eta (t) asNamely, it isWhere Λ represents the spectral density matrix,representing random processes with spectral density distribution, so random differential equations for the service robot are available
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
Wherein
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
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,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 directionAnd predicted input for each wheel speedThe constraints of (2) are as follows:
whereinPredictive input representing speed, NCIn order to control the time domain,upper and lower predicted input bounds representing speeds, respectively;which represents the predicted actual speed of movement,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
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 incrementIn the form of
Wherein
And then have
The objective function J is established as follows
WhereinIndicating 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
Thus, by solving the quadratic programming optimization problem equations (15) and (13), the velocity input increments are obtainedWill be provided withFirst speed increment ofThe 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 directionStep 3) utilizing the restricted movement speedAnd 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 motionSpecified speed of movementSetting the tracking error e1(t) and velocity tracking error e2(t) are each independently
e1(t)=X(t)-Xd(t) (16)
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)
the Lyapunov function is designed as
Based on the random stabilization theory to obtain
Where I represents an identity matrix of appropriate dimensions. According to Young's inequality, for a given constant ρ1>0,ρ2Greater than 0, has
Further, the controller u (t) is designed as follows:
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) andan 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
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:
wherein
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,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:
The random noise η (t) is expressed asWherein upsilon represents a 3-dimensional independent random process, and
Further, the formula (3) is represented by
Setting the spectral density of the random noise eta (t) asNamely, it isWhere Λ represents the spectral density matrix,representing a random process with a spectral density distribution, thus obtaining a random differential equation for the service robot
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:
wherein B isG(t) represents a coefficient matrix, and
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 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
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,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 constructedAnd predicted input for each wheel speedThe constraints of (2) are as follows:
whereinPredictive input representing speed, NCIn order to control the time domain,upper and lower predicted input bounds representing speeds, respectively;which represents the predicted actual speed of movement,an upper bound and a lower bound representing the actual movement speed, respectively;
from equation (9), the predicted speed model is obtained as follows:
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 incrementIn the form of
Wherein
b1minAnd b1maxRespectively representLower and upper limits of constraints; b2minAnd b2maxRespectively representLower and upper limits of constraints;
and then have
The objective function J is established as follows:
whereinIndicating a specified speed of movement, Q1And Q2Respectively positive definite regulating matrixes; by substituting formula (11) into formula (14), the objective function is expressed as
Thus, by solving the quadratic programming optimization problem equations (15) and (13), the velocity input increments are obtainedWill be provided withFirst inIncrement of speedSubstituting 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
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 motionAnd 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 motionSpecified speed of movementSetting the tracking error e1(t) and velocity tracking error e2(t) are each independently
e1(t)=X(t)-Xd(t) (16)
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)
the Lyapunov function is designed as
Based on the random stabilization theory to obtain
Wherein I represents an identity matrix of appropriate dimensions; according to Young's inequality, for a given constant ρ1>0,ρ2Greater than 0, has
further, the controller u (t) is designed as follows:
thus, the random exponential settling of the tracking error system (16) (17) is achieved by the controller (24) and in accordance with equation (21).
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202010076151 | 2020-01-23 | ||
CN2020100761510 | 2020-01-23 |
Publications (2)
Publication Number | Publication Date |
---|---|
CN112034842A true CN112034842A (en) | 2020-12-04 |
CN112034842B CN112034842B (en) | 2024-03-26 |
Family
ID=73576819
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202010794629.3A Active CN112034842B (en) | 2020-01-23 | 2020-08-10 | Speed constraint tracking control method of service robot applicable to different users |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN112034842B (en) |
Cited By (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN113377115A (en) * | 2021-07-05 | 2021-09-10 | 沈阳工业大学 | Stability control method for autonomous learning transient motion time of service robot |
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 |
CN116627138A (en) * | 2023-05-29 | 2023-08-22 | 东北大学 | Control method for self-adaptive weight mass of mobile robot with speed interval constraint |
WO2024075081A1 (en) * | 2022-10-06 | 2024-04-11 | 1Qb Information Technologies Inc. | Systems and methods for simulating at least one solution of a stochastic differential equation and methods for using thereof for generative machine learning |
US12051005B2 (en) | 2019-12-03 | 2024-07-30 | 1Qb Information Technologies Inc. | System and method for enabling an access to a physics-inspired computer and to a physics-inspired computer simulator |
Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN104932488A (en) * | 2015-06-30 | 2015-09-23 | 南京工业大学 | Model predictive control performance evaluation and diagnosis method |
KR20160024110A (en) * | 2014-08-25 | 2016-03-04 | 주식회사 바로텍시너지 | Legs rehabilitation robot capable of movable gait training and stationary gait training |
CN107272640A (en) * | 2017-06-12 | 2017-10-20 | 华中科技大学 | A kind of modeling quality control method and system based on model predictive controller |
CN108245380A (en) * | 2018-03-13 | 2018-07-06 | 西安交通大学 | A kind of human body lower limbs recovery exercising robot |
-
2020
- 2020-08-10 CN CN202010794629.3A patent/CN112034842B/en active Active
Patent Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
KR20160024110A (en) * | 2014-08-25 | 2016-03-04 | 주식회사 바로텍시너지 | Legs rehabilitation robot capable of movable gait training and stationary gait training |
CN104932488A (en) * | 2015-06-30 | 2015-09-23 | 南京工业大学 | Model predictive control performance evaluation and diagnosis method |
CN107272640A (en) * | 2017-06-12 | 2017-10-20 | 华中科技大学 | A kind of modeling quality control method and system based on model predictive controller |
CN108245380A (en) * | 2018-03-13 | 2018-07-06 | 西安交通大学 | A kind of human body lower limbs recovery exercising robot |
Non-Patent Citations (6)
Title |
---|
JING TANG: "Direct force control of upper-limb exoskeleton based on fuzzy adaptive algorithm", 《JOURNAL OF VIBROENGINEERING》 * |
单芮: "全方向康复步行训练机器人的迭代学习控制研究", 《中国优秀硕博士学位论文全文数据库》, pages 3 * |
孙平: "Finite-time tracking control with velocity constraints for the stochastic rehabilitative training walker systems considering different rehabilitee masses", 《ORIGINAL PAPER》 * |
孙平: "考虑人机作用力的康复训练机器人各运动轴最优轨迹跟踪预测控制", 《北京理工大学学报》, pages 1076 - 1079 * |
孙平;: "不确定康复训练机器人速度与加速度同时约束的跟踪控制", 北京理工大学学报, no. 10 * |
张立勋: "助行康复机器人减重支撑单元控制仿真研究", 《康复工程》 * |
Cited By (7)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US12051005B2 (en) | 2019-12-03 | 2024-07-30 | 1Qb Information Technologies Inc. | System and method for enabling an access to a physics-inspired computer and to a physics-inspired computer simulator |
CN113377115A (en) * | 2021-07-05 | 2021-09-10 | 沈阳工业大学 | Stability control method for autonomous learning transient motion time of service robot |
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 |
WO2024075081A1 (en) * | 2022-10-06 | 2024-04-11 | 1Qb Information Technologies Inc. | Systems and methods for simulating at least one solution of a stochastic differential equation and methods for using thereof for generative machine learning |
CN116627138A (en) * | 2023-05-29 | 2023-08-22 | 东北大学 | Control method for self-adaptive weight mass of mobile robot with speed interval constraint |
CN116627138B (en) * | 2023-05-29 | 2024-09-06 | 东北大学 | Control method for self-adaptive weight mass of mobile robot with speed interval constraint |
Also Published As
Publication number | Publication date |
---|---|
CN112034842B (en) | 2024-03-26 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN112034842A (en) | Service robot speed constraint tracking control method suitable for different users | |
CN110989589B (en) | Tracking control method for rehabilitation walking robot with different trainers with randomly changed quality | |
Ishiguro et al. | A neural network compensator for uncertainties of robotics manipulators | |
CN107479381B (en) | Optimal prediction control method for tracking error of each axis of redundant rehabilitation walking training robot | |
Lin et al. | Development of a self-balancing human transportation vehicle for the teaching of feedback control | |
CN112433495B (en) | Rehabilitation robot rapid finite time control based on SCN man-machine uncertain model | |
Duchaine et al. | Computationally efficient predictive robot control | |
Yu | Nonlinear PD regulation for ball and beam system | |
CN112506054B (en) | Rehabilitation robot random finite time stable control based on SCN observation active thrust | |
JP2005535025A (en) | Intelligent mechatronics controlled suspension system based on quantum soft arithmetic | |
CN113093538A (en) | Non-zero and game neural-optimal control method of modular robot system | |
CN105945925A (en) | Control method of bionic snake-shaped robot | |
Jin et al. | Flexible actuator with variable stiffness and its decoupling control algorithm: Principle prototype design and experimental verification | |
CN112433475A (en) | SCN system offset identification-based cushion robot time-limited learning control method | |
CN113325720B (en) | Self-adaptive tracking control method for rehabilitation training robot with movement speed decision | |
Teodorescu et al. | Probabilistic shared control for a smart wheelchair: A stochastic model-based framework | |
CN116000917A (en) | Motion trail safety triggering data driving control method of rehabilitation walking robot | |
CN113419433B (en) | Design method of tracking controller of under-actuated system of self-balancing electric wheelchair | |
Bian et al. | Design, analysis, and test of a novel 2-DOF spherical motion mechanism | |
Richter et al. | Motion optimization for musculoskeletal dynamics: A flatness-based polynomial approach | |
CN113359767B (en) | Method for controlling safe driving of limited track tracking error of robot structure with slow change | |
CN115338871A (en) | Limited self-adaptive robust control method and system of two-degree-of-freedom mechanical arm | |
CN113419423B (en) | Tracking control method for service robot to adapt to structural change in limited time | |
CN112571424A (en) | Direct constraint control of each axis speed of rehabilitation robot based on SCN walking force estimation | |
CN113741469A (en) | Output feedback trajectory tracking control method with preset performance and dead zone input constraint for electromechanical system |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
SE01 | Entry into force of request for substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
GR01 | Patent grant | ||
GR01 | Patent grant |