CN108015763B - Anti-noise-interference redundant manipulator path planning method - Google Patents
Anti-noise-interference redundant manipulator path planning method Download PDFInfo
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Abstract
The invention discloses a redundant manipulator path planning method and a redundant manipulator path planning system capable of resisting noise interference, wherein the method comprises the following steps: 1) establishing a time-varying quadratic programming model according to the parameter index of the actual redundant manipulator, and introducing the performance index of the redundant manipulator; 2) optimizing the optimal value of the time-varying quadratic programming model by using a Lagrange multiplier method; 3) designing a standard matrix equation according to an optimization formula; 4) designing a deviation function equation of the system according to the actual physical model system and a standard matrix equation; 5) an anti-noise interference redundant manipulator path planning method is designed according to a deviation function equation and a power-type variable parameter recurrent neural dynamics method, and a network state solution obtained by the method is an optimal solution. Under the interference of an external noise environment, the actual motion path of the redundant manipulator can be superposed with the expected path, so that the calculation speed is greatly improved, and the method has the characteristics of high precision, high convergence, strong instantaneity, good robustness and the like.
Description
Technical Field
The invention relates to a mechanical arm path planning method, in particular to an anti-noise-interference redundant mechanical arm path planning method.
Background
Noise interference is interference that is caused by various changes to a machine that is performing an operation task, such as turning on and off, a generator, and radio communication of peripheral load devices, when the machine performs the operation task. The noise interference often causes failure of precision instruments or computer equipment, and may cause errors in the execution of programs and files. Therefore, it is necessary to take the influence of the noise term into account when considering the path planning and operation of a complex mechanical system.
Redundancy is an excess from a safety point of view, which is to ensure that an instrument, equipment or a work can operate normally even in abnormal situations. At present, most modern products and engineering designs apply the idea and theory of redundancy. The redundant manipulator means that the number of degrees of freedom of the manipulator is more than the number of degrees of freedom necessary for completing tasks, and the redundant manipulator can complete additional work such as obstacle avoidance, joint angle limit constraint, manipulator singularity and the like simultaneously when completing various tasks of the end effector due to more degrees of freedom. The traditional method for solving the inverse kinematics problem of the redundant manipulator is a pseudo-inverse-based method, and the method has the advantages of large calculated amount, poor real-time performance and single problem constraint, and is greatly restricted in practical manipulator application and operation. In recent years, solutions for redundant manipulator motion planning based on quadratic planning problems have been proposed and developed. These are divided into numerical method solvers and neural network solvers. Compared with the traditional numerical method solver, the newly emerging neural network solver is more and more pursued by people due to the characteristics of good real-time performance, high efficiency and the like.
While in the prior art the closest approach to solving the quadratic programming problem is the discrete numerical method, such a method is clearly inefficient and unstable in the face of large and complex data. Thus, a gradient descent based neural network model is proposed and used to solve the quadratic programming problem. However, such a gradient descent-based neural network does not solve the quadratic programming problem well, because the actual situation is often related to the event, which inevitably results in some residual errors that cannot be estimated by the experiment, and these errors cannot converge to zero. This means that we need faster convergence speed and higher convergence accuracy when dealing with the quadratic programming problem. In such a context, the tensor neural network is proposed and well developed. The neural network is a traditional method for solving the path planning of the mechanical arm, and the neural network model can solve the quadratic planning problem under the time-varying condition. Through the derived time coefficient, the neural network can obtain the most effective solution of the quadratic programming problem. However, when the calculation data becomes huge, especially when complex noise interference is to be considered, we often need more time to calculate the result, which is disadvantageous for practical operation.
Because the traditional fixed parameter recurrent neural network methods such as the gradient neural network and the tensor neural network require that the convergence parameter (the inverse value of the inductance parameter or the capacitance parameter in the actual circuit system) needs to be set as large as possible, faster convergence performance is obtained. Such a requirement is unrealistic and difficult to satisfy when the neural network is applied in a practical system. In addition, in practical systems, the reciprocal of the inductance parameter value and the reciprocal of the capacitance parameter value are usually time-varying, and in particular, in large-scale power electronic systems, ac motor control systems, power network systems, and the like, it is not reasonable to set the system parameters to fixed values.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides the anti-noise-interference redundant manipulator path planning method, which can enable the actual motion path of the redundant manipulator to be coincident with the expected path under the interference of the external noise environment, greatly improves the calculation speed, and has the characteristics of high precision, high convergence speed, strong real-time performance, good robustness and the like.
It is another object of the present invention to provide a redundant manipulator path planning system that is immune to noise interference.
The purpose of the invention can be achieved by adopting the following technical scheme:
a method of noise interference resistant redundant robotic arm path planning, the method comprising:
1) establishing a time-varying quadratic programming model according to the actual parameter index of the redundant manipulator, and introducing a performance index coefficient vector of the motion planning of the redundant manipulator;
2) optimizing the optimal value of the time-varying quadratic programming model by using a Lagrange multiplier method;
3) designing a standard matrix equation according to an optimization formula;
4) designing a deviation function equation of the system according to the actual physical model system and a standard matrix equation;
5) an anti-noise interference redundant manipulator path planning method is designed according to a deviation function equation and a power-type variable parameter recurrent neural dynamics method, and a network state solution obtained by the method is an optimal solution.
Further, the establishing of the time-varying quadratic programming model according to the actual parameter index of the redundant manipulator and the introduction of the performance index coefficient vector of the motion planning of the redundant manipulator specifically include:
the following equation expressions of the kinematics of the redundant manipulator can be obtained by formulating and modeling the parameter indexes of the actual redundant manipulator:
f(θ(t))＝r(t) (1)
wherein theta (t) is the mechanical joint angle of the redundant manipulator; r (t) is the desired end trajectory of the redundant manipulator; f (-) is a nonlinear equation representing the angle of the joint of the redundant manipulator; the following inverse kinematics equation expressions on the velocity layer of the redundant manipulator can be obtained by simultaneously deriving the two ends of the equation:
wherein
The matrix is a Jacobian matrix of the redundant manipulator, n represents the number of the degrees of freedom of the manipulator, and m represents the space dimension of the tail end track of the manipulator;
the derivatives of the joint angle and the tail end track of the redundant manipulator with respect to time are respectively; according to the physical model, the following time-varying quadratic programming model can be established:
subject to J(θ(t))x(t)＝B(t) (4)
wherein
Q (t) ═ i (t) is an identity matrix; j (theta (t)) is a Jacobian matrix of the redundant manipulator; p (t) is a performance index coefficient vector;
introducing a performance index coefficient vector P (t) of the redundant manipulator, wherein the specific design formula is as follows:
wherein
Indicating joint deviationThe motion response coefficients theta (t) and theta (0) respectively represent the joint state and the initial joint state in the motion process of the redundant manipulator.
Further, the optimizing the time-varying quadratic programming model by using the lagrangian multiplier method specifically includes:
to obtain partial derivative information about the optimal solution and the lagrangian multiplier for the time-varying quadratic programming problem, using the lagrangian multiplier method for the time-varying quadratic programming problem (3) (4) can obtain the following:
wherein
Is the Lagrangian multiplier; according to Lagrange's theorem, if
And
exist and are continuous, then the following two equations hold, namely
Wherein, the time-varying parameter matrix and the vector Q (t), P (t), J (theta (t)), B (t) are composed of the signals obtained by the system sensor of the actual physical model, the signals of the expected running state of the system, and the like; time-varying parameter matrices and vectors Q (t), P (t), J (θ (t)), B (t), and their time derivatives
Are known or can be estimated within certain accuracy requirements; there is a time-varying quadratic programming problem (3) (4) about the optimal solution and about the partial derivative information of the lagrangian multiplier, and the lagrangian multiplier method can be used to represent the above information as optimization equations (6) (7).
Further, the designing a standard matrix equation according to the optimization formula specifically includes:
according to the optimization formulas (6) and (7), the following standard matrix equation about the time-varying quadratic programming problems (3) and (4) can be designed:
W(t)Y(t)＝G(t) (8)
wherein
The time-varying coefficient matrix and vectors W (t), Y (t), G (t) are continuous and smooth in the real domain.
Further, the designing a deviation function equation of the system according to the actual physical model system and the standard matrix equation specifically includes:
designing a deviation function equation of the obtained system according to a matrix equation (8) of the smooth time-varying quadratic programming problem of the obtained actual physical model system or numerical solution system; to obtain the optimal solution of the time-varying quadratic programming problem (3) (4), a deviation function equation in the form of a matrix is defined as follows:
optimal solution x of time-varying quadratic programming problem (3) (4) when deviation function equation (t) converges to zero*(t) can be obtained.
Further, the method for planning the path of the redundant manipulator resisting the noise interference is designed according to a deviation function equation and a power-type variable parameter recurrent neural dynamics method, and a network state solution obtained by the method is an optimal solution, and specifically comprises the following steps:
the data in the time-varying parameter matrix can be input into a processing unit (a computer, a singlechip, a microprocessor and the like); by combining the obtained time-varying parameter matrix and derivative information thereof with a real number domain power-varying parameter-varying recurrent neural dynamics method and by utilizing a monotone increasing odd activation function, a redundant manipulator path planning method for resisting noise interference can be designed; according to the power parameter varying recursive neurodynamic method, the time derivative of the deviation function equation (t) needs to be negative; different from a fixed parameter recursive neurodynamics method, the design parameters determining the convergence performance of the novel neurodynamics method are time-varying; a power-type time-varying parameter is designed and used in the invention, and the design formula is as follows:
wherein gamma > 0 is a constant coefficient parameter of artificial design, and phi (-) is a monotonically increasing odd activation array.
Substituting the deviation function equation and the derivative information thereof into the design formula (8), the real number domain power type variable parameter recurrent neural network model can be expressed by the following implicit kinetic equation
Wherein
Is the partial derivative information.
If noise interference and hardware operation errors exist, the following noise-containing power variant recurrent neural network model can be obtained:
where Δ d (t) is the noise term of the coefficient matrix; Δ k (t) is the error term when the hardware is running.
According to pairs
Definition of (1), to know
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 an initial value
According to an implicit kinetic equation (12), a real-number-domain anti-noise-interference redundant manipulator path planning method and network implementation can be obtained; and the output result of the network is the optimal solution of the real number domain time-varying quadratic programming problems (3) and (4).
The network state solution obtained by solving the redundancy mechanical arm path planning method based on the anti-noise interference is the optimal solution of the time-varying quadratic programming problems (3) and (4) of the actual physical system or the numerical solving system; and outputting the optimal solution of the solver obtained by the processor, and completing the optimal solution of an actual physical system or a numerical solving system in the form of a real number domain smooth time-varying quadratic programming problem, wherein the obtained network state solution is the optimal solution of the redundancy mechanical arm motion planning interfered by the noise.
The other purpose of the invention can be achieved by adopting the following technical scheme:
and the external environment input module is used for acquiring and analyzing data input by the external environment, and forms the basis of the time-varying parameter matrix content.
The input interface circuit module is used for externally setting data and interface channels among the processors, and can be realized by circuits and protocols of different interfaces according to different sensors.
The processor module is used for processing external input data and solving the optimal solution of the redundant manipulator motion path planning method which is designed based on the power-type variable parameter recurrent neural dynamics method and is used for being interfered by noise.
And the output interface module is used as an interface of the optimal solution data of the redundant manipulator motion path planning method and the output environment module, wherein the interface can be a circuit interface or a return value of a program and is different according to different design systems.
And the output environment module is used for realizing the purpose of the redundant manipulator motion path planning method which is based on the power type variable parameter recurrent neural dynamics method and is used for being interfered by noise.
Further, the external environment input module specifically includes:
the external sensor data acquisition subunit collects dynamic parameters of the system, such as physical quantities of displacement, speed, acceleration, angular velocity and the like through the sensor;
and the data analysis subunit of the expected target realization state performs theoretical analysis of the system by analyzing known or acquired physical quantities.
Further, the processor module specifically includes:
the time-varying parameter matrix subunit is used for completing matrixing or vectorization of external input data;
the redundant manipulator motion path planning method for resisting the noise interference is a core part of a system, a system model obtained by mathematical modeling is used for modeling, formulating, analyzing and designing the configuration in advance through data of the system, so that a deviation function equation is designed, and the redundant manipulator motion path planning method for resisting the noise interference is designed by utilizing a power-type variable parameter recursive neural dynamics method.
Further, the output environment module specifically includes:
the optimal solution request terminal unit is used for a request end which needs to obtain the optimal solution of the real number domain smooth time-varying quadratic programming problem of the actual physical system or the numerical solving system, and the port sends an instruction request to the solving system when solving parameters need to be obtained and receives a solving result;
and the redundant manipulator path planning terminal unit is used for converting the parameters output by the optimal solution request end into related poems and finally inputting the poems into a manipulator control program to plan and control the path of the manipulator.
The invention has the following beneficial effects for the prior art:
the method for planning the motion path of the redundant manipulator interfered by noise has the characteristics of global convergence, the deviation can be converged to zero at a speed exceeding an exponential, the calculation speed is greatly improved, and the method has the characteristics of high precision, high convergence speed, strong real-time property, good robustness and the like. The method adopts a ubiquitous hidden dynamics model for description, can respectively fully utilize derivative information of each time-varying parameter from two aspects of the method and the system, and can quickly, accurately and real-timely approach the optimal solution of the problem; the system and the method can well solve a series of related problems such as redundant manipulator motion planning and the like.
Drawings
Fig. 1 is a flowchart of a redundant manipulator motion path planning method with noise interference resistance according to embodiment 1 of the present invention.
FIG. 2 is a block diagram of an implementation of the noise interference immune redundant robotic arm motion path planning system of the present invention.
Fig. 3(a) is a trajectory diagram of a redundant manipulator interfered by noise and adopting the planning method of the present invention when executing a motion path planning task.
Fig. 3(b) is a trajectory diagram of a redundant manipulator interfered by noise and adopting a conventional planning method when executing a motion path planning task.
Fig. 4(a) is a graph of an actual path and a desired path when a noise-disturbed redundant manipulator using the planning method of the present invention performs a motion path planning task.
Fig. 4(b) is a graph of an actual path and a desired path when a noise-disturbed redundant manipulator using a conventional planning method performs a motion path planning task.
Fig. 5(a) is a graph showing error curves in the directions of the X axis, the Y axis, and the Z axis when the noise-disturbed redundant manipulator using the planning method of the present invention performs a motion path planning task.
Fig. 5(b) is a graph showing error curves in the directions of the X axis, the Y axis, and the Z axis when the redundant manipulator interfered by noise performs a motion path planning task by using a conventional planning method.
Fig. 6(a) is a graph of norm errors when a noise-disturbed redundant manipulator using the planning method of the present invention performs a motion path planning task.
Fig. 6(b) is a graph of norm errors when a noise-disturbed redundant manipulator using a conventional planning method performs a motion path planning task.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Example 1:
as shown in fig. 1, the present embodiment provides a redundant manipulator path planning method resistant to noise interference, which includes the following steps:
s1, establishing a time-varying quadratic programming model according to the actual parameter indexes of the redundant manipulator, and introducing a performance index coefficient vector of the redundant manipulator;
s11, establishing a time-varying quadratic programming model:
the following equation expressions of the kinematics of the redundant manipulator can be obtained by formulating and modeling the parameter indexes of the actual redundant manipulator:
f(θ(t))＝r(t) (1)
wherein theta (t) is the mechanical joint angle of the redundant manipulator; r (t) is the desired end trajectory of the redundant manipulator; f (-) is a nonlinear equation representing the angle of the joint of the redundant manipulator; the following inverse kinematics equation expressions on the velocity layer of the redundant manipulator can be obtained by simultaneously deriving the two ends of the equation:
wherein
The matrix is a Jacobian matrix of the redundant manipulator, n represents the number of the degrees of freedom of the manipulator, and m represents the space dimension of the tail end track of the manipulator;
the derivatives of the joint angle and the tail end track of the redundant manipulator with respect to time are respectively; according to the physical model, the following time-varying quadratic programming model can be established:
subject to J(θ(t))x(t)＝B(t) (4)
wherein
Q (t) ═ i (t) is an identity matrix; j (theta (t)) is a Jacobian matrix of the redundant manipulator; p (t) is a performance index coefficient vector;
s12, introducing a performance index coefficient vector P (t) of the redundant manipulator, wherein the specific design formula is as follows:
wherein
And the joint deviation response coefficient is represented, and theta (t) and theta (0) respectively represent the joint state and the initial joint state in the motion process of the redundant manipulator.
S2, optimizing the optimal value of the time-varying quadratic programming model by using a Lagrange multiplier method;
to obtain partial derivative information about the optimal solution and the lagrangian multiplier for the time-varying quadratic programming problem, using the lagrangian multiplier method for the time-varying quadratic programming problem (3) (4) can obtain the following:
wherein
Is the Lagrangian multiplier; according to Lagrange's theorem, if
And
exist and are continuous, then the following two equations hold, namely
Wherein, the time-varying parameter matrix and the vector Q (t), P (t), J (theta (t)), B (t) are composed of the signals obtained by the system sensor of the actual physical model, the signals of the expected running state of the system, and the like; time-varying parameter matrices and vectors Q (t), P (t), A (t), B (t), and their time derivatives
Are known or can be estimated within certain accuracy requirements; in existence becomes twiceThe planning problem (3) (4) is about the optimal solution and about the partial derivative information of the lagrangian multiplier, and the lagrangian multiplier method can be used to represent the above information as optimization equations (6) (7).
S3, designing a standard matrix equation according to the optimization formula;
according to the optimization formulas (6) and (7), the following standard matrix equation about the time-varying quadratic programming problems (3) and (4) can be designed:
W(t)Y(t)＝G(t) (8)
wherein
The time-varying coefficient matrix and vectors W (t), Y (t), G (t) are continuous and smooth in the real domain.
S4, designing a deviation function equation of the system according to the actual physical model system and the standard matrix equation;
designing a deviation function equation of the obtained system according to a matrix equation (8) of the smooth time-varying quadratic programming problem of the obtained actual physical model system or numerical solution system; to obtain the optimal solution of the time-varying quadratic programming problem (3) (4), a deviation function equation in the form of a matrix is defined as follows:
when the deviation function equation (t) converges to zero, an optimal solution x (t) for the time-varying quadratic programming problem (3) (4) can be obtained.
S5, designing an anti-noise-interference redundant manipulator path planning method according to a deviation function equation and a power-type variable parameter recurrent neural dynamics method, wherein the network state solution obtained by the method is an optimal solution;
the data in the time-varying parameter matrix can be input into a processing unit (a computer, a singlechip, a microprocessor and the like); by combining the obtained time-varying parameter matrix and derivative information thereof with a real number domain power-varying parameter-varying recurrent neural dynamics method and by utilizing a monotone increasing odd activation function, a redundant manipulator path planning method for resisting noise interference can be designed; according to the power parameter varying recursive neurodynamic method, the time derivative of the deviation function equation (t) needs to be negative; different from a fixed parameter recursive neurodynamics method, the design parameters determining the convergence performance of the novel neurodynamics method are time-varying; a power-type time-varying parameter is designed and used in the invention, and the design formula is as follows:
wherein gamma > 0 is a constant coefficient parameter of artificial design, and phi (-) is a monotonically increasing odd activation array.
Substituting the deviation function equation and the derivative information thereof into the design formula (8), the real number domain power type variable parameter recurrent neural network model can be expressed by the following implicit kinetic equation
Wherein
Is the partial derivative information.
If noise interference and hardware operation errors exist, the following noise-containing power variant recurrent neural network model can be obtained:
where Δ d (t) is the noise term of the coefficient matrix; Δ k (t) is the error term when the hardware is running.
According to pairs
Definition of (1), to know
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 an initial value
According to an implicit kinetic equation (12), a real-number-domain anti-noise-interference redundant manipulator path planning method and network implementation can be obtained; and the output result of the network is the optimal solution of the real number domain time-varying quadratic programming problems (3) and (4).
The network state solution obtained by solving the redundancy mechanical arm path planning method based on the anti-noise interference is the optimal solution of the time-varying quadratic programming problems (3) and (4) of the actual physical system or the numerical solving system; and outputting the optimal solution of the solver obtained by the processor, and completing the optimal solution of an actual physical system or a numerical solving system in the form of a real number domain smooth time-varying quadratic programming problem, wherein the obtained network state solution is the optimal solution of the redundancy mechanical arm motion planning interfered by the noise.
Example 2:
as shown in fig. 2, the present embodiment provides a redundant manipulator path planning system with noise interference resistance, and the specific applications of the various modules are as follows: and the external environment input module is used for acquiring and analyzing the data input by the external environment.
The input interface circuit module is used as an interface channel between external setting data and a processor and can be realized by circuits and protocols of different interfaces according to different sensors.
The processor module is used for processing external input data, namely solving the optimal solution of the anti-noise-interference redundant manipulator motion path planning method designed on the basis of the power-type variable parameter recurrent neural dynamics method.
And the output interface module is used as an interface of the optimal solution data of the redundant manipulator motion path planning method for resisting the noise interference and the output environment module, wherein the interface can be a circuit interface or a return value of a program and is different according to different design systems.
And the output environment module is used for realizing the anti-noise interference redundant manipulator motion path planning method based on the power type variable parameter recurrent neural dynamics method.
The external environment input module specifically comprises:
the external sensor data acquisition subunit collects dynamic parameters of the system, such as physical quantities of displacement, speed, acceleration, angular velocity and the like through the sensor;
and the data analysis subunit of the expected target realization state performs theoretical analysis of the system by analyzing known or acquired physical quantities.
The processor module specifically includes:
the time-varying parameter matrix subunit is used for completing matrixing or vectorization of external input data;
the redundant manipulator motion path planning method for resisting the noise interference is a core part of a system, a system model obtained by mathematical modeling is used for modeling, formulating, analyzing and designing the configuration in advance through data of the system, so that a deviation function equation is designed, and the redundant manipulator motion path planning method for resisting the noise interference is designed by utilizing a power-type variable parameter recursive neural dynamics method.
The output environment module specifically comprises:
the optimal solution request terminal unit is used for a request end which needs to obtain the optimal solution of the real number domain smooth time-varying quadratic programming problem of the actual physical system or the numerical solving system, and the port sends an instruction request to the solving system when solving parameters need to be obtained and receives a solving result;
and the redundant manipulator path planning terminal unit is used for converting the parameters output by the optimal solution request end into related poems and finally inputting the poems into a manipulator control program to plan and control the path of the manipulator.
Example 3:
the MATLAB simulation experiment of this example was established in Kinova-JACO2On the basis of the light bionic mechanical arm. The total weight of the mechanical arm is 4.4kg, and the maximum control distance is 77 cm.
The type of redundant manipulator comprises 6 degrees of freedom in total, namely theta (t) comprises 6 elements; the space dimensions of the tail end of the mechanical arm are 3, namely the tail end of the mechanical arm comprises an X axis, a Y axis and a Z axis; the Jacobian matrix of which is
The starting joint angle of the redundant robot arm is set to θ (0) [1.675, 2.843, -3.216, 4.187, -1.710, -2.650 ]](ii) a The task execution period t is set to 8 s; the parameter γ is set to 80. In the present example, in order to show the superiority of the variable parameter neural solver for redundant manipulator motion planning proposed by the present invention, the Kinova-JACO2The expected trajectory of the lightweight biomimetic redundant manipulator is set to a complex butterfly shape with a parametric diameter of 45 cm. According to Kinova-JACO set as above2The redundancy mechanical arm physical model is solved on a speed layer, and the following time-varying quadratic programming model can be established:
wherein I (t) is an identity matrix;
while
Respectively as follows:
from the steps and methods described above, a matrix equation can be designed that yields
W(t)Y(t)＝G(t) (16)
Wherein
To obtain the optimal solution of the time-varying quadratic programming model for solving the motion path of the redundant manipulator, a deviation function equation in the form of a matrix is defined as follows
(t)＝W(t)Y(t)-G(t) (17)
According to the power type variable parameter recursive neurodynamic method, a power type time-varying parameter is designed and used in the invention, and the design formula is as follows
Wherein the parameter γ is set to 80.
From the deviation function equation and the derivative information thereof, the real number domain power type variable parameter recurrent neural network model can be expressed by the following implicit kinetic equation
Wherein
Is partial derivative information; Δ d (t) is the noise term of the coefficient matrix; Δ k (t) is the error term when the hardware is running. In order to better simulate the noise interference suffered by the redundant manipulator in actual operation, in this example, the noise term Δ d (t) and the error term Δ k (t) are composed of a series of complex sine and cosine functions, and the specific expressions are as follows:
according to the definition of Y (t), it can be seen 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 an initial value of Y (0) ═ Y0。
According to the implicit kinetic equation, a real-number-domain anti-noise-interference redundant manipulator path planning method and network implementation can be obtained; and the output result of the network is the optimal solution of the real number domain time-varying quadratic programming problem. And outputting the optimal solution of the solver obtained by the processor, and completing the optimal solution of the actual physical system or the numerical solution system in the form of a real number domain smooth time-varying quadratic programming problem. The obtained network state solution is the optimal solution of the redundancy mechanical arm system motion planning which is interfered by the noise and is obtained by the simulation example.
The results of the experiments of the simulation example are shown in fig. 3(a), 3(b), 4(a), 4(b), 5(a), 5(b), 6(a), and 6 (b). Fig. 3(a) and 3(b) are track diagrams of a redundant manipulator interfered by noise when executing a motion path planning task, respectively applying the novel method and the conventional method of the present invention. Fig. 4(a) and 4(b) are graphs of an actual path and a desired path when a redundant manipulator interfered by noise performs a motion path planning task, respectively, when the novel method and the conventional method of the present invention are applied. Fig. 5(a) and 5(b) are graphs of error curves in the directions of the X axis, the Y axis and the Z axis when the redundant manipulator interfered by noise executes a motion path planning task, respectively, when the novel method and the conventional method of the present invention are applied. Fig. 6(a) and 6(b) are graphs of norm errors when the redundant manipulator interfered by noise executes a motion path planning task under the condition that the novel method and the conventional method are applied respectively, where the norm errors | | e (t) | | i2The 2-norm is defined as the sum of errors of the redundant manipulator in three directions of an X axis, a Y axis and a Z axis when the redundant manipulator executes a path planning task.
As can be seen from fig. 3(a), 3(b), 4(a), and 4(b), when the method for planning a motion path of a redundant manipulator with noise interference resistance according to the present invention is applied to plan a motion path of the manipulator, an actual motion path may coincide with an expected path, that is, a path deviation may rapidly converge to zero; when the traditional method is applied to planning the path of the mechanical arm, a large deviation always exists between an actual motion path and an expected path, and the requirement on accuracy is difficult to meet in the actual operation of the redundant mechanical arm.
As can be seen from fig. 5(a) and 5(b), when the method for planning a motion path of a redundant manipulator with noise interference resistance according to the present invention is applied to plan a motion path of the manipulator, errors in the three directions of the X axis, the Y axis, and the Z axis can converge to zero at a fast speed, i.e., a deviation between an actual motion path and an expected path of the manipulator can be well eliminated; when the traditional method is applied to planning the path of the mechanical arm, large deviation always exists between the actual motion path and the expected path in the three directions of the X axis, the Y axis and the Z axis, and the accuracy requirement is difficult to meet in the actual redundant mechanical arm operation.
As can be seen from fig. 6(a) and 6(b), when the method for planning a motion path of a redundant manipulator with noise immunity according to the present invention is applied to plan a manipulator path, a norm error of the redundant manipulator with noise immunity can converge to zero at a fast speed; when the traditional method is applied to the path planning of the mechanical arm, norm errors always exist, namely certain errors always exist when the mechanical arm executes a path planning task, and the accuracy requirement is difficult to meet.
The experimental results of the simulation embodiment well show the superiority of the method for planning the motion path of the redundant manipulator resisting the noise interference.
The above description is only for the preferred embodiments of the present invention, but the protection scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution and the inventive concept of the present invention within the scope of the present invention.
Claims (7)
1. An anti-noise-interference redundant manipulator path planning method is characterized by comprising the following steps: the method comprises the following steps:
1) establishing a time-varying quadratic programming model according to the actual parameter index of the redundant manipulator, and introducing the performance index of the motion planning of the redundant manipulator into the time-varying quadratic programming model;
2) optimizing the optimal value of the time-varying quadratic programming model by using a Lagrange multiplier method to obtain an optimization formula;
3) designing a standard matrix equation according to an optimization formula;
4) designing a deviation function equation of the system according to the actual physical model system and a standard matrix equation;
5) and establishing a power variable parameter recurrent neural network model containing noise according to the deviation function equation and the power variable parameter recurrent neural dynamics method, wherein the network state solution output by the model is the optimal solution.
2. The method for noise-immune redundant robotic arm path planning according to claim 1, wherein: the method comprises the following steps of establishing a time-varying quadratic programming model according to actual redundant manipulator parameter indexes, and introducing performance indexes of redundant manipulator motion planning, and specifically comprises the following steps:
the parameter indexes of the actual redundancy mechanical arm are formulated and modeled to obtain the following inverse kinematics equation expression of the redundancy mechanical arm:
f(θ(t))＝r(t) (1)
wherein theta (t) is the mechanical joint angle of the redundant manipulator; r (t) is the desired end trajectory of the redundant manipulator; f (-) is a nonlinear equation representing the angle of the joint of the redundant manipulator; simultaneously deriving the two ends of the equation to obtain the following inverse kinematics equation expression on the speed layer of the redundant manipulator:
wherein
The matrix is a Jacobian matrix of the redundant manipulator, n represents the number of the degrees of freedom of the manipulator, and m represents the space dimension of the tail end track of the manipulator;
the derivatives of the joint angle and the tail end track of the redundant manipulator with respect to time are respectively; according to the physical model, the following time-varying quadratic programming model can be established:
subject to J(θ(t))x(t)＝B(t) (4)
wherein
Q (t) ═ i (t) is an identity matrix; j (theta (t)) is a Jacobian matrix of the redundant manipulator; p (t) is a performance index coefficient vector;
introducing a performance index coefficient vector P (t) of the redundant manipulator, wherein the specific design formula is as follows:
wherein
The joint deviation response coefficient is shown, and theta (t) and theta (0) respectively show the joint state and the initial joint state in the motion process of the redundant manipulator.
3. The method for noise-immune redundant robotic arm path planning according to claim 2, wherein: the optimization of the optimal value of the time-varying quadratic programming model by using the Lagrange multiplier method specifically comprises the following steps:
a time-varying quadratic programming model:
subject to J(θ(t))x(t)＝B(t) (4)
to obtain partial derivative information about the optimal solution and the lagrangian multiplier for the time-varying quadratic programming problem, using the lagrangian multiplier method for the time-varying quadratic programming problem (3) (4) can obtain the following:
wherein
Is the Lagrangian multiplier; according to Lagrange's theorem, if
And
exist and are continuous, then the following two equations hold, namely
Wherein, the time-varying parameter matrix and the vector Q (t), P (t), J (t), B (t) are composed of the signals obtained by the sensor of the actual physical model system and the signals of the expected operation state of the system; time-varying parameter matrices and vectors Q (t), P (t), J (θ (t)), B (t), and their time derivatives
Are known or can be estimated within certain accuracy requirements; there is a time-varying quadratic programming problem (3) (4) about the optimal solution and about the partial derivative information of the lagrangian multiplier, and the lagrangian multiplier method can be used to represent the above information as optimization equations (6) (7).
4. The method for noise immunity redundant manipulator path planning according to claim 3, wherein: the designing of a standard matrix equation according to the optimization formula specifically includes:
optimizing a formula:
according to the optimization formulas (6) and (7), the following standard matrix equation about the time-varying quadratic programming problems (3) and (4) can be designed:
W(t)Y(t)＝G(t) (8)
wherein
The time-varying coefficient matrix and vectors W (t), Y (t), G (t) are continuous and smooth in the real domain.
5. The noise immune redundant manipulator path planning method according to claim 4, wherein: the method for designing the deviation function equation of the system according to the actual physical model system and the standard matrix equation specifically comprises the following steps:
standard matrix equation:
W(t)Y(t)＝G(t) (8)
designing a deviation function equation of the obtained system according to a standard matrix equation (8) of the smooth time-varying quadratic programming problem of the obtained actual physical model system or numerical solution system; to obtain the optimal solution of the time-varying quadratic programming problem (3) (4), a deviation function equation in the form of a matrix is defined as follows:
optimal solution x of time-varying quadratic programming problem (3) (4) when deviation function equation (t) converges to zero*(t) can be obtained.
6. The method of claim 5, wherein the method comprises: the method for planning the path of the redundant manipulator resisting the noise interference is designed according to a deviation function equation and a power-type variable parameter recurrent neural dynamics method, a network state solution obtained by the method is an optimal solution, and the method specifically comprises the following steps:
the data in the time-varying parameter matrix can be input into the processing unit; by combining the obtained time-varying parameter matrix and derivative information thereof with a real number domain power-varying parameter-varying recurrent neural dynamics method and by utilizing a monotone increasing odd activation function, a redundant manipulator path planning method for resisting noise interference can be designed; according to the power parameter varying recursive neurodynamic method, the time derivative of the deviation function equation (t) needs to be negative; different from a fixed parameter recursive neurodynamics method, the design parameters determining the convergence performance of the novel neurodynamics method are time-varying; the design formula of a power type time-varying parameter is as follows:
wherein gamma > 0 is a constant coefficient parameter of artificial design, and phi (-) is a monotone increasing odd activation array;
substituting the deviation function equation and the derivative information thereof into a design formula (8),
if noise interference and hardware operation errors exist, the following noise-containing power variant recurrent neural network model can be obtained:
where Δ d (t) is the noise term of the coefficient matrix; Δ K (t) is an error term when the hardware runs; it is composed ofIn
Is partial derivative information;
according to pairs
Definition of (1), to know
Wherein Y (t) has an initial value
According to an implicit kinetic equation (11), a real-number-domain anti-noise-interference redundant manipulator path planning method and network implementation can be obtained; and the output result of the network is the optimal solution of the real number domain time-varying quadratic programming problems (3) and (4).
7. A redundant robotic arm motion path planning system for achieving noise immunity as claimed in any one of claims 1-6, characterized by: the system comprises:
the external environment input module is used for acquiring and analyzing data input by the external environment to form the basis of the time-varying parameter matrix content;
the input interface circuit module is used for externally setting data and interface channels among the processors and can be realized by circuits and protocols of different interfaces according to different sensors;
the processor module is used for processing external input data and solving the optimal solution of the redundant manipulator motion path planning method for resisting the noise interference, which is designed on the basis of the power-type variable parameter recurrent neural dynamics method;
the output interface module is used as an interface between optimal solution data of the redundant manipulator motion path planning method and the output environment module, wherein the data is solved by the redundant manipulator motion path planning method resisting noise interference, and the interface can be a circuit interface or a return value of a program and is different according to different design systems;
and the output environment module is used for realizing the anti-noise interference redundant manipulator motion path planning method based on the power type variable parameter recurrent neural dynamics method.
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| CN109015657B (en) * | 2018-09-07 | 2021-12-10 | 浙江科技学院 | Final state network optimization method for redundant mechanical arm repetitive motion planning |
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| CN110076770B (en) * | 2019-03-28 | 2022-12-06 | 陕西理工大学 | Self-movement method for redundant mechanical arm |
| CN110103225B (en) * | 2019-06-04 | 2023-04-11 | 兰州大学 | Data-driven method and device for controlling repeated motion of mechanical arm |
| CN111716357A (en) * | 2020-06-18 | 2020-09-29 | 南京邮电大学 | Track generation and modulation method based on dynamic neural network |
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