CN109773794A - A kind of 6 axis Identification of Dynamic Parameters of Amanipulator method neural network based - Google Patents

A kind of 6 axis Identification of Dynamic Parameters of Amanipulator method neural network based Download PDF

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CN109773794A
CN109773794A CN201910143907.6A CN201910143907A CN109773794A CN 109773794 A CN109773794 A CN 109773794A CN 201910143907 A CN201910143907 A CN 201910143907A CN 109773794 A CN109773794 A CN 109773794A
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kinetic parameter
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CN109773794B (en
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泮求亮
林旭军
王进
陆国栋
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Zhejiang University ZJU
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Abstract

The invention discloses a kind of 6 axis Identification of Dynamic Parameters of Amanipulator methods neural network based.Steps are as follows: step 1: Dynamic Modeling in Robotics and linearisation;Step 2: excitation track optimizing, optimizes excitation track using Artificial Immune Algorithm;Step 3: experiment sampling, allows robot to follow the movement of excitation track, multiple groups observing matrix and joint moment are obtained as experimental data.Step 4: data processing, pre-processes the data of experiment acquisition using three standard deviation criterion and the way of median average filter, reducing data noise bring influences.Step 5: Chemical kinetic parameter estimation, estimates kinetic parameter using neural network.Step 6: Verification, robot is allowed to follow an executable track different from excitation track again, sampling experimental data again evaluate the reliability of the kinetic parameter of identification with torque residual error root according to resulting kinetic parameter is recognized come prediction theory joint moment.

Description

A kind of 6 axis Identification of Dynamic Parameters of Amanipulator method neural network based
Technical field
The present invention relates to a kind of methods of Identification of Dynamic Parameters of Amanipulator, are based on nerve net more particularly, to a kind of 6 axis Identification of Dynamic Parameters of Amanipulator methods of network, are related to widely used series connection work in the fields such as industrial production, logistics transportation Industry robot, accurate kinetic parameter are the bases of robot high-precision control.
Background technique
Robot dynamics are the bases for inquiring into robot control, so dynamic parameters identification is non-in robot control A technology of Chang Guanjian, industrial robot realize high-precision control, and smooth motion trajectories require high-precision dynamics ginseng Number.At present robot dynamics pass parameter identification mostly use genetic algorithm greatly optimize excitation track, with least square method come into The iterative estimate of action mechanics parameter, Chemical kinetic parameter estimation precision is not high, and industrial robot is caused to be difficult to accurately control.
Summary of the invention
In view of the deficiencies of the prior art, the invention discloses a kind of 6 axis robot dynamics' parameters neural network based Discrimination method improves the estimated accuracy of kinetic parameter, fault-tolerance with higher.
A kind of method of 6 axis Identification of Dynamic Parameters of Amanipulator neural network based, including the following steps:
First step Dynamic Modeling establishes the D-H link rod coordinate system of 6 axis robots, constructs its kinetics equation, because after Three axis mainly influence robot end's posture, and the influence to joint moment is small, therefore does not consider, and are substantially carried out first three joint power Learn the identification of parameter.According to Lagrange's dynamical equations, the dominant linear representation of robot is derived, it is former according to minimum inertia Expression formula is simplified to linear forms by reason, provides the kinetic parameter for needing to recognize, observing matrix.
Second step motivates track optimizing to carry out the Fourier expansion of joint angles, and boundary is continuous in order to obtain, joint Angular speed, angular acceleration is equal to 0 Fourier space in period starting, needs to optimize it (improvement), multinomial with five times Formula replaces constant term, obtains improved Fourier space as follows:
Wherein i is the i-th joint, wfFor the fundamental frequency of Fourier space, aik, bikFor Fourier space,For constant term coefficient, M is the order of Fourier space.
Optimize the excitation track for obtaining the coefficient of Fourier space, being optimized with immune clone algorithm;
Third step experiment sampling allows robot to follow the movement of excitation track, multiple periods, different moments photoelectric encoder The joint angles for acquiring multiple groups robot, obtain multiple groups joint moment as experiment sample, while obtaining motor feedback current, root According to torque coefficient, finding out motor output torque is joint moment;
The processing of 4th step data counts the data of experiment acquisition by three standard deviations and the way of median average filter Data preprocess, to reduce influence of the data noise to experiment;
The multiple groups observing matrix and joint moment that 5th step Chemical kinetic parameter estimation is obtained according to experiment, pass through nerve net Network picks out kinetic parameter.
6th step Verification provides one article of executable track for being different from excitation track, and robot follows track to move, Multiple periods, different moments acquire the joint angles of multiple groups robot, and motor feedback current is obtained according to required kinetic parameter Joint moment is obtained with experiment to theoretical joint moment to compare, and the reliable of kinetic parameter is evaluated with torque residual error root Property.
Further, immune clone algorithm optimization Fourier space is specially each pass in improved excitation track Section has 10 freedom degrees, and 3 joints amount to 30 freedom degree coefficients, meanwhile, the joint position of robot, velocity and acceleration by To constraint, using Immune Clonal Selection Algorithm, to obtain optimum results, optimizing index is that the conditional number of observing matrix is minimum, is exempted from Steps are as follows for the optimizing of epidemic disease clonal selection algorithm:
(1) antigen is identified first, i.e., to needing the problem of optimizing to analyze, selects optimization feature.For need The feature to be optimized carries out feasibility analysis, then constructs its affinity function, as the evaluation index of problem, while structure Produce the constraint condition of problem.Optimization problem herein is 30 freedom degree coefficients, and minimal condition number is as its affinity letter Number, the range of motion of robot, maximum speed and peak acceleration are as its constraint condition.
(2) then antibody is initialized.Since there are low efficiencys and " Hamming steep cliff " for binary-coded mode Disadvantage, therefore initial solution is by the way of real coding.The feasible solution of problem is converted into Immune Clonal Selection Algorithm by encoding In antibody, generate one group of random initial solution for meeting constraint condition.
(3) affinity is calculated to each of population antibody individual.By calculating the affinity of individual, evaluated with this The performance of antibody.
(4) antibody in population is ranked up according to affinity size, selects preceding 50% defect individual as excellent Individual.
(5) defect individual chosen is cloned, make a variation and clone inhibition operation, delete choosing and obtain same amount of filial generation Individual.
(6) random to generate the newborn population equal with original population quantity, calculate its affinity, and delete select preceding 50% it is excellent Good filial generation.
(7) the immune population that (5) (6) generate is merged with newborn population, replaces original population.
(8) whether the new population that judgement obtains meets the termination condition of algorithm, and termination condition is that the number of iterations is more than 200 It is secondary, if meeting termination condition, searching process is terminated, otherwise continues iteration optimizing.
Further, the 4th step is specially the multiple groups observing matrix data obtained to sampling, first carries out three standards Poor criterion removes gross error;Experimental data is handled with the way of median average filter again later, to reduce data noise Bring influences.
Further, the 5th step is specially that experiment is obtained input of the observing matrix as neural network, initially Weight be set as the random value of 0-1, the label that the joint moment tested is exported as neural network, theoretical joint power Output of the square as neural network.Using batch gradient optimization algorithm come estimated driving force parameter, the nerve net trained The weight of network is kinetic parameter to be estimated.
Further, in the first step, for the robot system in the joint n, consider the influence of joint-friction, move Mechanical equation can be indicated with Second-order Non-linear Differential Equation:
Wherein M (q) represents inertial matrix, and q is joint angles vector;For joint angular velocity vector;For joint angle acceleration Spend vector;For centrifugal force and coriolis force matrix;G (q) is robot gravity item;τ is control force vector.
Its kinetic model can be linearized and be simplified:
Wherein W is the observing matrix of each joint variable composition of robot,For kinetic parameter to be identified.
Further, in the third step, the joint angles that experiment is obtained are fitted to Fourier space, right It differentiates to obtain joint angular speed, then to differentiating to obtain joint angular acceleration, composition multiple groups observing matrix is as experiment sample This.
Advantage and beneficial effect of the invention is following several points:
The conventional method of dynamic parameters identification has disintegration mensuration, CAD method, whole identification method, side proposed by the present invention One kind owned by France in whole identification method, compared to it, they two plant method, and lump-sum analysis method is obtained by robot actual motion , more meet actual scene, the result of identification be actually more nearly, and do not need to disintegrate to robot, facilitate peace Entirely.
Current dynamic parameters identification method mostly uses greatly equalization filtering method to data processing, the present invention propose with Three standard deviation criterion and the way of median average filter handle data, remove because operation error or it is incorrect bring it is coarse The advantages of error, median average filter combines two kinds of filtering algorithms, can inhibit random disturbances and filter out apparent arteries and veins Punching interference.It mostly using genetic algorithm to optimize greatly excitation track, is easily trapped into local optimum, calculating is more complicated, this The case where invention can effectively avoid local optimum using Artificial Immune Algorithm generation, convergence speed of the algorithm are very fast.
Current dynamic parameters identification method mostly uses greatly weighted least-squares iterative method to Chemical kinetic parameter estimation, this Invention proposition carrys out estimated driving force parameter with neural network, and neural network has higher fault-tolerance and high speed to find what optimization solved Ability accurately can estimate the kinetic parameter of robot quickly by neural network very much.
Detailed description of the invention
Fig. 1 is the flow diagram of robot dynamics' parameter Estimation in the present invention;
Fig. 2 is the flow chart of immune clone optimization algorithm in the present invention;
Fig. 3 is the schematic diagram of immune clone algorithm effect of optimization in the present invention;
Fig. 4 is the schematic diagram of the structure of neural network in the present invention;
Fig. 5 is the schematic diagram of gradient optimization algorithm of the invention;
Fig. 6 is the flow chart of verifying kinetic parameter reliability of the invention.
Specific embodiment
With reference to the accompanying drawings of the specification, technical solution of the present invention is described further.
Suitable 6 axis robot is selected, the information such as the D-H parameter of robot are obtained.
D-H parameter
Alpha1=pi/2;A1=160;D1=0;Theta1=q1;Init_theta1=0
Alpha2=0;A2=575;D2=0;Theta2=q2;Init_theta2=pi/2
Alpha3=pi/2;A3=130;D3=644;Theta3=q3;Init_theta3=0
Alpha4=-pi/2;A4=0;D4=0;Theta4=q4;Init_theta4=0
Alpha5=pi/2;A5=0;D5=0;Theta5=q5;Init_theta5=-pi/2
Alpha6=0;A6=0;D6=109.5;Theta6=q6;Init_theta6=pi/2
The present invention uses following steps:
A kind of method of 6 axis Identification of Dynamic Parameters of Amanipulator neural network based, mainly including the following steps:
First step Dynamic Modeling establishes the D-H link rod coordinate system of 6 axis robots, constructs its kinetics equation, because after Three axis mainly influence robot end's posture, and the influence to joint moment is smaller, therefore does not consider, and it is dynamic to be substantially carried out first three joint The identification of mechanics parameter.According to Lagrange's dynamical equations, the dominant linear representation of robot is derived, according to minimum inertia Expression formula is simplified to linear forms by Parameter Principle, and provides the kinetic parameter for needing to recognize, observing matrix.
For the robot system in the joint n, the influence of joint-friction is considered, kinetics equation can use second nonlinear The differential equation indicates:
Wherein M (q) represents inertial matrix, and q is joint angles vector;For joint angular velocity vector;For joint angle acceleration Spend vector;For centrifugal force and coriolis force matrix;G (q) is robot gravity item;τ is control force vector.
Its kinetic model can be linearized and be simplified:
Wherein W is the observing matrix of each joint variable composition of robot,For kinetic parameter to be identified.
Second step motivates track optimizing to carry out Fourier expansion to joint angles, and boundary is continuous in order to obtain, joint Angular speed, angular acceleration is equal to 0 Fourier space in period starting, needs to optimize it (improvement), multinomial with five times Formula replaces constant term, obtains improved Fourier space:
Wherein i is the i-th joint, wfFor the fundamental frequency of Fourier space, aik, bikFor Fourier space,For constant term coefficient, M is the order of Fourier space.
Optimize to obtain the coefficient of Fourier space with immune clone algorithm, immune clone algorithm optimizes Fourier space tool Body is that each joint in improved excitation track has 10 freedom degrees, and 3 joints amount to 30 freedom degree coefficients.Meanwhile machine The joint position of people, velocity and acceleration suffer restraints, so the optimization problem of excitation track is that the optimal of multiple constraint is asked Topic.Optimizing index is that the conditional number of observing matrix is minimum, and traditional method is solved complex and therefore selected using immune clone Algorithm is selected, to obtain preferable optimum results.
Steps are as follows for Immune Clonal Selection Algorithm optimizing:
(1) antigen is identified first, i.e., to needing the problem of optimizing to analyze, selects optimization feature.For need The feature to be optimized carries out feasibility analysis, then constructs its affinity function, and the as conditional number of observing matrix is minimum, As the evaluation index of problem, while constructing the constraint condition to go wrong.Optimization problem herein is 30 freedom degree coefficients, Minimal condition number is as its affinity function, the range of motion of robot, maximum speed and peak acceleration as it about Beam condition.
(2) then antibody is initialized.Since there are low efficiencys and " Hamming steep cliff " for binary-coded mode Disadvantage, therefore initial solution is by the way of real coding.The feasible solution of problem is converted into Immune Clonal Selection Algorithm by encoding In antibody, generate one group of random initial solution for meeting constraint condition.
(3) affinity is calculated to each of population antibody individual.By calculating the affinity of individual, evaluated with this The performance of antibody.
(4) antibody in population is ranked up according to affinity size, selects preceding 50% defect individual as excellent Individual.
(5) defect individual chosen is cloned, make a variation and clone inhibition operation, delete choosing and obtain same amount of filial generation Individual.
(6) random to generate the newborn population equal with original population quantity, calculate its affinity, and delete select preceding 50% it is excellent Good filial generation.
(7) the immune population that (5) (6) generate is merged with newborn population, replaces original population.
The second step specially judges whether obtained new population meets the termination condition of algorithm, and termination condition is repeatedly Generation number is more than 200 times.If meeting termination condition, searching process is terminated, otherwise continues iteration optimizing.Immune clone The Fourier space coefficient of optimization is calculated in algorithm iteration, generates the excitation track of optimization.Algorithm flow chart such as attached drawing 2, people The effect picture of work immune algorithm optimization, such as attached drawing 3.
Third step experiment sampling allows robot to follow the movement of excitation track, multiple periods, different moments photoelectric encoder The joint angles for acquiring multiple groups robot, the joint angles that experiment is obtained, are fitted to Fourier space, are differentiated to it Joint angular speed is obtained, then to differentiating to obtain joint angular acceleration, composition multiple groups observing matrix is used as experiment sample, according to being used to Property matrix and coriolis force matrix derive observing matrix specifically:
W1_1=ddq1;W1_2=ddq1*sin (q2) ^2+dq1*dq2*sin (2*q2);W1_3=-ddq1*sin (2* q2)
-2*dq1*dq2*cos(2*q2);W1_4=ddq2*sin (q2)+dq2^2*cos (q2);W1_5=ddq2*cos (q2)
-dq2^2*sin(q2);W1_6=0;W1_7=2*a2* (ddq1*cos (q2)-dq1*dq2*sin (q2));w1_8 =
-2*a2*(ddq1*sin(q2)-dq1*dq2*cos(q2));W1_9=-0.5*ddq1*cos (2*q2+2*q3)+
dq1*(dq2+dq3)*sin(2*q2+2*q3);W1_10=-ddq1*sin (2*q2+2*q3)-
2*dq1*(dq2+dq3)*cos(2*q2+2*q3);
W1_11=(ddq2+ddq3) * sin (q2+q3)+(dq2+dq3) ^2*cos (q2+q3);
W1_12=(ddq2+ddq3) * cos (q2+q3)+(dq2+dq3) ^2*sin (q2+q3);
W1_13=0;
W1_14=ddq1* (a3*cos (q3)+a3*cos (2*q2+q3)+2*a2*cos (q2+q3))
-2*dq1*dq2*(a3*sin(2*q2+q3)+a2*sin(q2+q3))
-dq1*dq3*(2*a2*sin(q2+q3)+a3*sin(q3)+a3*sin(q3+2*q2));
W1_15=-ddq1* (a3*sin (q3)+a3*sin (2*q2+q3)+2*a2*sin (q2+q3))
-2*dq1*dq2*(a3*cos(2*q2+q3)+a2*cos(q2+q3))
-dq1*dq3*(2*a2*cos(q2+q3)+a3*cos(q3)+a3*cos(q3+2*q2));
W2_1=0;W2_2=-dq1^2*sin (q2) * cos (q2);W2_3=dq1^2*cos (2*q2);
W2_4=ddq1*sin (q2);W2_5=ddq1*cos (q2);W2_6=ddq2;
W2_7=dq1^2*a2*sin (q2)+g*cos (q2);W2_8=dq1^2*a2*cos (q2)-g*sin (q2);
W2_9=-dq1^2*sin (q2+q3) * cos (q2+q3);W2_10=dq1^2*cos (2*q2+2*q3);
W2_11=ddq1*sin (q2+q3);W2_12=ddq1*cos (q2+q3);W2_13=ddq2+ddq3;
W2_14=(2*ddq2*ddq3) * a3*cos (q3)-a3*sin (q3) * (2*dq2+dq3) * dq3
+(a2*sin(q2+q3)+a3*sin(q3+2*q2))*ddq1^2+g*cos(q2+q3);
W2_15=- (2*ddq2*ddq3) * a3*sin (q3)-a3*cos (q3) * (2*dq2+dq3) * dq3
+(a2*cos(q2+q3)+a3*cos(q3+2*q2))*ddq1^2-g*sin(q2+q3);
W3_1=0;W3_2=0;W3_3=0;W3_4=0;W3_5=0;W3_6=0;W3_7=0;
W3_8=0;W3_9=-ddq1*sin (q2+q3) * cos (q2+q3);W3_10=dq1^2*cos (2*q2+2* q3);
W3_11=ddq1*sin (q2+q3);W3_12=ddq1*cos (q2+q3);W3_13=ddq2+ddq3;
W3_14=ddq2*a3*cos (q3)+q1^2* (a2*sin (q2+q3)+a3*sin (q2+q3) * cos (q2)+
dq2^2*a3*sin(q3)+g*cos(q2+q3);
W3_15=-ddq2*a3*sin (q3)+dq1^2* (a2*cos (q2+q3)+0.5*a3* (cos (q3)+cos (2*q2 +q3)))
+dq2^2*a3*cos(q3)-g*sin(q2+q3);
Wherein q1, q2, q3 represent the angle in each joint, and dq1, dq2, dq3 represent the angular speed in each joint, ddq1, ddq2, Ddq3 represents the angular acceleration in each joint, and g represents acceleration of gravity.
Motor feedback current is obtained simultaneously, according to torque coefficient, the motor output torque found out is joint moment.
T=K*Ia
Wherein T is joint moment, and K is current torque coefficient, and Ia is motor feedback current;
The processing of 4th step data removes the gross error in experimental data, is passing through median by three standard deviation criterion Average filter method handles the data of experiment acquisition, to reduce influence of the data noise to experiment.
The multiple groups observing matrix and joint moment that 5th step Chemical kinetic parameter estimation is obtained according to experiment, pass through nerve net Network picks out kinetic parameter.Experiment is specially obtained into multiple groups observing matrix as the input of neural network, initial power The random value for being set to 0-1 is reseted, the label that the multiple groups joint moment tested is exported as neural network, theoretical joint power Output of the square as neural network.Using batch gradient descent method come training pattern, the weight of the neural network of training completion is For kinetic parameter to be identified, the Structure Figure 4 of neural network, gradient optimization algorithm schematic diagram attached 5.
6th step Verification provides one article of executable track for being different from excitation track, and robot follows track to move, Multiple periods, different moments acquire the joint angles of multiple groups robot, and motor feedback current is obtained according to required kinetic parameter Joint moment is obtained with experiment to theoretical joint moment to compare, and the reliable of kinetic parameter is evaluated with torque residual error root Property.Verification flow chart such as attached drawing 6.

Claims (6)

1. a kind of 6 axis Identification of Dynamic Parameters of Amanipulator method neural network based, it is characterised in that the following steps are included:
First step Dynamic Modeling establishes the D-H link rod coordinate system of 6 axis robots, constructs its kinetics equation, because of rear three axis Main to influence robot end's posture, the influence to joint moment is small, therefore does not consider, and is substantially carried out first three joint power ginseng Several identifications;According to Lagrange's dynamical equations, the dominant linear representation of robot is derived, it will according to minimum principle of inertia Expression formula is simplified to linear forms, provides the kinetic parameter for needing to recognize, observing matrix;
Second step motivates track optimizing to carry out the Fourier expansion of joint angles, and boundary is continuous in order to obtain, joint angle speed Degree, angular acceleration are equal to 0 Fourier space in period starting, need to optimize it, normal to replace with quintic algebra curve It is several, it is as follows to obtain improved Fourier space:
Wherein i is the i-th joint, wfFor the fundamental frequency of Fourier space, aik, bikFor Fourier space,For constant term coefficient, M is The order of Fourier space.
Optimize the excitation track for obtaining the coefficient of Fourier space, being optimized with immune clone algorithm;
Third step experiment sampling allows robot to follow the movement of excitation track, and in multiple periods, different moments are acquired with photoelectric encoder The joint angles of multiple groups robot obtain multiple groups joint moment as experiment sample, while obtaining motor feedback current, according to turn Moment coefficient, finding out motor output torque is joint moment;
The processing of 4th step data is pre- to the data progress data of experiment acquisition by three standard deviations and the way of median average filter Processing, to reduce influence of the data noise to experiment;
The multiple groups observing matrix and joint moment that 5th step Chemical kinetic parameter estimation is obtained according to experiment, pass through neural network To pick out kinetic parameter;
6th step Verification provides one article of executable track for being different from excitation track, and robot follows track to move, multiple Period, different moments acquire the joint angles of multiple groups robot, and motor feedback current is managed according to required kinetic parameter The joint moment of opinion obtains joint moment with experiment and compares, and the reliability of kinetic parameter is evaluated with torque residual error root.
2. one kind 6 axis Identification of Dynamic Parameters of Amanipulator method neural network based according to claim 1, feature It is that the immune clone algorithm optimization Fourier space is specially that each joint in improved excitation track there are 10 freedom Degree, 3 joints amount to 30 freedom degree coefficients, meanwhile, the joint position of robot, velocity and acceleration suffers restraints, and uses Immune Clonal Selection Algorithm, to obtain optimum results, optimizing index is that the conditional number of observing matrix is minimum, and immune clonal selection is calculated Steps are as follows for method optimizing:
(1) antigen is identified first, i.e., to needing the problem of optimizing to analyze, selects optimization feature, it is excellent for needing The feature of change carries out feasibility analysis, and the affinity function for then constructing it constructs simultaneously as the evaluation index of problem The constraint condition of problem, the optimization problem in the present invention are 30 freedom degree coefficients, minimal condition number as its affinity function, The range of motion of robot, maximum speed and peak acceleration are as its constraint condition;
(2) then antibody is initialized, initial solution is turned the feasible solution of problem by the way of real coding, through coding It changes the antibody in Immune Clonal Selection Algorithm into, generates one group of random initial solution for meeting constraint condition;
(3) affinity is calculated to each of population antibody individual, by calculating the affinity of individual, antibody is evaluated with this Performance;
(4) antibody in population is ranked up according to affinity size, selects preceding 50% defect individual as defect individual;
(5) defect individual chosen cloned, made a variation and clone inhibition operation, deleted choosing and obtain same amount of filial generation Body;
(6) random to generate the newborn population equal with original population quantity, calculate its affinity, and delete select preceding 50% excellent son Generation;
(7) the immune population that (5) (6) generate is merged with newborn population, replaces original population;
(8) whether the new population that judgement obtains meets the termination condition of algorithm, and termination condition is that the number of iterations is more than 200 times, such as Fruit meets termination condition, then terminates searching process, otherwise continues iteration optimizing.
3. one kind 6 axis Identification of Dynamic Parameters of Amanipulator method neural network based according to claim 1, feature Be: the 4th step is specially the multiple groups observing matrix data obtained to sampling, first carries out three standard deviation criterion, is removed thick Big error;Experimental data is handled with the way of median average filter again later, is influenced to reduce data noise bring.
4. one kind 6 axis Identification of Dynamic Parameters of Amanipulator method neural network based according to claim 1, feature Be: the 5th step is specially the input that experiment is obtained observing matrix as neural network, and initial weight is set as The random value of 0-1, the label that the joint moment tested is exported as neural network, theoretical joint moment is as nerve net The output of network, using batch gradient optimization algorithm come estimated driving force parameter, the weight for the neural network trained is Kinetic parameter to be estimated.
5. one kind 6 axis Identification of Dynamic Parameters of Amanipulator method neural network based according to claim 1, feature It is in the first step, for the robot system in the joint n, considers the influence of joint-friction, kinetics equation can be with It is indicated with Second-order Non-linear Differential Equation:
Wherein M (q) represents inertial matrix, and q is joint angles vector;For joint angular velocity vector;For joint angular acceleration arrow Amount;For centrifugal force and coriolis force matrix;G (q) is robot gravity item;τ is control force vector;
Its kinetic model can be linearized and be simplified:
Wherein W is the observing matrix of each joint variable composition of robot,For kinetic parameter to be identified.
6. one kind 6 axis Identification of Dynamic Parameters of Amanipulator method neural network based according to claim 1, feature It is in the third step, the joint angles that experiment is obtained are fitted to Fourier space, differentiate and closed to it Angular speed is saved, then to differentiating to obtain joint angular acceleration, forms multiple groups observing matrix as experiment sample.
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