CN105867130B - The track following error constraints method of controlling security of rehabilitation ambulation training robot - Google Patents
The track following error constraints method of controlling security of rehabilitation ambulation training robot Download PDFInfo
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Abstract
The track following error constraints method of controlling security of rehabilitation ambulation training robot belongs to the control field of wheeled healing robot more particularly to a kind of track following error constraints method of controlling security of rehabilitation ambulation training robot.The present invention, which provides one kind, making rehabilitation ambulation training robot during the motion, the track following error constraints method of controlling security of transient period and steady-state process track following error while controlled rehabilitation ambulation training robot.The present invention is based on the kinetic models of rehabilitation ambulation training robot, design gamma controller, establish x, the track following error state equation of three directions of motion of y-axis and rotation angle；Based on Lyapunov stable theories, build each asymptotically stable constraints of track following error system, obtain the method for solving of gamma controller parameter matrix, within the specified range by the actual motion TRAJECTORY CONTROL of rehabilitation ambulation training robot transient period and steady-state process, rehabilitation clients' safety is ensured.
Description
Technical field
The invention belongs to the control field of wheeled healing robot more particularly to a kind of rails of rehabilitation ambulation training robot
Mark tracking error constrains method of controlling security.
Background technology
Walking is that the daily self-support of the mankind is lived important one of basic activity, as advanced age population increases, the elderly leg
Muscle strength gradually weakens, if reinforcing the elderly's ambulation training not in time, walking-function can be caused gradually to lose, cannot achieve
It is daily to live on one's own life.Since China lacks care-giving professional, while family's youth population is reduced, and how the elderly to be helped to restore
Walking movement function becomes serious social concern.Therefore, development rehabilitation ambulation training robot, help the elderly safely into
Row ambulation training is of great significance.
The track that rehabilitation ambulation training robot needs tracking doctor to specify is trained patient, related healing robot
There are many achievements in research for Trajectory Tracking Control method, however these achievements all have ignored the tracking performance of transient period.Machine
People's operation is indoors in circumstances not known, if transient period track following error is excessive, robot can collide surrounding people or object,
Threaten the safety of trainer.Existing result of study only only accounts for the tracking performance of robot steady-state process, leads to these controls
Method all has certain limitation in practical applications.Up to the present, there are no constrain transient period and stable state rank simultaneously
The control method of section track following error.How the method for controlling security of research track tracking error constraint of the present invention, constrain health
Track following error of the multiple ambulation training robot in entire motion process, ensures that the safety of user is of great significance.
Invention content
The present invention addresses the above problem, and providing one kind making rehabilitation ambulation training robot during the motion, transient state
The track following error constraints of stage and steady-state process track following error while controlled rehabilitation ambulation training robot peace
Full control method.
To achieve the above object, the present invention adopts the following technical scheme that, the present invention includes the following steps：
Step 1) establishes x, the track following error state equation of three directions of motion of y-axis and rotation angle, the movement of system
It is as follows to learn model：
Wherein
X (t) is the practical run trace of rehabilitation ambulation training robot, and u (t) indicates that control input power, M indicate rehabilitation step
The quality of row image training robot, m indicate the quality of rehabilitation clients, I0Indicate rotary inertia,For coefficient square
Battle array；θ indicates the angle between trunnion axis and robot center and first wheel subcenter line, θ=θ1, according to rehabilitation walking robot
People's structure,θ3=θ+π,liIndicate system gravity to the distance of each wheel subcenter, r0Table
Show center to the distance of center of gravity, φiIndicate x ' axis and the corresponding l of each wheeliBetween angle, i=1,2,3,4；f1,f2,f3,
f4The control input power of four driving wheels, λ are indicated respectively1,λ2,λ3,λ4Indicate center of gravity to the distance of each wheel, φ respectively1,φ2,
φ3,φ4Indicate respectively horizontal axis and center of gravity to each wheel subcenter line angle；
The practical run trace X (t) of step 2) rehabilitation ambulation training robot, the specified training track X of doctord(t), rail is moved
Mark and movement velocity tracking error e1(t) and e2(t) it is respectively
e1(t)=X (t)-Xd(t) (2)
Wherein X (t)=[x (t) y (t) θ (t)]TIndicate x, the actual motion track of y-axis and rotation angular direction, Xd(t)=
[xd(t) yd(t) θd(t)]TIndicate x, the expectation pursuit movement track of y-axis and rotation angular direction；e1(t)=[e11(t) e12
(t) e13(t)]TIndicate x, the track following error of y-axis and rotation angular direction, e2(t)=[e21(t) e22(t) e23(t)]TTable
Show x, the tracking error of y-axis direction speed and angular velocity of rotation；
Gamma controller is arranged in step 3)：
Wherein Kd=diag { Kd1,Kd2,Kd3}’Kp=diag { Kp1,Kp2,Kp3}’Indicate B
The pseudo inverse matrix of (θ), Kd,KpIndicate controller parameter matrix；
Controller formula (4) is substituted into system model formula (1), is obtained
X can be obtained by formula (2), (3), (5), y-axis and rotation angular direction track following error system state equation are
Lyapunov functions are arranged in step 4)：
Wherein
Along track following error system (6) to formula (8) derivation, when following constraints is set up,
Have
It sets up, i.e. x, the track following error system Asymptotic Stability of three directions of motion of y-axis and rotation angle, wherein εiIt indicates
The small positive number being arbitrarily designated；
Step 5) integrates formula (10) both ends from 0 to t, obtains
Further arrange
Vi(t)-Vi(0)≤-εi(|e1i(t)|-|e1i(0)|) (12)
When following condition is set up
There is following formula establishment
It is obtained by formula (8), (14), (12)
Then have
|e1i(t)|≤εi+|e1i(0)| (16)
The safety movement of the actual path X (t) of rehabilitation ambulation training robot is ranging from
|x(t)-xd(t)|≤ε1+|x(0)-xd(0)| (17)
|y(t)-yd(t)|≤ε2+|y(0)-yd(0)| (18)
|θ(t)-θd(t)|≤ε2+|θ(0)-θd(0)| (19)。
As a preferred embodiment, the present invention is based on MSP430 series monolithics is supplied to motor to drive output pwm signal
Moving cell makes the track following error of rehabilitation ambulation training robot limit within the specified range；With MSP430 series monolithics
For master controller, the input of master controller connects motor speed measuring module, output connects motor drive module；Motor-drive circuit and direct current
Motor is connected；Power-supply system gives each power electrical apparatus.
As another preferred embodiment, main controller controls method of the present invention is：Read the feedback of motor encoder
The control command signal X that signal gives with master controllerd(t) andError signal is calculated；It is main according to error signal
Controller calculates the controlled quentity controlled variable of motor according to scheduled control algolithm, gives electric-motor drive unit, and motor rotation drives wheel
It maintains Equilibrium and is moved by specific mode.
Advantageous effect of the present invention.
The present invention is based on the kinetic models of rehabilitation ambulation training robot, are missed according to movement velocity and movement position tracking
Difference designs gamma controller, establishes x, the track following error state equation of three directions of motion of y-axis and rotation angle；It is based on
Lyapunov stable theories build each asymptotically stable constraints of track following error system, obtain gamma controller ginseng
The method for solving of matrix number is referring to the actual motion TRAJECTORY CONTROL of rehabilitation ambulation training robot transient period and steady-state process
Determine in range, ensures rehabilitation clients' safety.
Binding kinetics model of the present invention, the gamma controller of design can establish x, three movement sides of y-axis and rotation angle
To track following error state equation；The Asymptotic Stability condition for building three track following error systems respectively, in constraint rail
On the basis of mark tracking error, the safety movement position range of rehabilitation ambulation training robot is sought.Controller design of the present invention
Simply, it is easy to accomplish, controller not only makes rehabilitation ambulation training robot realize track following, but also can the practical fortune of active constraint
Dynamic rail mark realizes that the tracking performance of transient period and steady-state process, the control method can improve training in safety movement region
The safety of person.
Description of the drawings
The present invention will be further described with reference to the accompanying drawings and detailed description.The scope of the present invention not only limits to
In the statement of the following contents.
Fig. 1 is controller of the present invention work block diagram；
Fig. 2 is present system coordinate diagram；
Fig. 3 is MSP430 single-chip minimum systems of the present invention；
Fig. 4 is master controller peripheral expansion circuit of the present invention；
Fig. 5 is hardware general principles circuit of the present invention.
In Fig. 2, xOy is fixed coordinate system, and x ' Cy ' are robot mechanism coordinate system, and G is that robot constitutes people with rehabilitation clients
The center of gravity of machine system.
Specific implementation mode
As shown, general steps of the present invention are as follows：
1) movement velocity of the specified training track of doctor and movement position tracking are missed according to rehabilitation ambulation training robot
Difference designs gamma controller, and binding kinetics model establishes x, and the track following of three directions of motion of y-axis and rotation angle misses
Poor state equation；
2) Lyapunov functions are designed, each asymptotically stable constraints of track following error system is built, are obtained non-thread
The method for solving of property controller parameter matrix, makes rehabilitation ambulation training robot transient period and the actual motion rail of steady-state process
Mark constrains within the specified range；
3) output pwm signal is supplied to by electric-motor drive unit based on MSP430 series monolithics, makes rehabilitation ambulation training
Robot tracks the training track that doctor specifies within the scope of home.
The present invention is as follows：
Kinetic model of the step 1) based on rehabilitation ambulation training robot is missed according to movement velocity and movement position tracking
Difference, establishes x, the track following error state equation of three directions of motion of y-axis and rotation angle, and the kinematics model of system is as follows
Wherein
X (t) is the practical run trace of rehabilitation ambulation training robot, and u (t) indicates that control input power, M indicate rehabilitation step
The quality of row image training robot, m indicate the quality of rehabilitation clients, I0Indicate rotary inertia,For coefficient square
Battle array.θ indicates the angle between trunnion axis and robot center and first wheel subcenter line, i.e. θ=θ1, by rehabilitation walking robot
People's structure it is found thatθ3=θ+π,liIndicate system gravity to each wheel subcenter distance,
r0Expression center is to the distance of center of gravity, φiIndicate x ' axis and the corresponding l of each wheeliBetween angle, i=1,2,3,4.
Kinetic model of the step 2) based on rehabilitation ambulation training robot is missed according to movement velocity and movement position tracking
Difference establishes x, the track following error state equation of three directions of motion of y-axis and rotation angle, rehabilitation ambulation training robot reality
Run trace X (t), the specified training track X of doctord(t), if movement locus and movement velocity tracking error e1(t) and e2(t) divide
It is not
e1(t)=X (t)-Xd(t) (2)
Wherein X (t)=[x (t) y (t) θ (t)]TIndicate x, the actual motion track of y-axis and rotation angular direction, Xd(t)=
[xd(t) yd(t) θd(t)]TIndicate x, the expectation pursuit movement track of y-axis and rotation angular direction.e1(t)=[e11(t) e12
(t) e13(t)]TIndicate x, the track following error of y-axis and rotation angular direction, e2(t)=[e21(t) e22(t) e23(t)]TTable
Show x, the tracking error of y-axis direction speed and angular velocity of rotation.
It is as follows to design gamma controller
Wherein Kd=diag { Kd1,Kd2,Kd3, Kp=diag { Kp1,Kp2,Kp3,Indicate B
The pseudo inverse matrix of (θ).
Controller (4) is substituted into system model (1), is obtained
X can be obtained by formula (2), (3), (5), y-axis and rotation angular direction track following error system state equation are
Step 3) designs Lyapunov functions, builds each asymptotically stable constraints of track following error system, obtains
The method for solving of gamma controller parameter matrix makes the practical fortune of rehabilitation ambulation training robot transient period and steady-state process
Dynamic TRAJECTORY CONTROL is within the specified range；It is as follows to design Lyapunov functions
Wherein
Along track following error system (6) to formula (8) derivation, when following constraints is set up,
Have
It sets up, i.e. x, the track following error system Asymptotic Stability of three directions of motion of y-axis and rotation angle, wherein εiIt indicates
The small positive number being arbitrarily designated.
Step 4) designs Lyapunov functions, builds each asymptotically stable constraints of track following error system, obtains
The method for solving of gamma controller parameter matrix makes the practical fortune of rehabilitation ambulation training robot transient period and steady-state process
Dynamic rail mark constrains within the specified range；It is characterized in that：Formula (10) both ends are integrated from 0 to t, are obtained
Further arrange
Vi(t)-Vi(0)≤-εi(|e1i(t)|-|e1i(0)|) (12)
When following condition is set up
There is following formula establishment
It is obtained by formula (8), (14), (12)
Then have
|e1i(t)|≤εi+|e1i(0)| (16)
Therefore, the safety movement of the actual path X (t) of rehabilitation ambulation training robot is ranging from
|x(t)-xd(t)|≤ε1+|x(0)-xd(0)| (17)
|y(t)-yd(t)|≤ε2+|y(0)-yd(0)| (18)
|θ(t)-θd(t)|≤ε2+|θ(0)-θd(0)| (19)
Output pwm signal is supplied to electric-motor drive unit by step 5) based on MSP430 series monolithics, makes rehabilitation walking
The track following error of image training robot limits within the specified range, using MSP430 series monolithics as master controller, main control
The input of device connects motor speed measuring module, output connects motor drive module；Motor-drive circuit is connected with direct current generator；Power-supply system
To each power electrical apparatus.
Main controller controls method is the control command letter for reading the feedback signal of motor encoder and being given with master controller
Number Xd(t) andError signal is calculated.According to error signal, master controller is calculated according to scheduled control algolithm
The controlled quentity controlled variable of motor, gives electric-motor drive unit, and motor rotation drives wheel to maintain Equilibrium and moved by specific mode.
The present invention solves the Security Control Problem of rehabilitation ambulation training manipulator trajectory tracking error constraints, is based on power
Model and gamma controller are learned, x, the track following error state equation of three directions of motion of y-axis and rotation angle are established.Pass through
Lyapunov functions build each asymptotically stable constraints of track following error system, to solve controller parameter matrix,
Within the specified range by the actual motion TRAJECTORY CONTROL of rehabilitation ambulation training robot transient period and steady-state process, it effectively improves
The safety of trainer.
It is understood that above with respect to the specific descriptions of the present invention, it is merely to illustrate the present invention and is not limited to this
Technical solution described in inventive embodiments, it will be understood by those of ordinary skill in the art that, still the present invention can be carried out
Modification or equivalent replacement, to reach identical technique effect；As long as meet use needs, all protection scope of the present invention it
It is interior.
Claims (1)
1. the track following error constraints method of controlling security of rehabilitation ambulation training robot, it is characterised in that including following step
Suddenly：
Kinetic model of the step 1) based on rehabilitation ambulation training robot, according to movement velocity and movement position tracking error,
Establish x, the track following error state equation of three directions of motion of y-axis and rotation angle, the kinematics model of system is as follows：
Wherein
X (t) is the practical run trace of rehabilitation ambulation training robot, and u (t) indicates that control input power, M indicate rehabilitation walking instruction
Practice the quality of robot, m indicates the quality of rehabilitation clients, I0Indicate rotary inertia,For coefficient matrix；θ
Indicate the angle between trunnion axis and robot center and first wheel subcenter line, θ=θ1, according to rehabilitation walking robot knot
Structure,θ3=θ+π,liIndicate system gravity to the distance of each wheel subcenter, r0In expression
The heart is to the distance of center of gravity, φiIndicate x ' axis and the corresponding l of each wheeliBetween angle, i=1,2,3,4；f1,f2,f3,f4Point
Not Biao Shi four driving wheels control input power, λ1,λ2,λ3,λ4Indicate center of gravity to the distance of each wheel, φ respectively1,φ2,φ3,
φ4Indicate respectively horizontal axis and center of gravity to each wheel subcenter line angle；
Kinetic model of the step 2) based on rehabilitation ambulation training robot, according to movement velocity and movement position tracking error,
Establish x, the track following error state equation of three directions of motion of y-axis and rotation angle, the practical row of rehabilitation ambulation training robot
Walk track X (t), the specified training track X of doctord(t), movement locus and movement velocity tracking error e1(t) and e2(t) it is respectively
e1(t)=X (t)-Xd(t) (2)
Wherein X (t)=[x (t) y (t) θ (t)]TIndicate x, the actual motion track of y-axis and rotation angular direction, Xd(t)=[xd
(t) yd(t) θd(t)]TIndicate x, the expectation pursuit movement track of y-axis and rotation angular direction；e1(t)=[e11(t) e12(t)
e13(t)]TIndicate x, the track following error of y-axis and rotation angular direction, e2(t)=[e21(t) e22(t) e23(t)]TIndicate x, y
The tracking error of axis direction speed and angular velocity of rotation；
Gamma controller is arranged in step 3)：
Wherein Kd=diag { Kd1,Kd2,Kd3, Kp=diag { Kp1,Kp2,Kp3,Indicate the puppet of B (θ)
Inverse matrix, Kd,KpIndicate controller parameter matrix；
Controller formula (4) is substituted into system model formula (1), is obtained
X can be obtained by formula (2), (3), (5), y-axis and rotation angular direction track following error system state equation are
Step 4) builds each asymptotically stable constraints of track following error system, obtains gamma controller parameter matrix
Method for solving makes the actual motion TRAJECTORY CONTROL of rehabilitation ambulation training robot transient period and steady-state process in specified range
It is interior；Lyapunov functions are set：
Wherein
Along track following error system (6) to formula (8) derivation, when following constraints is set up,
Have
It sets up, i.e. x, the track following error system Asymptotic Stability of three directions of motion of y-axis and rotation angle, wherein εiIndicate arbitrary
Specified small positive number；
Step 5) builds each asymptotically stable constraints of track following error system, obtains gamma controller parameter matrix
Method for solving makes rehabilitation ambulation training robot transient period and the actual motion profile constraints of steady-state process in specified range
It is interior；Formula (10) both ends are integrated from 0 to t, are obtained
Further arrange
Vi(t)-Vi(0)≤-εi(|e1i(t)|-|e1i(0)|) (12)
When following condition is set up
There is following formula establishment
It is obtained by formula (8), (14), (12)
Then have
|e1i(t)|≤εi+|e1i(0)| (16)
The safety movement of the actual path X (t) of rehabilitation ambulation training robot is ranging from
|x(t)-xd(t)|≤ε1+|x(0)-xd(0)| (17)
|y(t)-yd(t)|≤ε2+|y(0)-yd(0)| (18)
|θ(t)-θd(t)|≤ε2+|θ(0)-θd(0)| (19)；
Output pwm signal is supplied to electric-motor drive unit based on MSP430 series monolithics, makes rehabilitation ambulation training robot
Track following error limitation within the specified range；Using MSP430 series monolithics as master controller, the input of master controller connects
Motor speed measuring module, output connect motor drive module；Motor-drive circuit is connected with direct current generator；Power-supply system is to each electrical
Equipment is powered；
The main controller controls method is：Read the control command letter that the feedback signal of motor encoder gives with master controller
Number Xd(t) andError signal is calculated；According to error signal, master controller is calculated according to scheduled control algolithm
The controlled quentity controlled variable of motor, gives electric-motor drive unit, and motor rotation drives wheel to maintain Equilibrium and moved by specific mode；
According to rehabilitation ambulation training robot to the movement velocity and movement position tracking error of the specified training track of doctor, design
Gamma controller, binding kinetics model establish x, the track following error state side of three directions of motion of y-axis and rotation angle
Journey；
Lyapunov functions are designed, each asymptotically stable constraints of track following error system is built, obtain nonlinear Control
The method for solving of device parameter matrix makes rehabilitation ambulation training robot transient period and the actual motion profile constraints of steady-state process
Within the specified range；
Output pwm signal is supplied to electric-motor drive unit based on MSP430 series monolithics, makes rehabilitation ambulation training robot
The training track that doctor specifies is tracked within the scope of home.
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