CN109129486A - A kind of repetitive motion planning method for redundant manipulator inhibiting periodic noise - Google Patents
A kind of repetitive motion planning method for redundant manipulator inhibiting periodic noise Download PDFInfo
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- CN109129486A CN109129486A CN201811120185.4A CN201811120185A CN109129486A CN 109129486 A CN109129486 A CN 109129486A CN 201811120185 A CN201811120185 A CN 201811120185A CN 109129486 A CN109129486 A CN 109129486A
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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
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
- B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
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- Mechanical Engineering (AREA)
- Automation & Control Theory (AREA)
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Abstract
The present invention provides a kind of repetitive motion planning method for redundant manipulator for inhibiting periodic noise, include the following steps: 1) to parse the inverse kinematics of mechanical arm on angular acceleration layer using quadratic form optimization, the minimum performance index of design can be angular speed norm, torque norm, it is constrained in angular acceleration Jacobi's equation with angular speed and position feedback；2) the quadratic form optimization of step 1) is converted standard quadratic programming by the equivalence transformation for carrying out angular speed index and angular acceleration index；3) the standard quadratic programming of step 2) is solved with circadian rhythm neural network Solution To The Network device；4) solving result of step 3) is driven into manipulator motion.The present invention is planned in the repeating motion using the circadian rhythm neural fusion control redundancy mechanical arm based on quadratic programming, effectively prevent the interference of periodic noise, being overlapped for mechanical arm actual path and expected path is realized, mechanical arm repeating motion is planned.
Description
Technical field
The present invention relates to redundancy mechanical arm control fields, and in particular to a kind of redundancy mechanical arm for inhibiting periodic noise
Repetitive motion planning method.
Background technique
Redundancy mechanical arm is a kind of active mechanical device in end of least degree of freedom needed for freedom degree is greater than task space,
Its motor task includes welding, painting, assemble, excavate and draw etc., is widely used in equipment manufacturing, product is processed, machine work
In the national economy production activity such as industry.The Inverse Kinematics Problem of redundancy mechanical arm refers to known mechanical arm end pose, determines
The joint angle problem of mechanical arm.When redundancy mechanical arm end task is a closed curve, each joint may be returned not
To initial position, this phenomenon is called joint angle bias phenomenon or non-duplicate motion problems；And repeating motion programme is just
It is to design index appropriate, when so that mechanical arm tail end having executed closed curve task, each joint angle can return to it
Initial position.
Previous repeating motion analytic method does not account for the influence of periodic noise, and obtained result is default cycles
What noise was not present, this does not meet actual conditions.In fact periodic noise is present in various control systems, to reduce control
Performance even results in out of control.Periodic noise may result from twiddle factor, such as motor and vibrating elements.Redundant mechanical arm
Also it will receive the interference of periodic noise, may therefore lead to redundant mechanical arm repeating motion planning failure.
Summary of the invention
In order to overcome the defects of the prior art, the present invention at least provides the following technical solutions:
A kind of repetitive motion planning method for redundant manipulator inhibiting periodic noise comprising following steps:
1) inverse kinematics of mechanical arm is parsed on angular acceleration layer using quadratic form prioritization scheme, the minimality of design
Can index can be angular speed norm and torque norm, it is constrained in the angular acceleration Jacobi etc. with angular speed and position feedback
Formula；
2) quadratic form optimization is converted standard two by the equivalence transformation for carrying out angular speed index and angular acceleration index
Secondary planning；
3) the standard quadratic programming is solved with circadian rhythm neural network Solution To The Network device；
4) result of the solution is driven into manipulator motion.
Further, the quadratic form Optimization Plan of the step 1) are as follows: minimize
It is constrained in angular acceleration Jacobi's equation with angular speed and position feedback
Wherein σ ∈ [0,1] is weight parameter,It is joint angular velocity vector, a (t) is a parameter vector,Represent joint torque vector, M (θ) ∈ Rn×nIt is an inertial matrix,
It is centrifugal force and Coriolis force vector, g (θ) ∈ RnGravitational vectors, J is the Jacobian matrix of mechanical arm, θ andIt is respectively
Joint angle vector sum joint angular velocity vector,Indicate joint velocity vector, r (t) andRespectively indicate mechanical arm tail end
Actuator position vector sum velocity vector,Indicate robot arm end effector acceleration, λa, λb∈ R is as feedback
Control coefrficient.
Further, the step 2) specifically,
Carry out angular speed indexWith angular acceleration indexEquivalence transformation, two
Secondary type optimization is converted into a standard quadratic programming, designs its performance indicator to minimize xTQx/2+μTX, it is constrained in Jx=y,
Wherein, T indicates transposition,Q:=(1- σ) I+ σ M (θ), wherein I ∈ Rn×nIt is unit matrix； θ (0) is
Joint initial angle, α and β are positive weights coefficients；
Further, the step 3) is specifically, standard quadratic programming is converted into the solution of a matrix equation WX=Y,
WhereinM is flute
The dimension in karr space, n are the dimension of joint space, and λ indicates Lagrange multiplier vector；
Then, matrix equation is solved with circadian rhythm Neural Networks Solution device.Designing it and calculating error is ∈ (t)=WX-
Y, when error is zero, corresponding X value is just the solution of matrix equation.The kinetics equation of circadian rhythm neural network isWhereinIt is first derivative of the ∈ (t) to the time, γ > 0 designs to adjust
Convergence rate, F () indicate that activation primitive, φ (t) represent periodic noise.χ(t)∈Rn+mIt is an auxiliary vector, is defined as χ
(t)=χ (t-T)+ρ ∈ (t), wherein T is periodic noisePeriod, and ρ > 0 is a feedback factor；In conjunction with error ∈
(t) and the kinetics equation of circadian rhythm neural network, the kinetics equation of available circadian rhythm Neural Networks Solution device
Given initial value X0∈Rn+m, X is obtained by circadian rhythm Neural Networks Solution device, error ∈ (t) is converged to
0, it is constantly solved by circadian rhythm Neural Networks Solution device, the solution of matrix equation WX=Y can be obtained, to obtain acceleration
The optimal solution of layer repeating motion planning quadratic programming.
Further, the matrix equation, with circadian rhythm Neural Networks Solution device solve result drive mechanical arm into
Row repeating motion planning.
Further, the activation primitive is linear activation primitive, sinh activation primitive, bipolar sigmoid activation
Function or tunable activation primitive；The periodic noise is that period random noise, constant noise, square wave noise or triangular wave are made an uproar
Sound.
Compared with prior art, the present invention at least has the following beneficial effects:
The present invention uses the redundancy mechanical arm repeating motion planning side of the circadian rhythm neural network based on quadratic programming
Method, and the present invention considers the interference of a variety of periodic noises, effectively prevents the interference of periodic noise, realizes mechanical arm reality
Border track is overlapped with expected path, and mechanical arm repeating motion is planned.
Detailed description of the invention
Fig. 1 is the process of the repetitive motion planning method for redundant manipulator of the inhibition periodic noise of the embodiment of the present invention
Figure.
Fig. 2 is mechanical arm non-duplicate motion planning schematic diagram under period random noise disturbance.
The mechanical arm of Fig. 3 to realize the present invention schematic diagram that repeating motion is planned under period random noise disturbance.
Specific embodiment
It is next below that the present invention will be further described in detail.
Repetitive motion planning method for redundant manipulator shown in FIG. 1 mainly by acceleration layer repeating motion performance indicator with
Constraint 1, standard quadratic programming 2, the circadian rhythm Neural Networks Solution device 3 based on matrix equation, the next machine controller 4 and machinery
Arm 5 forms.Specifically, this method includes following steps:
1) inverse kinematics of mechanical arm is parsed on angular acceleration layer using quadratic form optimization, the minimum performance of design refers to
Mark can be angular speed norm and torque norm, it is constrained in angular acceleration Jacobi's equation with angular speed and position feedback；
2) quadratic form optimization is converted standard two by the equivalence transformation for carrying out angular speed index and angular acceleration index
Secondary planning；
3) the standard quadratic programming is solved with circadian rhythm neural network Solution To The Network device；
4) result of the solution is driven into manipulator motion.
Shown in Fig. 2, mechanical arm is under period random noise disturbance, and after completion task, joint of mechanical arm is not returned to initially
Position, i.e. each final states joint angle of mechanical arm are not equal to initial joint angle, and cannot complete closing motion；The reality of mechanical arm
Track cannot be overlapped with expected path.Mechanical arm can not achieve repeating motion planning.
Schematic diagram is planned in the repeating motion under period random noise disturbance of the mechanical arm of Fig. 3 to realize the present invention.The present invention
The quadratic form prioritization scheme of design, i.e. acceleration layer repeating motion programme are
It minimizes
Constraint condition
Wherein σ ∈ [0,1] is weight parameter,It is joint angular velocity vector, a (t) is a parameter vector,Represent joint torque vector, M (θ) ∈ Rn×nIt is an inertial matrix,It is centrifugal force and Coriolis force vector, g (θ) ∈ RnIt is gravitational vectors, J is the Jacobian matrix of mechanical arm,
θ andIt is joint angle vector sum joint angular velocity vector respectively,Indicate joint velocity vector, r (t) andIt respectively indicates
Robot arm end effector position vector and velocity vector,Indicate robot arm end effector acceleration, λa, λb∈
R is as feedback control coefficient.
In view of the minimum index of above-mentioned prioritization scheme is joint angular speed, and constraint condition is joint angular acceleration,
It therefore need to be by the angular speed index of mechanical armWith angular acceleration indexIt carries out of equal value
Transformation, then quadratic form prioritization scheme (1)-(2) can be described as following standard quadratic programming scheme:
Minimize xTQx/2+μTx (3)
Jx=y (4)
Wherein, transposition is indicated,Q:=(1- σ) I+ σ M (θ), wherein I ∈ Rn×nIt is unit matrix；θ(0)
It is joint initial angle, α and β are positive weights coefficients；
Above-mentioned standard quadratic programming scheme can be converted into the solution of a matrix equation WX=Y, whereinM is Descartes
The dimension in space, n are the dimension of joint space, and λ indicates Lagrange multiplier vector.
Then, above-mentioned matrix equation is solved with circadian rhythm Neural Networks Solution device.Design its calculate error be ∈ (t)=
WX-Y, when error is zero, corresponding X value is just the solution of matrix equation.The kinetics equation of circadian rhythm neural network isWhereinIt is first derivative of the ∈ (t) to the time, the design of γ > 0 restrains to adjust
Speed, F () expression activation primitive (such as linear activation primitive, sinh activation primitive, bipolar sigmoid activation primitive,
Tunable activation primitive), φ (t) represent various periodic noises (for example, period random noise, constant noise, square wave noise, three
Angle wave noise etc.), it is noted that it can be handled using constant noise as a periodic noise with any period.χ
(t)∈Rn+mIt is an auxiliary vector, is defined as χ (t)=χ (t-T)+ρ ∈ (t), wherein T is periodic noisePeriod, and
ρ > 0 is a feedback factor.In conjunction with the kinetics equation of error ∈ (t) and circadian rhythm neural network, the available period
Restrain the kinetics equation of Neural Networks Solution device
Given initial value X0∈Rn+m, X is obtained by circadian rhythm Neural Networks Solution device, error ∈ (t) is converged to
0, it is constantly solved by circadian rhythm Neural Networks Solution device, the solution of matrix equation WX=Y can be obtained, to obtain acceleration
The optimal solution of layer repeating motion planning quadratic programming.
It is carried out now in conjunction with workflow of the specific example operation to this method as described below.
During acceleration layer repeating motion planning implementation, the parameter of HTVO (i.e. mixing torque and speed-optimization) scheme
It is set as σ=0.6, λa=20, λbThe joint angle original state θ (0) of=20, α=50, β=50, redundant mechanical arm are set as
[1.675,2.843, -3.216,4.187, -1.710, -2.650]TRad defaults n=6, m=3, repeating motion tracing task
The execution period is set as T=8s, and activation primitive uses linear activation primitive F (e)=e.The acceleration being calculated is transmitted again
The movement of mechanical arm is controlled to mechanical arm controller.
Mechanical arm is under period random noise disturbance, and after completion task, mechanical arm has returned to initial position, completes closure
Movement, meanwhile, each final states joint angle of mechanical arm is equal to initial joint angle；The actual path of mechanical arm also with desired trajectory weight
It closes.Mechanical arm realizes repeating motion planning.
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 (6)
1. a kind of repetitive motion planning method for redundant manipulator for inhibiting periodic noise, it is characterised in that include the following steps:
1) inverse kinematics of mechanical arm is parsed on angular acceleration layer using quadratic form prioritization scheme, the minimum performance of design refers to
Mark can be angular speed norm and torque norm, it is constrained in angular acceleration Jacobi's equation with angular speed and position feedback；
2) quadratic form optimization is converted the secondary rule of standard by the equivalence transformation for carrying out angular speed index and angular acceleration index
It draws；
3) the standard quadratic programming is solved with circadian rhythm neural network Solution To The Network device；
4) result of the solution is driven into manipulator motion.
2. the repetitive motion planning method for redundant manipulator according to claim 1 for inhibiting periodic noise, feature exist
In the quadratic form Optimization Plan of the step 1) are as follows: minimizeIt is constrained in
Angular acceleration Jacobi's equation with angular speed and position feedbackIts
Middle σ ∈ [0,1] is weight parameter,It is joint angular velocity vector, a (t) is a parameter vector,Represent joint torque vector, M (θ) ∈ Rn×nIt is an inertial matrix,It is centrifugal force and Coriolis force vector, g (θ) ∈ RnIt is gravitational vectors, J is the Jacobian matrix of mechanical arm,
θ andIt is joint angle vector sum joint angular velocity vector respectively,Indicate joint velocity vector, r (t) andIt respectively indicates
Robot arm end effector position vector and velocity vector,Indicate robot arm end effector acceleration, λa, λb∈
R is as feedback control coefficient.
3. the repetitive motion planning method for redundant manipulator according to claim 1 or 2 for inhibiting periodic noise, feature
Be, the step 2) specifically,
Carry out angular speed indexWith angular acceleration indexEquivalence transformation, quadratic form
Optimization is converted into a standard quadratic programming, designs its performance indicator to minimize xTQx/2+μTX, it is constrained in Jx=y,
In, T indicates transposition,Q:=(1- σ) I+ σ M (θ), wherein I ∈ Rn×nIt is unit matrix； θ
It (0) is joint initial angle, α and β are positive weights coefficients；
4. the repetitive motion planning method for redundant manipulator according to claim 3 for inhibiting periodic noise, feature exist
In, the step 3) specifically, standard quadratic programming is converted into the solution of a matrix equation WX=Y, whereinM is Descartes
The dimension in space, n are the dimension of joint space, and λ indicates Lagrange multiplier vector；
Then, matrix equation is solved with circadian rhythm Neural Networks Solution device.Designing it and calculating error is ∈ (t)=WX-Y, when
When error is zero, corresponding X value is just the solution of matrix equation.The kinetics equation of circadian rhythm neural network isWhereinIt is first derivative of the ∈ (t) to the time, γ > 0 designs to adjust
Convergence rate, F () indicate that activation primitive, φ (t) represent periodic noise.χ(t)∈Rn+mIt is an auxiliary vector, is defined as χ
(t)=χ (t-T)+ρ ∈ (t), wherein T is periodic noisePeriod, and ρ > 0 is a feedback factor；In conjunction with error ∈
(t) and the kinetics equation of circadian rhythm neural network, the kinetics equation of available circadian rhythm Neural Networks Solution device
Given initial value X0∈Rn+m, X is obtained by circadian rhythm Neural Networks Solution device, error ∈ (t) is made to converge to 0, passed through
Circadian rhythm Neural Networks Solution device constantly solves, and can obtain the solution of matrix equation WX=Y, to obtain acceleration layer repetition
The optimal solution of motion planning quadratic programming.
5. the repetitive motion planning method for redundant manipulator according to claim 4 for inhibiting periodic noise, feature exist
In the matrix equation, the result driving mechanical arm solved with circadian rhythm Neural Networks Solution device carries out repeating motion planning.
6. the repetitive motion planning method for redundant manipulator according to claim 4, which is characterized in that the activation primitive
For linear activation primitive, sinh activation primitive, bipolar sigmoid activation primitive or tunable activation primitive；The period
Noise is period random noise, constant noise, square wave noise or triangular noise.
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| CN116901063A (en) * | 2023-07-13 | 2023-10-20 | 长春通视光电技术股份有限公司 | Redundant space mechanical arm track planning method based on quadratic programming |
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