CN115042190A - Optimization method for series robot dynamics parameter identification excitation track - Google Patents
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Abstract
The invention discloses an optimization method for identifying excitation tracks by kinetic parameters of a series robot, which comprises the following steps: s1: establishing a Newton-Euler dynamic model of the series robot; s2: linearizing the nonlinear terms in the kinetic model in the step S1, and obtaining a linear kinetic model based on the modified DH method; s3: solving the minimum parameter set of the multi-joint mechanical arm dynamics to obtain a simplified model of the multi-joint mechanical arm dynamics model; s4: and recombining the standard parameters by a numerical method of QR decomposition or linear relation mapping to obtain an observation matrix W. The optimization method for identifying the excitation track by the kinetic parameters of the series robot can find the excitation track parameters meeting the constraint in the shortest time, can reduce the complexity in the calculation process, and can reduce the required condition number, thereby improving the accuracy of parameter identification and the robustness of the identification result to noise.
Description
Technical Field
The invention relates to track optimization of an industrial robot, in particular to an optimization method for identifying an excitation track by using kinetic parameters of a serial robot.
Background
Modern robotic arm applications require high precision and high speed, such as advanced manufacturing and multi-robot system control. These applications typically require advanced model-based control algorithms or torque input-based control algorithms. Such a control scheme requires accurate knowledge of the kinetic parameters of the robot arm. However, many robot manufacturers do not provide these parameters or provide only partial information. Therefore, identification or calibration by experiment is a relatively reliable method to obtain this information. The design of the excitation trajectory is very important in the parameter identification of the robot. During the excitation of the trajectory, the dynamic parameters of the manipulator should be completely simulated and the influence of noise on the measurements should be minimized, in order to estimate the parameters only quickly and accurately and to ensure the identification accuracy.
According to the publication: CN111775140A, published as the invention patent application 2020-10-16, discloses an optimization method for multi-joint mechanical arm dynamics parameter identification excitation track, which is carried out according to the following steps: step 1, establishing a dynamic model of the multi-joint mechanical arm by using a Newton-Euler method, and carrying out linearization processing on a nonlinear item in the dynamic model so as to obtain a linearized dynamic model of the multi-joint mechanical arm; step 2, solving the linearized dynamic model of the multi-joint mechanical arm based on a random digital-analog parameter method to obtain the minimum dynamic parameter set of the multi-joint mechanical arm and obtain a simplified model of the dynamic model of the multi-joint mechanical arm; step 3, establishing a mathematical model of the multi-joint mechanical arm dynamics parameter identification excitation track, obtaining an observation matrix function according to a simplified model of the multi-joint mechanical arm dynamics model, and establishing an identification excitation track model consisting of an optimization objective function of the identification excitation track and constraint conditions according to the observation matrix function; and 4, optimizing the identification excitation track model according to a quantum genetic algorithm to obtain an excitation track meeting joint constraint conditions and changing in a space range, wherein the excitation track is used for parameter identification of multi-joint mechanical arm dynamics. The main technical effects are as follows: establishing a multi-joint mechanical arm linearization dynamic model through analyzing the dynamic performance of the multi-joint mechanical arm, determining a minimum kinetic parameter set of the multi-joint mechanical arm by a random number method, establishing an identification excitation track by introducing a finite term Fourier series method, setting a condition number of the minimum kinetic parameter set corresponding to a generalized observation matrix as an identification excitation track optimization objective function, optimizing the excitation track suitable for identifying the kinetic parameters of the multi-joint mechanical arm by adopting a quantum genetic algorithm, solving the problems that the excitation track optimization algorithm has more iteration times and is easy to fall into a local extreme value, optimizing the excitation track meeting joint constraint conditions and changing in a space range based on the quantum genetic algorithm, the optimization algorithm can quickly converge the optimized excitation track, has better robustness, and provides a new method for optimizing the excitation track required by the multi-joint mechanical arm dynamics parameter identification.
Regarding the optimization criterion of the excitation trajectory, in order to obtain good performance and reduce the influence of noise errors on parameter estimation, the condition number Cond (-) of the minimization regression matrix is usually adopted as an optimization target criterion. Or the logarithm of the Fisher information matrix determinant, Log { det (·) }, can be used as an optimization criterion to optimize the trajectory. Can also be judged by a method based on a Hadamard inequality
As an optimization criterion to reduce the complexity and computation time of finding the optimal trajectory. Another common method is to add disturbance features, such as noise, during the optimization process, which can effectively improve the accuracy of parameter identification. The method for optimizing the kinetic parameters of the series robot to identify the excitation track adopts disturbance characteristics to optimize, so that the calculation complexity and the time loss in the optimization process are increased, the influence of noise errors on parameter identification can be reduced in the excitation track optimization process, the calculation complexity in the optimization process is reduced, the time loss is reduced, and the optimized identification excitation track meets the boundary requirement and has better excitation.
Disclosure of Invention
The invention aims to provide an optimization method for identifying excitation tracks by kinetic parameters of a series robot, so that the influence of noise errors on parameter identification can be reduced in the excitation track optimization process, the computational complexity in the optimization process is reduced, the time loss is reduced, and the optimized identification excitation tracks meet the boundary requirements and have better excitation.
In order to achieve the above purpose, the invention provides the following technical scheme: an optimization method for identifying excitation tracks by kinetic parameters of a series robot comprises the following steps:
s1: establishing a Newton-Euler dynamic model of the series robot;
s2: linearizing the nonlinear terms in the kinetic model in the step S1, and obtaining a linear kinetic model based on the modified DH method;
s3: solving the minimum parameter set of the multi-joint mechanical arm dynamics to obtain a simplified model of the multi-joint mechanical arm dynamics model;
s4: recombining the standard parameters by a numerical method of QR decomposition or linear relation mapping to obtain an observation matrix W;
s5: establishing a mathematical model for identifying the excitation trajectory by the kinetic parameters of the serial robot based on Fourier series;
s6: by introducing a Hadamard inequality optimization criterion as one of constraint conditions and taking the condition Cond (W) of an observation matrix as an optimization standard for identifying an excitation track optimization objective function, an optimal excitation track fully representing mechanical characteristics of an actual robot system is obtained and is used for parameter identification of multi-joint mechanical arm dynamics.
Preferably, step S6 is performed as follows:
s6.1: setting an optimized approach value delta, and setting joint positions and constraint conditions of acceleration;
s6.2: randomly generating 2N +1 parameters of a Fourier excitation track of a single joint in an interval of [ -2,2], wherein the harmonic number N is usually 5, and the sampling frequency is 100 HZ;
s6.3, generating an initial coefficient through preliminary optimization, establishing an optimized objective function according to a Hadamard inequality, and performing optimization solution on the optimized objective function through sequential quadratic programming using an fmincon function in an MATLAB toolbox; in solving quadratic programmingIn the iterative process of the subproblem, the Hessian approximate matrix is updated to the optimal solution, so that the initial position q under the constraint space is quickly generated i,0 And Fourier coefficient a i,k 、b i,k ；
S6.4: optimizing an objective function Cond (W) through an fmincon function based on an interior point method according to the initial optimization local optimal value obtained in the S6.3 until a feasible solution meets a constraint objective;
s6.5: at this time, whether the condition number of the result after the optimization of S6.4 is smaller than the optimization approach value delta set by the joint is judged, if so, the optimization result is retained and the process enters S6.6, if not, the group of parameters is abandoned, and the process returns to S6.2 to regenerate a group of random parameters and re-execute S6.2-S6.5;
s6.6: substituting the optimization result obtained in the step S6.5 into the mathematical model for identifying the excitation track established in the step S3, respectively judging whether the mathematical model meets joint position, speed and acceleration constraint conditions, and if so, obtaining the optimal excitation track which meets the joint constraint conditions and changes in a space range; if not, the set of parameters is discarded, and the process returns to S6.2 to regenerate a set of random parameters and repeats S6.2-S6.6.
Preferably, in step 6.1, the constraint conditions of joint position and acceleration are as shown in equation (8):
in the formula,
respectively represents the joint angle, angular velocity and angular acceleration of the ith joint at the time point t, q max Is the maximum value of the joint angle,
is the maximum value of the angular velocity of the joint,
maximum value of angular acceleration of joint, t 0 、t f Respectively representing a start point and an end point.
Preferably, in step 6.3, first, according to the Hadamard inequality, as shown in equation (9):
an optimization objective function established based on the Hadamard inequality is shown as the formula (10):
W kg sequence quadratic programming pairs using fmincon functions in MATLAB toolbox for the kth-column-wise kth element of the observation matrix W
Carrying out optimization solution; in the iterative process of solving the quadratic programming subproblem, the Hessian approximate matrix is updated until the optimal solution is obtained, so that the initial position q under the constraint space is quickly generated i,0 And Fourier coefficient a i,k 、b i,k 。
Preferably, in step 6.4, the objective function cond (w) is optimized by fmincon function based on the interior point method according to the local optimal value obtained in step 6.3 until the feasible solution meets the constraint objective.
In the technical scheme, the optimization method for identifying the excitation track by the kinetic parameters of the series robot, provided by the invention, has the following beneficial effects:
1. according to the method, an accurate series robot dynamics model is established, a minimum dynamics parameter set is obtained, the model for identifying the excitation track is designed according to finite term Fourier series parameters, so that an observation matrix W is obtained, the condition number of the observation matrix is still used as an optimal target function for identifying the excitation track, the Hadamard inequality is introduced as one of constraint conditions, the excitation track parameters meeting the constraint can be found in the shortest time, and the complexity in the calculation process can be reduced.
2. The method can reduce the required condition number after optimization, thereby improving the accuracy of parameter identification and the robustness of the identification result to noise, and providing a new method for excitation track optimization required by the kinetic parameter identification of the tandem robot.
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In order to more clearly illustrate the embodiments of the present application or technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present invention, and other drawings can be obtained by those skilled in the art according to the drawings.
FIG. 1 is a flow chart of optimizing the excitation trajectory based on the criteria set forth in step S6 according to the present invention;
FIG. 2 is a graph of the number of conditions over time during an optimization process provided by an embodiment of the present invention;
FIG. 3a is a graph of the relationship between the angle of each joint and the time of the optimized excitation trajectory according to the embodiment of the present invention
FIG. 3b is a graph of angular velocity of each joint of the optimized excitation trajectory versus time provided by an embodiment of the present invention;
FIG. 3c is a graph of angular acceleration of each joint versus time for an optimized excitation trajectory provided by an embodiment of the present invention;
fig. 4 is a graph of the number of conditions over time during the control optimization provided by an embodiment of the 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.
An optimization method for identifying excitation tracks by kinetic parameters of a series robot comprises the following steps:
s1: establishing a Newton-Euler dynamic model of the series robot;
establishing an n-degree-of-freedom series robot Newton-Euler dynamic model as shown in the formula (1):
in the formula (1), τ d Shows the torque of each joint of the robot arm, q,
Representing the joint angular position, joint angular velocity, and joint angular acceleration of the mechanical arm, m (q) is an inertia matrix,
in order to write the friction force as a linear relationship, a coulomb-viscous friction force model is used to describe the term, which is expressed as formula (2):
in the formula (2), f c 、f v Respectively representing the Coulomb and viscous friction coefficients, f b Representing viscous friction compensation, and adding the formula (2) into the identification model for identification;
s2: linearizing the nonlinear terms in the kinetic model in the step S1, and obtaining a linear kinetic model based on the modified DH method;
linear models are usually based on a modified DH method, and can be obtained to contain N s A linear model of the standard parameters is represented by the following formula (3):
in the formula (3), the reaction mixture is,
a regression matrix of a non-linear function of the joint position, velocity and acceleration vectors,
is a standard parameter vector to be estimated;
s3: solving the minimum parameter set of the multi-joint mechanical arm dynamics to obtain a simplified model of the multi-joint mechanical arm dynamics model;
s4: the standard parameters are recombined by a numerical method of QR decomposition or linear relation mapping, and N is obtained from the standard parameters b The observation matrix of the estimated parameters is expressed by equation (4):
wherein,
is the number of samples, ω s For sampling frequency, ω f Is a periodic track base;
s5: establishing a mathematical model for identifying the excitation trajectory by the kinetic parameters of the serial robot based on Fourier series;
the motion trajectory of the ith joint can be defined as a function of time t in the following way, the function is composed of the finite sum of N harmonic sine and cosine functions, and the formula is as follows (5):
in the formula, ω fi A fundamental frequency that is a Fourier series; the joints of the mechanical arm adopt the same fundamental frequency to ensure the periodicity of excitation tracks, and the parameterized motion track of each joint of the space robot contains 13 Fourier coefficients [ q [ [ q ] i,0 ,a i,1 ...a i,5 ,b i,1 ...b i,5 ]；q i,0 In order to set the i-th joint initial position,a i,k 、b i,k the amplitudes of the sine and cosine functions.
The first and second derivatives with respect to time for equation (5) can yield the angular velocity of joint i
And angular acceleration
As shown in formulas (6) and (7):
the above steps S1-S5 are conventional in the art and do not perform excessive unfolding.
S6: by introducing a Hadamard inequality optimization criterion as one of constraint conditions and taking the condition Cond (W) of an observation matrix as an optimization standard for identifying an excitation track optimization objective function, an optimal excitation track which fully represents the mechanical characteristics of an actual robot system is obtained and is used for parameter identification of multi-joint mechanical arm dynamics;
step S6 is performed as follows:
s6.1: setting an optimized approach value delta, and setting joint positions and constraint conditions of acceleration;
the constraint conditions of the joint position and the acceleration are shown in formula (8):
in the formula,
respectively showing the joint angle and angle of the ith joint at time tVelocity, angular acceleration, q max Is the maximum value of the joint angle,
is the maximum value of the angular velocity of the joint,
maximum value of angular acceleration of joint, t 0 、t f Respectively representing a starting point and an end point;
s6.2: randomly generating 2N +1 parameters of a Fourier excitation track of a single joint in an interval of [ -2,2], wherein the harmonic number N is usually 5, and the sampling frequency is 100 HZ;
s6.3, generating an initial coefficient through preliminary optimization;
establishing an optimization objective function according to a Hadamard inequality, wherein the Hadamard inequality is shown as a formula (9):
an optimization objective function established based on the Hadamard inequality is shown as the formula (10):
wherein, W kg For observing the kth element of the g-th column of the matrix W, a pair of sequence quadratic plans (sqp) in the MATLAB toolbox using the fmincon function
Carrying out optimization solution; in the iterative process of solving the quadratic programming subproblem, the Hessian approximate matrix is updated until the optimal solution is obtained, so that the initial position q under the constraint space is quickly generated i,0 And Fourier coefficient a i,k 、b i,k M is a radical of formula (4) in S4 above, N b Is obtained in the above S4;
s6.4: optimizing an objective function Cond (W) through an fmincon function based on an interior point method according to the initial optimization local optimal value obtained in the S6.3 until a feasible solution meets a constraint target;
the excitation trajectory optimization problem can therefore be described in the form:
the above objective function is expressed as:
arg min(Cond(W))≤Δ
the constraint targets are expressed as:
s6.5: at this time, whether the condition number of the result after the optimization of S6.4 is smaller than the optimization approach value delta set by the joint is judged, if so, the optimization result is retained and the process enters S6.6, if not, the group of parameters is abandoned, and the process returns to S6.2 to regenerate a group of random parameters and re-execute S6.2-S6.5;
s6.6: substituting the optimization result obtained in the step S6.5 into the mathematical model for identifying the excitation track established in the step S3, respectively judging whether the mathematical model meets joint position, speed and acceleration constraint conditions, and if so, obtaining the optimal excitation track which meets the joint constraint conditions and changes in a space range; if not, the set of parameters is discarded, and the process returns to S6.2 to regenerate a set of random parameters and repeats S6.2-S6.6.
As a first embodiment provided by the present invention, the specific implementation of the excitation trajectory identification optimization method for the kinetic parameters of a seven-degree-of-freedom series robot is performed as follows:
s1, establishing a Newton-Euler dynamic model of the series robot;
s2, processing nonlinear terms in the dynamic model in a linearization mode, and therefore obtaining a dynamic model based on the improved DH method;
s3, solving the minimum parameter set of the multi-joint mechanical arm dynamics to obtain a simplified model of the multi-joint mechanical arm dynamics model;
s4, recombining the standard parameters by a numerical method of QR decomposition or linear relation mapping to obtain an observation matrix W;
s5: establishing a mathematical model for identifying excitation tracks by kinetic parameters of the serial robot based on Fourier series, wherein the fundamental frequency is 0.1 pi, the total time is 20s, five Fourier series (N is 5) are contained in the tracks, and the constraint value of the optimized excitation tracks is shown in a table 2;
s6: the optimization target value Δ is set to 6.40, and the joint position and the constraint conditions of the acceleration are set as shown in table 1;
TABLE 1 seven-DOF robot motion constraint
Step 6.1: in the interval [ -2,2 [)]6.5 undetermined coefficients [ q ] of excitation track of each joint of internally generated serial robot i,0 ,a i,1 ...a i,5 ,b i,1 ...b i,5 ]；
Step 6.2: the excitation trajectory optimization execution flow is shown in fig. 1, and the condition number of the observation matrix is used as an optimization standard for identifying an excitation trajectory optimization target function by introducing a Hadamard inequality optimization criterion as one of constraint conditions, so that an optimal excitation trajectory fully representing the dynamic characteristics of an actual robot system is obtained. The iterative optimization process of the objective function is as shown in fig. 2, and it can be seen from the figure that the objective function approaches stability around 15 generations, the change of the optimization objective function value after 20 generations is small, and finally the iteration is finished and the condition number optimal value 60.046.23 is reached when the iteration reaches 23 generations, and fig. 3a, fig. 3b and fig. 3c are excitation locus diagrams after optimization. In order to embody the rapid convergence of the present invention, a single optimization criterion (cond (w)) is used to obtain the excitation trajectory as a control group, and fig. 4 is an optimization process of one control group. A comparison of the two optimization methods is given in table 2.
TABLE 2 time comparison of execution times
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The principle and the implementation mode of the invention are explained by applying specific embodiments in the invention, and the description of the embodiments is only used for helping to understand the method and the core idea of the invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present specification should not be construed as a limitation to the present invention.
An embodiment of the present application further provides a specific implementation manner of an electronic device, which is capable of implementing all steps in the method in the foregoing embodiment, where the electronic device specifically includes the following contents:
a processor (processor), a memory (memory), a communication Interface (Communications Interface), and a bus;
the processor, the memory and the communication interface complete mutual communication through the bus;
the processor is configured to call a computer program in the memory, and the processor implements all the steps of the method in the above embodiments when executing the computer program, for example, the processor implements the following steps when executing the computer program:
s1: establishing a Newton-Euler dynamic model of the series robot;
s2: linearizing the nonlinear terms in the kinetic model in the step S1, and obtaining a linear kinetic model based on the modified DH method;
s3: solving the minimum parameter set of the multi-joint mechanical arm dynamics to obtain a simplified model of the multi-joint mechanical arm dynamics model;
s4: recombining the standard parameters by a numerical method of QR decomposition or linear relation mapping to obtain an observation matrix W;
s5: establishing a mathematical model for identifying the excitation trajectory by the kinetic parameters of the serial robot based on Fourier series;
s6: by introducing a Hadamard inequality optimization criterion as one of constraint conditions and taking the condition Cond (W) of an observation matrix as an optimization standard for identifying an excitation track optimization objective function, an optimal excitation track fully representing mechanical characteristics of an actual robot system is obtained and is used for parameter identification of multi-joint mechanical arm dynamics.
Embodiments of the present application also provide a computer-readable storage medium capable of implementing all the steps of the method in the above embodiments, where the computer-readable storage medium stores thereon a computer program, and the computer program when executed by a processor implements all the steps of the method in the above embodiments, for example, the processor implements the following steps when executing the computer program:
s1: establishing a Newton-Euler dynamic model of the series robot;
s2: linearizing the nonlinear terms in the kinetic model in the step S1, and obtaining a linear kinetic model based on the modified DH method;
s3: solving the minimum parameter set of the multi-joint mechanical arm dynamics to obtain a simplified model of the multi-joint mechanical arm dynamics model;
s4: recombining the standard parameters by a numerical method of QR decomposition or linear relation mapping to obtain an observation matrix W;
s5: establishing a mathematical model for identifying the excitation trajectory by the kinetic parameters of the serial robot based on Fourier series;
s6: by introducing a Hadamard inequality optimization criterion as one of constraint conditions and taking the condition Cond (W) of an observation matrix as an optimization standard for identifying an excitation track optimization objective function, an optimal excitation track fully representing mechanical characteristics of an actual robot system is obtained and is used for parameter identification of multi-joint mechanical arm dynamics.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the hardware + program class embodiment, since it is substantially similar to the method embodiment, the description is simple, and the relevant points can be referred to the partial description of the method embodiment. Although embodiments of the present description provide method steps as described in embodiments or flowcharts, more or fewer steps may be included based on conventional or non-inventive means. The order of steps recited in the embodiments is merely one manner of performing the steps in a multitude of orders and does not represent the only order of execution. When an actual apparatus or end product executes, it may execute sequentially or in parallel (e.g., parallel processors or multi-threaded environments, or even distributed data processing environments) according to the method shown in the embodiment or the figures. The terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, the presence of additional identical or equivalent elements in a process, method, article, or apparatus that comprises the recited elements is not excluded. For convenience of description, the above devices are described as being divided into various modules by functions, and are described separately. Of course, in implementing the embodiments of the present description, the functions of each module may be implemented in one or more software and/or hardware, or a module implementing the same function may be implemented by a combination of multiple sub-modules or sub-units, and the like. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and other divisions may be realized in practice, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form. The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
As will be appreciated by one skilled in the art, embodiments of the present description may be provided as a method, system, or computer program product. Accordingly, embodiments of the present description may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, embodiments of the present description may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and so forth) having computer-usable program code embodied therein. The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the system embodiment, since it is substantially similar to the method embodiment, the description is simple, and for the relevant points, reference may be made to the partial description of the method embodiment. In the description of the specification, reference to the description of "one embodiment," "some embodiments," "an example," "a specific example," or "some examples" or the like means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the embodiments of the specification.
In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction. The above description is only an example of the embodiments of the present disclosure, and is not intended to limit the embodiments of the present disclosure. Various modifications and variations to the embodiments described herein will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the embodiments of the present specification should be included in the scope of the claims of the embodiments of the present specification.
Claims (6)
1. An optimization method for identifying excitation tracks by dynamic parameters of a series robot is characterized by comprising the following steps:
s1: establishing a Newton-Euler dynamic model of the series robot;
s2: linearizing the nonlinear terms in the kinetic model in the step S1, and obtaining a linear kinetic model based on the modified DH method;
s3: solving the minimum parameter set of the multi-joint mechanical arm dynamics to obtain a simplified model of the multi-joint mechanical arm dynamics model;
s4: recombining the standard parameters by a numerical method of QR decomposition or linear relation mapping to obtain an observation matrix W;
s5: establishing a mathematical model for identifying the excitation trajectory by the kinetic parameters of the serial robot based on Fourier series;
s6: by introducing a Hadamard inequality optimization criterion as one of constraint conditions and taking the condition Cond (W) of an observation matrix as an optimization standard for identifying an excitation track optimization objective function, an optimal excitation track fully representing mechanical characteristics of an actual robot system is obtained and is used for parameter identification of multi-joint mechanical arm dynamics.
2. The optimization method for identifying the excitation trajectory according to the kinetic parameters of the tandem robot as claimed in claim 1, wherein the step S6 is performed as follows:
s6.1: setting an optimized approach value delta, and setting joint positions and constraint conditions of acceleration;
s6.2: randomly generating 2N +1 parameters of a Fourier excitation track of a single joint in an interval of [ -2,2], wherein the harmonic number N is usually 5, and the sampling frequency is 100 HZ;
s6.3, generating initial coefficients through preliminary optimization, establishing an optimized target function according to a Hadamard inequality, and using a sequence two of fmincon functions in an MATLAB toolboxThe secondary planning optimizes and solves the optimized objective function; in the iterative process of solving the quadratic programming subproblem, the Hessian approximate matrix is updated to an optimal solution, so that the initial position q under the constraint space is quickly generated i,0 And Fourier coefficient a i,k 、b i,k ；
S6.4: optimizing an objective function Cond (W) through an fmincon function based on an interior point method according to the initial optimization local optimal value obtained in the S6.3 until a feasible solution meets a constraint objective;
s6.5: at this time, whether the condition number of the result after the optimization of S6.4 is smaller than the optimization approach value delta set by the joint is judged, if so, the optimization result is retained and the process enters S6.6, if not, the group of parameters is abandoned, and the process returns to S6.2 to regenerate a group of random parameters and re-execute S6.2-S6.5;
s6.6: substituting the optimization result obtained in the step S6.5 into the mathematical model for identifying the excitation track established in the step S3, respectively judging whether the mathematical model meets joint position, speed and acceleration constraint conditions, and if so, obtaining the optimal excitation track which meets the joint constraint conditions and changes in a space range; if not, the set of parameters is discarded, and the process returns to S6.2 to regenerate a set of random parameters and repeats S6.2-S6.6.
3. The optimization method for the series robot dynamics parameter identification excitation trajectory according to claim 2, wherein in step 6.1, the constraint conditions of joint position and acceleration are as shown in formula (8):
in the formula, q i (t)、
Respectively represents the joint angle, angular velocity and angular acceleration of the ith joint at the time t, q max Is the maximum value of the joint angle,
is the maximum value of the angular velocity of the joint,
maximum value of angular acceleration of joint, t 0 、t f Respectively representing a start point and an end point.
4. The optimization method for series robot dynamics parameter identification excitation trajectory according to claim 2, characterized in that in step 6.3, first, according to Hadamard inequality, as shown in equation (9):
an optimization objective function established based on the Hadamard inequality is shown as the formula (10):
W kg sequence quadratic programming pairs using fmincon functions in MATLAB toolbox for observing the kth element of the g-th column of the matrix W
Carrying out optimization solution; in the iterative process of solving the quadratic programming subproblem, the Hessian approximate matrix is updated until the optimal solution is obtained, so that the initial position q under the constraint space is quickly generated i,0 And Fourier coefficient a i,k 、b i,k 。
5. The optimization method for series robot dynamics parameter identification excitation trajectory according to claim 2, characterized in that in step 6.4, the objective function cond (w) is optimized by fmincon function based on the interior point method according to the local optimal value obtained in step 6.3 until the feasible solution meets the constraint objective.
6. The method for optimizing the excitation trajectory for the kinetic parameter identification of the tandem robot as claimed in claim 5, wherein the objective function Cond (W) is:
argmin(Cond(W))≤Δ；
the constraint objectives are:
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