CN107479381A - Each axle tracking error optimal preventive control method of redundancy rehabilitation ambulation training robot - Google Patents

Each axle tracking error optimal preventive control method of redundancy rehabilitation ambulation training robot Download PDF

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CN107479381A
CN107479381A CN201710753885.6A CN201710753885A CN107479381A CN 107479381 A CN107479381 A CN 107479381A CN 201710753885 A CN201710753885 A CN 201710753885A CN 107479381 A CN107479381 A CN 107479381A
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track
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CN107479381B (en
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孙平
张帅
孙桐
李树江
孟奇
张文娇
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Shenyang University of Technology
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    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

A kind of each axle tracking error optimal preventive control method of redundancy rehabilitation ambulation training robot, the control method are based on redundant robot's feature and kinetic model, design nonlinear feedback predictive controller, establish each sub-system discretization forecast model；Respectively using each track shaft tracking error as variable, establish objective optimization performance function, and build the constraints of each track shaft tracking error, speed tracing error and controlling increment, obtain optimal preventive control, so as to realize each track shaft tracking error optimal performance, and, ensure rehabilitation clients's safety training by the track following error of redundancy rehabilitation ambulation training robot and speed tracing error constraints within the specified range.The control method can not only improve tracking accuracy, and the security of energy Support Training person.

Description

Each axle tracking error optimal preventive control method of redundancy rehabilitation ambulation training robot
Technical field：
The present invention relates to the control field of wheeled redundancy healing robot, especially with respect to wheeled lower limb redundancy rehabilitation machine The control method of people.
Background technology：
As the increase of advanced age population and traffic accident take place frequently, lower extremity motor function obstacle person is caused to increase year by year.Due to me State's rehabilitation medical resource-constrained, the lower limb rehabilitation for the person that can not solve the problems, such as obstacle in time.Therefore, rehabilitation ambulation training machine is developed People, lower limb obstacle person is helped safely to carry out ambulation training significant.
Rehabilitation ambulation training robot usually requires the movement locus that tracking doctor specifies and helps obstacle person to be trained, essence Really the training track of tracking doctor can effectively improve rehabilitation efficacy.On rehabilitation ambulation training robotic tracking control method Existing many achievements in research, however be fruitful all do not realize respectively x-axis, three direction of motion tracks of y-axis and rotary shaft with The optimal performance of track, and not while by track following error and speed tracing error constraints within the specified range.Rehabilitation machine People is different from industrial robot, if track following error is excessive, healing robot may collide the barrier of surrounding；If Speed tracing error is excessive, healing robot will be caused to be moved with rehabilitation clients uncoordinated, these can all threaten the safety of trainer. Up to the present, it is optimal to be also not carried out each track shaft tracking performance, and constrained trajectory tracking error and speed tracing miss simultaneously The control method of difference.Existing healing robot mostly uses redundancy structure design method.
The content of the invention：
Goal of the invention：
In order to solve the above problems, the invention provides one kind to make redundancy rehabilitation ambulation training robot in motion process In, each track shaft tracking error is minimum, and track following error and speed tracing error constrain within the specified range pre- simultaneously Survey control method.
Technical scheme：
The present invention is achieved through the following technical solutions：
A kind of each axle tracking error optimal preventive control method of redundancy rehabilitation ambulation training robot, in the control method Rehabilitation ambulation training robot is a kind of redundant robot, it is necessary to complete x-axis, the track of three direction of motion of y-axis and rotary shaft Tracking, based on redundant robot's feature and kinetic model, design nonlinear feedback predictive controller, establish each sub-system from Dispersion forecast model；Respectively using each track shaft tracking error as variable, objective optimization performance function is established, and builds each track shaft The constraints of tracking error, speed tracing error and controlling increment, obtain optimal preventive control, so as to realize each track shaft with Track error optimization performance, and the track following error of redundancy rehabilitation ambulation training robot and speed tracing error constraints are being referred to Determine in scope, ensure rehabilitation clients's safety training.
Optimal preventive control method and step is as follows：
1) redundancy based on rehabilitation ambulation training robot, and binding kineticses model, design nonlinear feedback prediction Controller, so as to obtain the kinetic model of decoupling form；On this basis, x-axis, y-axis and the rotary shaft direction of motion are built Subsystem model, according to Taylor expansion method, establish each sub-system discretization forecast model；
2) subsystem discretization forecast model is utilized, obtaining each axle respectively has the movement locus and fortune of controlling increment form Dynamic speed state equation；Using each track shaft tracking error as variable, establish objective optimization performance function, and build each track shaft with The constraints of track error, speed tracing error and controlling increment；Asked by solving the quadratic programming with controlling increment form Topic, safe prediction control is obtained, while, ensure rehabilitation by track following error and speed tracing error constraints within the specified range Person's safety training.
1) redundancy based on rehabilitation ambulation training robot, and binding kineticses model, design nonlinear feedback prediction Controller, so as to obtain the kinetic model of decoupling form；On this basis, x-axis, y-axis and the rotary shaft direction of motion are built Subsystem model, according to Taylor expansion method, establish each sub-system discretization forecast model；
2) subsystem discretization forecast model is utilized, obtaining each axle respectively has the movement locus and fortune of controlling increment form Dynamic speed state equation；Using each track shaft tracking error as variable, establish objective optimization performance function, and build each track shaft with The constraints of track error, speed tracing error and controlling increment；Asked by solving the quadratic programming with controlling increment form Topic, safe prediction control is obtained, while, ensure rehabilitation by track following error and speed tracing error constraints within the specified range Person's safety training.
Step is as follows：
Redundancy of the step 1) based on rehabilitation ambulation training robot, and binding kineticses model, design nonlinear feedback Predictive controller, so as to obtain the kinetic model of decoupling form, it is characterised in that：System dynamics model is described as follows
Wherein
X (t)=[x (t), y (t), θ (t)]TThe actual walking of three x-axis, y-axis and rotary shaft directions of motion is represented respectively Track, u (t)=[f1,f2,f3,f4]TThe control input power of four wheels motor is represented respectively, and M represents rehabilitation ambulation training machine The quality of people, m represent the quality of rehabilitation clients, I0Represent rotary inertia,For coefficient matrix；θ represents water Angle between flat axle and robot center and first wheel subcenter line, i.e. θ=θ1, from the robot architecture,θ3=θ+π,lnRepresent system gravity to the distance of each wheel subcenter, r0Expression center is arrived The distance of center of gravity, φnRepresent l corresponding to x ' axles and each wheelnBetween angle, λnRepresent system gravity to each wheel Distance, n=1,2,3,4；And define alphabetical p and q expression-form as above.
The redundancy designed according to rehabilitation ambulation training robot mechanism, makes input power f2=f4, system (1) turns to as follows Form
Wherein
Design nonlinear feedback predictive controller
Wherein v (t) is control variable to be designed.
Make actual motion track X (t)=x1(t), actual motion speedThen system (3) turns to following solution The kinetic model of coupling form
Wherein x1(t)=[x11(t) x12(t) x13(t)]TX-axis, y-axis and rotary shaft three directions of motion are represented respectively Actual run trace, x2(t)=[x21(t) x22(t) x23(t)]TX-axis, y-axis and rotary shaft three directions of motion are represented respectively The actual speed of travel, v (t)=[v1(t) v2(t) v3(t)]TRepresent that three x-axis, y-axis and rotary shaft directions of motion are waited to set respectively The control variable of meter.
The subsystem model of step 2) structure x-axis, y-axis and the rotary shaft direction of motion, according to Taylor expansion method, establish each Sub-system discretization forecast model, it is characterised in that：Following subsystem model can be obtained according to formula (4)
If T is the sampling period, xi(k)=[x1i(k) x2i(k)]TRepresent subsystem in the state variable at k moment, yi(k) =x1i(k) represent subsystem in the output variable at k moment, vi(k-1) represent subsystem in the control variable at k-1 moment, Δ vi (k) controlling increment of the subsystem at the k moment is represented.Then according to Taylor expansion method, it is discrete that each sub-system can be obtained by formula (5) It is as follows to change forecast model
Wherein
Step 3) utilizes subsystem discretization forecast model, and obtaining each axle respectively has the movement locus of controlling increment form With speed movement status equation.It is characterized in that：Can be obtained according to formula (6) has the movement locus state of controlling increment form as follows Equation
x1i=F1xi(k)+Φ1vi(k-1)+G1ΔVi (7)
Wherein N is to predict time domain, NCTo control time domain, and
Equally, the speed movement status equation as follows with controlling increment form can be obtained according to formula (6)
x2i=F2xi(k)+Φ2vi(k-1)+G2ΔVi (8)
Wherein
x1i(k+j/k), j=1,2 ..., N, each sub-system is represented in prediction of the k moment to k+j moment movement locus, x2i(k+j/k), j=1,2 ..., N, represent each sub-system in prediction of the k moment to k+j moment movement velocitys, Δ vi(k+j/ K), j=0,1 ..., NC- 1, represent each sub-system in prediction of the k moment to k+j moment controlling increments.
Step 4) establishes objective optimization performance function using each track shaft tracking error as variable, and build each track shaft with The constraints of track error, speed tracing error and controlling increment.It is characterized in that：Establish objective optimization performance function JiIt is as follows
Ji=min (x1i-Xdi)T(x1i-Xdi) (9)
Wherein Xd=[Xd1 Xd2 Xd3]TRepresent the training track that doctor specifies, Xdi(i=1,2,3) three axles are represented respectively The movement locus that direction is specified.e1(t)=X (t)-Xd=x1(t)-XdRepresent track following error, x1i(t)-XdiThree are represented respectively The track following error of individual direction of principal axis；Speed tracing error is represented,Respectively Represent the speed tracing error of three direction of principal axis.Then each track shaft tracking error, speed tracing error and controlling increment are built Constraints it is as follows：
WhereinThe track following error upper limit that expression system is specified from the k+1 moment to the k+N moment in three direction of principal axis, AndExpression system is from the k+1 moment to the k+N moment in the speed tracing error that three direction of principal axis are specified Limit, andRepresent the upper limit of controlling increment, and Δ Vimin=-Δ Vimax。
By solve with controlling increment form quadratic programming problem, obtain optimal preventive control, while by track with Track error and speed tracing error constraints within the specified range, ensure rehabilitation clients's safety training.It is characterized in that：It is excellent to obtain target Change functional expression (9) and the controlling increment expression-form of constraint equation (10).Formula (7) is substituted into formula (9), obtained
OrderJ can be obtainediOn controlling increment Δ ViTable It is as follows up to form：
Formula (7) and formula (8) are substituted into formula (10), can there must be the constraints of controlling increment form as follows：
Further abbreviation is
GΔVi≤bi (14)
Wherein
Can there must be the quadratic programming problem of controlling increment form as follows according to formula (11) and formula (13)：
Step 5) obtains optimal preventive control, simultaneously will by solving the quadratic programming problem with controlling increment form Track following error and speed tracing error constraints within the specified range, ensure rehabilitation clients's safety training.It is characterized in that：Solve The step of safe prediction controls is as follows：
Step1：The k=0 moment, to xiAnd v (k)i(k-1) initial value is assigned.
Step2：The k moment, by formula (7) and the rehabilitation ambulation training robot at N number of moment after formula (8) the calculating k moment Movement locus x1iWith movement velocity x2i, calculate G and bi。
Step3：Quadratic programming problem formula (15) is solved, makes each track shaft tracking error minimum, while track following is missed Difference and speed tracing error constrain within the specified range simultaneously, obtain the optimal control sequence Δ V of subsystemsi, according to control Time domain processed determines subsystem controls increment Delta vi(k) subsystems controlled quentity controlled variable v, is calculated according to formula (6)i(k), and then controlled Variable v (k) processed.
Step4：At the k+1 moment, according to the predicted position and speed of v (k) computation models (6), while v (k) is substituted into and controlled DeviceActual motion position and the speed of rehabilitation ambulation training robot are obtained, and calculates prediction error.
Step5：According to the prediction error obtained in Step4, the predicted position and speed of feedback compensation subsystems, make Forecast model position and velocity correction output are identical with the reality output of rehabilitation ambulation training robot；Update xiAnd v (k)i(k- 1) value, Step2 is returned.
In order to realize optimal preventive controlUsing MSP430 series monolithics as master controller, the input of master controller connects Motor speed measuring module, output connect motor drive module；Motor drive module is connected with direct current generator；Power-supply system is to each electric Equipment is powered.What the optimal preventive control method of master controller gave to read the feedback signal of motor encoder with master controller Control command signal XdWithError signal is calculated.According to error signal, master controller is according to predetermined control algolithm meter The controlled quentity controlled variable of motor is calculated, gives motor drive module, motor rotates driven wheel and maintains Equilibrium and transported by specific mode It is dynamic.
Advantage and effect：
The present invention is a kind of each axle tracking error optimal preventive control method of redundancy rehabilitation ambulation training robot, is had such as Lower advantage：
Redundancy based on rehabilitation ambulation training robot, research are made each track shaft tracking performance optimal by the present invention, and The optimal preventive control method of constrained trajectory tracking error and speed tracing error simultaneously, to improving tracking accuracy and ensureing The security of trainer is significant.
The present invention combines the redundancy and kinetic model of rehabilitation ambulation training robot, designs the pre- observing and controlling of nonlinear feedback Device processed, establish x-axis, the subsystem discretization forecast model of three directions of motion of y-axis and rotary shaft；Tracked respectively with each track shaft Error is variable, establishes objective optimization performance function, and builds each track shaft tracking error, speed tracing error and controlling increment Constraints, optimal preventive control is obtained, so as to realize each track shaft tracking error optimal performance, and by redundancy rehabilitation walking The track following error and speed tracing error of image training robot constrain within the specified range simultaneously.Controller of the present invention not only makes Each track shaft tracking error is minimum, and energy while constrained trajectory tracking error and speed tracing error, and the control method can not only Improve tracking accuracy, and the security of energy Support Training person.
Brief description of the drawings：
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.
Embodiment：
The present invention is described further below in conjunction with the accompanying drawings, but the scope of the present invention should not be limited by the examples.
A kind of each axle tracking error optimal preventive control method of redundancy rehabilitation ambulation training robot, in the control method Rehabilitation ambulation training robot is a kind of redundant robot, it is necessary to complete x-axis, the track of three direction of motion of y-axis and rotary shaft Tracking, based on redundant robot's feature and kinetic model, design nonlinear feedback predictive controller, establish each sub-system from Dispersion forecast model；Respectively using each track shaft tracking error as variable, objective optimization performance function is established, and builds each track shaft The constraints of tracking error, speed tracing error and controlling increment, obtain optimal preventive control, so as to realize each track shaft with Track error optimization performance, and the track following error of redundancy rehabilitation ambulation training robot and speed tracing error constraints are being referred to Determine in scope, ensure rehabilitation clients's safety training.
Optimal preventive control method and step is as follows：
1) redundancy based on rehabilitation ambulation training robot, and binding kineticses model, design nonlinear feedback prediction Controller, so as to obtain the kinetic model of decoupling form；On this basis, x-axis, y-axis and the rotary shaft direction of motion are built Subsystem model, according to Taylor expansion method, establish each sub-system discretization forecast model；
2) subsystem discretization forecast model is utilized, obtaining each axle respectively has the movement locus and fortune of controlling increment form Dynamic speed state equation；Using each track shaft tracking error as variable, establish objective optimization performance function, and build each track shaft with The constraints of track error, speed tracing error and controlling increment；Asked by solving the quadratic programming with controlling increment form Topic, optimal preventive control is obtained, while, ensure rehabilitation by track following error and speed tracing error constraints within the specified range Person's safety training.
Step is as follows：
Redundancy of the step 1) based on rehabilitation ambulation training robot, and binding kineticses model, design nonlinear feedback Predictive controller, so as to obtain the kinetic model of decoupling form, it is characterised in that：System dynamics model is described as follows
Wherein
X (t) is x-axis, the actual run trace of three directions of motion of y-axis and rotary shaft, and u (t) represents control input power, M The quality of rehabilitation ambulation training robot is represented, m represents the quality of rehabilitation clients, I0Represent rotary inertia, For coefficient matrix.θ represents the angle between trunnion axis and robot center and first wheel subcenter line, i.e. θ=θ1, by the machine Knowable to device people structure,θ3=θ+π,lnRepresent system gravity to each wheel subcenter away from From r0Expression center is to the distance of center of gravity, φnRepresent l corresponding to x ' axles and each wheelnBetween angle, n=1,2,3,4.
The redundancy designed according to rehabilitation ambulation training robot mechanism, makes input power f2=f4, system (1) turns to as follows Form
Wherein
Design nonlinear feedback predictive controller
Wherein v (t) is control variable to be designed.
Make actual motion track X (t)=x1(t), actual motion speedThen system (3) turns to following solution The kinetic model of coupling form
Wherein x1(t)=[x11(t) x12(t) x13(t)]TX-axis, y-axis and rotary shaft three directions of motion are represented respectively Actual run trace, x2(t)=[x21(t) x22(t) x23(t)]TX-axis, y-axis and rotary shaft three directions of motion are represented respectively The actual speed of travel, v (t)=[v1(t) v2(t) v3(t)]TRepresent that three x-axis, y-axis and rotary shaft directions of motion are waited to set respectively The control variable of meter.
The subsystem model of step 2) structure x-axis, y-axis and the rotary shaft direction of motion, according to Taylor expansion method, establish each Sub-system discretization forecast model, it is characterised in that：Following subsystem model can be obtained according to formula (4)
If T is the sampling period, xi(k)=[x1i(k) x2i(k)]TRepresent subsystem in the state variable at k moment, yi(k) =x1i(k) represent subsystem in the output variable at k moment, vi(k-1) represent subsystem in the control variable at k-1 moment, Δ vi (k) controlling increment of the subsystem at the k moment is represented.Then according to Taylor expansion method, it is discrete that each sub-system can be obtained by formula (5) It is as follows to change forecast model
Wherein
Step 3) utilizes subsystem discretization forecast model, and obtaining each axle respectively has the movement locus of controlling increment form With speed movement status equation.It is characterized in that：Can be obtained according to formula (6) has the movement locus state of controlling increment form as follows Equation
x1i=F1xi(k)+Φ1vi(k-1)+G1ΔVi (7)
Wherein N is to predict time domain, NCTo control time domain, and
x1i(k+j/k), j=1,2 ..., N, represent each sub-system in prediction of the k moment to k+j moment movement locus, Δ vi(k+j/k), j=0,1 ..., NC- 1, represent each sub-system in prediction of the k moment to k+j moment controlling increments；
Equally, the speed movement status equation as follows with controlling increment form can be obtained according to formula (6)
x2i=F2xi(k)+Φ2vi(k-1)+G2ΔVi (8)
Wherein
x2i(k+j/k), j=1,2 ..., N, represent each sub-system in prediction of the k moment to k+j moment movement velocitys.
Step 4) establishes objective optimization performance function using each track shaft tracking error as variable, and build each track shaft with The constraints of track error, speed tracing error and controlling increment.It is characterized in that：Establish objective optimization performance function JiIt is as follows
Ji=min (x1i-Xdi)T(x1i-Xdi) (9)
Wherein Xd=[Xd1 Xd2 Xd3]TRepresent the training track that doctor specifies, Xdi(i=1,2,3) three axles are represented respectively The movement locus that direction is specified.e1(t)=X (t)-Xd=x1(t)-XdRepresent track following error, x1i(t)-XdiThree are represented respectively The track following error of individual direction of principal axis；Speed tracing error is represented,Respectively Represent the speed tracing error of three direction of principal axis.Then each track shaft tracking error, speed tracing error and controlling increment are built Constraints it is as follows：
WhereinThe track following error upper limit that expression system is specified from the k+1 moment to the k+N moment in three direction of principal axis, And Expression system is from the k+1 moment to the k+N moment in the speed tracing error that three direction of principal axis are specified Limit, andΔVimaxRepresent the upper limit of controlling increment, and Δ Vimin=-Δ Vimax。
By solve with controlling increment form quadratic programming problem, obtain optimal preventive control, while by track with Track error and speed tracing error constraints within the specified range, ensure rehabilitation clients's safety training.It is characterized in that：It is excellent to obtain target Change functional expression (9) and the controlling increment expression-form of constraint equation (10).Formula (7) is substituted into formula (9), obtained
OrderJ can be obtainediOn controlling increment Δ ViTable It is as follows up to form：
Formula (7) and formula (8) are substituted into formula (10), can there must be the constraints of controlling increment form as follows：
Further abbreviation is
GΔVi≤bi (14)
Wherein
Represent NCThe unit matrix of dimension.
Can there must be the quadratic programming problem of controlling increment form as follows according to formula (11) and formula (13)：
Step 5) obtains optimal preventive control, simultaneously will by solving the quadratic programming problem with controlling increment form Track following error and speed tracing error constraints within the specified range, ensure rehabilitation clients's safety training.It is characterized in that：Solve The step of optimal preventive control, is as follows：
Step1：The k=0 moment, to xiAnd v (k)i(k-1) initial value is assigned.
Step2：The k moment, by formula (7) and the rehabilitation ambulation training robot at N number of moment after formula (8) the calculating k moment Movement locus x1iWith movement velocity x2i, calculate G and bi。
Step3：Quadratic programming problem formula (15) is solved, makes each track shaft tracking error minimum, while track following is missed Difference and speed tracing error constrain within the specified range simultaneously, obtain the optimal control sequence Δ V of subsystemsi, according to control Time domain processed determines subsystem controls increment Delta vi(k) subsystems controlled quentity controlled variable v, is calculated according to formula (6)i(k), and then controlled Variable v (k) processed.
Step4：At the k+1 moment, according to the predicted position and speed of v (k) computation models (6), while v (k) is substituted into and controlled DeviceActual motion position and the speed of rehabilitation ambulation training robot are obtained, and calculates prediction error.
Step5：According to the prediction error obtained in Step4, the predicted position and speed of feedback compensation subsystems, make Forecast model position and velocity correction output are identical with the reality output of rehabilitation ambulation training robot；Update xiAnd v (k)i(k- 1) value, Step2 is returned.
In order to realize optimal preventive controlUsing MSP430 series monolithics as master controller, the input of master controller connects Motor speed measuring module, output connect motor drive module；Motor drive module is connected with direct current generator；Power-supply system is to each electric Equipment is powered.What the optimal preventive control method of master controller gave to read the feedback signal of motor encoder with master controller Control command signal XdWithError signal is calculated.According to error signal, master controller is according to predetermined control algolithm meter The controlled quentity controlled variable of motor is calculated, gives motor drive module, motor rotates driven wheel and maintains Equilibrium and transported by specific mode It is dynamic.
Conclusion：
The present invention solves each track shaft tracking error best performance of redundancy rehabilitation ambulation training robot, and constrains simultaneously The optimal preventive control problem of track following error and speed tracing error.By establishing three x-axis, y-axis and rotary shaft motions The subsystem discretization forecast model in direction, builds objective optimization performance function and each track shaft tracking error, speed tracing miss The constraints of difference and controlling increment, based on the quadratic programming problem with controlling increment form is solved, obtain optimum prediction Control.Control method of the present invention can not only improve tracking accuracy, and the security of energy Support Training person.

Claims (6)

  1. A kind of 1. each axle tracking error optimal preventive control method of redundancy rehabilitation ambulation training robot, it is characterised in that：The control Rehabilitation ambulation training robot in method processed is a kind of redundant robot, it is necessary to complete three x-axis, y-axis and rotary shaft motions The track following in direction, based on redundant robot's feature and kinetic model, nonlinear feedback predictive controller is designed, established each Sub-system discretization forecast model；Respectively using each track shaft tracking error as variable, objective optimization performance function, and structure are established The constraints of each track shaft tracking error, speed tracing error and controlling increment is built, safe prediction control is obtained, so as to realize Each track shaft tracking error optimal performance, and the track following error of redundancy rehabilitation ambulation training robot and speed tracing are missed Difference constraint within the specified range, ensures rehabilitation clients's safety training.
  2. 2. each axle tracking error optimal preventive control method of redundancy rehabilitation ambulation training robot according to claim 1, It is characterized in that：Optimal preventive control method and step is as follows：
    1) redundancy based on rehabilitation ambulation training robot, and binding kineticses model, nonlinear feedback PREDICTIVE CONTROL is designed Device, so as to obtain the kinetic model of decoupling form；On this basis, the subsystem of x-axis, y-axis and the rotary shaft direction of motion is built System model, according to Taylor expansion method, establishes each sub-system discretization forecast model；
    2) subsystem discretization forecast model is utilized, obtaining each axle respectively has the movement locus and motion speed of controlling increment form Spend state equation；Using each track shaft tracking error as variable, objective optimization performance function is established, and builds each track shaft tracking and misses The constraints of difference, speed tracing error and controlling increment；By solving the quadratic programming problem with controlling increment form, obtain Optimal preventive control is obtained, while, ensures rehabilitation clients's peace by track following error and speed tracing error constraints within the specified range Full training.
  3. 3. each axle tracking error optimal preventive control method of redundancy rehabilitation ambulation training robot according to claim 2, It is characterized in that：Optimal preventive control method and step is as follows：
    Step 1), the redundancy based on rehabilitation ambulation training robot, and binding kineticses model, design nonlinear feedback prediction Controller, so as to obtain the kinetic model of decoupling form, system dynamics model is described as follows
    Wherein
    X (t)=[x (t), y (t), θ (t)]TX-axis, the actual run trace of three directions of motion of y-axis and rotary shaft, u are represented respectively (t)=[f1,f2,f3,f4]TThe control input power of four wheels motor is represented respectively, and M represents the matter of rehabilitation ambulation training robot Amount, m represent the quality of rehabilitation clients, I0Represent rotary inertia, M0,K(θ),B (θ) is coefficient matrix；θ represent trunnion axis and Angle between robot center and first wheel subcenter line, i.e. θ=θ1, from the robot architecture, θ3=θ+π,lnRepresent system gravity to the distance of each wheel subcenter, r0Expression center to center of gravity distance, φnRepresent l corresponding to x ' axles and each wheelnBetween angle, λnSystem gravity is represented to the distance of each wheel, n=1,2, 3,4；And define alphabetical p and q expression-form as above；
    The redundancy designed according to rehabilitation ambulation training robot mechanism, makes input power f2=f4, system (1) turns to following form
    Wherein
    Design nonlinear feedback predictive controller
    Wherein v (t) is control variable to be designed；
    Make actual motion track X (t)=x1(t), actual motion speedThen system (3) turns to following decoupling shape The kinetic model of formula
    Wherein x1(t)=[x11(t) x12(t) x13(t)]TX-axis, the reality of three direction of motion of y-axis and rotary shaft are represented respectively Run trace, x2(t)=[x21(t) x22(t) x23(t)]TX-axis, the reality of three direction of motion of y-axis and rotary shaft are represented respectively The speed of travel, v (t)=[v1(t) v2(t) v3(t)]TRepresent that x-axis, y-axis and three directions of motion of rotary shaft are to be designed respectively Control variable；
    Step 2), the subsystem model for building x-axis, y-axis and the rotary shaft direction of motion, according to Taylor expansion method, establish each axle Subsystem discretization forecast model, following subsystem model is obtained according to formula (4)：
    If T is the sampling period, xi(k)=[x1i(k) x2i(k)]TRepresent movement locus and movement velocity of the subsystem at the k moment State variable, yi(k)=x1i(k) represent subsystem in the movement locus output variable at k moment, vi(k-1) represent that subsystem exists The control variable at k-1 moment, Δ vi(k) controlling increment of the subsystem at the k moment is represented；Then foundation Taylor expansion method, by It is as follows that formula (5) can obtain each sub-system discretization forecast model
    Wherein
    C=[1 0]；
    Step 3), using subsystem discretization forecast model, obtain respectively each axle have controlling increment form movement locus and Speed movement status equation；Obtained according to formula (6) has the movement locus state equation of controlling increment form as follows
    x1i=F1xi(k)+Φ1vi(k-1)+G1ΔVi (7)
    Wherein N is to predict time domain, NCTo control time domain, and
    x1i(k+j/k), j=1,2 ..., N, represent each sub-system in prediction of the k moment to k+j moment movement locus, Δ vi(k + j/k), j=0,1 ..., NC- 1, represent each sub-system in prediction of the k moment to k+j moment controlling increments；
    Equally, the speed movement status equation as follows with controlling increment form is obtained according to formula (6)
    x2i=F2xi(k)+Φ2vi(k-1)+G2ΔVi (8)
    Wherein
    C1=[0 1],
    x2i(k+j/k), j=1,2 ..., N, represent each sub-system in prediction of the k moment to k+j moment movement velocitys；
    Step 4), using each track shaft tracking error as variable, establish objective optimization performance function, and build the tracking of each track shaft and miss The constraints of difference, speed tracing error and controlling increment；
    Step 5) obtains optimal preventive control by solving the quadratic programming problem with controlling increment form, while by track Tracking error and speed tracing error constraints within the specified range, ensure rehabilitation clients's safety training.
  4. 4. each axle tracking error optimal preventive control method of redundancy rehabilitation ambulation training robot according to claim 3, It is characterized in that：Objective optimization performance function J is established in step 4iIt is as follows：
    Ji=min (x1i-Xdi)T(x1i-Xdi) (9)
    Wherein Xd=[Xd1 Xd2 Xd3]TRepresent the training track that doctor specifies, Xdi(i=1,2,3) represent that each direction of principal axis refers to respectively Fixed movement locus；e1(t)=X (t)-Xd=x1(t)-XdRepresent track following error, x1i(t)-XdiEach direction of principal axis is represented respectively Track following error；Speed tracing error is represented,Each axle is represented respectively The speed tracing error in direction；Then the constraints of each track shaft tracking error, speed tracing error and controlling increment is built It is as follows：
    WhereinThe track following error upper limit that expression system is specified from the k+1 moment to the k+N moment in each direction of principal axis, and The speed tracing error upper limit that expression system is specified from the k+1 moment to the k+N moment in each direction of principal axis, andΔVimaxRepresent the upper limit of controlling increment, and Δ Vimin=-Δ Vimax；
    By solving the quadratic programming problem with controlling increment form, optimal preventive control is obtained, while track following is missed Difference and speed tracing error constraints within the specified range, ensure rehabilitation clients's safety training；Obtain objective optimization functional expression (9) peace treaty The controlling increment expression-form of beam conditional (10)；Formula (7) is substituted into formula (9), obtained
    OrderJ can be obtainediOn controlling increment Δ ViExpression shape Formula is as follows：
    Formula (7) and formula (8) are substituted into formula (10), can there must be the constraints of controlling increment form as follows：
    Further abbreviation is
    GΔVi≤bi (14)
    Wherein
    Represent NCThe unit matrix of dimension；
    Can there must be the quadratic programming problem of controlling increment form as follows according to formula (11) and formula (13)：
    。
  5. 5. each axle tracking error optimal preventive control method of redundancy rehabilitation ambulation training robot according to claim 3, It is characterized in that：The step of solution optimal preventive control in step 5), is as follows：
    Step1：The k=0 moment, to xiAnd v (k)i(k-1) initial value is assigned；
    Step2：At the k moment, the motion rail of N number of moment rehabilitation ambulation training robot after the k moment is calculated by formula (7) and formula (8) Mark x1iWith movement velocity x2i, calculate G and bi；
    Step3：Solve quadratic programming problem formula (15), make each track shaft tracking error minimum, at the same by track following error and Speed tracing error constrains within the specified range simultaneously, obtains the optimal control sequence Δ V of subsystemsi, according to control when Domain determines subsystem controls increment Delta vi(k) subsystems controlled quentity controlled variable v, is calculated according to formula (6)i(k), and then obtain controlling change Measure v (k)；
    Step4：At the k+1 moment, controller is substituted into according to the predicted position and speed of v (k) computation models (6), while by v (k)Actual motion position and the speed of rehabilitation ambulation training robot are obtained, and calculates prediction error；
    Step5：According to the prediction error obtained in Step4, the predicted position and speed of feedback compensation subsystems, make prediction Modal position and velocity correction output are identical with the reality output of rehabilitation ambulation training robot；Update xiAnd v (k)i(k-1) Value, return to Step2.
  6. 6. each axle tracking error optimal preventive control method of redundancy rehabilitation ambulation training robot according to claim 5, It is characterized in that：In order to realize optimal preventive controlUsing MSP430 series monolithics as master controller, master controller it is defeated Enter to connect motor speed measuring module, output connects motor drive module；Motor drive module is connected with direct current generator；Power-supply system is to each Power electrical apparatus；The optimal preventive control method of master controller is given to read the feedback signal of motor encoder with master controller Fixed control command signal XdWithError signal is calculated；According to error signal, master controller is calculated according to predetermined control Method calculates the controlled quentity controlled variable of motor, gives motor drive module, and motor rotates driven wheel and maintains Equilibrium and by designated parties Formula is moved.
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