CN114378812A - Parallel mechanical arm prediction control method based on discrete recurrent neural network model - Google Patents

Parallel mechanical arm prediction control method based on discrete recurrent neural network model Download PDF

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CN114378812A
CN114378812A CN202111520250.4A CN202111520250A CN114378812A CN 114378812 A CN114378812 A CN 114378812A CN 202111520250 A CN202111520250 A CN 202111520250A CN 114378812 A CN114378812 A CN 114378812A
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mechanical arm
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neural network
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CN114378812B (en
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石杨
王杰
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Yangzhou University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/003—Programme-controlled manipulators having parallel kinematics
    • 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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    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
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Abstract

The invention provides a parallel mechanical arm prediction control method based on a discrete recurrent neural network model, which is characterized by establishing a parallel mechanical arm dynamic model and initializing a physical model of the parallel mechanical arm; constructing a parallel mechanical arm discrete recurrent neural network model, wherein the discrete recurrent neural network model is limited by a general five-instantaneous discretization formula; constructing an expected path of the parallel mechanical arms, and acquiring an initial value of a Stewart platform nonlinear power system; and performing predictive control on the path of the parallel mechanical arm nonlinear power system based on the discrete recurrent neural network model. The invention theoretically analyzes how to keep the tracking precision of the Stewart platform based on the truncation error, constructs a discrete recurrent neural network model, and realizes the prediction and high-precision real-time tracking of the path of the Stewart mechanical arm.

Description

Parallel mechanical arm prediction control method based on discrete recurrent neural network model
Technical Field
The invention belongs to the field of mechanical arm tracking control, and particularly relates to a parallel mechanical arm prediction control method based on a discrete recurrent neural network model.
Background
In the field of redundant parallel robots, the stuart platform has attracted extensive attention from practitioners and researchers, and has found applications in many areas, such as mechatronics, cybernetics, telescope design, insect science, and the like. For example, the design and analysis of parallel-supported bumpers based on 18-cycle stewart platforms to prevent external impacts from damaging the inertial navigation system; the research of scientific researchers provides a six-degree-of-freedom real-time motion tracking system for the position and posture measurement of an industrial robot in a three-dimensional space. Many effective methods have been investigated for tracking control problems of the stewart platform.
Kumaret gives a robust finite time tracking of a Stutt platform based on an overtorque sliding-mode observer. Mohammed and Li have designed a dynamic neural network in the middle for the motion control problem of the Stewart platform. Na nuaet al, moreover, proposes a solution to the direct kinematics problem of 6 prism actuators making up 3 parallel pairs at the base or hand.
It is worth noting that in the past decades, Recurrent Neural Networks (RNNs) have become a powerful alternative to real-time engineering problems. Unlike the classical RNN model, a special class of RNN models was designed and discussed herein for solving the continuous time-varying problem. For example, Chen and Yi investigate the robustness of the recently proposed hybrid RNN for solving online matrix inversion; based on the effective solution of the dynamic Lyapunov equation, a system construction method for designing a control law by using a return-to-zero neural network is provided.
However, a great deal of research has considered the design of RNN models in a continuous time environment. In view of the potential implementation of the tracking control of the stewart platform, it is also necessary to build and study a corresponding discrete-time model. However, in a discrete time environment, the conventional tracking control method is essentially established in a continuous time environment, and the performance of the conventional tracking control method is often not satisfactory. Specifically, at a time during tracking control, the input signal anchors the desired output at that time. It is clear that the real-time calculation and transmission of the control signals is time consuming and the required output may vary. If the conventional method is applied to real-time tracking control, the result is likely to be a delay.
In recent years, many studies on discrete models have appeared, and many studies have fully demonstrated the advantages of good convergence and high precision. However, most of these studies do not allow for a rigorous efficiency analysis. In fact, in practical applications, efficiency is regarded as an important objective in the tracking control process of the stewart platform. Namely, on the premise of not influencing the result precision, the calculation time and the calculation space cost of the tracking control of the Stewart platform are reduced as much as possible.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a discrete recurrent neural network model prediction control method of a parallel mechanical arm, which can realize path prediction and high-precision real-time tracking of a Stutt mechanical arm.
The technical scheme provided by the invention is as follows:
the invention discloses a discrete recurrent neural network model prediction control method of parallel mechanical arms, which comprises the following steps:
establishing a parallel mechanical arm dynamic model and initializing a physical model of the parallel mechanical arm;
constructing a parallel mechanical arm discrete recurrent neural network model, wherein the discrete recurrent neural network model is limited by a general five-instantaneous discretization formula;
constructing an expected path of the parallel mechanical arm, and acquiring an initial value of a nonlinear power system of the parallel mechanical arm;
and performing predictive control on the path of the parallel mechanical arm nonlinear power system based on the discrete recurrent neural network model.
The parallel mechanical arm is a Stewart platform and is provided with six independent brakes, the six independent brakes are respectively connected with three fixed points on a platform bottom plate and six mounting points on a platform top plate, and the Stewart platform controls an end effector to track a preset path by adjusting the lengths of the six independent brakes.
The method is further characterized in that the discrete recurrent neural network model comprises a discrete recurrent neural network tracking model and a discrete recurrent neural network prediction model, the discrete recurrent neural network tracking model is used for tracking the length change of the independent brakes of the parallel mechanical arms, and the discrete recurrent neural network prediction model is used for performing prediction control on the paths of the non-linear dynamic systems of the parallel mechanical arms.
Further, the parallel mechanical arm dynamic model is constructed in the following specific steps: constructing a discrete equation of tracking control of the parallel mechanical arm:
Figure BDA0003407054230000021
wherein ,sa(tk+1) For parallel connection of the actual path of the arm at tk+1Path vector of time, sd(tk+1) Desired path at t for parallel robot armk+1A path vector of a time;
constructing an error vector under continuous time:
e(tk)＝sa(tk)-sd(tk) (2)
introducing an RNN design formula:
Figure BDA0003407054230000031
wherein, λ is a design formula parameter;
deducing by combining the formula (2) and the formula (3):
Figure BDA0003407054230000032
wherein ,
Figure BDA00034070542300000310
is tkThe time instants are connected in parallel to the time derivative of the actual path of the robot,
Figure BDA0003407054230000034
is tkTime-series connection is carried out on the time derivative of the expected path of the mechanical arm;
deducing based on formula (4):
Figure BDA0003407054230000035
constructing a kinematic equation of the parallel mechanical arm:
Figure BDA0003407054230000036
where C is a coefficient matrix of positive kinematics of the parallel manipulator, l (t)k) Is tkLength matrix of independent brake of parallel mechanical arm at moment, D (t)k) Is tkThe global position matrix of the end effector of the parallel mechanical arm is connected,
Figure BDA0003407054230000037
is tkAnd connecting the speed of the independent brake of the mechanical arm in parallel at any moment.
And (3) deriving and connecting a mechanical arm dynamic model by combining the formula (5) and the formula (6):
Figure BDA0003407054230000038
further, the discrete recurrent neural network tracking model is specifically as follows:
Figure BDA0003407054230000039
wherein ,l(tk+1) Is tk+1The length of the independent brake of the parallel mechanical arm at the moment, g is the sampling gap of the general five-instantaneous discretization formula, k is a selection parameter of the general five-instantaneous discretization formula, and h is g lambda, O (g)4) Is the truncation error.
Further, the discrete recurrent neural network prediction model is specifically as follows:
Figure BDA0003407054230000041
wherein ,sa(tk+1) Is tk+1Predicted value s of nonlinear power system of mechanical arm connected in parallel at any timea(tk) Is tkHistorical value, s, of the nonlinear power system of the mechanical arm connected in parallel at any timea(tk-1) Is tk-1Historical value, s, of the nonlinear power system of the mechanical arm connected in parallel at any timea(tk-2) Is tk-2Historical value, s, of the nonlinear power system of the mechanical arm connected in parallel at any timea(tk-3) Is tk-3The historical value of the nonlinear power system of the mechanical arm is connected in parallel at any time, g is the sampling interval of the general five-instantaneous discretization formula, k is the selection parameter of the general five-instantaneous discretization formula, C+Is an inverse kinematics coefficient matrix.
Further, the error of the discrete recurrent neural network prediction model is calculated by the following formula:
||e(tk+1)||2＝||sa(tk+1)-sd(tk+1)||2
wherein ,e(tk+1) Prediction error vector, s, for a discrete recurrent neural network prediction modela(tk+1) For parallel connection of the actual path of the arm at tk+1Path vector of time, sd(tk+1) Desired path at t for parallel robot armk+1A path vector for a time instant.
Further, the inverse kinematics coefficient matrix is obtained by converting the positive kinematics coefficient matrix of the mechanical arm according to the inverse kinematics principle.
Further, the parallel mechanical arm nonlinear power system is characterized in that a plurality of constraint terms exist, and at least comprise a selection parameter kappa and a design formula parameter lambda of a general five-instantaneous discretization formula.
In the prior art, under a discrete time environment, a traditional tracking control method used is essentially established under a continuous time environment, strict efficiency analysis is not considered, and the performance is often unsatisfactory. Compared with the prior art, the parallel mechanical arm prediction control method based on the discrete recurrent neural network model theoretically analyzes how to keep the tracking precision of the Stewart platform based on the truncation error, constructs the discrete recurrent neural network model, realizes the prediction and high-precision real-time tracking of the path of the Stewart mechanical arm, researches the influence of the discrete recurrent neural network model on the tracking precision under different sampling gap values and different selection parameter values based on an inverse kinematics technical method, and further improves the tracking control efficiency of the discrete recurrent neural network model.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings which are required to be used in the technical solution description will be briefly introduced below, it is obvious that the exemplary embodiments of the present invention and the description thereof are only used for explaining the present invention and do not constitute an unnecessary limitation of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without inventive labor. In the drawings:
FIG. 1 is a schematic flow chart of a discrete recurrent neural network model established in a predictive control method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a simplified Stewart platform model with an end effector and a moving platform on top and a fixed platform on the bottom, both platforms connected by six independent prism drivers, for use in a predictive control method according to an embodiment of the invention;
FIG. 3 is a schematic structural diagram of a discrete recurrent neural network prediction model in a prediction control method according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a change trajectory of coordinates of the actual trajectory of the stewart platform calculated by the discrete recurrent neural network tracking model at each moment on the X, Y, Z axis in the prediction control method according to the embodiment of the present invention;
FIG. 5 is a schematic diagram of a change trajectory of a speed of each leg of the Stewart platform at each moment, which is calculated by a discrete recurrent neural network tracking model in the predictive control method according to the embodiment of the invention;
FIG. 6 is a drawing of the Stewart platform l calculated by the discrete recurrent neural network tracking model in the prediction control method according to the embodiment of the present invention1、l2、l3Variation track of length of number leg at each momentA schematic diagram;
FIG. 7 is a drawing of the Stewart platform l calculated by the discrete recurrent neural network tracking model in the prediction control method according to the embodiment of the present invention4、l5、l6The length change track diagram of the number leg at each moment is shown;
fig. 8 is a schematic diagram of an actual path traced by the discrete recurrent neural network prediction model through the end effector and an expected path of the function itself under the conditions that the sampling gap g is 0.01 and the selection parameter k is 1/11 in the prediction control method according to the embodiment of the present invention;
fig. 9 is a schematic diagram of an actual path traced by the discrete recurrent neural network prediction model through the end effector and an expected path of the function itself under the conditions that the sampling gap g is 0.01 and the selection parameter k is 1/11 in the prediction control method according to the embodiment of the present invention, and the angle in fig. 8 is adjusted;
fig. 10 is a schematic diagram of an actual path traced by the discrete recurrent neural network prediction model through the end effector and an expected path of the function itself under the conditions that the sampling gap g is 0.001 and the selection parameter k is 1/11 in the prediction control method according to the embodiment of the present invention;
fig. 11 is a schematic diagram of an actual path traced by the discrete recurrent neural network prediction model through the end effector and an expected path of the function itself under the conditions that the sampling gap g is 0.001 and the selection parameter k is 1/11 in the prediction control method according to the embodiment of the present invention, and the angle in fig. 10 is adjusted;
fig. 12 is a schematic diagram illustrating the influence of values of different selection parameters κ (1/11< κ <1/6) on residual error under the condition that the sampling gap g is 0.01 in the prediction control method according to the embodiment of the present invention;
fig. 13 is a schematic diagram illustrating the influence of values of different selection parameters κ (1/11< κ <1/6) on residual errors under the condition that the sampling gap g is 0.001 in the prediction control method according to the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment provides a parallel mechanical arm prediction control method based on a discrete recurrent neural network model, and with reference to fig. 1, the method includes the following steps:
the method described in this embodiment is applied to a stewart platform, which is a parallel robotic arm having six independent prismatic actuators attached to three locations on the platform's bottom plate (i.e., fixed base) and spanning to six mounting points on the top plate (i.e., moving platform). The tracking control process of the stewart platform is to adjust the lengths of the six independent prism actuators to control the end effector of the stewart platform (which is considered as the center point of the moving platform) so that the end effector of the stewart platform can track the required path.
S11: establishing a Stewart platform dynamic model and initializing a physical model;
specifically, the discrete recurrent neural network described in this embodiment is defined by a general five-instantaneous discretization formula (FID formula), which is specifically as follows:
Figure BDA0003407054230000061
where g is the sampling gap, κ is a selection parameter, O (g)3) To truncate the error, k is the current instant,
k +1 is the future instant.
The stewart platform tracking control discrete equation:
Figure BDA0003407054230000062
in the formula ,sa(tk+1) For the actual path of the Stewart platform at tk+1Way of timeRadial vector, sd(tk+1) The expected path at t for the stewart platformk+1A path vector of a time;
constructing an error vector under continuous time:
e(tk)＝sa(tk)-sd(tk) (3)
introducing an RNN design formula:
Figure BDA0003407054230000071
wherein, λ is a design formula parameter;
combining equation (3) and equation (4) yields:
Figure BDA0003407054230000072
wherein ,
Figure BDA0003407054230000073
is tkThe time derivative of the actual path of the time-of-day stewart platform,
Figure BDA0003407054230000074
is tkThe time derivative of the expected path of the time-of-day stewart platform;
further based on equation (5):
Figure BDA0003407054230000075
according to the kinematic system, the kinematic equation is as follows:
Figure BDA0003407054230000076
wherein C is coefficient matrix of positive kinematics of the mechanical arm, and l (t)k) Is tkLength matrix of the mechanical arm brake at time, D (t)k) Is tkA global position matrix of the end effector at the time,
Figure BDA0003407054230000077
is tkThe speed of the mechanical arm independent brake is obtained at the moment.
Combining the formula (6) and the formula (7) to further obtain a stewart control equation, namely a parallel mechanical arm dynamics model:
Figure BDA0003407054230000078
initializing a physical model, specifically including the positions of an initial base and an upper platform, and setting the initial lengths, positions and angles of six independent prismatic crystal brakes and the central position of an end effector.
S12: constructing a discrete recurrent neural network model (FID formula DTRNN model) of a Stewart platform;
specifically, according to formula (1), a discrete time-varying recurrent neural network tracking model is obtained:
Figure BDA0003407054230000081
where λ is h/g, the value of h therefore depends on the values of λ and g.
According to the formula (9), an inverse discretization formula is obtained:
Figure BDA0003407054230000082
further, the formula (7) is subjected to pseudo-inversion to obtain:
Figure BDA0003407054230000083
further, a discrete time-varying recurrent neural network prediction model is established, and the structure of the model refers to fig. 3:
Figure BDA0003407054230000084
wherein ,sa(tk+1) Is tk+1Predicted value, s, of nonlinear dynamical system of time Stewart platforma(tk) Is tkHistorical values, s, of the nonlinear dynamical system of the Stewart platform at the momenta(tk-1) Is tk-1Historical values, s, of the nonlinear dynamical system of the Stewart platform at the momenta(tk-2) Is tk-2Historical values, s, of the nonlinear dynamical system of the Stewart platform at the momenta(tk-3) Is tk-3The historical value of the nonlinear power system of the Stewart platform at the moment, g is the sampling interval of the general five-instantaneous discretization formula, k is the selection parameter of the general five-instantaneous discretization formula, C is a constant between 1/12 and 1/6+Is an inverse kinematics coefficient matrix.
C+For the inverse kinematics coefficient matrix, when predicting the path of the mechanical arm at the time k +1, the embodiment adopts the inverse kinematics principle to convert the coefficient matrix of the positive kinematics of the mechanical arm into the inverse kinematics coefficient matrix.
S13: acquiring an initial value of a Stewart platform nonlinear power system;
inputting a constructed expected path of the Stutt platform nonlinear power system, wherein the nonlinear power system has a plurality of constraint terms, the constraint terms comprise a parameter lambda in an RNN design formula and a selection parameter k in an FID formula, and a prism driver length (leg length) vector l (t) of the mechanical arm is obtained0) Velocity vector of leg
Figure BDA0003407054230000085
Actual position vector sa(t0) And the time derivative of the actual position vector
Figure BDA0003407054230000086
Acquiring physical model parameters of the parallel mechanical arms, such as Euler angle theta, platform coordinate a, global coordinate b and total zero position of the platform coordinateLocal coordinates p;
s14: performing predictive control on the path of the parallel mechanical arm nonlinear power system based on a discrete recurrent neural network model;
adjusting the hyper-parameters of a discrete recurrent neural network model, wherein the hyper-parameters comprise time domain, step length, sampling gap g and selection parameter k in an FID formula, training the model to research the influence of different hyper-parameter settings on the tracking precision of the discrete recurrent neural network model, and performing analog simulation on the discrete recurrent neural network model obtained by training by using MATLAB (matrix laboratory), thereby obtaining a path prediction value s output by a Stewart platform nonlinear power systema(tk+1)；
S15: calculating the precision of the discrete recurrent neural network model of the Stewart platform and optimizing the model;
calculating the error of the predicted value of the discrete recurrent neural network model by using the error vector calculation formula under the continuous time defined in the step S1 according to the expected path input in the step S13, so as to obtain the prediction precision of the model, and returning to the step S13 when the shape of the mechanical arm path is changed, and re-adjusting the hyper-parameters of the discrete recurrent neural network model and training the model;
specifically, an error formula for obtaining the predicted value of the discrete recurrent neural network model at each moment is as follows:
||e(tk+1)||2＝||sa(tk+1)-sd(tk+1)||2 (13)
wherein ,e(tk+1) Prediction error vector, s, for a discrete recurrent neural network prediction modela(tk+1) For the actual path of the Stewart platform at tk+1Path vector of time, sd(tk+1) The expected path at t for the stewart platformk+1And (4) the path vector of the moment is subjected to modular evaluation.
It is to be noted that the discrete-time tracking control of the stewart platform is defined as being generated by the smooth continuous-time tracking control of the stewart platform. In the solution process, all discrete-time matrices/vectors can be regarded as discrete mappings of the respective continuous-time matrices/vectors. That is, the time derivatives of the discrete-time matrix/vector are meaningful and solvable.
In order to verify the accuracy and effectiveness of the discrete recurrent neural network model predictive control method of the parallel mechanical arm, the simulation experiment is performed based on MATLAB software, and the simulation process specifically includes the following steps:
s21: specifying a desired trajectory;
in particular, the amount of the solvent to be used,
Figure BDA0003407054230000101
s22: defining a Stewart platform rotation matrix A;
in particular, a rotation matrix in the X-axis component
Figure BDA0003407054230000102
Rotation matrix in the Y-axis component
Figure BDA0003407054230000103
Rotation matrix in the Z-axis component
Figure BDA0003407054230000104
The rotation matrix a is AxAyAz, where θ is euler angle, θ is θ x, θ y, θ z]TIn the present simulation example, the initial value of θ is vector (0, 0, π/2).
S23: setting discrete recurrent neural network model parameters;
specifically, given a sampling interval g, a parameter k is selected, a parameter λ is designed, and a trajectory is predicted using a discrete recurrent neural network model, and in this embodiment, comparative simulation experiments are performed on the conditions that the sampling interval g is 0.01 and the g is 0.001, (where g is 0.01, the design parameter λ is 3 and g is 0.001, the design parameter λ is 30), the selection parameters κ is 1/7, κ 1/8, κ is 1/9, κ is 1/10, and κ is 1/11, respectively.
S24: analyzing a track tracking prediction result;
specifically, referring to fig. 4, fig. 4 shows a variation trajectory of coordinates of the actual trajectory of the stuart platform calculated by the discrete recurrent neural network model at each time on the X, Y, Z axis;
referring to fig. 5, fig. 5 shows a variation trajectory of the velocity of each leg of the stewart platform at each moment calculated by the discrete recurrent neural network model;
referring to FIG. 6, FIG. 6 shows a discrete recurrent neural network model calculating a Stewart platform1、l2、l3The change track of the length of the number leg at each moment;
referring to FIG. 7, FIG. 7 illustrates a discrete recurrent neural network model calculating a Stewart platform4、l5、l6The change track of the length of the number leg at each moment;
as can be seen from the figure, as time increases, the component of the actual trajectory at the X, Y, Z axis at each moment, the six leg lengths of the stuart platform, and the speed of each mechanical arm periodically and regularly change, which fully explains that the discrete recurrent neural network model has successfully completed the real-time tracking task;
in addition, the embodiment uses the tracking data in the real-time tracking task to control the end effector to draw the track according to the inverse kinematics principle. The trajectories and the trajectory tracking results are shown in fig. 8, 9, 10, and 11. Note that fig. 8 and 9 are obtained in the case where the sampling gap g is 0.01; fig. 10, 11 were obtained with a sampling gap g of 0.001, where the solid line represents the actual trajectory of the end effector and the dashed line represents the expected trajectory generated by the discrete recurrent neural network model of the manipulator within the interval;
in order to better show the results of the numerical experiments, the state of another viewing angle of fig. 8 is shown in fig. 9. Similarly, fig. 11 is also rotated by fig. 10, and the actual trajectory is identical to the expected trajectory at two different sampling intervals, which fully proves the accuracy and effectiveness of the proposed trajectory prediction tracking of the discrete recurrent neural network model.
S25: analyzing the influence of the selection parameter kappa on the discrete recurrent neural network model;
specifically, for the discrete recurrent neural network model, the present embodiment selects parameters k of 1/7, k of 1/8, k of 1/9, k of 1/10 and k of 1/11 respectively under the condition that the sampling gap g is 0.01 and g is 0.001 for comparison experiments;
first, the influence of the selection parameter on the solution error was investigated with the sampling interval g being 0.01, and the experimental result is shown in fig. 12, where the maximum steady-state solution error of the discrete recurrent neural network model converged to 10-8Indicating that the precision meets the expectation, and as the parameter k is reduced, the error of the solution is reduced, and the reduction degree is consistent;
similarly, the influence of the parameter on the solution error is studied by taking the sampling gap g to be 0.001, and as a result, as shown in fig. 13, the maximum steady-state solution error of the discrete recurrent neural network model converges to 10-12The accuracy is still as expected, and when the sampling gap g is 0.001, the variation trend of the residual error is consistent with the result when the sampling gap g is 0.01.
The simulation experiment of the embodiment proves that the accuracy of the prediction control of the discrete recurrent neural network model is high, and real-time control and prediction can be carried out. Research shows that the selection of the parameter k has a decisive effect on improving the efficiency of the model, if the efficiency of the model needs to be improved, the accuracy is highest when the sampling parameter k is 1/11, and the system efficiency can be effectively improved in practical operation.
According to the discrete recurrent neural network model predictive control method for the parallel mechanical arms with high precision and high efficiency, the neural network is combined with model predictive control, and the method has excellent system control performance. Furthermore, this method may also achieve the following technical advantages: the method is simple to implement, easy to operate and free from adjusting too many parameters; and has higher control precision and certain robustness.
In addition, an embodiment of the present invention further provides a computer-readable storage medium, where the computer-readable storage medium may store a program, and when the program is executed, the program includes some or all of the steps of any of the discrete recurrent neural network model-based parallel manipulator prediction control methods described in the above method embodiments.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.
The integrated unit, if implemented in the form of a software functional unit and sold or used as a stand-alone product, may be stored in a computer readable memory. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a memory and includes several instructions for causing a computer device (which may be a personal computer, a server, a network device, or the like) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned memory comprises: a U-disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a removable hard disk, a magnetic or optical disk, and other various media capable of storing program codes.
Those skilled in the art will appreciate that all or part of the steps in the methods of the above embodiments may be implemented by associated hardware instructed by a program, which may be stored in a computer-readable memory, which may include: flash memory disks, read-only memory, random access memory, magnetic or optical disks, and the like.
The above-mentioned embodiments, objects, technical solutions and advantages of the present application are further described in detail, it should be understood that the above-mentioned embodiments are only examples of the present application, and are not intended to limit the scope of the present application, and any modifications, equivalent substitutions, improvements and the like made on the basis of the technical solutions of the present application should be included in the scope of the present application.

Claims (10)

1. A parallel mechanical arm prediction control method based on a discrete recurrent neural network model is characterized by comprising the following steps:
establishing a parallel mechanical arm dynamic model and initializing a physical model of the parallel mechanical arm;
constructing a parallel mechanical arm discrete recurrent neural network model, wherein the discrete recurrent neural network model is limited by a general five-instantaneous discretization formula;
constructing an expected path of the parallel mechanical arm, and acquiring an initial value of a nonlinear power system of the parallel mechanical arm;
and performing predictive control on the path of the parallel mechanical arm nonlinear power system based on the discrete recurrent neural network model.
2. The parallel mechanical arm prediction control method based on the discrete recurrent neural network model as claimed in claim 1, wherein the parallel mechanical arm is a stewart platform, and has six independent brakes, the six independent brakes are respectively connected with three fixed points on the platform bottom plate and six mounting points on the platform top plate, and the stewart platform controls the end effector to track the preset path by adjusting the lengths of the six independent brakes.
3. The parallel mechanical arm prediction control method based on the discrete recurrent neural network model as claimed in claim 1, wherein the discrete recurrent neural network model comprises a discrete recurrent neural network tracking model and a discrete recurrent neural network prediction model, the discrete recurrent neural network tracking model is used for tracking length changes of independent brakes of the parallel mechanical arms, and the discrete recurrent neural network prediction model is used for performing prediction control on paths of the non-linear power system of the parallel mechanical arms.
4. The parallel mechanical arm prediction control method based on the discrete recurrent neural network model as claimed in claim 1, wherein the parallel mechanical arm dynamics model is constructed by the following specific process: constructing a discrete equation of tracking control of the parallel mechanical arm:
Figure FDA0003407054220000011
wherein ,sa(tk+1) For parallel connection of the actual path of the arm at tk+1Path vector of time, sd(tk+1) Desired path at t for parallel robot armk+1A path vector of a time;
constructing an error vector under continuous time:
e(tk)＝sa(tk)-sd(tk) (2)
introducing an RNN design formula:
Figure FDA0003407054220000012
wherein, λ is a design formula parameter;
deducing by combining the formula (2) and the formula (3):
Figure FDA0003407054220000021
wherein ,
Figure FDA0003407054220000022
is tkThe time instants are connected in parallel to the time derivative of the actual path of the robot,
Figure FDA0003407054220000023
is tkTime-series connection is carried out on the time derivative of the expected path of the mechanical arm;
deducing based on formula (4):
Figure FDA0003407054220000024
constructing a kinematic equation of the parallel mechanical arm:
Figure FDA0003407054220000025
where C is a coefficient matrix of positive kinematics of the parallel manipulator, l (t)k) Is tkLength matrix of independent brake of parallel mechanical arm at moment, D (t)k) Is tkThe global position matrix of the end effector of the parallel mechanical arm is connected,
Figure FDA0003407054220000026
is tkAnd connecting the speed of the independent brake of the mechanical arm in parallel at any moment.
And (3) deriving and connecting a mechanical arm dynamic model by combining the formula (5) and the formula (6):
Figure FDA0003407054220000027
5. the parallel mechanical arm prediction control method based on the discrete recurrent neural network model as claimed in claim 3, wherein the discrete recurrent neural network tracking model is specifically as follows:
Figure FDA0003407054220000028
wherein ,l(tk+1) Is tk+1The length of the independent brake of the parallel mechanical arm at the moment, g is the sampling gap of the general five-instantaneous discretization formula, k is a selection parameter of the general five-instantaneous discretization formula, and h is g lambda, O (g)4) Is the truncation error.
6. The parallel mechanical arm prediction control method based on the discrete recurrent neural network model as claimed in claim 3, wherein the discrete recurrent neural network prediction model is specifically as follows:
Figure FDA0003407054220000029
wherein ,sa(tk+1) Is tk+1Predicted value s of nonlinear power system of mechanical arm connected in parallel at any timea(tk) Is tkHistorical value, s, of the nonlinear power system of the mechanical arm connected in parallel at any timea(tk-1) Is tk-1Historical value, s, of the nonlinear power system of the mechanical arm connected in parallel at any timea(tk-2) Is tk-2Historical value, s, of the nonlinear power system of the mechanical arm connected in parallel at any timea(tk-3) Is tk-3The historical value of the nonlinear power system of the mechanical arm is connected in parallel at any time, g is the sampling interval of the general five-instantaneous discretization formula, k is the selection parameter of the general five-instantaneous discretization formula, C+Is an inverse kinematics coefficient matrix.
7. The parallel mechanical arm prediction control method based on the discrete recurrent neural network model as claimed in claim 6, wherein the error of the discrete recurrent neural network prediction model is calculated by the following formula:
||e(tk+1)||2＝||sa(tk+1)-sd(tk+1)||2
wherein ,e(tk+1) Prediction error vector, s, for a discrete recurrent neural network prediction modela(tk+1) For parallel connection of the actual path of the arm at tk+1Path vector of time, sd(tk+1) Desired path at t for parallel robot armk+1A path vector for a time instant.
8. The parallel mechanical arm prediction control method based on the discrete recurrent neural network model as claimed in claim 6, wherein the inverse kinematics coefficient matrix is obtained by converting a positive kinematics coefficient matrix of the mechanical arm according to an inverse kinematics principle.
9. The parallel mechanical arm prediction control method based on the discrete recurrent neural network model is characterized in that a plurality of constraint terms exist in the parallel mechanical arm nonlinear power system, and the constraint terms at least comprise a selection parameter k and a design formula parameter λ of a general five-instantaneous discretization formula.
10. A computer-readable storage medium, wherein the storage medium contains the discrete recurrent neural network model-based parallel manipulator prediction control method according to any one of claims 1 to 9.
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Citations (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2002059384A (en) * 2000-08-22 2002-02-26 Sony Corp Learning system and learning method for robot
CN1472673A (en) * 2003-06-05 2004-02-04 上海交通大学 Data merging method based linear constrainted cut minimum binary multiply
US20120290131A1 (en) * 2011-05-09 2012-11-15 King Fahd University Of Petroleum And Minerals Parallel kinematic machine trajectory planning method
CN103472724A (en) * 2013-09-16 2013-12-25 江苏大学 Real-time control dynamics modeling method for multi-freedom-degree parallel mechanism
CN109726045A (en) * 2017-10-27 2019-05-07 百度（美国）有限责任公司 System and method for the sparse recurrent neural network of block
CN110769985A (en) * 2017-12-05 2020-02-07 谷歌有限责任公司 Viewpoint-invariant visual servoing of a robot end effector using a recurrent neural network
CN111618864A (en) * 2020-07-20 2020-09-04 中国科学院自动化研究所 Robot model prediction control method based on adaptive neural network
CN111801693A (en) * 2018-03-06 2020-10-20 Tdk株式会社 Neural network device, signal generation method, and program
CN112817231A (en) * 2020-12-31 2021-05-18 南京工大数控科技有限公司 High-precision tracking control method for mechanical arm with high robustness
CN113239545A (en) * 2021-05-13 2021-08-10 嘉兴学院 Efficient method for multi-objective optimization design of parallel robot

Patent Citations (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2002059384A (en) * 2000-08-22 2002-02-26 Sony Corp Learning system and learning method for robot
CN1472673A (en) * 2003-06-05 2004-02-04 上海交通大学 Data merging method based linear constrainted cut minimum binary multiply
US20120290131A1 (en) * 2011-05-09 2012-11-15 King Fahd University Of Petroleum And Minerals Parallel kinematic machine trajectory planning method
CN103472724A (en) * 2013-09-16 2013-12-25 江苏大学 Real-time control dynamics modeling method for multi-freedom-degree parallel mechanism
CN109726045A (en) * 2017-10-27 2019-05-07 百度（美国）有限责任公司 System and method for the sparse recurrent neural network of block
CN110769985A (en) * 2017-12-05 2020-02-07 谷歌有限责任公司 Viewpoint-invariant visual servoing of a robot end effector using a recurrent neural network
CN111801693A (en) * 2018-03-06 2020-10-20 Tdk株式会社 Neural network device, signal generation method, and program
CN111618864A (en) * 2020-07-20 2020-09-04 中国科学院自动化研究所 Robot model prediction control method based on adaptive neural network
CN112817231A (en) * 2020-12-31 2021-05-18 南京工大数控科技有限公司 High-precision tracking control method for mechanical arm with high robustness
CN113239545A (en) * 2021-05-13 2021-08-10 嘉兴学院 Efficient method for multi-objective optimization design of parallel robot

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