CN114378812B - 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 PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
- B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
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- 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
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
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Abstract
The application provides a parallel mechanical arm prediction control method based on a discrete recurrent neural network model, which comprises the steps of 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 defined by a general five-instant discretization formula; constructing an expected path of the parallel mechanical arm, and acquiring an initial value of a Stuttgart platform nonlinear power system; and carrying out predictive control on the paths of the nonlinear power systems of the parallel mechanical arms based on the discrete recurrent neural network model. Based on the truncation error, the application analyzes how to maintain the tracking precision of the Stuttgart platform in theory, builds a discrete recurrent neural network model, and realizes the prediction and high-precision real-time tracking of the Stuttgart mechanical arm path.
Description
Technical Field
The application 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 redundancy parallel robots, the Stuttgart platform has attracted considerable attention from practitioners and researchers and has found application in many areas such as electromechanical integration, control theory, telescope design, insect science, and the like. For example, the design and analysis of an 18-stoker platform based parallel support bumper to prevent external impacts from damaging the inertial navigation system; the scientific research workers research provides a six-degree-of-freedom real-time motion tracking system for measuring the position and the posture of the industrial robot in a three-dimensional space. Many effective methods have been studied for tracking control problems of the Stuttgart platform.
Kumaret gives a robust finite time tracking of the schart platform based on a super twisted sliding mode observer. Aiming at the motion control problem of the Stuttgart platform, mohammed and Li design a dynamic neural network. Furthermore, p.nanuaet al proposes a solution to the direct kinematic problem of 6 prism actuators forming 3 parallel pairs at the base or hand.
It is worth noting that Recurrent Neural Networks (RNNs) have become a powerful alternative to solving engineering problems in real time during the last decades. Unlike classical RNN models, a special class of RNN models is designed herein and explored for solving continuous time-varying problems. For example, chen and Yi studied the robustness of the recently proposed hybrid RNN for solving on-line matrix inversion; based on the effective solution of the dynamic Lyapunov equation, a system construction method for designing a control law by utilizing a return-to-zero neural network is provided.
However, a great deal of research has considered the design of RNN models in continuous time environments. In view of the potential implementation of the Stuttgart platform tracking control, 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 thereof tends to be unsatisfactory. Specifically, at a certain point in the tracking control process, the input signal anchors the desired output at that point. Obviously, the real-time computation and transmission of control signals takes time, and the required output may vary. If the conventional method is applied to real-time tracking control, the result is likely to be delay.
In recent years, many researches on discrete models are also presented, and many researches fully prove the advantages of good convergence and high precision. However, most of these studies do not take into account strict efficiency analysis. In fact, in practical applications, efficiency is considered as an important goal in the process of the Stuttgart platform tracking control. On the premise of not influencing the result precision, the calculation time and the calculation space cost of the Stuttgart platform tracking control are reduced as much as possible.
Disclosure of Invention
Aiming at the defects in the prior art, the application provides a discrete recurrent neural network model prediction control method of a parallel mechanical arm, which can realize the path prediction and high-precision real-time tracking of a Stuttgart mechanical arm.
The technical scheme provided by the application is as follows:
the application discloses a discrete recurrent neural network model predictive control method of a parallel mechanical arm, 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 defined by a general five-instant 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 carrying out predictive control on the paths of the nonlinear power systems of the parallel mechanical arms based on the discrete recurrent neural network model.
Further, the parallel mechanical arm is a Stuttgart 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 Stuttgart platform controls the end effector to track a preset path by adjusting the lengths of the six independent brakes.
Further, the method is 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 brake of the parallel mechanical arm, and the discrete recurrent neural network prediction model is used for performing predictive control on the path of the nonlinear power system of the parallel mechanical arm.
Further, the method is characterized in that the construction process of the parallel mechanical arm dynamics model is specifically as follows: constructing a parallel mechanical arm tracking control discrete equation:
wherein ,sa (t k+1 ) The actual path of the parallel mechanical arm is at t k+1 Path vector of time, s d (t k+1 ) The expected path for the parallel robot arm is at t k+1 A path vector of time;
constructing an error vector under continuous time:
e(t k )＝s a (t k )-s d (t k ) (2)
introducing an RNN design formula:
wherein lambda is a design formula parameter;
the combination of equation (2) and equation (3) yields:
wherein ,at t k Time derivative of real path of moment parallel mechanical arm, < ->At t k Time derivative of expected path of mechanical arm connected in parallel at moment;
derived based on equation (4):
constructing a kinematic equation of the parallel mechanical arm:
wherein C is a coefficient matrix of the positive kinematics of the parallel mechanical arm, l (t k ) At t k Length matrix of independent brakes of mechanical arm connected in parallel at moment, D (t k ) At t k A global position matrix of the end effector of the mechanical arm is connected in parallel at any time,at t k The speed of the independent brake of the mechanical arm is connected in parallel at any time.
And (3) pushing out a parallel mechanical arm dynamics model by combining the formula (5) and the formula (6):
further, the discrete recurrent neural network tracking model is characterized by comprising the following specific steps:
wherein ,l(tk+1 ) At t k+1 The length of the independent brake of the mechanical arm in parallel at moment, g is the sampling gap of the general five-moment discretization formula, κ is the selection parameter of the general five-moment discretization formula, h=gλ, O (g 4 ) Is a truncation error.
Further, the discrete recurrent neural network prediction model is characterized by comprising the following specific steps:
wherein ,sa (t k+1 ) At t k+1 Predicted value s of nonlinear power system of mechanical arm connected in parallel at moment a (t k ) At t k Historical value s of nonlinear power system of mechanical arm connected in parallel at moment a (t k-1 ) At t k-1 Historical value s of nonlinear power system of mechanical arm connected in parallel at moment a (t k-2 ) At t k-2 Historical value s of nonlinear power system of mechanical arm connected in parallel at moment a (t k-3 ) At t k-3 Historical value of moment parallel mechanical arm nonlinear power system, g is sampling gap of general five-instantaneous discretization formula, kappa is selection parameter of general five-instantaneous discretization formula, C + Is a matrix of inverse kinematics coefficients.
Further, the method is characterized in that the error of the discrete recurrent neural network prediction model is calculated by the following formula:
||e(t k+1 )|| 2 ＝||s a (t k+1 )-s d (t k+1 )|| 2
wherein ,e(tk+1 ) Prediction error vector s for discrete recurrent neural network prediction model a (t k+1 ) The actual path of the parallel mechanical arm is at t k+1 Path vector of time, s d (t k+1 ) The expected path for the parallel robot arm is at t k+1 Path vector of time.
Further, the inverse kinematics coefficient matrix is obtained by converting a mechanical arm positive kinematics coefficient matrix according to an inverse kinematics principle.
Further, the parallel mechanical arm nonlinear power system is characterized in that a plurality of constraint terms exist, and the constraint terms at least comprise a selection parameter kappa and a design formula parameter lambda of a general five-instant discretization formula.
The prior art is built in a discrete time environment, while the traditional tracking control method is built in a continuous time environment, and strict efficiency analysis is not considered, so that performance is often not satisfactory. Compared with the prior art, the parallel mechanical arm prediction control method based on the discrete recurrent neural network model provided by the application has the advantages that based on the cut-off error, how to keep the tracking precision of the Stuttgart platform is analyzed theoretically, the discrete recurrent neural network model is constructed, the prediction and high-precision real-time tracking of the Stuttgart mechanical arm path are realized, the influence of the discrete recurrent neural network model on the tracking precision under different sampling gap values and different selection parameter values is researched based on the inverse kinematics technology method, and the tracking control efficiency of the discrete recurrent neural network model is further improved.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for the description of the technical solutions will be briefly described below, and it is obvious that the exemplary embodiments of the present application and the descriptions thereof are only for explaining the present application and are not to be construed as unduly limiting the present application, and other drawings can be obtained according to the provided drawings without the need for inventive labor for those skilled in the art. 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 application;
FIG. 2 is a simplified schematic illustration of a Style's platform model with an end effector at the top and a moving platform at the bottom, the two platforms being connected by six independent prism drives for use in the predictive control method of an embodiment of the application;
FIG. 3 is a schematic diagram of a discrete recurrent neural network prediction model in a predictive control method according to an embodiment of the application;
FIG. 4 is a schematic diagram of a change track of coordinates of a Stuttgart platform actual track calculated by a discrete recurrent neural network tracking model at each moment on a X, Y, Z axis in the predictive control method according to the embodiment of the application;
FIG. 5 is a schematic diagram of a variation trace of the velocity of each leg of the Stuttgart platform at each moment calculated by a discrete recurrent neural network tracking model in a predictive control method according to an embodiment of the present application;
FIG. 6 is a schematic diagram of a discrete recurrent neural network tracking model calculation Stuttgart platform l in a predictive control method according to an embodiment of the application 1 、l 2 、l 3 A change track schematic diagram of the length of the number leg at each moment;
FIG. 7 is a schematic diagram of a discrete recurrent neural network tracking model calculation of a Stuttgart platform l in a predictive control method according to an embodiment of the application 4 、l 5 、l 6 A change track schematic diagram of the length of the number leg at each moment;
fig. 8 is a schematic diagram of an actual path and an expected path of a function by an end effector, wherein the actual path and the expected path are drawn by a discrete recurrent neural network prediction model in the prediction control method according to the embodiment of the application under the condition that a sampling gap g=0.01 and a selection parameter k=1/11;
fig. 9 is a schematic diagram of an actual path drawn by a model through an end effector and an expected path of a function itself under the condition that a sampling gap g=0.01 and a selection parameter k=1/11 in a discrete recurrent neural network prediction model in a prediction control method according to an embodiment of the present application, where an angle of fig. 8 is adjusted;
fig. 10 is a schematic diagram of an actual path and an expected path of a function by an end effector, which are drawn by a discrete recurrent neural network prediction model in the prediction control method according to the embodiment of the present application, under the condition that a sampling gap g=0.001 and a selection parameter k=1/11;
fig. 11 is a schematic diagram of an actual path drawn by a model through an end effector and an expected path of a function itself under the condition that a sampling gap g=0.001 and a selection parameter k=1/11 in a discrete recurrent neural network prediction model in a prediction control method according to an embodiment of the present application, where an angle of fig. 10 is adjusted;
fig. 12 is a schematic diagram showing the effect of the values of different selection parameters κ (1/11 < κ < 1/6) on residual error under the condition of sampling gap g=0.01 in the prediction control method according to the embodiment of the present application;
fig. 13 is a schematic diagram showing the effect of the values of different selection parameters κ (1/11 < κ < 1/6) on residual error under the condition of sampling gap g=0.001 in the prediction control method according to the embodiment of the present application.
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
The embodiment provides a parallel mechanical arm prediction control method based on a discrete recurrent neural network model, and referring to fig. 1, the method comprises the following steps:
the method described in this embodiment is applied to a Style platform, which is a parallel robotic arm having six independent prismatic actuators connected to three locations on the floor (i.e., stationary base) of the platform, spanning six mounting points on the ceiling (i.e., mobile platform). The tracking control process of the Stuttgart's stage is to adjust the lengths of the six independent prism actuators to control the Stuttgart's stage's end effector (which is considered the center point of the moving stage) so that the Stuttgart's stage's end effector can track the desired path.
S11: establishing a Stuttgart platform dynamics model and initializing a physical model;
specifically, the discrete recurrent neural network described in this embodiment is defined by a general five-transient discretization formula (FID formula), which is specifically as follows:
wherein g is a sampling gap, κ is a selection parameter, O (g 3 ) For truncation errors, k is the current instant,
k+1 is the future instant in time.
The Stuttgart platform tracking control discrete equation:
in the formula ,sa (t k+1 ) The actual path is at t for the Stuttgart platform k+1 Path vector of time, s d (t k+1 ) The path is expected to be at t for the Stuttgart platform k+1 A path vector of time;
constructing an error vector under continuous time:
e(t k )＝s a (t k )-s d (t k ) (3)
introducing an RNN design formula:
wherein lambda is a design formula parameter;
the combination of equation (3) and equation (4) can be obtained:
wherein ,at t k Time derivative of the actual path of the time-of-day Stuttgart platform,/>At t k The time derivative of the desired path of the time-of-day Stuttgart platform;
further derived based on equation (5):
according to the kinematic system, the kinematic equation is as follows:
wherein C is a coefficient matrix of the mechanical arm positive kinematics, l (t k ) At t k Length matrix of moment arm brake, D (t k ) At t k A global position matrix of the end effector at the moment in time,at t k The speed of the independent brake of the mechanical arm at the moment.
The Stuttgart control equation, namely the parallel mechanical arm dynamics model, is further obtained by combining the formula (6) and the formula (7):
the physical model is initialized, and specifically comprises the positions of an initial base and an upper platform, and initial lengths, positions and angles of six independent prismatic brakes and the central position of an end effector are set.
S12: constructing a Stuttgart platform discrete recurrent neural network model (FID formula DTRNN model);
specifically, according to formula (1), a discrete time-varying recurrent neural network tracking model is obtained:
where λ=h/g, and therefore the value of h depends on the values of λ and g.
According to equation (9), an inverse discretization equation is obtained:
further, performing pseudo inversion on the formula (7) to obtain:
further, a discrete time-varying recurrent neural network prediction model is established, and the structure of the model is shown in fig. 3:
wherein ,sa (t k+1 ) At t k+1 Predicted value s of time Stuttgart platform nonlinear power system a (t k ) At t k Historical value s of time Stuttgart platform nonlinear power system a (t k-1 ) At t k-1 Historical value s of time Stuttgart platform nonlinear power system a (t k-2 ) At t k-2 Historical value s of time Stuttgart platform nonlinear power system a (t k-3 ) At t k-3 Historical values of a nonlinear power system of a time Stuttgart platform, g is a sampling gap of a general five-instantaneous discretization formula, and kappa is a general five-instantaneousThe selection parameter of the time discretization formula is a constant between 1/12 and 1/6, C + Is a matrix of inverse kinematics coefficients.
C + In order to predict 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 coefficient matrix of the inverse kinematics.
S13: acquiring an initial value of a Stuttgart platform nonlinear power system;
inputting a constructed Stuttgart platform nonlinear power system expected path, 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 acquiring a prism driver length (leg length) vector l (t) of the mechanical arm 0 ) Leg speed vectorActual position vector s a (t 0 ) And the time derivative of the actual position vector +.>Obtaining physical model parameters of the parallel mechanical arm, such as Euler angle theta, platform coordinate a, global coordinate b and global coordinate p of the zero position of the platform coordinate;
s14: carrying out predictive control on paths of the nonlinear power system of the parallel mechanical arm based on a discrete recurrent neural network model;
adjusting super parameters of a discrete recurrent neural network model, wherein the super parameters comprise a time domain, a step length and a sampling gap g in an FID formula, selecting parameters kappa, performing model training to study the influence of setting of different super parameters on the tracking precision of the discrete recurrent neural network model, performing simulation on the discrete recurrent neural network model obtained by training by using MATLAB, and obtaining a path predicted value s output by a Stuttgart platform nonlinear power system a (t k+1 )；
S15: calculating the precision of a Stuttgart platform discrete recurrent neural network model 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, so as to carry out the adjustment of the super parameters of the discrete recurrent neural network model and the training of the model again;
specifically, an error formula for obtaining the predicted value of the discrete recurrent neural network model at each moment is:
||e(t k+1 )|| 2 ＝||s a (t k+1 )-s d (t k+1 )|| 2 (13)
wherein ,e(tk+1 ) Prediction error vector s for discrete recurrent neural network prediction model a (t k+1 ) The actual path is at t for the Stuttgart platform k+1 Path vector of time, s d (t k+1 ) The path is expected to be at t for the Stuttgart platform k+1 The path vector at the moment is modulo-evaluated.
The discrete-time tracking control of the stutter platform is defined as being generated by the smooth continuous-time tracking control of the stutter platform. In the solving process, all discrete time matrices/vectors can be regarded as discrete mappings of corresponding continuous time matrices/vectors. That is, the time derivative of the discrete time matrix/vector is 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 embodiment carries out a simulation experiment based on MATLAB software, and the simulation process is specifically as follows:
s21: specifying a desired trajectory;
in particular, the method comprises the steps of,
s22: defining a Stuttgart platform rotation matrix A;
specifically, the rotation matrix on the X-axis component
Rotation matrix on Y-axis component
Rotation matrix on Z-axis component
Rotation matrix a=axayaz, where θ is the euler angle, θ= [ θx, θy, θz] T In this simulation example, the initial value of θ is a vector (0, pi/2).
S23: setting discrete recurrent neural network model parameters;
specifically, given a sampling gap g, a selection parameter k, a design parameter λ, and tracking prediction of a trajectory using a discrete recurrent neural network model, in this embodiment, comparative simulation experiments were performed on the sampling gaps g=0.01, g=0.001, (where when g=0.01, the design parameter λ=3, and when g=0.001, the design parameter λ=30) and the selection parameters are k=1/7, k=1/8, k=1/9, k=1/10, and k=1/11, respectively.
S24: analyzing a track tracking prediction result;
specifically, referring to fig. 4, fig. 4 shows a change track of coordinates of a actual track of the stuttt platform calculated by the discrete recurrent neural network model at each moment on the X, Y, Z axis;
referring to fig. 5, fig. 5 shows a trajectory of the velocity of each leg of the stutter platform calculated by the discrete recurrent neural network model at each time;
referring to FIG. 6, FIG. 6 shows a discrete recurrent neural network model calculation of the Stuttgart platform l 1 、l 2 、l 3 The length change track of the number leg at each moment;
referring to FIG. 7, FIG. 7 shows a discrete recurrent neural network model calculation of the Stuttgart platform l 4 、l 5 、l 6 Length of number leg at each momentA change track;
as can be seen from the graph, with the increase of time, the component of the actual track at X, Y, Z axis, the length of the six legs of the ston platform and the speed of each mechanical arm all change periodically and regularly, which fully indicates 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 track and the track tracking result are shown in fig. 8, 9, 10 and 11. Note that fig. 8, 9 are obtained with the sampling gap g=0.01; fig. 10, 11 are obtained with a sampling gap g=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;
to better show the results of the numerical experiments, the state of another view of fig. 8 is shown in fig. 9. Similarly, fig. 11 is also rotated by fig. 10, and the actual trajectory is completely consistent with the expected trajectory at two different sampling intervals, which fully demonstrates the accuracy and effectiveness of the proposed discrete recurrent neural network model trajectory prediction tracking.
S25: analyzing the influence of the selection parameter kappa on the discrete recurrent neural network model;
specifically, for the discrete recurrent neural network model, in this embodiment, under the condition of sampling gap g=0.01 and g=0.001, parameters k=1/7, k=1/8, k=1/9, k=1/10 and k=1/11 are selected respectively for comparison experiments;
firstly, taking the sampling gap g=0.01 to study the influence of the selection parameters on the solving error, and the experimental result is that the maximum steady-state solving error of the discrete recurrent neural network model is converged to 10 as shown in fig. 12 -8 The accuracy of the representation meets the expectations, as the parameter kappa decreases, the error of the solution also decreases, and the degree of decrease is consistent;
similarly, taking the sampling gap g=0.001 to study the effect of parameters on solution error, the results are shown in fig. 13, the most discrete recurrent neural network modelLarge steady state solution error converges to 10 -12 The accuracy still meets the expectations, and when the sampling gap g=0.001, the variation trend of the residual error is consistent with the result when the sampling gap g=0.01.
Simulation experiments of the embodiment prove that the prediction control accuracy of the discrete recurrent neural network model is high, and real-time control and prediction can be performed. Research shows that the selection of the parameter kappa has a decisive effect on improving the efficiency of the model, if the model efficiency needs to be improved, the accuracy is highest when the sampling parameter kappa=1/11, and the system efficiency can be effectively improved in actual operation.
According to the discrete recurrent neural network model predictive control method for the parallel mechanical arm with high precision and high efficiency, the neural network is combined with model predictive control, so that the system control performance is excellent. In addition, the method can realize the following technical advantages: the method is simple to realize and easy to operate, and does not need to adjust too many parameters; and has higher control precision and certain robustness.
In addition, the embodiment of the application also provides a computer readable storage medium, wherein the computer readable storage medium can store a program, and the program when executed comprises part or all of the steps of any parallel mechanical arm prediction control method based on the discrete recurrent neural network model described in the embodiment of the method.
In addition, each functional unit in the embodiments of the present application may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit. The integrated units may be implemented in hardware or in software functional units.
The integrated units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable memory. Based on this understanding, the technical solution of the present application may be embodied essentially or partly in the form of a software product, or all or part of the technical solution, 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 perform all or part of the steps of the method according to the embodiments of the present application. And the aforementioned memory includes: a U-disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a removable hard disk, a magnetic disk, or an optical disk, or other various media capable of storing program codes.
Those of ordinary skill in the art will appreciate that all or a portion of the steps in the various methods of the above embodiments may be implemented by a program that instructs associated hardware, and the program may be stored in a computer readable memory, which may include: flash disk, read-only memory, random access memory, magnetic or optical disk, etc.
The foregoing embodiments have been provided for the purpose of illustrating the general principles of the present application in further detail, and are not to be construed as limiting the scope of the application, but are merely intended to cover any modifications, equivalents, improvements, etc. based on the teachings of the application.
Claims (9)
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 defined by a general five-instant 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;
carrying out predictive control on paths of the nonlinear power system of the parallel mechanical arm based on a discrete recurrent neural network model;
the discrete recurrent neural network model comprises a discrete recurrent neural network tracking model and a discrete recurrent neural network prediction model, wherein the discrete recurrent neural network tracking model is used for tracking the length change of the independent brake of the parallel mechanical arm, and the discrete recurrent neural network prediction model is used for performing predictive control on the path of the nonlinear power system of the parallel mechanical arm.
2. The parallel mechanical arm prediction control method based on the discrete recurrent neural network model according to claim 1, wherein the parallel mechanical arm is a Stuttgart 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 Stuttgart platform controls an end effector to track a 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 according to claim 2, wherein the construction process of the parallel mechanical arm dynamics model is specifically as follows: constructing a parallel mechanical arm tracking control discrete equation:
wherein ,sa (t k+1 ) The actual path of the parallel mechanical arm is at t k+1 Path vector of time, s d (t k+1 ) The expected path for the parallel robot arm is at t k+1 A path vector of time;
constructing an error vector under continuous time:
e(t k )＝s a (t k )-s d (t k ) (2)
introducing an RNN design formula:
wherein lambda is a design formula parameter;
the combination of equation (2) and equation (3) yields:
wherein ,at t k Time derivative of real path of moment parallel mechanical arm, < ->At t k Time derivative of expected path of mechanical arm connected in parallel at moment;
derived based on equation (4):
constructing a kinematic equation of the parallel mechanical arm:
wherein C is a coefficient matrix of the positive kinematics of the parallel mechanical arm, l (t k ) At t k Length matrix of independent brakes of mechanical arm connected in parallel at moment, D (t k ) At t k A global position matrix of the end effector of the mechanical arm is connected in parallel at any time,at t k The speed of the independent brake of the mechanical arm is connected in parallel at any moment;
and (3) pushing out a parallel mechanical arm dynamics model by combining the formula (5) and the formula (6):
4. the parallel mechanical arm prediction control method based on the discrete recurrent neural network model according to claim 3, wherein the discrete recurrent neural network tracking model is specifically as follows:
wherein ,l(tk+1 ) At t k+1 The length of the independent brake of the mechanical arm in parallel at moment, g is the sampling gap of the general five-moment discretization formula, κ is the selection parameter of the general five-moment discretization formula, h=gλ, O (g 4 ) Is a truncation error.
5. The parallel robot prediction control method based on the discrete recurrent neural network model as claimed in claim 4, wherein the discrete recurrent neural network prediction model is specifically as follows:
wherein ,sa (t k+1 ) At t k+1 Predicted value s of nonlinear power system of mechanical arm connected in parallel at moment a (t k ) At t k Historical value s of nonlinear power system of mechanical arm connected in parallel at moment a (t k-1 ) At t k-1 Historical value s of nonlinear power system of mechanical arm connected in parallel at moment a (t k-2 ) At t k-2 Historical value s of nonlinear power system of mechanical arm connected in parallel at moment a (t k-3 ) At t k-3 Historical value of moment parallel mechanical arm nonlinear power system, g is sampling gap of general five-instantaneous discretization formula, kappa is selection parameter of general five-instantaneous discretization formula, C + Is a matrix of inverse kinematics coefficients.
6. The parallel robot prediction control method based on the discrete recurrent neural network model according to claim 5, wherein the error of the discrete recurrent neural network prediction model is calculated by the following formula:
||e(t k+1 )|| 2 ＝||s a (t k+1 )-s d (t k+1 )|| 2
wherein ,e(tk+1 ) Prediction error vector s for discrete recurrent neural network prediction model a (t k+1 ) The actual path of the parallel mechanical arm is at t k+1 Path vector of time, s d (t k+1 ) The expected path for the parallel robot arm is at t k+1 Path vector of time.
7. The parallel robot prediction control method based on the discrete recurrent neural network model according to claim 6, wherein the inverse kinematics coefficient matrix is obtained by converting a robot forward kinematics coefficient matrix according to an inverse kinematics principle.
8. The parallel mechanical arm prediction control method based on the discrete recurrent neural network model according to claim 1, wherein a plurality of constraint terms exist in the nonlinear power system of the parallel mechanical arm, and the constraint terms at least comprise a selection parameter kappa and a design formula parameter lambda of a general five-instant discretization formula.
9. A computer-readable storage medium, wherein the storage medium contains the parallel robot arm predictive control method based on the discrete recurrent neural network model according to any one of claims 1 to 8.
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