CN111775140A - Optimization method for multi-joint mechanical arm dynamics parameter identification excitation track - Google Patents

Optimization method for multi-joint mechanical arm dynamics parameter identification excitation track Download PDF

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CN111775140A
CN111775140A CN202010854347.8A CN202010854347A CN111775140A CN 111775140 A CN111775140 A CN 111775140A CN 202010854347 A CN202010854347 A CN 202010854347A CN 111775140 A CN111775140 A CN 111775140A
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mechanical arm
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卢剑伟
陈新法
朱汉子
任远凯
杨凡
韩建辉
陈佳枫
郭嘉豪
吴勃夫
郑敏毅
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Hefei University of Technology
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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
    • B25J9/06—Programme-controlled manipulators characterised by multi-articulated arms
    • 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
    • B25J9/16—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 invention discloses an optimization method for multi-joint mechanical arm dynamics parameter identification excitation tracks, which comprises the steps of selecting a finite term Fourier series as a model of the multi-joint mechanical arm dynamics parameter identification excitation tracks, taking the condition number of a minimum dynamics parameter set of a multi-joint mechanical arm corresponding to an observation matrix as an identification excitation track optimization objective function, and optimizing the identification excitation tracks meeting boundary conditions by adopting a quantum genetic algorithm of quantum coding and a revolving door change strategy. The quantum genetic algorithm can quickly realize optimization convergence, the optimized excitation identification track meets the boundary requirement and has better excitation, and the better excitation track can be identified and optimized for the dynamic parameters of the multi-joint mechanical arm.

Description

Optimization method for multi-joint mechanical arm dynamics parameter identification excitation track
Technical Field
The invention relates to a multi-joint mechanical arm dynamics parameter identification excitation track optimization method.
Background
In recent years, control based on a dynamic model becomes more and more important for improving the dynamic performance of a multi-joint mechanical arm. However, due to the complexity of the dynamics of the multi-joint mechanical arm, it is difficult to obtain accurate kinetic parameters, and the inaccurate kinetic parameters result in that an accurate kinetic model cannot be established, so that the model-based control is difficult to realize. Therefore, the study of mastering accurate kinetic models and kinetic parameters by a kinetic parameter identification method is gaining attention.
The accurate kinetic parameter identification depends on four parts of the derivation of a kinetic model of the multi-joint mechanical arm, the design and optimization of an excitation track, the acquisition and cleaning of identification data and an identification algorithm. The design and optimization of the identification excitation track can fully excite the dynamic performance of the mechanical arm, disturbance factors caused by inaccurate modeling, actual measurement data noise and the like are avoided to a great extent, the deviation of dynamic parameter identification is reduced, and the identification precision of the dynamic parameters of the mechanical arm is improved.
Commonly used optimization solving methods mainly include Fmincon, particle swarm algorithm, improved genetic algorithm and the like, and the methods are all used for finding a non-local minimum optimization target value in an excitation track constraint boundary. The Fmincon method for optimizing the excitation track is easy to fall into a local extreme value and needs a large amount of screening work. The genetic algorithm searches the optimal solution of the optimization problem in the constraint range by simulating the genetic characteristics of the biological world in a random mode from the aspect of probability, but the genetic algorithm is slow in convergence speed and premature due to the immutability of the evolution of the biological world, has multiple iteration times and is easy to fall into a local extreme value, and thus the kinetic parameter identification is influenced.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides an optimization method for identifying excitation tracks of dynamic parameters of a multi-joint mechanical arm, so that a better excitation track can be identified and optimized for the dynamic parameters of the multi-joint mechanical arm, and the optimized identification excitation track meets boundary requirements and has better excitation, thereby laying a foundation for further improving the dynamic performance of the multi-joint mechanical arm.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the invention relates to an optimization method for multi-joint mechanical arm dynamics parameter identification excitation track, which is characterized by comprising 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 optimization method for the multi-joint mechanical arm dynamics parameter identification excitation track is also characterized in that the step 4 is carried out according to the following process:
step 4.1, setting the population number n, and setting the maximum evolution algebra Tmax and the rotation angle of a quantum revolving door, wherein the current evolution algebra is t; initializing t ═ 1; the optimization parameters for initializing the t generation evolution of the excitation track model are all
Figure BDA0002645853010000021
Setting an optimization target as a global minimum value of an optimization objective function;
step 4.2, generating n groups of random numbers evolved in the t generation in the interval [0,1] and comparing the random numbers with the optimized parameters evolved in the t generation so as to obtain binary solutions corresponding to all the optimized parameters evolved in the t generation;
4.3, obtaining a generalized observation matrix function value consisting of the observation matrix function through a binary solution of the optimization parameters evolved in the t generation, and further solving the condition number of the generalized observation matrix function value evolved in the t generation to obtain an optimized objective function value evolved in the t generation;
4.4, selecting the smaller value of the optimization objective function value evolved in the t generation and the optimization objective function value evolved in the t-1 generation as a judgment standard; when t is 1, the binary solutions of the evolutionary optimization parameters of the t-1 generation are all '1', and the optimization objective function value is infinite;
step 4.5, adjusting the optimized parameters corresponding to the judgment standards by using a quantum revolving door to obtain the optimized parameters evolved in the t +1 th generation;
step 4.6, after assigning t +1 to t, judging whether t is greater than Tmax, if so, saving the optimized parameters evolved in the Tmax generation and the corresponding optimized objective function values as local optimal parameters and objective function values; otherwise, returning to the step 4.2 for sequential execution;
and 4.7, selecting the minimum value of all local optimal objective function values in the population as a global optimal objective function value, and outputting an optimization parameter value corresponding to the global optimal objective function value, so that the optimization parameter value is brought into the mathematical model for identifying the excitation track established in the step 3, and further the excitation track meeting joint constraint conditions and changing in a space range is obtained.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the method, a multi-joint mechanical arm linearization dynamics model is established through analyzing the multi-joint mechanical arm dynamics performance, the minimum dynamics parameter set of the multi-joint mechanical arm is determined through a random number method, a finite Fourier series method is introduced to establish an identification excitation track, the condition number of the minimum dynamics parameter set corresponding to a generalized observation matrix is set as an identification excitation track optimization objective function, an excitation track suitable for multi-joint mechanical arm dynamics parameter identification is optimized through a quantum genetic algorithm, and the problems that the excitation track optimization algorithm is large in iteration times and prone to falling into a local extreme value are solved.
2. The excitation trajectory meeting joint constraint conditions and changing in a space range is optimized based on the quantum genetic algorithm, the excitation trajectory optimized by the optimization algorithm can be rapidly converged and has better robustness, and a new method is provided for excitation trajectory optimization required by multi-joint mechanical arm dynamics parameter identification.
Drawings
FIG. 1 is a flow chart of the quantum genetic algorithm optimized excitation trajectory in the present invention;
FIG. 2 is a diagram of an objective function optimization process according to the present invention;
FIG. 3a is a graph of the relationship between the first three joint angles and time of the optimized excitation trajectory in the present invention;
FIG. 3b is a graph of angular velocity versus time for the first three joints of the optimized excitation trajectory in accordance with the present invention;
FIG. 3c is a graph of angular acceleration versus time for the first three joints of the excitation trajectory after optimization in accordance with the present invention.
Detailed Description
In this embodiment, a method for optimizing the kinetic parameter identification excitation trajectory of a multi-joint mechanical arm based on a quantum genetic algorithm is performed as follows:
step 1, establishing a dynamic model of the multi-joint mechanical arm by using a Newton-Euler method, wherein the dynamic model is shown as a formula (1):
Figure BDA0002645853010000031
in the formula (1), τ represents the joint moments of the robot arm, q,
Figure BDA0002645853010000032
The joint angular position, the joint angular velocity, and the joint angular acceleration of the robot arm are represented, M represents an inertia matrix, C represents coriolis force and centrifugal force, and G represents gravity.
Nonlinear terms in the dynamic model are linearized, and the linearized dynamic model of the multi-joint mechanical arm is obtained as shown in the formula (2):
Figure BDA0002645853010000033
in the formula (2), W is the angle q and angular velocity of the joint of the mechanical arm
Figure BDA0002645853010000034
And angular acceleration of joint
Figure BDA0002645853010000035
And phi is a standard kinetic parameter of the mechanical arm.
Step 2, 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;
step 2.1, setting generalized observation matrix functions of n acquisition points according to a linearized dynamic model of the multi-joint mechanical arm as shown in a formula (3):
Figure BDA0002645853010000036
in the formula (3), psi is a generalized observation matrix of n acquisition points, z is the number of the kinematic joints, and m is the number of the standard kinetic parameters.
The smallest linearly independent group of psi corresponds to the base parameter space of the standard kinetic parameter set phi. The minimum number of linearly independent columns is also the spatial dimension k of ψ, while the m-k columns are required to be deleted and linearly integrated. The spatial dimension k of ψ corresponds to the number of basis parameters of the standard kinetic parameter set φ, and this k column contributes most. The screened m-k columns correspond to parameters with contribution degree of almost zero and parameters with contribution degree of correlation in the standard parameter set phi, wherein the parameters with contribution degree of zero need to be deleted, and the parameters with contribution degree of correlation need to be linearly combined based on the base parameters.
Step 2.2, generating a group of random numbers for simulating the motion parameters of the mechanical arm joint, thereby establishing a random generalized observation matrix psirandomAnd the random generalized observation matrix is a non-column full rank matrix;
step 2.3, carrying out random generalized observation on the matrix psirandomPerforming QR decomposition to obtain a first Q matrix and a first R matrix as shown in a formula (4):
Figure BDA0002645853010000041
by aligning psirandomAnd decomposing and solving the contribution degree of the kinetic parameters. However, the regression matrix psi due to the dynamic parameters of the multi-joint manipulatorrandomIs a non-column full rank matrix with no uniqueness to its standard QR decomposition. But QR decomposition by Householder can solve ψrandomIs not the only problem.
The original vector Θ is transformed using the construction column of equation (5):
Figure BDA0002645853010000042
in the formula (5), the reaction mixture is,
Figure BDA0002645853010000043
for the first R matrix diagonal value ofThe column position of zero is set by the column position,
Figure BDA0002645853010000044
column positions for which the diagonal value of the first R matrix is non-zero;
step 2.4, defining a column transformation unit vector set [ E1,E2,…,Ei,…,Em]；EiA column transformation unit vector in which the ith element is '1' and the other elements are '0';
step 2.5, solving the random generalized matrix psi by using the formula (6)randomThe column transformation rotation matrix p:
p＝[EΘ1EΘ2... EΘi... EΘm](6)
in equation (6), Θ i is the ith element of the column-transformed original vector Θ, EΘiA column transformation unit vector in which the theta i element is '1' and the other elements are '0';
step 2.6, utilizing the formula (7) to carry out random generalized observation matrix psirandomAnd (3) performing column transformation:
ψrandomp＝[ψ1,ψ2](7)
in formula (7), phi1For k independent column vectors, psi2M-k column vectors to be deleted and combined;
step 2.7, solving the basic parameter phi of the minimum dynamic parameter set of the multi-joint mechanical arm by using the formula (8)1Parameter phi linearly combinable with a base parameter2：
Figure BDA0002645853010000051
Step 2.8, Pair psi using equation (9)randomCarrying out QR decomposition on p to obtain a second Q matrix [ Q ]1,Q2]And a second R matrix [ R ]kRm-k]；
Figure BDA0002645853010000052
In the formula (9), RkFor k independent column vectors, R, in a second R matrixm-kAre m-k column vectors in the second R matrix.
Step 2.9, solving the minimum parameter set phi of the multi-joint mechanical arm dynamics by using the formula (10)min：
φmin＝φ1+βφ2(10)
In the formula (10), β is the basic parameter phi of the multi-joint mechanical arm dynamics1With a linearly combinable parameter phi2And has the following combination coefficients:
β＝Rk -1Rm-k(11)
the simplified dynamic model of the multi-joint mechanical arm is shown as the formula (12):
Figure BDA0002645853010000053
in the formula (12), WminGeneralized observation matrix psi corresponding to the minimum parameter set of the mechanical arm dynamics1The basis observation matrix of (1).
Step 3, establishing a mathematical model of the multi-joint mechanical arm dynamics parameter identification excitation track as shown in formula (13):
Figure BDA0002645853010000054
in formula (13), ωfRepresenting the fundamental frequency, αl,i、βl,iIs an N-order Fourier series excitation track identification optimization parameter, wherein l is 1, 2, … …, N, qi0Is a constant term for the ith joint position.
According to the simplified model of the multi-joint mechanical arm dynamics model in the step 2, a generalized observation matrix function is obtained as shown in a formula (14):
Figure BDA0002645853010000061
the optimization of the excitation track is a multivariable nonlinear constraint optimization problem, the condition number cond (psi) of the generalized observation matrix psi is selected as an optimization target function of the excitation track, on one hand, a least square method is selected for parameter identification calculation, and when the cond (psi) is smaller, the psi matrix is smaller in pathological state, and the identification calculation result is accurate; on the other hand, in a practical physical sense, the smaller cond (ψ) is, the more the excitation trajectory of the optimal calculation can be changed within a large constraint range, and the dynamic performance of the robot arm can be sufficiently excited. An optimization objective function and a constraint function for identifying the excitation track are established according to the generalized observation matrix function, and the functions are shown in a formula (15):
Figure BDA0002645853010000062
in the formula (15), qimin，qimaxRespectively the minimum value and the maximum value of the ith joint angle,
Figure BDA0002645853010000063
is the maximum value of the i-th joint angular velocity,
Figure BDA0002645853010000064
is the maximum value of the i-th joint angular acceleration.
Step 4, as shown in figure 1, optimizing the excitation track in the step 3 according to a quantum genetic algorithm;
step 4.1, setting the population number n, and setting the maximum evolution algebra Tmax, wherein the current evolution algebra is t; initializing t ═ 1; setting an optimization target as a global minimum value of an optimization objective function; the optimization parameters for initializing the t generation evolution of the excitation track model are all
Figure BDA0002645853010000065
As shown in equation (16):
Figure BDA0002645853010000066
step 4.2, generating n groups of random numbers evolved in the t generation in the [0,1] interval and comparing the random numbers with the optimized parameters evolved in the t generation, so as to obtain binary solutions corresponding to all the optimized parameters evolved in the t generation, as shown in a formula (17):
Figure BDA0002645853010000071
in the formula (17), j is a computer-generated random number, Al,i、Bl,iOptimization parameters α for the excitation trajectoryl,i、βl,iThe corresponding binary solution.
4.3, obtaining a generalized observation matrix function value consisting of an observation matrix function through a binary solution of the optimization parameters evolved in the t generation, and further solving the condition number of the generalized observation matrix function value evolved in the t generation to obtain an optimized objective function value evolved in the t generation;
4.4, selecting the smaller value of the optimization objective function value evolved in the t generation and the optimization objective function value evolved in the t-1 generation as a judgment standard; when t is 1, the binary solutions of the evolutionary optimization parameters of the t-1 generation are all 1, and the optimization objective function value is infinite;
and 4.5, adjusting the optimized parameters corresponding to the discrimination criteria by using a quantum revolving door to obtain the optimized parameters evolved in the t +1 th generation, as shown in the formula (18):
Figure BDA0002645853010000072
from formula (18), α'l,i，β'l,iFor the adjusted excitation trajectory optimization parameter, U (theta) is a quantum rotation gate function, and
Figure BDA0002645853010000073
theta is the rotation angle of the quantum revolving door, and the value of theta is shown in table 1:
table 1: rotation angle adjusting strategy of quantum revolving door
Figure BDA0002645853010000074
X in Table 1i＝[Al,iBl,i]Binary solution of optimized parameter values for the t-th evolution, bestiIs a binary solution of the current optimum optimization parameter value, f (x)i) Is the optimized objective function value corresponding to the binary solution of the optimized parameter value evolved in the t generation, f (best)i) Is the optimization objective function value, s (α), corresponding to the binary solution of the current optimal optimization parameter valuel,i,βl,i) Is the direction of the angle of rotation,iis the magnitude of the rotation angle theta, i.e. theta equals s (α)l,i,βl,i)·i。
Step 4.6, after assigning t +1 to t, judging whether t is greater than Tmax, if so, saving the optimized parameters evolved in the Tmax generation and the corresponding optimized objective function values as local optimal parameters and objective function values; otherwise, the step 4.2 is returned to and executed in sequence.
And 4.7, selecting the minimum value of all local optimal objective function values in the population as a global optimal objective function value, and outputting an optimization parameter value corresponding to the global optimal objective function value, so that the optimization parameter value is brought into the mathematical model for identifying the excitation track established in the step 3, and the excitation track meeting joint constraint conditions and changing in a space range is obtained.
Example 1:
the multi-joint mechanical arm dynamics parameter identification excitation track optimization method comprises the following steps:
step 1, establishing a dynamic model of the multi-joint mechanical arm, and carrying out linearization processing on the dynamic model.
And 2, solving a minimum dynamic parameter set.
Step 3, establishing a mathematical model of the excitation track, wherein the fundamental frequency is 0.2 pi, the total time is 10s, and the constraint value of the optimized excitation track is shown in table 2:
table 2: joint angle, angular velocity and angular acceleration constraint values of three anterior joints of mechanical arm
Figure BDA0002645853010000081
And 4, initializing optimization parameters of the excitation track, and solving a corresponding binary solution and an optimization objective function value.
And 5, comparing to obtain the minimum value of the optimization objective function, recording the optimal excitation track optimization parameter value, and taking the optimal excitation track optimization parameter value as the object of the next iterative evolution. And when the iteration times reach the maximum value, outputting the result. Fig. 2 is a diagram of the optimization process of the objective function, and it can be seen from the diagram that the optimization process approaches stability around 25 generations, the change of the optimization objective function value is very small after 100 generations, and the final optimization target value is around 9.47, and the algorithm has rapid convergence. 3a, 3b and 3c are diagrams of the optimized excitation locus, and it can be seen from the curves in the diagrams that the optimized excitation locus meets the constraint of each joint and occupies the motion space of the mechanical arm in a larger range, which illustrates that the excitation locus optimization requirement is met by the algorithm.

Claims (2)

1. An optimization method for multi-joint mechanical arm dynamics parameter identification excitation track is characterized by comprising 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.
2. The optimization method for multi-joint mechanical arm dynamics parameter identification excitation trajectory according to claim 1, wherein the step 4 is performed as follows:
step 4.1, setting the population number n, and setting the maximum evolution algebra Tmax and the rotation angle of a quantum revolving door, wherein the current evolution algebra is t; initializing t ═ 1; the optimization parameters for initializing the t generation evolution of the excitation track model are all
Figure FDA0002645851000000011
Setting an optimization target as a global minimum value of an optimization objective function;
step 4.2, generating n groups of random numbers evolved in the t generation in the interval [0,1] and comparing the random numbers with the optimized parameters evolved in the t generation so as to obtain binary solutions corresponding to all the optimized parameters evolved in the t generation;
4.3, obtaining a generalized observation matrix function value consisting of the observation matrix function through a binary solution of the optimization parameters evolved in the t generation, and further solving the condition number of the generalized observation matrix function value evolved in the t generation to obtain an optimized objective function value evolved in the t generation;
4.4, selecting the smaller value of the optimization objective function value evolved in the t generation and the optimization objective function value evolved in the t-1 generation as a judgment standard; when t is 1, the binary solutions of the evolutionary optimization parameters of the t-1 generation are all '1', and the optimization objective function value is infinite;
step 4.5, adjusting the optimized parameters corresponding to the judgment standards by using a quantum revolving door to obtain the optimized parameters evolved in the t +1 th generation;
step 4.6, after assigning t +1 to t, judging whether t is greater than Tmax, if so, saving the optimized parameters evolved in the Tmax generation and the corresponding optimized objective function values as local optimal parameters and objective function values; otherwise, returning to the step 4.2 for sequential execution;
and 4.7, selecting the minimum value of all local optimal objective function values in the population as a global optimal objective function value, and outputting an optimization parameter value corresponding to the global optimal objective function value, so that the optimization parameter value is brought into the mathematical model for identifying the excitation track established in the step 3, and further the excitation track meeting joint constraint conditions and changing in a space range is obtained.
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