CN109352656A - A kind of multi-joint mechanical arm control method with time-varying output constraint - Google Patents
A kind of multi-joint mechanical arm control method with time-varying output constraint Download PDFInfo
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- CN109352656A CN109352656A CN201811441894.2A CN201811441894A CN109352656A CN 109352656 A CN109352656 A CN 109352656A CN 201811441894 A CN201811441894 A CN 201811441894A CN 109352656 A CN109352656 A CN 109352656A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
- B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
Abstract
The invention discloses a kind of multi-joint mechanical arm control method with time-varying output constraint, specific steps include: the multi-joint mechanical arm kinetic model and desired pursuit path that (1) is established under time-varying output constraint；(2) transfer function that the system with time-varying output constraint is converted to abandoned new system is established；(3) former mechanical arm system, is converted to new mechanical arm system by the transfer function obtained according to step (2)；(4) tracking error signal of mechanical arm system after converting is defined；(5) for the neural network control device of the mechanical arm system design stability after conversion.The present invention can be totally unknown in system parameter and realizes that the exact trajectory of mechanical arm tracks in the case where having time-varying output constraint, and ensures the satisfaction of time-varying output constraint.
Description
Technical field
The present invention relates to automatic field more particularly to a kind of multi-joint mechanical arm controlling parties with time-varying output constraint
Method.
Background technique
The fast development of science and technology provides power-assisted for the further application of mechanical arm, and multi-joint mechanical arm is using most
Extensive automated machine equipment, in the fields extensive application such as industry manufacture, military, medical treatment, amusement even space probation.
In practical applications, there is various constraint conditions for mechanical arm control system, such as input saturation, task space are limited, speed
It is limited.Once these constraint conditions are breached, it is possible to which the decline for leading to mechanical arm system performance even results in the damage of system
Safety that is bad and threatening mechanical arm system relevant staff.With scientific and technological further development, the concept quilt of human-computer interaction
It is proposed, future will have the work of more and more robots the mankind at one's side, therefore set for the mechanical arm system with specified constraint
Meter controller has important theoretical significance and practical application value.However in current most of researchs, mainly for machine
The stability and control precision of device people's system are studied, and seem insufficient in terms of the controller design for considering output constraint.
Using existing recursive design method, most of result of study can only all solve to have the mechanical arm of constant output constraint to control
Problem, and usually it is arranged more relaxed to the bound of limited output, this also makes while the conservative for increasing algorithm
The practicability for obtaining algorithm is restricted.
Multi-joint mechanical arm is as time-varying, the Complex Nonlinear System of the multiple-input and multiple-output of coupling, movement
Control and its complexity, and during actual control design case, the parameter of mechanical arm is often unknown or parameter measurement is deposited
In biggish error, it is therefore desirable to there is the controller design tool for unknown parameter model.Mind is utilized in artificial neural network
Approximation through network, the Unknown kinetic model of mechanical arm system is approached by using neural network, to reach and be
The purpose that still can be accurately controlled in the case where uniting there are unknown parameter.Selection and nerve net to neural network topology structure
The adjustment of network weight has all had stringent theoretical analysis method, therefore neural network has obtained widely in mechanical arm control
Using.
Summary of the invention
It is an object of the invention to overcome the deficiencies of the prior art and provide a kind of multi-joint machines with time-varying output constraint
Tool arm control method.The present invention can be realized in the case where parameter is totally unknown to the multi-joint machine with time-varying output constraint
Tool arm carries out high-precision tracing control.The present invention is by establishing transform method, by the system with time-varying output constraint
Abandoned new system is converted to, solves the problems, such as mechanical arm unknown parameters by using neural network, and combine Backstepping
Neural network control device is established for the nonlinear system after conversion to realize Trajectory Tracking Control.The present invention is guaranteeing
While the time-varying output constraint of mechanical arm, the tracing control of fast and stable is realized.
The purpose of the present invention can be achieved through the following technical solutions:
A kind of multi-joint mechanical arm control method with time-varying output constraint, specific steps include:
(1) the multi-joint mechanical arm kinetic model and desired pursuit path under time-varying output constraint are established；
(2) transfer function that the system with time-varying output constraint is converted to abandoned new system is established；
(3) former mechanical arm system, is converted to new mechanical arm system by the transfer function obtained according to step (2)；
(4) tracking error signal of mechanical arm system after converting is defined；
(5) for the neural network control device of the mechanical arm system design stability after conversion.
Specifically, in step (1), multi-joint mechanical arm kinetic model is with strong non-under the time-varying output constraint
The mechanical arm dynamic model of linear coupling indicates are as follows:
Wherein, X1=q,τ indicates control moment, M (X1) indicate inertial matrix, Cm(X1,X2) indicate centripetal force
Matrix, G (X1) indicate gravitation vector, JT(X1) indicate mechanical arm Jacobian matrix, F (X2) indicate friction force vector, f
(t) it indicates from people and extraneous disturbance term；M(X1),Cm(X1,X2),G(X1),F(X2),JT(X1), f (t) is unknown；Mechanical arm
Time-varying output constraint indicate are as follows:
Further, the mechanical arm dynamic model established is using joint of mechanical arm angular displacement and joint angular displacement as state
Variable indicates are as follows:
Wherein, q=[q1 q2 ... qn]TIndicate angular displacement, qd=[qd1 qd2 ... qdn]TIndicate given output with
Track track, e=[e1 e2 ... en]TIndicate output tracking error,Withq=[q 1 q 2 ... q n]
The upper bound and the lower bound of the time-varying output constraint of mechanical arm are respectively indicated, n indicates the Rigid Robot Manipulator with time-varying output constraint
Joint number,And ηiIt (t) is intermediate variable.
It specifically, is first the tracking to mechanical arm output angle by the constraints conversion of time-varying output in the step (2)
The mechanical arm system of script belt restraining is converted to the new mechanical arm system of not belt restraining by the constraint of error, redesign transfer function
System.
Design a new state variable siAnd one about siWith ηiStrictly monotone increasing smooth function Qi(si,
ηi), it indicates are as follows:
Only need siBounded may make output to meet time-varying output constraint.
Further, strictly monotone increasing smooth function is embodied as with transition status variable:
Wherein,Indicate converted variable siTo the derivative of time.
Specifically, in the step (3), the new system after the conversion obtained according to specific transfer function is indicated are as follows:
Wherein,Indicate that the derivative of conversion intermediate variable, H and R indicate are as follows:
Specifically, in the step (4), the tracking error of mechanical arm system is indicated after conversion are as follows:
z1=[z11,z12,...,z1n]T=[s1,s2,...,sn]T
z2=[z21,z22,...,z2n]T=X2-α
Wherein, z1,z2Indicate the error variance that Backstepping design process is used in new system.α is virtual controlling amount, is indicated
Are as follows:
Wherein, k1=diag { k11,k12,...,k1nIndicate the parameter matrix for needing to be arranged.
Specifically, in the step (5), the multi-joint mechanical arm adaptive neural network with time-varying output constraint of design
Network controller indicates are as follows:
Wherein, k2=diag { k21,k22,...,k2nIndicate the parameter matrix being arranged,Indicate local RBF neural, it is unknown dynamic in closed-loop system for approaching
State,Indicate that Gaussian bases, N are mind
Quantity through nodes, ξj, j=1 ... the different nodes in N representation space, the referred to as central point of Gaussian function, ηj,j
=1 ... N indicates center width,Indicate the input of neural network,Indicate institute
With the estimate vector of RBF neural weight.
Further, the right value update rate of the neural network are as follows:
Wherein,Indicate the constant of expression learning rate that can be artificially arranged, σiThe expression of > 0 can artificially be set
The small constant set.
The present invention compared to the prior art, have it is below the utility model has the advantages that
1, control method provided by the present invention does not need mechanical arm system parameter, and can have in system extraneous unknown
In the case where disturbance, high performance tracing control is carried out to mechanical arm, without destroying time-varying output constraint.
2, the present invention is converted the multi-joint mechanical arm with time-varying output constraint to not by establishing transform method
Constrained new system reduces the conservative of controlling plan design.
3, the controller in the present invention can be under any given known time-varying output constraint, when guaranteeing that mechanical arm meets
Change output constraint condition solves existing conventional neural network control device and faces that may be present when time-varying output constraint get over
Boundary's problem.
Detailed description of the invention
Fig. 1 is linkage plane mechanical arm schematic diagram in the embodiment of the present invention.
Fig. 2 is a kind of multi-joint mechanical arm control method with time-varying output constraint provided in an embodiment of the present invention.
Fig. 3 is the analogous diagram that joint of mechanical arm angular displacement tracks situation in the embodiment of the present invention.
Fig. 4 is the analogous diagram that joint of mechanical arm angular displacement tracks situation in the embodiment of the present invention.
Fig. 5 is the Error Graph in the embodiment of the present invention between joint angular displacement and given trail angle deformation trace.
Fig. 6 is the change curve of converted variable in the embodiment of the present invention.
Fig. 7 is the analogous diagram of mechanical arm control input in the embodiment of the present invention.
Fig. 8 is the analogous diagram of mechanical arm control input in the embodiment of the present invention.
Specific embodiment
Present invention will now be described in further detail with reference to the embodiments and the accompanying drawings, but embodiments of the present invention are unlimited
In this.
Embodiment
In the present embodiment, mechanical arm is two linkage plane mechanical arms, and specific structure is as shown in Figure 1.
It is illustrated in figure 2 a kind of specific flow chart of multi-joint mechanical arm control method with time-varying output constraint, is had
Body step includes:
(1) the multi-joint mechanical arm kinetic model and desired pursuit path under time-varying output constraint are established；
The two connecting rods mechanical arm is made of 2 connecting rods, and angular displacement sensor and speed are housed in each artis of connecting rod
Sensor is spent to measure joint Angle Position, angular speed.The kinetic model of two linkage plane mechanical arms indicates are as follows:
Wherein, X1=q,Joint angle motion vector is q=[q1,q2]T, joint angular velocity vector isIndicate that friction term, τ indicate that control moment, M (q) indicate inertial matrix,Indicate centripetal force
Matrix, G (q) indicate gravitation vector；J (q) expression mechanical arm Jacobian matrix, the unknown disturbance of f (t) expression, M (q),G(q),J(q),It is unknown.
In the present embodiment, giving reference locus is indicated are as follows:
Xd1=[sin (t), cos (t)]T
Time-varying output constraint is further set, is indicated are as follows:
q(t)=[- 0.1 × 2-0.8-0.04+sin(t) -0.495×2-1.2t-0.03+cos(t)]T
In the present embodiment, need guaranteeing time-varying output constraintUnder, realize the rail of two linkage plane mechanical arms
Mark tracing control.
M(q),G(q),J(q),Representation are as follows:
Wherein, q1, q2Respectively indicate the angular displacement in joint 1 and joint 2；m1, m2Respectively indicate the matter of connecting rod 1 and connecting rod 2
Amount；l1, l2Respectively indicate the length of connecting rod 1 and connecting rod 2；I1,I2Respectively indicate the inertia of connecting rod 1 and connecting rod 2；G indicates that gravity adds
Speed；
In the present embodiment, the relevant parameter of system specifically:
l1=0.36m, l2=0.32m, m1=2.2Kg, m2=0.86Kg, g=9.8m/s2
I1=64.25 × 10-3kgm2,I2=22.42 × 10-3kgm2
Friction term indicates are as follows:
Disturbance term from environment indicates are as follows:
F (t)=[+1 cos (t)+0.5 of sin (t)]T
(2) transfer function that the system with time-varying output constraint is converted to abandoned new system is established；
Design a new state variable siAnd one about siWith ηiStrictly monotone increasing smooth function Qi(si,
ηi), strictly monotone increasing smooth function is embodied as with transition status variable:
Wherein,Indicate converted variable siTo the derivative of time, ei,ηi,Expression are as follows:
(3) former mechanical arm system, is converted to new mechanical arm system by the transfer function obtained according to step (2)；According to
New system after the conversion that specific transfer function obtains indicates are as follows:
Wherein,Indicate that the derivative of conversion intermediate variable, H and R indicate are as follows:
(4) tracking error signal of mechanical arm system after converting is defined；
In the present embodiment, since the kinetic model of mechanical arm is totally unknown, using neural networkIt approaches and closes
The unknown dynamic of loop system.
The input of neural networkAnd have:
Wherein, k1=diag { k11,k12Indicate the feedback oscillator parameter designed.
(5) for the neural network control device of the mechanical arm system design stability after conversion.
The multi-joint mechanical arm neural network control device with time-varying output constraint of design indicates are as follows:
Wherein, k2=diag { k21,k22Indicate control gain matrix, Local RBF neural is indicated, for approaching the unknown dynamic in closed-loop system, Si
(Z)=[si1(||Z-ξ1||),…,siN(||Z-ξN||)]T,Indicate Gaussian bases, N table
Show the number of Gaussian bases in neural network, ξj, j=1 ... different nodes in N representation space, referred to as Gaussian function
Central point, ηj, j=1 ... N indicates center width,Indicate the input of neural network,Indicate that the estimate vector of RBF neural weight used, N indicate the node number of neural network.
Further, the right value update rate of the neural network are as follows:
Wherein,Indicate the constant of expression learning rate that can be artificially arranged, σiThe expression of > 0 can artificially be set
The small constant set.
In the present embodiment, system primary condition are as follows:
X (0)=[0,1；0,0]
Controller parameter: neural network weight initial valueNeural network node number N=4096, Γ=diag
{ 70 }, η=0.7, δ=0.01, k1=diag { 80 40 }, k2=diag { 88 86 }.
Fig. 3 is joint of mechanical arm angular displacement q1Tracking situation analogous diagram.Fig. 4 is the joint angular displacement q of mechanical arm2With
Track situation analogous diagram.Fig. 5 is joint angular displacement q1,q2With given trail angle deformation trace qd1,qd2Between Error Graph.Pass through figure
3, Fig. 4 and Fig. 5 can be seen that under designed controller, and mechanical arm is able to achieve good output trajectory tracking effect, and its
Output is able to satisfy given time-varying output constraint condition.Fig. 6 is designed joint angle displacement tracking error converted variable s1,s2's
Variation diagram, error converted variable s1,s2Boundedness also ensure the satisfaction of time-varying output constraint.Fig. 7 is mechanical arm control input
u1Analogous diagram.Fig. 8 is mechanical arm control input u2Analogous diagram.
The above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are not by above-described embodiment
Limitation, other any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present invention,
It should be equivalent substitute mode, be included within the scope of the present invention.
Claims (9)
1. a kind of multi-joint mechanical arm control method with time-varying output constraint, which is characterized in that specific steps include:
(1) the multi-joint mechanical arm kinetic model and desired pursuit path under time-varying output constraint are established；
(2) transfer function that the system with time-varying output constraint is converted to abandoned new system is established；
(3) former mechanical arm system, is converted to new mechanical arm system by the transfer function obtained according to step (2)；
(4) tracking error signal of mechanical arm system after converting is defined；
(5) for the neural network control device of the mechanical arm system design stability after conversion.
2. a kind of multi-joint mechanical arm control method with time-varying output constraint according to claim 1, feature exist
In in step (1), multi-joint mechanical arm kinetic model is the machine coupled with strong nonlinearity under the time-varying output constraint
Tool arm dynamic model indicates are as follows:
Wherein, X1=q,Q=[q1 q2 ... qn]TIndicate angular displacement, τ indicates control moment, M (X1) indicate inertia
Matrix, Cm(X1,X2) indicate centripetal force matrix, G (X1) indicate gravitation vector, JT(X1) indicate mechanical arm Jacobean matrix
Battle array, F (X2) indicating friction force vector, f (t) is indicated from people and extraneous disturbance term；M(X1),Cm(X1,X2),G(X1),F
(X2),JT(X1), f (t) is unknown；The time-varying output constraint of mechanical arm indicates are as follows:
3. a kind of multi-joint mechanical arm control method with time-varying output constraint according to claim 2, feature exist
In the mechanical arm dynamic model established is indicated using joint of mechanical arm angular displacement and joint angular displacement as state variable are as follows:
Wherein, q=[q1 q2 ... qn]TIndicate angular displacement, qd=[qd1 qd2 ... qdn]TIndicate given output tracking rail
Mark, e=[e1 e2 ... en]TIndicate output tracking error,Withq=[q 1 q 2 ... q n] respectively
Indicate that the upper bound and the lower bound of the time-varying output constraint of mechanical arm, n indicate the joint with the Rigid Robot Manipulator of time-varying output constraint
Number,And ηiIt (t) is intermediate variable.
4. a kind of multi-joint mechanical arm control method with time-varying output constraint according to claim 1, feature exist
In, in the step (2), one new state variable s of designiAnd one about siWith ηiStrictly monotone increasing it is smooth
Function Qi(si,ηi), it indicates are as follows:
Wherein, e=[e1 e2 ... en]TIndicate output tracking error,Withq=[q 1 q 2 ... q n]
The upper bound and the lower bound of the time-varying output constraint of mechanical arm are respectively indicated, n indicates the Rigid Robot Manipulator with time-varying output constraint
Joint number,And ηiIt (t) is intermediate variable；
Only need siBounded may make output to meet time-varying output constraint.
5. a kind of multi-joint mechanical arm control method with time-varying output constraint according to claim 4, feature exist
In strictly monotone increasing smooth function is embodied as with transition status variable:
Wherein,Indicate converted variable siTo the derivative of time.
6. a kind of multi-joint mechanical arm control method with time-varying output constraint according to claim 1, feature exist
In in the step (3), the new system after the conversion obtained according to specific transfer function is indicated are as follows:
Wherein,Indicate that the derivative of conversion intermediate variable, H and R indicate are as follows:
Wherein,Q=[q1 q2 ... qn]TIndicating angular displacement, M (q) indicates inertial matrix,Indicate centripetal
Torque battle array, G (q) indicate gravitation vector, JT(q) indicate that the Jacobian matrix of mechanical arm, f (t) indicate to come from people and the external world
Disturbance term, e=[e1 e2 ... en]TIndicate output tracking error, And ηiIt (t) is intermediate variable.
7. a kind of multi-joint mechanical arm control method with time-varying output constraint according to claim 1, feature exist
In in the step (4), the tracking error of mechanical arm system is indicated after conversion are as follows:
z1=[z11,z12,...,z1n]T=[s1,s2,...,sn]T
z2=[z21,z22,...,z2n]T=X2-α
Wherein, z1,z2Indicate the error variance that Backstepping design process is used in new system,α is virtual controlling amount,
It indicates are as follows:
Wherein, k1=diag { k11,k12,...,k1nIndicate the parameter matrix for needing to be arranged, qd=[qd1 qd2 ... qdn]TTable
Show given output tracking track.
8. a kind of multi-joint mechanical arm control method with time-varying output constraint according to claim 1, feature exist
In, in the step (5), the multi-joint mechanical arm neural network control device table with time-varying output constraint of design
It is shown as:
Wherein, k2=diag { k21,k22,...,k2nIndicate the parameter matrix being arranged,Indicate local RBF neural, Si(Z)=[si1(||Z-ξ1||),…,siN(|
|Z-ξN||)]T,Indicate that Gaussian bases, N indicate of Gaussian bases in neural network
Number, ξj, j=1 ... the different nodes in N representation space, the referred to as central point of Gaussian function, ηj, j=1 ... N indicates center
Width,Indicate the input of neural network,Indicate RBF neural power used
The estimate vector of value, z1,z2Indicate that the error variance in new system, α are virtual controlling amount.
9. a kind of multi-joint mechanical arm control method with time-varying output constraint according to claim 8, feature exist
In the right value update rate of the neural network are as follows:
Wherein,Indicate the constant of expression learning rate that can be artificially arranged, σiThe expression of > 0 can artificially be arranged small
Constant.
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| CN110187637A (en) * | 2019-06-03 | 2019-08-30 | 重庆大学 | Robot system control method in the case where control direction and desired trajectory are uncertain |
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| CN116690561A (en) * | 2023-05-30 | 2023-09-05 | 渤海大学 | Self-adaptive optimal backstepping control method and system for single-connecting-rod mechanical arm |
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