CN108015763A - A kind of redundancy mechanical arm paths planning method of anti-noise jamming - Google Patents

A kind of redundancy mechanical arm paths planning method of anti-noise jamming Download PDF

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CN108015763A
CN108015763A CN201711147249.5A CN201711147249A CN108015763A CN 108015763 A CN108015763 A CN 108015763A CN 201711147249 A CN201711147249 A CN 201711147249A CN 108015763 A CN108015763 A CN 108015763A
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mechanical arm
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redundancy mechanical
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CN108015763B (en
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张智军
孔令东
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South China University of Technology SCUT
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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
    • 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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  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses the redundancy mechanical arm paths planning method and system of a kind of anti-noise jamming, the described method includes：1) time-varying quadratic programming model is established according to active redundancy mechanical arm parameter index, and introduces the performance indicator of redundancy mechanical arm；2) lagrange's method of multipliers is used, optimal value optimization is carried out to time-varying quadratic programming model；3) a canonical matrix equation is designed according to optimization formula；4) according to actual physics model system and canonical matrix equation, the departure function equation of system is designed；5) ginseng recurrent neural dynamic method is become according to departure function equation and power type and designs a kind of redundancy mechanical arm paths planning method of anti-noise jamming, the network state solution obtained required by this method is optimal solution.Under the interference of extraneous noise circumstance, the actual motion path of redundancy mechanical arm can also overlap the present invention with expected path, substantially increase calculating speed, have the characteristics that precision is high, convergence is fast, real-time, robustness is good.

Description

A kind of redundancy mechanical arm paths planning method of anti-noise jamming
Technical field
The present invention relates to a kind of robotic arm path planing method, more particularly to a kind of redundancy mechanical arm of anti-noise jamming Paths planning method.
Background technology
So-called noise jamming, is exactly switching on and shutting down, the power generation of perimeter load equipment when mechanical equipment performs operation task The responsible interference of various change caused by the machinery for being carrying out operation task such as machine, radio communication.Noise jamming Failure often is caused to precision instruments or computer equipment, it is also possible to cause program and the execution mistake of archives etc..Therefore, exist It is very necessary influencing to take into account caused by noise item when the path planning of one complicated mechanical system of consideration and operation 's.
So-called redundancy, is exactly a unnecessary from safety considerations amount, this amount is exactly to ensure instrument, equipment Or a certain be operated under abnormal condition can also run well.At present redundancy is all applied in Most modern product and engineering design Spend this thought and theory.The quantity that redundancy mechanical arm refers to the mechanical arm free degree is more than the free degree necessary to completion task Quantity, since with more frees degree, redundancy mechanical arm, can also be same when completing the various tasks of end effector When complete the extra works such as Obstacle avoidance, joint angle limit restraint, mechanical arm be unusual.It is conventionally used to solve redundancy machine The method of tool arm Inverse Kinematics Problem is the method based on pseudoinverse, and this method is computationally intensive, real-time is poor, problem constraint is single, Applied in actual mechanical arm with greatly being restricted in operation.In recent years, based on quadratic programming problem be used for solve redundancy The scheme of degree manipulator motion planning is suggested, and has obtained certain development.Among these again be divided into Numerical Methods Solve device and Neural Networks Solution device.Compared to traditional Numerical Methods Solve device, the Neural Networks Solution device of nearest emerging appearance is due to it The features such as real-time performance is good, efficient, is increasingly subject to people to pursue.
And in the prior art, closest to solve quadratic programming problem method be discrete values method, but in face of During huge and complicated data, such a method is clearly that efficiency is insufficient and unstable.Then, it is a kind of to be declined based on gradient Neural network model be suggested, and for solving quadratic programming problem.However, such a nerve net declined based on gradient Network can not solve quadratic programming problem well, because actual conditions are often related to event, so inevitably result in experiment Some inestimable remainder errors are produced, and these errors can not converge to zero.It means that we are handling secondary rule , it is necessary to the convergence precision of faster convergence rate and higher during the problem of drawing.Under such a background, a neutral net is suggested And good development is obtained.It is a kind of conventional method for being used to solve robotic arm path planning to open neutral net, such a Neural network model can solve the quadratic programming problem under time dependant conditions.Pass through the time coefficient derived, a neutral net Can obtain quadratic programming problem most has neutralizing.However, becoming huge calculating data, the noise of complexity is especially considered During interference, we generally require more times and go result of calculation, this is unfavorable for practice operation.
Since the preset parameter recurrent neural network method such as traditional Gradient Neural Networks and a neutral net requires convergence Parameter (being inductance parameters value or the reciprocal value of capacitance parameter in actual circuit system) needs to be set big as far as possible, with To faster constringency performance.When Application of Neural Network is in actual system, such a requirement is unreal and is difficult to meet 's.In addition, in systems in practice, the inverse of inductance parameters value and capacitance parameter value is typically time-varying, particularly large-scale Power electronic system, AC Motor Control system, electric power networks system etc., system parameter settings are unreasonable for fixed value 's.
The content of the invention
It is an object of the invention to overcome the deficiencies of the prior art and provide a kind of redundancy mechanical arm road of anti-noise jamming Footpath planing method, this method under the interference of extraneous noise circumstance, can make the actual motion path of redundancy mechanical arm also can It is enough to be overlapped with expected path, calculating speed is substantially increased, there is the spies such as precision is high, convergence is fast, real-time, robustness is good Point.
Another object of the present invention is to provide a kind of redundancy mechanical arm path planning system of anti-noise jamming.
The purpose of the present invention can be reached by adopting the following technical scheme that：
A kind of redundancy mechanical arm paths planning method of anti-noise jamming, the described method includes：
1) time-varying quadratic programming model is established according to active redundancy mechanical arm parameter index, and introduces redundancy mechanical arm Performance indicator coefficient vector；
2) lagrange's method of multipliers is used, optimal value optimization is carried out to time-varying quadratic programming model；
3) a canonical matrix equation is designed according to optimization formula；
4) according to actual physics model system and canonical matrix equation, the departure function equation of system is designed；
5) ginseng recurrent neural dynamic method is become according to departure function equation and power type and designs a kind of the superfluous of anti-noise jamming Remaining robotic arm path planing method, the network state solution obtained required by this method is optimal solution.
Further, it is described that time-varying quadratic programming model is established according to active redundancy mechanical arm parameter index, and draw Enter the performance indicator coefficient vector of redundancy mechanical arm, specifically include：
By active redundancy mechanical arm parameter index formulation, modelling, following redundancy mechanical arm fortune can be obtained It is dynamic to learn equation expression formula：
F (θ (t))=r (t) (1)
Wherein θ (t) is the mechanical joint angle of redundancy mechanical arm；R (t) is the expectation end rail of redundancy mechanical arm Mark；F () is the nonlinear equation for representing redundancy mechanical arm joint angles；The derivation at the same time of equation both ends can obtain following superfluous Inverse kinematics equation expression formula on remaining mechanical arm velocity layer：
WhereinFor the Jacobian matrix of redundancy mechanical arm, n represents the quantity of the mechanical arm free degree, M represents the space dimensionality of mechanical arm tail end track；The respectively joint angles and end orbit of redundancy mechanical arm Derivative on the time；According to above-mentioned physical model, following time-varying quadratic programming model can be established：
Subject to J (θ (t)) x (t)=B (t) (4)
WhereinQ (t)=I (t) is unit matrix；J (θ (t)) is redundancy mechanical arm Jacobian matrix；P (t) is performance indicator coefficient vector；
The performance indicator coefficient vector P (t) of redundancy mechanical arm is introduced, its specific design formula is：WhereinRepresent joint offset response coefficient, θ (t), θ (0) represent redundancy mechanical arm respectively Joint states and initial joint states in motion process.
Further, the use lagrange's method of multipliers, carries out time-varying quadratic programming model optimal value optimization, tool Body includes：
It is right in order to obtain on time-varying quadratic programming problem on optimal solution and the partial derivative information of Lagrange's multiplier Time-varying quadratic programming problem (3) (4) can obtain following formula using lagrange's method of multipliers：
WhereinFor Lagrange's multiplier；From Lagrange's theorem, ifWithIn the presence of and it is continuous, then two formula of following formula is set up, i.e.,
Wherein time-varying parameter matrix and vector Q (t), P (t), J (t), B (t) are obtained by actual physics model system sensor Signal and system are expected operating state signal etc. and are formed；Time-varying parameter matrix and vector Q (t), P (t), J (t), B (t), and Their time-derivative It is It is known or can be estimated in the range of certain precise requirements；There are time-varying quadratic programming problem (3) (4) on Optimal solution and the partial derivative information on Lagrange's multiplier, and can be expressed as above- mentioned information using lagrange's method of multipliers Optimize formula (6) (7).
Further, it is described that a canonical matrix equation is designed according to optimization formula, specifically include：
One following mark on time-varying quadratic programming problem (3) (4) can be designed that according to optimization formula (6) (7) Quasi- matrix equality：
W (t) Y (t)=G (t) (8)
Wherein
Time-varying coefficient matrix and vector W (t), Y (t), G (t) are continuous and smooth in real number field.
Further, it is described according to actual physics model system and canonical matrix equation, design the deviation letter of system Number equation, specifically includes：
According to the matrix of the smooth time-varying quadratic programming problem of obtained actual physics model system or numerical solution system Equation (8), design can obtain the departure function equation of system；The optimal solution of time-varying quadratic programming problem (3) (4) in order to obtain, it is fixed The departure function equation of an adopted matrix form is as follows：
When departure function equation ε (t) converges to zero, the optimal solution x of time-varying quadratic programming problem (3) (4)*(t) can It is obtained.
Further, ginseng recurrent neural dynamic method is become according to departure function equation and power type and establishes Noise Power type becomes ginseng recurrent neural networks model, and the network state solution of model output is optimal solution, is specifically included：
Data in time-varying parameter matrix can be input in processing unit；Pass through obtained time-varying parameter matrix and its Derivative information, becomes ginseng recurrent neural dynamic method with reference to real number field power type and utilizes the strange activation primitive of monotonic increase, Ke Yijian The power type of a vertical Noise becomes ginseng recurrent neural networks model；Ginseng recurrent neural dynamic method, deviation letter are become according to power type The time-derivative of number equation ε (t) is needed for negative definite；Different from preset parameter recurrent neural dynamic method, power type becomes ginseng recurrence The design parameter that constringency performance is determined in neurodynamics method is time-varying, which is defined as follows：
Wherein γ ＞ 0 are the constant coefficient parameter artificially designed, and Φ () very activates array for monotonic increase.
Departure function equation and its derivative information are substituted into design formula (8), then real number field power type becomes ginseng recurrent neural net Network model can use following implicit kinetics equation to express
WhereinFor partial derivative information.
If there is noise jamming and hardware kinematic error, then it can obtain following Noise power type and become ginseng recurrent neural Network model：
Wherein Δ D (t) is the noise item of coefficient matrix；Δ K (t) is error term when hardware is run.
According to rightDefinition, it is known that
Y(t)：=[xT(t),λT(t)]T
=[x1(t),x2(t),…,xn(t),λ1(t),λ2(t),…,λm(t)]T (13)
Wherein Y (t) has initial value
According to implicit kinetics equation (12), the redundancy mechanical arm path planning of real number field anti-noise jamming can be obtained Method and real-time performance；The output result of network is the optimal solution of real number field time-varying quadratic programming problem (3) (4).
The network state solution that redundancy mechanical arm paths planning method based on anti-noise jamming solves is the reality The optimal solution of the time-varying quadratic programming problem (3) (4) of border physical system or numerical solution system；By the obtained solution of processor Device optimal solution exports, and completes the actual physics system with the smooth time-varying quadratic programming problem form of real number field or numerical solution system The optimal solution of system solves, and the obtained network state solution as required redundant manipulator motion planning by noise jamming is most Excellent solution.
Another object of the present invention, which can adopt the following technical scheme that, to be reached：
External environment input module, for the acquisition and analysis of the data inputted to external environment, above-mentioned data constitute The basis of time-varying parameter matrix content.
Input interface circuit module, for external setting-up data and as the interface channel between processor, according to sensing The different of device can be by the circuit and protocol realization of distinct interface.
Processor module, for the processing to outer input data, asks for becoming ginseng recurrent neural dynamics side based on power type The designed optimal solution for being used for the redundant manipulator motion paths planning method by noise jamming of method.
Output interface module, the data that the redundant manipulator motion paths planning method for anti-noise jamming is solved The interface of homologous ray optimal theoretical solution request end, the wherein interface can be the return value that circuit interface can also be program, root According to the different and different of design system.
Output environment module, is used for realization and is used for based on power type change ginseng recurrent neural dynamic method by noise jamming The purpose of redundant manipulator motion paths planning method.
Further, the external environment input module, specifically includes：
External sensor data gathers subelement, by the dynamic parameter of sensor collection system, such as displacement, speed, adds The physical quantitys such as speed, angular speed；
Target realizes the data analysis subelement of state, by analyzing each physical quantity that is known or collecting, The theory analysis of carry out system.
Further, the processor module, specifically includes：
Time-varying parameter matrix subelement, for completing matrixing or vector quantization to outer input data；
The redundancy mechanical arm paths planning method subelement of anti-noise jamming, the redundancy mechanical arm fortune of anti-noise jamming Dynamic paths planning method is the core of system, by the way that the data of system are modeled, formulate, analyze and are designed in advance Configuration, the system model obtained including mathematical modeling, so that design deviation functional equation, and passed using ginseng is become based on power type Neurodynamics method is returned to be designed for the redundant manipulator motion paths planning method by noise jamming.
Further, the output environment module, specifically includes：
Optimal solution asks terminal unit, for need to obtain the real number field light of actual physics system or numerical solution system The request end of sliding time-varying quadratic programming problem optimal solution, the port send instruction when needing to obtain solving parameter to solving system Request, and receive solving result；
Redundancy mechanical arm path planning terminal unit, the parameter for optimal solution request end to be exported are converted into dependency number According to, finally enter mechanical arm control program in mechanical arm carry out path planning with control.
The present invention has following beneficial effect for the prior art：
The present invention becomes ginseng recurrent neural kinetic model method based on power type, different from traditional preset parameter recurrent neural Dynamic method, it is of the present invention to be used for that to there is the overall situation by the trajectory path planning method of the redundancy mechanical arm of noise jamming Convergence property, and deviation can substantially increase calculating speed with hyperexponential speed convergence to zero, have precision is high, convergence is fast, Real-time, the features such as robustness is good.This method is described using the hidden kinetic model of generally existing, can be respectively from method , can quickly, accurately and real-time approximation problem be optimal with the derivative information that each time-varying parameter is made full use of in two aspects of system Solution；A series of relevant issues such as redundant manipulator motion planning can be solved well.
Brief description of the drawings
Fig. 1 is the flow chart of the redundant manipulator motion paths planning method of the anti-noise jamming of the embodiment of the present invention 1.
Fig. 2 realizes frame diagram for the redundant manipulator motion path planning system of the anti-noise jamming of the present invention.
Fig. 3 is trajectory diagram when the redundancy mechanical arm by noise jamming of the present invention performs trajectory path planning task.
Fig. 4 is the Actual path when redundancy mechanical arm by noise jamming of the invention performs trajectory path planning task With the curve map of expected path.
Fig. 5 is X-axis, Y-axis, Z when the redundancy mechanical arm by noise jamming of the present invention performs trajectory path planning task Error curve diagram on direction of principal axis.
Fig. 6 is the norm error when redundancy mechanical arm by noise jamming of the invention performs trajectory path planning task Curve map.
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 1：
As shown in Figure 1, present embodiments provide a kind of redundancy mechanical arm paths planning method of anti-noise jamming, the party Method includes the following steps：
S1, according to active redundancy mechanical arm parameter index establish time-varying quadratic programming model, and introduces redundancy machinery The performance indicator coefficient vector of arm；
S11, establish time-varying quadratic programming model：
By active redundancy mechanical arm parameter index formulation, modelling, following redundancy mechanical arm fortune can be obtained It is dynamic to learn equation expression formula：
F (θ (t))=r (t) (1)
Wherein θ (t) is the mechanical joint angle of redundancy mechanical arm；R (t) is the expectation end rail of redundancy mechanical arm Mark；F () is the nonlinear equation for representing redundancy mechanical arm joint angles；The derivation at the same time of equation both ends can obtain following superfluous Inverse kinematics equation expression formula on remaining mechanical arm velocity layer：
WhereinFor the Jacobian matrix of redundancy mechanical arm, n represents the quantity of the mechanical arm free degree, m Represent the space dimensionality of mechanical arm tail end track；Respectively the joint angles of redundancy mechanical arm and end orbit close In the derivative of time；According to above-mentioned physical model, following time-varying quadratic programming model can be established：
Subject to J (θ (t)) x (t)=B (t) (4)
WhereinQ (t)=I (t) is unit matrix；J (θ (t)) is redundancy mechanical arm Jacobian matrix；P (t) is performance indicator coefficient vector；
S12, the performance indicator coefficient vector P (t) for introducing redundancy mechanical arm, its specific design formula are：WhereinRepresent joint offset response coefficient, θ (t), θ (0) represent redundancy mechanical arm respectively Joint states and initial joint states in motion process.
S2, using lagrange's method of multipliers, optimal value optimization is carried out to time-varying quadratic programming model；
It is right in order to obtain on time-varying quadratic programming problem on optimal solution and the partial derivative information of Lagrange's multiplier Time-varying quadratic programming problem (3) (4) can obtain following formula using lagrange's method of multipliers：
WhereinFor Lagrange's multiplier；From Lagrange's theorem, ifWithIn the presence of and it is continuous, then two formula of following formula is set up, i.e.,
Wherein time-varying parameter matrix and vector Q (t), P (t), J (t), B (t) are obtained by actual physics model system sensor Signal and system are expected operating state signal etc. and are formed；Time-varying parameter matrix and vector Q (t), P (t), A (t), B (t), and Their time-derivative It is It is known or can be estimated in the range of certain precise requirements；There are time-varying quadratic programming problem (3) (4) on Optimal solution and the partial derivative information on Lagrange's multiplier, and can be expressed as above- mentioned information using lagrange's method of multipliers Optimize formula (6) (7).
S3, according to optimization formula design a canonical matrix equation；
One following mark on time-varying quadratic programming problem (3) (4) can be designed that according to optimization formula (6) (7) Quasi- matrix equality：
W (t) Y (t)=G (t) (8)
Wherein
Time-varying coefficient matrix and vector W (t), Y (t), G (t) are continuous and smooth in real number field.
S4, according to actual physics model system and canonical matrix equation, design the departure function equation of system；
According to the matrix of the smooth time-varying quadratic programming problem of obtained actual physics model system or numerical solution system Equation (8), design can obtain the departure function equation of system；The optimal solution of time-varying quadratic programming problem (3) (4) in order to obtain, it is fixed The departure function equation of an adopted matrix form is as follows：
When departure function equation ε (t) converges to zero, the optimal solution x of time-varying quadratic programming problem (3) (4)*(t) can It is obtained.
S5, become a kind of the superfluous of anti-noise jamming of ginseng recurrent neural dynamic method design according to departure function equation and power type Remaining robotic arm path planing method, the network state solution obtained required by this method is optimal solution；
Data in time-varying parameter matrix can be input in processing unit；Pass through obtained time-varying parameter matrix and its Derivative information, becomes ginseng recurrent neural dynamic method with reference to real number field power type and utilizes the strange activation primitive of monotonic increase, Ke Yijian The power type of a vertical Noise becomes ginseng recurrent neural networks model；Ginseng recurrent neural dynamic method, deviation letter are become according to power type The time-derivative of number equation ε (t) is needed for negative definite；Different from preset parameter recurrent neural dynamic method, power type becomes ginseng recurrence The design parameter that constringency performance is determined in neurodynamics method is time-varying, which is defined as follows：
Wherein γ ＞ 0 are the constant coefficient parameter artificially designed, and Φ () very activates array for monotonic increase.
Departure function equation and its derivative information are substituted into design formula (8), then real number field power type becomes ginseng recurrent neural net Network model can use following implicit kinetics equation to express
WhereinFor partial derivative information.
If there is noise jamming and hardware kinematic error, then it can obtain following Noise power type and become ginseng recurrent neural Network model：
Wherein Δ D (t) is the noise item of coefficient matrix；Δ K (t) is error term when hardware is run.
According to rightDefinition, it is known that
Y(t)：=[xT(t),λT(t)]T
=[x1(t),x2(t),…,xn(t),λ1(t),λ2(t),…,λm(t)]T (13)
Wherein Y (t) has initial value
According to implicit kinetics equation (12), the redundancy mechanical arm path planning of real number field anti-noise jamming can be obtained Method and real-time performance；The output result of network is the optimal solution of real number field time-varying quadratic programming problem (3) (4).
The network state solution that redundancy mechanical arm paths planning method based on anti-noise jamming solves is the reality The optimal solution of the time-varying quadratic programming problem (3) (4) of border physical system or numerical solution system；By the obtained solution of processor Device optimal solution exports, and completes the actual physics system with the smooth time-varying quadratic programming problem form of real number field or numerical solution system The optimal solution of system solves, and the obtained network state solution as required redundant manipulator motion planning by noise jamming is most Excellent solution.
Embodiment 2：
As shown in Fig. 2, present embodiments providing a kind of redundancy mechanical arm path planning system of anti-noise jamming, its is each The particular use of a module is as follows：
External environment input module, for the acquisition and analysis of the data inputted to external environment.
Input interface circuit module, for external setting-up data and as the interface channel between processor, according to sensing The different of device can be by the circuit and protocol realization of distinct interface.
Processor module, for the processing to outer input data, that is, asks for becoming ginseng recurrent neural dynamics based on power type The optimal solution of the redundant manipulator motion paths planning method of anti-noise jamming designed by method.
Output interface module, the data that the redundant manipulator motion paths planning method for anti-noise jamming is solved The interface of homologous ray optimal theoretical solution request end, the wherein interface can be the return value that circuit interface can also be program, root According to the different and different of design system.
Output environment module, is used for realization the redundancy for the anti-noise jamming for becoming ginseng recurrent neural dynamic method based on power type Spend manipulator motion paths planning method.
External environment input module, specifically includes：
External sensor data gathers subelement, by the dynamic parameter of sensor collection system, such as displacement, speed, adds The physical quantitys such as speed, angular speed；
Target realizes the data analysis subelement of state, by analyzing each physical quantity that is known or collecting, The theory analysis of carry out system.
Processor module, specifically includes：
Time-varying parameter matrix subelement, for completing matrixing or vector quantization to outer input data；
The redundancy mechanical arm paths planning method subelement of anti-noise jamming, the redundancy mechanical arm fortune of anti-noise jamming Dynamic paths planning method is the core of system, by the way that the data of system are modeled, formulate, analyze and are designed in advance Configuration, the system model obtained including mathematical modeling, so that design deviation functional equation, and passed using ginseng is become based on power type Neurodynamics method is returned to be designed for the redundant manipulator motion paths planning method by noise jamming.
Output environment module, specifically includes：
Optimal solution asks terminal unit, for need to obtain the real number field light of actual physics system or numerical solution system The request end of sliding time-varying quadratic programming problem optimal solution, the port send instruction when needing to obtain solving parameter to solving system Request, and receive solving result；
Redundancy mechanical arm path planning terminal unit, the parameter for optimal solution request end to be exported are converted into related poem Sentence, finally enters in mechanical arm control program and carries out path planning and control to mechanical arm.
Embodiment 3：
The MATLAB emulation experiments of the present embodiment are established in Kinova-JACO2On the basis of light-type biomimetic manipulator.Should Type mechanical arm gross weight 4.4kg, maximum of control distance 77cm.
The type redundancy mechanical arm includes 6 frees degree altogether, that is, θ (t) contains 6 elements；The sky of mechanical arm tail end Between dimension be 3, i.e., including three X-axis, Y-axis, Z axis directions；Its Jacobian matrix isRedundancy mechanical arm Starting joint angles be set to θ (0)=[1.675,2.843, -3.216,4.187, -1.710, -2.650]；Tasks carrying Cycle, t was set to 8s；Parameter γ is set to 80.In this example, proposed by the present invention it is used for redundancy machine to show The superiority of the neural solver of change ginseng of tool arm motion planning, the Kinova-JACO2The phase of the bionical redundancy mechanical arm of light-type Track is hoped to be set to a complicated butterfly-like shape, a diameter of 45cm of parameter of the butterfly-like shape track.According to as above set Kinova-JACO2Redundancy mechanical arm physical model, solves on velocity layer, can establish following time-varying quadratic programming Model：
Wherein, I (t) is unit matrix； AndRespectively：
According to step and method described previously, can design to obtain following matrix equality, i.e.,
W (t) Y (t)=G (t) (16)
Wherein
For obtain it is above-mentioned be used for solve redundant manipulator motion path time-varying quadratic programming model optimal solution, one The departure function equation of matrix form is defined as foloows
ε (t)=W (t) Y (t)-G (t) (17)
Ginseng recurrent neural dynamic method is become according to power type, a kind of time-varying parameter of power type is designed and makes in the present invention With its design formula is as follows
Wherein, parameter γ is set to 80.
By departure function equation and its derivative information, real number field power type change ginseng recurrent neural networks model can be used as follows Implicit kinetics equation expression
WhereinFor partial derivative information；ΔD(t) For the noise item of coefficient matrix；Δ K (t) is error term when hardware is run.In order to which more preferable simulation redundancy mechanical arm is actual The noise jamming being subject to during operation, in this example, noise item Δ D (t) and error term Δ K (t) by a series of complex sine, Cosine function is formed, its expression is as follows：
According to the definition to Y (t), it is known that
Y(t)：=[xT(t),λT(t)]T
=[x1(t),x2(t),…,xn(t),λ1(t),λ2(t),…,λm(t)]T (20)
Wherein Y (t) has initial value Y (0)=Y0。
According to above-mentioned shown implicit kinetics equation, the redundancy mechanical arm road of real number field anti-noise jamming can be obtained Footpath planing method and real-time performance；The output result of network is the optimal solution of real number field time-varying quadratic programming problem.Will processing The obtained solver optimal solution output of device, completes the actual physics system with the smooth time-varying quadratic programming problem form of real number field The optimal solution of system or numerical solution system solves.Obtained network state solution is that this simulation example is required by noise jamming The optimal solution of redundancy mechanical arm system motion planning.
The specific experiment result of the emulation embodiment such as Fig. 3 (a) (b), Fig. 4 (a) (b), Fig. 5 (a) (b) and Fig. 6 (a) (b) It is shown.In the case that wherein Fig. 3 (a) (b) is applies novel method of the present invention and conventional method respectively, done by noise The redundancy mechanical arm disturbed performs trajectory diagram during trajectory path planning task.Fig. 4 (a) (b) is applies institute of the present invention respectively In the case of the novel method and conventional method stated, when being performed trajectory path planning task by the redundancy mechanical arm of noise jamming Actual path and expected path curve map.Fig. 5 (a) (b) is to apply novel method of the present invention and tradition respectively In the case of method, X-axis, Y-axis when being performed trajectory path planning task by the redundancy mechanical arm of noise jamming, in Z-direction Error curve diagram.In the case that Fig. 6 (a) (b) is applies novel method of the present invention and conventional method respectively, made an uproar The redundancy mechanical arm of acoustic jamming performs norm error curve map during trajectory path planning task, the norm error | | e (t) | |2Be defined as redundancy mechanical arm in execution route planning tasks X-axis, Y-axis, on three directions of Z axis the sum of error 2- models Number.
From Fig. 3,4, in the redundant manipulator motion path planning side of application anti-noise jamming of the present invention When method carries out robotic arm path planning, actual motion path can coincide with expected path, i.e., Path error can be received rapidly Hold back to zero；And when application conventional method carries out robotic arm path planning, always exist between actual motion path and expected path Relatively large deviation, is difficult to meet precise requirements in actual redundancy mechanical arm operation.
As shown in Figure 5, in the redundant manipulator motion paths planning method of application anti-noise jamming of the present invention When carrying out robotic arm path planning, its X-axis, Y-axis, the error on three directions of Z axis can with speed convergence quickly to zero, The deviation between the actual motion path of mechanical arm and expected path can be eliminated well；And carried out in application conventional method When robotic arm path is planned, its actual motion path on three X-axis, Y-axis, Z axis directions and it is desirable to total between path There are relatively large deviation, is difficult to meet precise requirements in actual redundancy mechanical arm operation.
It will be appreciated from fig. 6 that in the redundant manipulator motion paths planning method of application anti-noise jamming of the present invention When carrying out robotic arm path planning, its norm error can be with speed convergence quickly to zero；And carried out in application conventional method When robotic arm path is planned, its norm error is constantly present, i.e., mechanical arm execution route planning tasks when always there are certain error, It is difficult to meet required precision.
The experimental result of above-mentioned emulation embodiment illustrates the redundancy of anti-noise jamming of the present invention well The superiority of manipulator motion paths planning method.
The above, is only patent preferred embodiment of the present invention, but the protection domain of patent of the present invention is not limited to This, any one skilled in the art is in the scope disclosed in patent of the present invention, the skill of patent according to the present invention Art scheme and its inventive concept are subject to equivalent substitution or change, belong to the protection domain of patent of the present invention.

Claims (10)

  1. A kind of 1. redundancy mechanical arm paths planning method of anti-noise jamming, it is characterised in that：The described method includes：
    1) time-varying quadratic programming model is established according to active redundancy mechanical arm parameter index, and in time-varying quadratic programming model Introduce the performance indicator of redundancy mechanical arm；
    2) lagrange's method of multipliers is used, optimal value optimization is carried out to time-varying quadratic programming model, obtains optimization formula；
    3) a canonical matrix equation is designed according to optimization formula；
    4) according to actual physics model system and canonical matrix equation, the departure function equation of system is designed；
    5) the power type change ginseng that a Noise is established according to departure function equation and power type change ginseng recurrent neural dynamic method is passed Return neural network model, the network state solution of model output is optimal solution.
  2. A kind of 2. redundancy mechanical arm paths planning method of anti-noise jamming according to claim 1, it is characterised in that： Described establishes time-varying quadratic programming model according to active redundancy mechanical arm parameter index, and introduces the fortune of redundancy mechanical arm Dynamic planning index, specifically includes：
    By active redundancy mechanical arm parameter index formulation, modelling, following redundancy mechanical arm inverse kinematics equation is obtained Expression formula：
    F (θ (t))=r (t) (1)
    Wherein θ (t) is the mechanical joint angle of redundancy mechanical arm；R (t) is the expectation end orbit of redundancy mechanical arm；f () is the nonlinear equation for representing redundancy mechanical arm joint angles；Following redundancy machine is obtained to the derivation at the same time of equation both ends Inverse kinematics equation expression formula on tool arm velocity layer：
    <mrow> <mi>J</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mover> <mrow> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mover> <mi>r</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    WhereinFor the Jacobian matrix of redundancy mechanical arm, n represents the quantity of the mechanical arm free degree, and m is represented The space dimensionality of mechanical arm tail end track；Respectively the joint angles of redundancy mechanical arm and end orbit on when Between derivative；According to above-mentioned physical model, following time-varying quadratic programming model can be established：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>min</mi> <mi>i</mi> <mi>m</mi> <mi>i</mi> <mi>z</mi> <mi>e</mi> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mi>x</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>P</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    Subject to J (θ (t)) x (t)=B (t) (4)
    WhereinQ (t)=I (t) is unit matrix；J (θ (t)) is the Ya Ke of redundancy mechanical arm Compare matrix；P (t) is performance indicator coefficient vector；
    The performance indicator coefficient vector P (t) of redundancy mechanical arm is introduced, its specific design formula is：WhereinExpression joint offset response coefficient, θ (t), θ (0) represents redundancy machinery respectively Joint states and initial joint states in arm motion process.
  3. A kind of 3. redundancy mechanical arm paths planning method of anti-noise jamming according to claim 2, it is characterised in that： It is described to use Lagrangian Arithmetic, optimal value optimization is carried out to time-varying quadratic programming model, is specifically included：
    Time-varying quadratic programming model：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>min</mi> <mi>i</mi> <mi>m</mi> <mi>i</mi> <mi>z</mi> <mi>e</mi> </mrow> </mtd> <mtd> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mi>x</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>P</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    Subject to J (θ (t)) x (t)=B (t) (4)
    In order to obtain on time-varying quadratic programming problem on optimal solution and the partial derivative information of Lagrange's multiplier, to time-varying Quadratic programming problem (3) (4) can obtain following formula using lagrange's method of multipliers：
    WhereinFor Lagrange's multiplier；From Lagrange's theorem, ifWithIn the presence of and it is continuous, then two formula of following formula is set up, i.e.,
    Wherein time-varying parameter matrix and vector Q (t), P (t), J (t), B (t) obtain signal by actual physics model system sensor And system is expected operating state signal and is formed；Time-varying parameter matrix and vector Q (t), P (t), J (t), B (t), and they Time-derivative It is known Or it can be estimated in the range of certain precise requirements；There are time-varying quadratic programming problem (3) (4) on optimal solution And the partial derivative information on Lagrange's multiplier, and can use lagrange's method of multipliers that above- mentioned information is expressed as optimization public affairs Formula (6) (7).
  4. A kind of 4. redundancy mechanical arm paths planning method of anti-noise jamming according to claim 3, it is characterised in that： It is described that a canonical matrix equation is designed according to optimization formula, specifically include：
    Optimize formula：
    One following standard square on time-varying quadratic programming problem (3) (4) can be designed that according to optimization formula (6) (7) Battle array equation：
    W (t) Y (t)=G (t) (8)
    Wherein
    Time-varying coefficient matrix and vector W (t), Y (t), G (t) are continuous and smooth in real number field.
  5. A kind of 5. redundancy mechanical arm paths planning method of anti-noise jamming according to claim 4, it is characterised in that： It is described according to actual physics model system and canonical matrix equation, design the departure function equation of system, it is specifically included：
    Canonical matrix equation：
    W (t) Y (t)=G (t) (8)
    According to the canonical matrix of the smooth time-varying quadratic programming problem of obtained actual physics model system or numerical solution system Equation (8), design can obtain the departure function equation of system；The optimal solution of time-varying quadratic programming problem (3) (4) in order to obtain, it is fixed The departure function equation of an adopted matrix form is as follows：
    When departure function equation ε (t) converges to zero, the optimal solution x of time-varying quadratic programming problem (3) (4)*(t) can be obtained .
  6. A kind of 6. redundancy mechanical arm paths planning method of anti-noise jamming according to claim 5, it is characterised in that： Become according to departure function equation and power type and join the power type change ginseng recurrent neural that recurrent neural dynamic method establishes a Noise Network model, the network state solution of model output is optimal solution, is specifically included：
    Data in time-varying parameter matrix can be input in processing unit；Pass through obtained time-varying parameter matrix and its derivative Information, becomes ginseng recurrent neural dynamic method with reference to real number field power type and utilizes the strange activation primitive of monotonic increase, can establish one The power type of a Noise becomes ginseng recurrent neural networks model；Ginseng recurrent neural dynamic method, departure function side are become according to power type The time-derivative of journey ε (t) is needed for negative definite；Different from preset parameter recurrent neural dynamic method, power type becomes ginseng recurrent neural The design parameter that constringency performance is determined in dynamic method is time-varying, which is defined as follows：
    <mrow> <mover> <mi>&amp;epsiv;</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>d</mi> <mi>&amp;epsiv;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <mi>&amp;gamma;</mi> <mo>+</mo> <msup> <mi>t</mi> <mi>&amp;gamma;</mi> </msup> <mo>)</mo> </mrow> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <mi>&amp;epsiv;</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    Wherein γ ＞ 0 are the constant coefficient parameter artificially designed, and Φ () very activates array for monotonic increase；
    Departure function equation and its derivative information are substituted into formula (8),
    If there is noise jamming and hardware kinematic error, then it can obtain following Noise power type and become ginseng recurrent neural network Model：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mover> <mi>Y</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <mover> <mi>W</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <mi>&amp;Delta;</mi> <mi>D</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>Y</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mrow> <mo>(</mo> <mi>&amp;gamma;</mi> <mo>+</mo> <msup> <mi>t</mi> <mi>&amp;gamma;</mi> </msup> <mo>)</mo> </mrow> <mi>&amp;Phi;</mi> <mrow> <mo>(</mo> <mi>W</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mi>Y</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>-</mo> <mi>G</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mover> <mi>G</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>&amp;Delta;</mi> <mi>K</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    Wherein Δ D (t) is the noise item of coefficient matrix；Δ K (t) is error term when hardware is run；WhereinFor partial derivative information；
    According to rightDefinition, it is known that
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>Y</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>:</mo> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msup> <mi>x</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <msup> <mi>&amp;lambda;</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>&amp;lambda;</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>&amp;lambda;</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>&amp;lambda;</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
    Wherein Y (t) has initial value
    According to implicit kinetics equation (11), the redundancy mechanical arm paths planning method of real number field anti-noise jamming can be obtained And real-time performance；The output result of network is the optimal solution of real number field time-varying quadratic programming problem (3) (4).
  7. 7. a kind of redundancy mechanical arm paths planning method for being used for realization any one of the claim 1-6 anti-noise jammings System, it is characterised in that：The system comprises：
    External environment input module, for obtaining and analyzing the acquisition and analysis of the data to external environment input, above-mentioned data Constitute the basis of time-varying parameter matrix content；
    Input interface circuit module, for external setting-up data and as the interface channel between processor, according to sensor Difference can be by the circuit and protocol realization of distinct interface；
    Processor module, for the processing to outer input data, and asks for becoming ginseng recurrent neural dynamics side based on power type The optimal solution of the redundant manipulator motion paths planning method for anti-noise jamming designed by method；
    Output interface module, the data homology that the redundant manipulator motion paths planning method for anti-noise jamming is solved The interface of optimal theoretical solution of uniting request end, which can be the return value that circuit interface can also be program, according to design department System it is different and different；
    Output environment module, for sending solution request to processor module, and after optimal solution result is obtained, parameter is converted For related data, for carrying out path planning and control to mechanical arm.
  8. 8. system according to claim 7, it is characterised in that the external environment input module, including：
    External sensor data gathers subelement, for the dynamic parameter by sensor collection system；
    Target realizes the data analysis subelement of state, for by analyzing each physical quantity that is known or collecting, The theory analysis of carry out system.
  9. 9. system according to claim 7, it is characterised in that the processor module includes：
    Time-varying parameter matrix subelement, for completing matrixing or vector quantization to outer input data；
    The redundancy mechanical arm paths planning method subelement of anti-noise jamming, by being modeled in advance to the data of system, Formulation, analysis and design configuration, the system model obtained including mathematical modeling, so that design deviation functional equation, and It is designed for being advised by the redundant manipulator motion path of noise jamming using ginseng recurrent neural dynamic method is become based on power type The method of drawing.
  10. 10. system according to claim 7, it is characterised in that the output environment module, including：
    Optimal solution asks terminal unit, to need to obtain the smooth time-varying two of real number field of actual physics system or numerical solution system The request end of secondary planning problem optimal solution, the port send finger when needing to obtain solving parameter to processor module solving system Order request, and receive solving result；
    Redundancy mechanical arm path planning terminal unit, for the parameter of optimal solution request terminal unit output to be converted into correlation Data, finally enter in mechanical arm control program and carry out path planning and control to mechanical arm.
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