CN106078741B - Limited performance flexible mechanical arm control method based on the definite theories of learning - Google Patents
Limited performance flexible mechanical arm control method based on the definite theories of learning Download PDFInfo
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- CN106078741B CN106078741B CN201610457032.3A CN201610457032A CN106078741B CN 106078741 B CN106078741 B CN 106078741B CN 201610457032 A CN201610457032 A CN 201610457032A CN 106078741 B CN106078741 B CN 106078741B
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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
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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
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1635—Programme controls characterised by the control loop flexible-arm control
Abstract
The invention discloses a kind of limited performance flexible mechanical arm control method based on the definite theories of learning, this method is directed to the uncertainty of flexible mechanical arm dynamic model, designs tracking error, is allowed to meet that constraints limits, and form error controller.Step of the present invention includes：Establish flexible mechanical arm dynamic model；Establish State Observer；Design tracking error performance constraints；Nerve network controller is designed based on the definite theories of learning；Utilize Heuristics modifier controller.Control method designed by the present invention can realize Fast Convergent, the dynamic property of low overshoot, meet the constraints limitation of setting, while avoid neural network weight on-line control, shorten control time.In addition, this method can utilize the Heuristics learnt to be directly realized by quick control to identical control task afterwards.
Description
Technical field
The invention belongs to the Trajectory Tracking Control field of flexible mechanical arm, especially for flexible mechanical arm system dynamic analog
The uncertainty of type, designs tracking error, is allowed to meet that constraints limits.Provide a kind of performance based on the definite theories of learning
Limited flexible mechanical arm control method.
Background technology
Nowadays, as robot develops towards high accuracy, quick direction, mechanical part increasingly tends to lightness.Phase
Than in traditional Rigid Robot Manipulator, flexible mechanical arm has the characteristics that structure is light, working space is big and efficient, so flexible member
Application of the part in fields such as manufacturing industry, aerospaces is more and more wider, but the flexible effect that flexible armed lever is brought, and can cause machinery
Vibration, this can cause the stationarity of TRAJECTORY CONTROL requirement to be more difficult to reach with accuracy, the track following control of flexible mechanical arm end
System is difficult all the more.And in practical application in industry, since the constraint of industrial environment limits, such as limit of motor maximum output torque
System, steady-state process end orbit tracking error limitation, the maximum overshoot of initial movement segment tracking error and convergence rate
Limitation, the control performance for often also needing to system meet certain constraints, this makes the control program of design not only ensure
Track following error system is stablized, and the tracking performance of tracking error will also meet the constraint under practical situation, this is to control
The design of scheme brings very big challenge.
For the Trajectory Tracking Control of flexible mechanical arm system, back stepping control, sliding formwork control, dynamic surface control etc. are intelligently controlled
Method combination ANN Control processed, can solve the stationarity of the TRAJECTORY CONTROL requirement in the case of system model Dynamic Uncertain
And accuracy problem.But in the case of having specific constraint for tracking performance, these control methods are unable to control tracking error
Meet the requirement that particular characteristic is limited.A kind of performance error changes adaptive neural network control method, by introduce performance by
Function is limited, is specially mathematical functional expression expression by the tracking error limited performance condition in actual environment, further passes through performance
Error is changed, and original affined tracking error control problem is converted to unconfinement transformed error stability control problem, pin
Neural network control is designed to unconfinement transformed error, and for immeasurablel Design of State state observation in system
Device, the stabilization of final unconfinement conversion error enable to end orbit tracking to meet that limited performance condition limits.Therefore pass through
The performance error conversion adaptive neural network control method of performance constraints function is introduced, can be according to specific actual performance about
Beam, designs corresponding limited performance function, realizes the Trajectory Tracking Control under the conditions of flexible mechanical arm limited performance.
It is existing using neutral net in flexible mechanical arm system Unknown Model dynamic approach during, it is necessary to
Continuous on-line tuning, every time during start runtime, controller needs to readjust neural network weight, in weighed value adjusting
Starting stage, neutral net is bigger for the dynamic approximate error of Unknown Model, and adjust process be it is very time-consuming,
This makes overall control effect be affected.For identical control task, the Unknown Model dynamic that neutral net is approached is base
This is consistent, so the neural network weight adjustment repeated is the operation of redundancy.In order to solve neutral net take redundancy
Line adjusts process, it is necessary to which the weights of neutral net are finally restrained, but this is extremely difficult reaches.Determine the theories of learning
(Wang C.and Hill D.J..Learning From Neural Control[J].IEEE Transactions
onNeural Networks,2006,17(1):130-145) the verified track for cycle or class cycle carries out nerve
When network approaches, neural network weight can finally restrain.The rail of limited performance flexible mechanical arm based on the definite theories of learning
Mark tracking and controlling method, the neural network weight after storage convergence, in next time identical control task, directly utilizes storage
Neural network weight, avoid repeat neutral net on-line tuning process, realize the constant value nerve net based on Heuristics
Network controls.
The content of the invention
The shortcomings that it is a primary object of the present invention to overcome the prior art and deficiency, propose that one kind is based on determining the theories of learning
Limited performance flexible mechanical arm Trajectory Tracking Control method, avoid for multiple identical control task, while meet reality
Control the Trajectory Tracking Control task in the case of specific tracking error performance constraints in environment.
In order to achieve the above object, the present invention uses following technical scheme：
The limited performance flexible mechanical arm control method based on the definite theories of learning of the present invention, comprises the following steps：
Step (1)：Establish flexible mechanical arm dynamic model：By state transformation, the decoupling of single connecting rod flexible mechanical arm is established
The dynamic model of the quadravalence canonical system form of conjunction；
Step (2)：Establish State Observer：The system mode design point not directly measured in model is observed
Device：
Wherein, p and riFor design parameter, i=1 ..., 4,Immeasurability shape respectively in system
State [υ2 υ3 υ4] state observer；
Step (3)：Design tracking error performance constraints：To connecting rod output angle and cycle reference track output angle
Between tracking error, the transient state and steady-state behaviour of design performance function pair tracking error constrained, and is specially：
Wherein, ρ (t) is performance function, ρ0、ρ∞、s、σ、For design constant, xdFor joint link lever angle reference periodically
Track, e1For track following error；
Design a strictly monotone increasing smooth function Ψ (ε1), by limited tracking error e1(t) transformed error ε is converted to1
(t)：
Step (4)：Nerve network controller is designed based on the definite theories of learning：It is adaptive using the definite theories of learning, design
Answer RBF neural learning controller：
Wherein,Exported for neutral net, k4For the controller gain constant of design, ε4To pass through following design
The median error amount that process calculates：
The state observer established according to step (2) exportsWith it is transformed non-in step (3)
Limited transformed error ε1, design Virtual Controller α1, α2, α3：
Wherein ki(i=1,2,3) be design Virtual Controller gain constant, xdFor joint link lever angle reference periodically
Track, γ, B are the middle control variable involved in virtual controlling；
The median error amount occurred in controller u
Step (5)：Utilize Heuristics modifier controller：According to the definite theories of learning, neutral net in step (4) is weighed
ValueConvergency value save asRealize and utilize the constant value RBF neural for expressing HeuristicsModifier controller,
I.e. controller form is：
As preferable technical solution, in step (1), the uncoupled quadravalence canonical system form of the flexible mechanical arm
Dynamic model be：
Wherein, x1And x2Respectively joint link lever angle and motor rotational angle, I and J are respectively the used of connecting rod and motor
Amount, M are the quality of connecting rod, and L is the length of connecting rod, and g is acceleration of gravity, and K is the coefficient of elasticity of flexible portion spring, and u is control
The control output of device processed, i.e. motor.
As preferable technical solution, in step (3), the limited tracking error e1(t) it is stringent by designing one
Monotonic increase smooth function Ψ (ε1) be converted to transformed error ε1(t), by controlling ε1(t) stabilization, makes e1(t) constraint is met
ConditionSo as to fulfill the Trajectory Tracking Control under constraints.
As preferable technical solution, in step (4), M signal variable γ, B tool that the Virtual Controller is related to
Body is：Neutral net exportsFor approaching mechanical arm system
Unknown multidate information, the input of neutral net isFor the neural network weight of online updating
Vector.
As preferable technical solution, in step (4), the neural network weight is convergent, based on definite study
Theory, the neutral net of tracking cycle track input, neural net regression vector S (X) meet persistent excitation condition, final god
Through network weightConverge to optimal value
As preferable technical solution, in step (5), the modified controller is contained in definite learning process
HeuristicsController allow for control task identical afterwards, realize Fast Convergent, low overshoot it is dynamic
State property energy.
Compared with prior art, the present invention having the following advantages that and beneficial effect：
1st, compared with the flexible mechanical arm Trajectory Tracking Control method that presently, there are, control method energy proposed by the present invention
Enough realize that track following error meets specific performance constraints, and not only realize what track following error finally went to zero
Inside one neighborhood, moreover it is possible to realize and the overshoot and convergence rate of error are limited.
2nd, for method of the invention by design performance function, the parameter of regulation performance function can be by performance constraints
Embodied by way of mathematical function, so as to further design controller.
3rd, method of the invention is by designing a strictly monotone increasing smooth function Ψ (ε1), by limited tracking error
e1(t) transformed error ε is converted to1(t), its essence is that limited tracking error control problem is converted into the steady of untethered error
Qualitative question, easy to controller design.
4th, method of the invention can learn the ambiguous model dynamic of system using the theories of learning are determined, and will
The Heuristics learnt is stored in the form of constant value neural network weight, when identical control task is carried out after being allowed to,
It can be directly controlled using the knowledge of storage, avoid the on-line tuning process of redundancy, realize neutral net Off-line control, saved
Improve the performance of dynamic tracking in the starting stage while making an appointment.
Brief description of the drawings
Fig. 1 is flexible mechanical arm system schematic of the present invention.
Fig. 2 is the overall control block diagram of flexible mechanical arm of the present invention.
Fig. 3 is the convergent analogous diagram of neural network learning stage tracking error of the present invention.
Fig. 4 is error analogous diagram between state observer of the present invention and institute's observation state.
Fig. 5 is neural network weight convergence analogous diagram of the present invention.
Fig. 6 is the controller output analogous diagram in neural network learning stage of the present invention.
Fig. 7 is that the present invention dynamically approaches analogous diagram using constant value neutral net is unknown to system.
Fig. 8 is that neural network learning stage of the present invention and knowledge recycle control stage tracking error convergence contrast simulation
Figure.
Embodiment
With reference to embodiment and attached drawing, the present invention is described in further detail, but embodiments of the present invention are unlimited
In this.
Embodiment
The present embodiment mainly studies Trajectory Tracking Control of the flexible mechanical arm under tracking performance limited situation, and Fig. 1 is soft
The schematic diagram of property mechanical arm system.
The overall control block diagram of limited performance flexible mechanical arm control method based on the definite theories of learning as shown in Fig. 2,
Its detailed implementation process includes：
Step (1)：Establish flexible mechanical arm dynamic model.
According to following flexible mechanical arm system model：
The dynamic model form for the quadravalence canonical system form being converted into after decoupling is as follows：
Wherein, x1And x2Respectively joint link lever angle and motor rotational angle, I and J are respectively the used of connecting rod and motor
Amount, M are the quality of connecting rod, and L is the length of connecting rod, and g is acceleration of gravity, and K is the coefficient of elasticity of flexible portion spring, and u is electricity
The control output of machine；
In this example, the systematic parameter for choosing flexible mechanical arm is respectively：
M=0.2kg, L=1m, I=2.3kgm2, K=15Nm/rad, J=0.5kgm2, g=9.8m/s2
Step (2)：Establish State Observer.
Since the state that can be measured in system is x1, and υ2, υ3, υ4It is immesurable, design point observation in system
Device is as follows：
Wherein p=1250, r1=r3=-2p, r2=-3p, r4=-p,Respectively can not in system
Measuring state [υ2 υ3 υ4] state observer.
Step (3)：Design tracking error performance constraints.
Select the reference locus in following cycle：
Wherein, xdFor the reference angle track of joint link lever angle at the end, and there are continuous derivativee1=
x1-xdFor the track following error of connecting rod end.
Tracking error is required to meet following limited performance constraints in this example：e1The maximum overshoot upper limit and under
Limit is respectively 1.44 and -1.2, e1Convergence rate cannot be below e-t, e1Steady-state error constrain between -0.05 and 0.05,
It is as follows that function is limited according to above-mentioned constraints design performance：
According to limited performance function, a strictly monotone increasing smooth function Ψ (ε is designed1), by limited track following
Error e1Be converted to untethered transformed error ε1：
Step (4)：Nerve network controller is designed based on the definite theories of learning.
Ensure transformed error ε by designing controller1Stabilization, so as to fulfill limited error e1Meet wanting for constraints
Ask, be specially：
Design firstVirtual Controller α1, and and state observerForm error variance ε2：
Wherein, k1=1,
Further designVirtual Controller α2, and and state observerForm error variance ε3：
Wherein, k2=4, γ=1/ (ρ+e1)+1/(1.2ρ-e1)。
Further designVirtual Controller α3, and and state observerForm error variance ε4：
Wherein, k3=10,
In this example, the system model dynamic of flexible mechanical arm is totally unknown, utilizes neutral netApproach unknown
Dynamic：The wherein input of neutral netAdaptive neural network
The following form of e-learning controller design：
Wherein, selection control gain k4=20.
Select neural network weightOnline updating regulation is：
The selection of system initial state and neural network parameter is as follows：
The primary condition of system：
Neural network parameter selects：Neural network node number N=9 × 9 × 11 × 11, weights initial value
Central point is evenly distributed on [- 0.9,0.9] × [- 0.9,0.9] × [- 1.5,1.5] × [- 1.5,1.5], neutral net turnover rate
Parameter Γ=12, o=0.0001.
According to nerve network controllerControl transformed error ε1Stablize, ε1Stabilization to be limited
Tracking error e1Meet constraints-ρ (t) ＜ e1(t) 1.2 ρ (t) of ＜, so as to fulfill the track following control under performance constraints
System.
Fig. 3 shows study stage tracking error e1Convergent analogous diagram, final tracking error e1In constraints-ρ (t)
＜ e1(t) fluctuation in 1.2 ρ (t) of ＜, and converge within the limited time inside zero small neighbourhood, so as to meet to set
Constraints requirement, realize the Trajectory Tracking Control under performance constraints.Fig. 4 is the state observer and system of design
Observation error change analogous diagram between middle institute's observation state.Fig. 5 is study weights of the neutral net to unknown system dynamic F (X)
Restrain analogous diagram.Fig. 6 is the wave simulation figure that neural network learning phase controller exports u.According to Fig. 5, in Neural Network Science
Habit stage, the weights of neutral net finally converge to constant value, store the weights constant value of these neutral nets, as system not
Know the expression of multidate information.
Step (5)：Utilize Heuristics modifier controller.
In this example, constant value nerve is calculated by averaging to convergent weights in the period [400s, 500s]
Network weight：
Design the nerve network controller based on Heuristics：
Wherein, the control parameter in controller is chosen consistent with the neural network learning stage.
Fig. 7 is constant value neutral netWith the Approximation effect analogous diagram between unknown system dynamic F (X), storage
Constant value neutral net can approach unknown system, unknown system is dynamically learnt so as to fulfill neutral net to recycle
Journey, avoids the online of redundancy from readjusting process.Fig. 8 recycles the tracking of control stage to miss for neural network learning stage and experience
Difference convergence contrast effect analogous diagram, for identical control task, the nerve network controller based on Heuristics has smaller
Overshoot, be better than the neural network learning stage in the dynamic characteristic of starting stage, shorten regulating time.
Above-described embodiment is the preferable embodiment of the present invention, but embodiments of the present invention and from above-described embodiment
Limitation, other any Spirit Essences without departing from the present invention with made under principle change, modification, replacement, combine, simplification,
Equivalent substitute mode is should be, is included within protection scope of the present invention.
Claims (6)
1. the limited performance flexible mechanical arm control method based on the definite theories of learning, it is characterised in that comprise the following steps：
Step (1)：Establish flexible mechanical arm dynamic model：By state transformation, it is uncoupled to establish single connecting rod flexible mechanical arm
The dynamic model of quadravalence canonical system form；
Step (2)：Establish State Observer：To the system mode design point observer not directly measured in model：
Wherein, p and riFor design parameter, i=1 ..., 4,Unmeasured state [υ respectively in system2
υ3 υ4] state observer；
Step (3)：Design tracking error performance constraints：To between connecting rod output angle and cycle reference track output angle
Tracking error, the transient state and steady-state behaviour of design performance function pair tracking error constrained, and is specially：
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Wherein, ρ (t) is performance function, ρ0、ρ∞、s、σ、For design constant, xdFor joint link lever angle reference periodicity track,
e1For track following error；
Design a strictly monotone increasing smooth function Ψ (ε1), by limited tracking error e1(t) transformed error ε is converted to1(t)：
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Step (4)：Nerve network controller is designed based on the definite theories of learning：Using the definite theories of learning, self_adaptive RBF is designed
Neural network learning controller：
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The median error amount calculated：
The state observer established according to step (2) exportsWith transformed untethered turn in step (3)
Change error ε1, design Virtual Controller α1, α2, α3：
Wherein ki(i=1,2,3) be design Virtual Controller gain constant, xdFor joint link lever angle reference periodicity track,
γ, B are the middle control variable involved in virtual controlling；
The median error amount ε occurred in controller u4：
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2. the limited performance flexible mechanical arm control method according to claim 1 based on the definite theories of learning, its feature
It is, in step (1), the dynamic model of the uncoupled quadravalence canonical system form of the flexible mechanical arm is：
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</msub>
</mrow>
</mtd>
</mtr>
<mtr>
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<mtable>
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<mi>J</mi>
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</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein, x1And x2Respectively joint link lever angle and motor rotational angle, I and J are respectively the inertia of connecting rod and motor, and M is
The quality of connecting rod, L are the length of connecting rod, and g is acceleration of gravity, and K is the coefficient of elasticity of flexible portion spring, u devices in order to control, i.e.,
The control output of motor.
3. the limited performance flexible mechanical arm control method according to claim 1 based on the definite theories of learning, its feature
It is, in step (3), the limited tracking error e1(t) by designing a strictly monotone increasing smooth function Ψ (ε1) turn
It is changed to transformed error ε1(t), by controlling ε1(t) stabilization, makes e1(t) constraints is met
So as to fulfill the Trajectory Tracking Control under constraints.
4. the limited performance flexible mechanical arm control method according to claim 1 based on the definite theories of learning, it is characterised in that
In step (4), M signal variable γ, B that the Virtual Controller is related to are specially： Neutral net exportsFor approaching the unknown multidate information of mechanical arm system, the input of neutral net
For For the neural network weight vector of online updating.
5. the limited performance flexible mechanical arm control method according to claim 1 based on the definite theories of learning, its feature
It is, in step (4), the neural network weight is convergent, based on the definite theories of learning, the input of tracking cycle track
Neutral net, neural net regression vector S (X) meets persistent excitation condition, final neural network weightConverge to optimal
Value
6. the limited performance flexible mechanical arm control method according to claim 1 based on the definite theories of learning, its feature
It is, in step (5), the modified controller contains the Heuristics in definite learning processSo that
Controller can realize Fast Convergent, the dynamic property of low overshoot for control task identical afterwards.
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| CN107160398B (en) * | 2017-06-16 | 2019-07-12 | 华南理工大学 | The safe and reliable control method of Rigid Robot Manipulator is limited based on the total state for determining study |
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| CN109227543B (en) * | 2018-10-19 | 2020-07-28 | 华南理工大学 | Mode-based intelligent control method for position-limited flexible joint robot |
| CN109352656B (en) * | 2018-11-29 | 2021-01-19 | 华南理工大学 | Multi-joint mechanical arm control method with time-varying output constraint |
| CN109782601B (en) * | 2019-01-31 | 2021-09-14 | 浙江大学 | Design method of self-adaptive neural network synchronous robust controller of coordinated mechanical arm |
| CN109884890B (en) * | 2019-02-15 | 2021-12-07 | 浙江工业大学 | Time-varying constraint inversion control method for servo system of electric drive mechanical arm |
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| CN111496796B (en) * | 2020-05-08 | 2020-12-22 | 哈尔滨工业大学 | Mechanical arm trajectory tracking control method and device based on instruction filter |
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