CN116141314A - Method and system for identifying dynamic parameters of robot based on projective geometry algebra - Google Patents
Method and system for identifying dynamic parameters of robot based on projective geometry algebra Download PDFInfo
- Publication number
- CN116141314A CN116141314A CN202310011748.0A CN202310011748A CN116141314A CN 116141314 A CN116141314 A CN 116141314A CN 202310011748 A CN202310011748 A CN 202310011748A CN 116141314 A CN116141314 A CN 116141314A
- Authority
- CN
- China
- Prior art keywords
- matrix
- rigid body
- parameters
- robot
- manifold
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Classifications
-
- 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
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1653—Programme controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Robotics (AREA)
- Mechanical Engineering (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
Abstract
The invention provides a method and a system for identifying dynamic parameters of a robot based on projective geometry algebra, wherein the method comprises the following steps: the acquisition step: according to a robot kinematics model, establishing a kinetic equation, arranging the kinetic equation into a linear equation on a positive definite matrix manifold, generating an optimal excitation track according to the coefficient matrix condition number of the linear equation, and collecting data; the processing steps are as follows: preprocessing the acquired data, filtering and identifying friction parameters, and eliminating the influence of friction on joint moment; solving: based on the processed data, on the symmetrical positive definite matrix manifold, the optimization technology on the manifold is used for solving, and the physical realizable dynamic parameters of each rigid body are obtained. When the friction of the passive joint is negligible, the invention can solve the problem of dynamic parameter identification of a general robot model, obtain the inertia matrix of each rigid body and the friction parameter of the active joint, and strictly maintain the physical realizability of the dynamic parameter.
Description
Technical Field
The invention relates to the field of robot dynamic parameter identification, in particular to a method and a system for identifying robot dynamic parameters based on projective geometry algebra.
Background
The dynamic parameters of the robot generally comprise inertial parameters such as mass, centroid position, rotational inertia and the like of each connecting rod and joint friction parameters, and the accurate identification of the parameters is a basis for further planning and controlling the motion of the system based on a model. Since the robot active joint generalized force is linear with respect to the inertial parameters, the inverse kinetic equation of the robot can always be organized into a linear equation with respect to the generalized force with respect to the inertial parameters. The conventional dynamic parameter identification method is based on the linear equation, and mainly comprises a least square method, a semi-positive programming method, a neural network method and the like. The existing methods still have some problems: 1) The least square method can only estimate a linearly independent minimum parameter set in the inertial parameters, and cannot ensure the physical realizability of the kinetic parameters, namely cannot ensure that the solved mass is positive, the inertial tensor is positive and the triangle inequality is satisfied; 2) The semi-positive planning method can obtain physically-realizable inertial parameters, but when the priori is lacking or the priori confidence is not high, the semi-positive result is obtained by solving, namely, the situation that the mass is 0 or the inertial tensor is semi-positive occurs; 2) The neural network method lacks the support of a physical model, has low interpretation and needs to consume a great deal of time for training, and the obtained model is difficult to apply to engineering actual scenes.
The Chinese patent document CN114800519A 'a friction-considered six-degree-of-freedom industrial robot dynamic parameter identification method', which uses a least square method to identify dynamic parameters, considers joint friction and motor parameters, and further improves the identification accuracy of the dynamic parameters by means of a heuristic algorithm. However, this approach does not take into account the physical availability of rigid body inertial parameters, which can cause problems in motion planning and control scenarios involving flexible joints.
The Chinese patent document CN109773794A is a 6-axis robot kinetic parameter identification method based on a neural network, wherein the kinetic parameters are identified by using a neural network type method, the input of the neural network is an observation matrix obtained according to a physical model, and the output is a moment, so that the kinetic parameters of a robot system with complex joints can be identified. However, the method does not consider the physical realizability of the rigid body inertia parameter, and the introduction of the neural network makes the model insufficient in interpretation.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method and a system for identifying the dynamic parameters of a robot based on projective geometry algebra.
The invention provides a method for identifying robot dynamic parameters based on projective geometry algebra, which comprises the following steps:
the acquisition step: according to a robot kinematics model, establishing a kinetic equation, arranging the kinetic equation into a linear equation on a positive definite matrix manifold, generating an optimal excitation track according to the coefficient matrix condition number of the linear equation, and collecting data;
the processing steps are as follows: preprocessing the acquired data, filtering and identifying friction parameters, and eliminating the influence of friction on joint moment;
solving: based on the processed data, on the symmetrical positive definite matrix manifold, the optimization technology on the manifold is used for solving, and the physical realizable dynamic parameters of each rigid body are obtained.
Preferably, the collecting step includes:
step 1.1: according to a kinematic model of the robot, calculating the pose, the speed and the acceleration of each rigid body and the position, the speed and the acceleration of a triple base vector fixedly connected to the rigid body, wherein the pose of the rigid body is an even-numbered unit multiple vector, the speed and the acceleration are double vectors, and the position, the speed and the acceleration of the triple base vector are triple vectors;
step 1.2: calculating an inertial force regression matrix of each rigid body, defining the inertial force regression matrix as a 4-order matrix, wherein each element in the matrix is a double vector and is only related to kinematic parameters; defining an inertia matrix as a 4-order symmetric positive definite matrix on a real number domain, and calculating the inertia force rotation of each rigid body by the inner products of the two 4-order matrices according to a correlation formula of projective geometry algebra;
step 1.3: calculating a generalized force regression matrix of each rigid body corresponding to each generalized force, arranging a dynamic equation of the robot system into a linear equation defined on a positive definite matrix manifold, and calculating the contribution of the inertial force of a connecting rod of the robot system to a certain generalized force by the inner product of the matrix of two 4-order matrixes, wherein the linear equation is calculated by the inner product of the matrix of the two 4-order matrixesOne matrix is an inertial matrix of a rigid body, the other matrix is defined as a generalized force regression matrix, the generalized force regression matrix is calculated by a kinematic model of the rigid body and the inertial force regression matrix, the generalized force regression matrix is a 4-order matrix defined on a real number domain, and a dynamics equation of the robot system after arrangement is Q=R*NWherein Q is a generalized force vector defined over the real number domain;Rthe ith row and the jth column of the matrix are generalized force regression matrices of inertia of the connecting rod j and generalized force i;Nthe j-th element is an inertia matrix of the connecting rod j, which is a special vector;
step 1.4: parameterizing the robot joint space trajectory and parameterizing the special matrix of step 1.3RReforming into regression matrices over real number domainYAnalyzing the minimum parameter set to obtain a regression matrix of the minimum parameter setY b Regression matrix with minimum parameter setY b The condition number of (2) is an objective function, and the optimal excitation track for dynamic parameter identification is obtained through optimization.
Preferably, the gradient of the objective function is calculated analytically by an algorithm in projective geometry algebra.
Preferably, the processing step comprises:
removing noise generated in the joint motion data and the joint moment data due to the signal acquisition process through Butterworth filtering or other filtering means;
and carrying out preliminary identification on dynamic parameters of the system by using a least square method, wherein the dynamic parameters comprise inertia parameters and friction parameters.
Preferably, the solving step includes: based on the linear equation, the physical realizability of the dynamic parameters is generalized to be the linear mapping of the rigid body's inverse dynamics from manifold to generalized force space on the symmetric positive definite matrix manifold, and the expression given in step 1.3 is provided, and in the embedded space of the symmetric positive definite matrix manifold, the gradient and the sea plug transformation are written analytically, and solved by the second-order optimization algorithm on manifold.
According to the invention, the system for identifying the dynamic parameters of the robot based on projective geometry algebra comprises the following components:
and the acquisition module is used for: according to a robot kinematics model, establishing a kinetic equation, arranging the kinetic equation into a linear equation on a positive definite matrix manifold, generating an optimal excitation track according to the coefficient matrix condition number of the linear equation, and collecting data;
the processing module is used for: preprocessing the acquired data, filtering and identifying friction parameters, and eliminating the influence of friction on joint moment;
and a solving module: based on the processed data, on the symmetrical positive definite matrix manifold, the optimization technology on the manifold is used for solving, and the physical realizable dynamic parameters of each rigid body are obtained.
Preferably, the acquisition module comprises:
module M1.1: according to a kinematic model of the robot, calculating the pose, the speed and the acceleration of each rigid body and the position, the speed and the acceleration of a triple base vector fixedly connected to the rigid body, wherein the pose of the rigid body is an even-numbered unit multiple vector, the speed and the acceleration are double vectors, and the position, the speed and the acceleration of the triple base vector are triple vectors;
module M1.2: calculating an inertial force regression matrix of each rigid body, defining the inertial force regression matrix as a 4-order matrix, wherein each element in the matrix is a double vector and is only related to kinematic parameters; defining an inertia matrix as a 4-order symmetric positive definite matrix on a real number domain, and calculating the inertia force rotation of each rigid body by the inner products of the two 4-order matrices according to a correlation formula of projective geometry algebra;
module M1.3: calculating a generalized force regression matrix corresponding to each generalized force of each rigid body, arranging a dynamic equation of a robot system into a linear equation defined on a positive definite matrix manifold, calculating the contribution of the inertial force of a connecting rod of the robot system to a certain generalized force by the inner product of matrixes of two 4-order matrixes, wherein one matrix is the inertial matrix of the rigid body, the other matrix is defined as the generalized force regression matrix, calculating by a kinematic model of the rigid body and the inertial force regression matrix and is the 4-order matrix defined on a real number domain, and arranging the dynamic equation of the robot system to be Q=after arrangingR*NWherein Q is a generalized forceVectors, defined in the real number domain;Rthe ith row and the jth column of the matrix are generalized force regression matrices of inertia of the connecting rod j and generalized force i;Nthe j-th element is an inertia matrix of the connecting rod j, which is a special vector;
module 1.4: parameterizing the robot joint space trajectory and parameterizing said special matrix of modules M1.3RReforming into regression matrices over real number domainYAnalyzing the minimum parameter set to obtain a regression matrix of the minimum parameter setY b Regression matrix with minimum parameter setY b The condition number of (2) is an objective function, and the optimal excitation track for dynamic parameter identification is obtained through optimization.
Preferably, the gradient of the objective function is calculated analytically by an algorithm in projective geometry algebra.
Preferably, the processing module includes:
removing noise generated in the joint motion data and the joint moment data due to the signal acquisition process through Butterworth filtering or other filtering means;
and carrying out preliminary identification on dynamic parameters of the system by using a least square method, wherein the dynamic parameters comprise inertia parameters and friction parameters.
Preferably, the solving module includes: based on the linear equation, the physical realizability of the dynamic parameters is generalized to be the linear mapping of the rigid body's inverse dynamics from manifold to generalized force space on the symmetric positive definite matrix manifold, and the expression given by the module 1.3 is provided, and in the embedded space of the symmetric positive definite matrix manifold, the gradient and the sea plug transformation are written analytically, and solved by the second-order optimization algorithm on manifold.
Compared with the prior art, the invention has the following beneficial effects:
when the friction of the passive joint is negligible, the invention can solve the problem of dynamic parameter identification of a general robot model, obtain the inertia matrix of each rigid body and the friction parameter of the active joint, and strictly maintain the physical realizability of the dynamic parameter.
Drawings
Other features, objects and advantages of the present invention will become more apparent upon reading of the detailed description of non-limiting embodiments, given with reference to the accompanying drawings in which:
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a reference diagram of projective geometry algebraic computation;
FIG. 3 is a diagram showing an initial state of a 6-degree-of-freedom serial industrial robot PUMA 560;
FIG. 4 is a plot of joint space optimal excitation trajectories;
FIG. 5 is a graph of joint moment after noise addition;
fig. 6 is a graph comparing torque estimation results of three methods.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications could be made by those skilled in the art without departing from the inventive concept. These are all within the scope of the present invention.
As shown in fig. 1, a method for identifying a robot dynamic parameter based on projective geometry algebra includes the following steps: 1. and establishing a kinetic equation according to the robot kinematic model, finishing the kinetic equation into a linear equation on a positive definite matrix manifold, generating an optimal excitation track according to the coefficient matrix condition number of the linear equation, and collecting data. 2. Preprocessing data, filtering and identifying friction parameters, and eliminating the influence of friction on generalized force. 3. On the symmetrical positive definite matrix manifold, the optimization technology on the manifold is used for solving, and the physical realizable dynamic parameters of each rigid body are obtained.
The step 1 comprises the following steps:
step 1.1: and calculating the pose, the speed and the acceleration of each rigid body and the position, the speed and the acceleration of the triple basis vector fixedly connected to the rigid body according to the kinematic model of the robot, wherein the pose of the rigid body is an even-numbered unit multiple vector, the speed and the acceleration are double vectors, and the position, the speed and the acceleration of the triple basis vector are triple vectors. The n-gram vector is a concept in projective geometry algebra.
According to the kinematic parameters of the robot, a kinematic model of the robot is established, each connecting rod of the robot is assumed to be a rigid body, the jacobian between the speed of each rigid body and the joint speed is analyzed, the pose, the speed and the acceleration of each rigid body are calculated, and the model is algebraic in projective geometry
Is indicated in (a). />
Is a 16-dimensional linear space with a distinction of the number of weights between basis vectors, including 0-fold vectors (scalar), vectors, double vectors, triple vectors, quadruple vectors (pseudo-scalar). Bilinear operators between basis vectors, geometry products, are defined in the linear space. The geometric product operation between substrates is shown in fig. 2. Pose M of rigid body i i Is the sum of scalar, double vector and pseudo scalar, is an even-numbered double vector, and satisfies the constraint +.>
Is M i Is negative. Velocity V i Is +.>
Are each represented as a double vector. The jacobian of rigid body velocity with respect to generalized coordinate velocity can be written as follows:
where n is the number of degrees of freedom of the system, L j Is a double vector.
Algebra of projective geometry
In which points are represented by triplet vectors, and the coordinates of points in euclidean space are represented as:
P＝xE 1 +yE 2 +zE 3 +E 0 (2)
wherein E is 1 ,E 2 ,E 3 ,E 0 The base vector, which is the triplet of vectors shown in Table 1, the coordinate array of points is
P＝[x,y,z,1] T (3)
The position, speed and acceleration of the point along with the rigid body motion are expressed as:
according to formulas (4) - (6), the position E 'of the triplet vector base vector Ek moving along with the rigid body i is calculated' i，k Speed and velocity of
Acceleration->
In the above-mentioned steps, the step of, i=1, 2,.. B ，N B Is the number of rigid bodies; k=0, 1,2,3./>
Step 1.2: an inertial force regression matrix for each rigid body is calculated. Defining an inertial force regression matrix as a special 4-order matrix, wherein each element in the matrix is a double vector and is only related to kinematic parameters; the inertia matrix is defined as a positive definite matrix of 4 th order symmetry over a real number domain. According to the correlation formula of projective geometry algebra, the inertia force rotation of each rigid body is calculated by the inner product of the two matrices of 4 th order.
The kinetic equation of rigid body i is expressed as
w＝tr(N T A)：＝N*A (7)
Wherein the method comprises the steps of
w＝f x e 23 +f y e 31 +f z e 12 +m x e 01 +m y e 02 +m z e 03 (8)
Is the sum of all force rotations to which the rigid body is subjected, [ f ] x ，f y ，f z ] T Is the main vector of the rigid body subjected to all external forces, [ m ] x ，m y ，m z ] T The main moment of the rigid body relative to the origin of the inertial system;
an inertial matrix that is a rigid body, wherein Ω is a spatial range that the rigid body contains; m is the mass of the rigid body; c is the centroid position of the rigid body; and Sigma is the moment of inertia of the rigid body. The physical realizability of the rigid body inertia parameter means that the matrix is positive, namely N is on the 4-order symmetric positive definite matrix manifold SPD (4).
A i For a special matrix related to rigid i motion only, an inertial force regression matrix is defined, where the element of the kth row and the first column is a double vector, considered a number, expressed as,
wherein, operation V is defined as:
wherein P is 1 ，P 2 Is a triplet vector;
for one-to-one mapping of triplet vectors, satisfy
J(E i )＝e i (12)
The operation lambda is the outer product, and the outer product of the two vectors a, b is defined as
a∧b＝0.5(ab-ba) (13)
After the outer product is generalized to the multiple vectors, the vector component with the highest weight in the geometric product results of the two multiple vectors is represented, for example, the outer product of the two double vectors is the pseudo scalar part in the multiple vectors obtained by geometric product operation of the two double vectors.
Step 1.3: and calculating a generalized force regression matrix of each rigid body corresponding to each generalized force, and arranging a dynamic equation of the robot system into a linear equation defined on a positive definite matrix manifold. The contribution of the inertia force of a certain connecting rod of the robot system to a certain generalized force is also calculated by the inner product of the matrix of two 4-order matrixes, wherein one matrix is the inertia matrix of the rigid body, the other matrix is defined as a generalized force regression matrix, and the contribution is calculated by the kinematic model of the rigid body and the inertia force regression matrix and is the 4-order matrix defined on the real number domain. The dynamics equation of the robot system after finishing is shaped as q=R*NIs an expression of (2). Wherein Q is a generalized force vector, defined on a real number domain;Rthe ith row and the jth column of the matrix are generalized force regression matrices of inertia of the connecting rod j and generalized force i;Nthe j-th element is an inertia matrix of the connecting rod j, which is a special vector.
According to the Dalangbeil principle and the virtual power principle, a kinetic equation of the robot system is obtained:
wherein, the liquid crystal display device comprises a liquid crystal display device,
virtual speed DeltaV of connecting rod i as the primary force i Virtual speed +.>
Satisfy relation of->
Substituted to obtain
Wherein, the liquid crystal display device comprises a liquid crystal display device,
for corresponding generalized coordinate q j Is the resultant torque of the joint torque and the friction torque. From the linear independence of the generalized coordinates and the linearity of the matrix trace, n equations are derived
Wherein, a generalized force regression matrix is defined as R ji ＝L j,i ∧A i A coefficient matrix representing the contribution of the inertia of the link i to the generalized force j. L (L) j,i ∧A i Represents L j,i And A is a i The outer product operation is performed on each double vector of the vector, the obtained pseudo scalar is directly mapped into scalar space in the actual operation, and R is ji Each element of (2) is a scalar real number, and the kth line and the first list expression are
The equation set is arranged to obtain the dynamic equation of the robot system as follows
If the robot system moves along a certain track, N times of measurement are carried out, and the movement data q of the active joint is obtained through the measurement of the sensor 1 ,q 2 ,…q N And moment data Q 1 ,Q 2 …Q N Each measurement satisfies the kinetic equation
Q＝R*N+ε (20)
Where ε is the error caused by measurement noise, etc.
After the group, get the equation
Wherein, the liquid crystal display device comprises a liquid crystal display device,
the kinetic parameter identification problem is summarized as manifold SPD (4) n Unconstrained optimization problem on
Wherein I II 2 Is the 2-norm of the vector.
Step 1.4: parameterizing the space track of the robot joint, and specially carrying out the step (1.3) on the space trackRReforming into regression matrices over real number domainYAnalyzing the minimum parameter set to obtain a regression matrix of the minimum parameter setY b And optimizing to obtain the optimal excitation track for identifying the dynamic parameters by taking the condition number of the matrix as an objective function. The gradient of the objective function is calculated analytically by an algorithm in projective geometry algebra.
To obtain the optimal excitation trajectory, the original kinetic equation is rearranged into
Wherein vecN is i Is N i Vectorization of (2) due to N i Symmetrical, with only 10 independent parameters, vecN i ＝[(N i ) 11 ，(N i ) 12 ，(N i ) 13 ，(N i ) 22 ，(N i ) 23 ，(N i ) 33 ，(N i ) 14 ，(N i ) 24 ，(N i ) 34 ，(N i ) 44 ] T ：＝[MXX，MXY，MXZ，MYY，MYZ，MZZ，MX，MY，MZ，M] T (24)
vecR ji Is R ji Vectorization, also 10-dimensional vector, has
vecR ji ＝[(R ji ) 11 ，(R ji ) 12 +(R ji ) 21 ，(R ji ) 13 +(R ji ) 31 ，(R ji ) 22 ，(R ji ) 23 +(R ji ) 32 ，(R ji ) 33 ，(R ji ) 14 +(R ji ) 41 ，(R ji ) 24 +(R ji ) 42 ，(R ji ) 34 +(R ji ) 43 ，(R ji ) 44 ] T (25)
Given the data of N measurements, the kinetic equation is obtained as
The robot joint space trajectory is parameterized using a fourier series, with, for each active joint,
the parameter vector p= [ a ] of the joint 1 ，b 1 ，a 2 ，b 2 ，...，a K ，b K ，c]The parameter set of all joint tracks is vectorp；ω k Selected based on sensor performance and motor performance. At this time, regression matrixY＝Y(p)。
Generation of optimal excitation trajectories yields optimization problems for the parameter space of the trajectories
subjecttop∈C
Wherein, the liquid crystal display device comprises a liquid crystal display device,Y b a regression matrix that is a minimum parameter set, the matrix is full of rank, and satisfiesY b π b ＝YPi; c is a constraint set which is satisfied by parameters and comprises an articulation range, a speed range, an acceleration range, a start-stop point constraint and the like.
In order to facilitate the rapid solution of the optimization problem, an objective function cond # -needs to be givenY b ) Wherein the more difficult one step is toYFor a pair of
Is a partial derivative of (c). According to the analysis expression of each term of the regression matrix provided by the dynamics model, the calculation rule of projective geometry algebra can be fully utilized, so that a more efficient algorithm can be obtained, and the specific algorithm refers to the related papers.
Step (a)3 using positive definite matrix manifold SPD (4) n The optimization algorithm solves the inertia matrix of each rigid body, namely
Thanks to the explicit expression of the robot dynamics equation obtained in step 1, it is possible to write the analytical expression of the gradient of the objective function on the manifold in the embedding euclidean space and the sea plug transformation, wherein
Wherein, the liquid crystal display device comprises a liquid crystal display device,Uis in combination withNA matrix vector of the same size, i.e. each element in the vector is a 4-order matrix. In the above operation involving transposition and vector inner product, the generalized force regression matrix
And inertial matrixNThe 4-th order matrix as an element of the matrix is taken as a number to participate in the operation, not a block matrix, such as
Hereinafter, the embodiment of the present invention will be described in detail with reference to the accompanying drawings by taking 6-degree-of-freedom serial industrial robot PUMA560 as an example, but the scope of the present invention is not limited to the following embodiments.
The specific flow of this embodiment includes: firstly, establishing a kinematic model according to kinematic parameters of a robot model; then randomly generating data of joint position, speed and acceleration, calculating a regression matrix and analyzing a minimum parameter set; secondly, parameterizing the joint space track by taking the condition number of a minimum parameter set regression matrix as an objective function and Fourier series, optimizing to obtain an optimal excitation track, outputting joint positions, speeds, accelerations and moments when moving along the excitation track by a robot simulation model, and adding white noise into moment data; and finally, according to the data of the last step, calculating a regression matrix, identifying the gradient of the objective function and the sea plug transformation of the kinetic parameters, and solving the kinetic parameters by using an optimization algorithm on the manifold.
In the following example, the robot model used is a 6-degree-of-freedom serial industrial robot PUMA560, the initial state of which is shown in fig. 3. According to MDH parameters of the robot, when the robot is in an initial state, the double vectors of six joint axes are expressed as
The rigid body motion caused by the joint i is,
the rigid motion of the connecting rod i is
The joint axis i is after rigid motion
The speed of the connecting rod i is
The acceleration of the connecting rod i is
Wherein g is gravity acceleration, and the value is 9.81e 03 。
According to the formula, the kinetic equation of the robot system is calculated as
The rearranged form is according to formulas (24) - (25)
τ＝Yπ＝Y b π b
Wherein the minimum parameters are 36, i.e b Is a 36-dimensional vector.
The joint space trajectory is parameterized by a trigonometric function with the frequency of 0.1Hz,0.2Hz and 0.4Hz, and an optimized excitation trajectory is obtained by using the dynamic model provided by the invention. The track parameters of the six joints are
Table 1 parameter table of optimum excitation trajectories
The track is a periodic track, the period is 10s, and the joint track is shown in fig. 4. Sampling rate 1kHz, collecting joint position q and joint speed along excitation track
Joint acceleration->
The inertia matrix of each link is set to be. The joint moment is obtained by using a reverse dynamics algorithm, white noise is added, the white noise of each joint is independent, the obeying mean value is 0, and the variance is sigma 2 Gaussian distribution, sigma 2 The simulated moment obtained by=20 is shown in fig. 5.
Using the method of the present invention, sigma is taken separately 2 And (0, 1, 20), carrying out dynamic parameter identification according to the generated data to obtain dynamic parameters of each rigid body, then randomly generating a track, predicting joint moment by using the identified parameters, comparing with the real moment, and evaluating the identification result. In addition, the results are shown in table 2, compared with the recognition result based on the iterative least square and the recognition result based on the semi-definite programming.
Therefore, the method of the invention is used for identifying the dynamic parameters, and can ensure the moment estimation precision and sigma which are the same as those of other methods under the same noise level 2 When=20, the estimation of the moment by the three methods is shown in fig. 6, and it can be seen that the prediction effect of the three methods on the moment is equivalent; the dynamic parameters obtained by the method are strictly and physically realizable and are closer to the true values of all the rigid bodies; when the measurement noise is increased, the method is more robust to the identification of the parameters, and the range from the identification result to the true value is not changed greatly.
Table 2 kinetic parameter identification result comparison table
The invention also provides a system for identifying the robot dynamics parameters based on the projective geometry algebra, which can be realized by executing the flow steps of the method for identifying the robot dynamics parameters based on the projective geometry algebra, namely, a person skilled in the art can understand the method for identifying the robot dynamics parameters based on the projective geometry algebra as a preferred implementation mode of the system for identifying the robot dynamics parameters based on the projective geometry algebra.
A system for identifying parameters of robot dynamics based on projective geometry algebra, comprising:
and the acquisition module is used for: and establishing a kinetic equation according to the robot kinematic model, finishing the kinetic equation into a linear equation on a positive definite matrix manifold, generating an optimal excitation track according to the coefficient matrix condition number of the linear equation, and collecting data.
The processing module is used for: preprocessing the acquired data, filtering and identifying friction parameters, and eliminating the influence of friction on joint moment.
And a solving module: based on the identified friction force parameters, on the symmetrical positive definite matrix manifold, the optimization technology on the manifold is used for solving, and the physical realizable dynamic parameters of each rigid body are obtained.
Those skilled in the art will appreciate that the invention provides a system and its individual devices, modules, units, etc. that can be implemented entirely by logic programming of method steps, in addition to being implemented as pure computer readable program code, in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers, etc. Therefore, the system and various devices, modules and units thereof provided by the invention can be regarded as a hardware component, and the devices, modules and units for realizing various functions included in the system can also be regarded as structures in the hardware component; means, modules, and units for implementing the various functions may also be considered as either software modules for implementing the methods or structures within hardware components.
The foregoing describes specific embodiments of the present invention. It is to be understood that the invention is not limited to the particular embodiments described above, and that various changes or modifications may be made by those skilled in the art within the scope of the appended claims without affecting the spirit of the invention. The embodiments of the present application and features in the embodiments may be combined with each other arbitrarily without conflict.
Claims (10)
1. A method for identifying the dynamic parameters of a robot based on projective geometry algebra is characterized by comprising the following steps:
the acquisition step: according to a robot kinematics model, establishing a kinetic equation, arranging the kinetic equation into a linear equation on a positive definite matrix manifold, generating an optimal excitation track according to the coefficient matrix condition number of the linear equation, and collecting data;
the processing steps are as follows: preprocessing the acquired data, filtering and identifying friction parameters, and eliminating the influence of friction on joint moment;
solving: based on the processed data, on the symmetrical positive definite matrix manifold, the optimization technology on the manifold is used for solving, and the physical realizable dynamic parameters of each rigid body are obtained.
2. The method for identifying the dynamic parameters of the robot based on the projective geometry algebra of claim 1, wherein the acquiring step comprises:
step 1.1: according to a kinematic model of the robot, calculating the pose, the speed and the acceleration of each rigid body and the position, the speed and the acceleration of a triple base vector fixedly connected to the rigid body, wherein the pose of the rigid body is an even-numbered unit multiple vector, the speed and the acceleration are double vectors, and the position, the speed and the acceleration of the triple base vector are triple vectors;
step 1.2: calculating an inertial force regression matrix of each rigid body, defining the inertial force regression matrix as a 4-order matrix, wherein each element in the matrix is a double vector and is only related to kinematic parameters; defining an inertia matrix as a 4-order symmetric positive definite matrix on a real number domain, and calculating the inertia force rotation of each rigid body by the inner products of the two 4-order matrices according to a correlation formula of projective geometry algebra;
step 1.3: calculating a generalized force regression matrix corresponding to each generalized force of each rigid body, arranging a dynamic equation of a robot system into a linear equation defined on a positive definite matrix manifold, calculating the contribution of the inertial force of a connecting rod of the robot system to a certain generalized force by the inner product of matrixes of two 4-order matrixes, wherein one matrix is the inertial matrix of the rigid body, the other matrix is defined as the generalized force regression matrix, calculating by a kinematic model of the rigid body and the inertial force regression matrix and is the 4-order matrix defined on a real number domain, and arranging the dynamic equation of the robot system to be Q=after arrangingR*NWherein Q is a generalized force vector defined over the real number domain;Rthe matrix is a special matrix, and the ith row and the jth outside of the matrix are generalized force regression matrices of inertia of the connecting rod j and generalized force i;Nthe j-th element is an inertia matrix of the connecting rod j, which is a special vector;
step 1.4: parameterizing the robot joint space trajectory and parameterizing the special matrix of step 1.3RReforming into regression matrices over real number domainYAnalyzing the minimum parameter set to obtain a regression matrix of the minimum parameter setY b Regression matrix with minimum parameter setY b The condition number of (2) is an objective function, and the optimal excitation track for dynamic parameter identification is obtained through optimization.
3. The method of claim 2, wherein the gradient of the objective function is calculated by an algorithm in the projective geometry algebra.
4. The method for identifying the robot dynamic parameters based on the projective geometry algebra of claim 1, wherein the processing step comprises:
removing noise generated in the joint motion data and the joint moment data due to the signal acquisition process through Butterworth filtering or other filtering means;
and carrying out preliminary identification on dynamic parameters of the system by using a least square method, wherein the dynamic parameters comprise inertia parameters and friction parameters.
5. The method for identifying the robot dynamic parameters based on projective geometry algebra of claim 2, wherein the solving step comprises: based on the linear equation, the physical realizability of the dynamic parameters is generalized to be the linear mapping of the rigid body's inverse dynamics from manifold to generalized force space on the symmetric positive definite matrix manifold, and the expression given in step 1.3 is provided, and in the embedded space of the symmetric positive definite matrix manifold, the gradient and the sea plug transformation are written analytically, and solved by the second-order optimization algorithm on manifold.
6. A system for identifying parameters of robot dynamics based on projective geometry algebra, comprising:
and the acquisition module is used for: according to a robot kinematics model, establishing a kinetic equation, arranging the kinetic equation into a linear equation on a positive definite matrix manifold, generating an optimal excitation track according to the coefficient matrix condition number of the linear equation, and collecting data;
the processing module is used for: preprocessing the acquired data, filtering and identifying friction parameters, and eliminating the influence of friction on joint moment;
and a solving module: based on the processed data, on the symmetrical positive definite matrix manifold, the optimization technology on the manifold is used for solving, and the physical realizable dynamic parameters of each rigid body are obtained.
7. The system of claim 6, wherein the acquisition module comprises:
module M1.1: according to a kinematic model of the robot, calculating the pose, the speed and the acceleration of each rigid body and the position, the speed and the acceleration of a triple base vector fixedly connected to the rigid body, wherein the pose of the rigid body is an even-numbered unit multiple vector, the speed and the acceleration are double vectors, and the position, the speed and the acceleration of the triple base vector are triple vectors;
module M1.2: calculating an inertial force regression matrix of each rigid body, defining the inertial force regression matrix as a 4-order matrix, wherein each element in the matrix is a double vector and is only related to kinematic parameters; defining an inertia matrix as a 4-order symmetric positive definite matrix on a real number domain, and calculating the inertia force rotation of each rigid body by the inner products of the two 4-order matrices according to a correlation formula of projective geometry algebra;
module M1.3: calculating a generalized force regression matrix corresponding to each generalized force of each rigid body, arranging a dynamic equation of a robot system into a linear equation defined on a positive definite matrix manifold, calculating the contribution of the inertial force of a connecting rod of the robot system to a certain generalized force by the inner product of matrixes of two 4-order matrixes, wherein one matrix is the inertial matrix of the rigid body, the other matrix is defined as the generalized force regression matrix, calculating by a kinematic model of the rigid body and the inertial force regression matrix and is the 4-order matrix defined on a real number domain, and arranging the dynamic equation of the robot system to be Q=after arrangingR*NWherein Q is a generalized force vector defined over the real number domain;Rthe ith row and the jth column of the matrix are generalized force regression matrices of inertia of the connecting rod j and generalized force i;Nthe j-th element is an inertia matrix of the connecting rod j, which is a special vector;
module 1.4: parameterizing the robot joint space trajectory and parameterizing said special matrix of modules M1.3RReforming into regression matrices over real number domainYAnalyzing the minimum parameter set to obtain a regression matrix of the minimum parameter setY b Regression matrix with minimum parameter setY b The condition number of (2) is an objective function, and the optimal excitation track for dynamic parameter identification is obtained through optimization.
8. The system of claim 7, wherein the gradient of the objective function is analytically calculated by an algorithm in the projective geometry algebra.
9. The system for identifying parameters of a robot based on projective geometry algebra of claim 6, wherein the processing module comprises:
removing noise generated in the joint motion data and the joint moment data due to the signal acquisition process through Butterworth filtering or other filtering means;
and carrying out preliminary identification on dynamic parameters of the system by using a least square method, wherein the dynamic parameters comprise inertia parameters and friction parameters.
10. The system of claim 7, wherein the solution module comprises: based on the linear equation, the physical realizability of the dynamic parameters is generalized to be the linear mapping of the rigid body's inverse dynamics from manifold to generalized force space on the symmetric positive definite matrix manifold, and the expression given by the module 1.3 is provided, and in the embedded space of the symmetric positive definite matrix manifold, the gradient and the sea plug transformation are written analytically, and solved by the second-order optimization algorithm on manifold.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310011748.0A CN116141314A (en) | 2023-01-05 | 2023-01-05 | Method and system for identifying dynamic parameters of robot based on projective geometry algebra |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310011748.0A CN116141314A (en) | 2023-01-05 | 2023-01-05 | Method and system for identifying dynamic parameters of robot based on projective geometry algebra |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN116141314A true CN116141314A (en) | 2023-05-23 |
Family
ID=86338302
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310011748.0A Pending CN116141314A (en) | 2023-01-05 | 2023-01-05 | Method and system for identifying dynamic parameters of robot based on projective geometry algebra |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116141314A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117331311A (en) * | 2023-09-21 | 2024-01-02 | 中山大学 | Robot dynamics parameter estimation method based on acceleration-free recursive filtering regression |
-
2023
- 2023-01-05 CN CN202310011748.0A patent/CN116141314A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117331311A (en) * | 2023-09-21 | 2024-01-02 | 中山大学 | Robot dynamics parameter estimation method based on acceleration-free recursive filtering regression |
| CN117331311B (en) * | 2023-09-21 | 2024-05-14 | 中山大学 | Robot dynamics parameter estimation method based on acceleration-free recursive filtering regression |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Gao et al. | Design optimization of a spatial six degree-of-freedom parallel manipulator based on artificial intelligence approaches | |
| Eski et al. | Fault detection on robot manipulators using artificial neural networks | |
| Wu et al. | An overview of dynamic parameter identification of robots | |
| Tan et al. | A prediction and compensation method of robot tracking error considering pose-dependent load decomposition | |
| Enferadi et al. | A Kane’s based algorithm for closed-form dynamic analysis of a new design of a 3RSS-S spherical parallel manipulator | |
| Liu et al. | Predicting the position-dependent dynamics of machine tools using progressive network | |
| Yang et al. | Robot kinematics and dynamics modeling | |
| Huang et al. | Dynamic parameter identification of serial robots using a hybrid approach | |
| Al Mashhadany | Virtual reality trajectory of modified PUMA 560 by hybrid intelligent controller | |
| CN116141314A (en) | Method and system for identifying dynamic parameters of robot based on projective geometry algebra | |
| Zhang et al. | Robot peg-in-hole assembly based on contact force estimation compensated by convolutional neural network | |
| Zhao et al. | A learning-based multiscale modelling approach to real-time serial manipulator kinematics simulation | |
| Oh et al. | Force/torque sensor calibration method by using deep-learning | |
| CN113618730B (en) | Robot motion analysis method and device, readable storage medium and robot | |
| Grazioso et al. | Modeling and simulation of hybrid soft robots using finite element methods: Brief overview and benefits | |
| Buffinton | Kane’s Method in Robotics | |
| Van Der Smagt et al. | Solving the ill-conditioning in neural network learning | |
| Beiki et al. | Optimal trajectory planning of a six DOF parallel stewart manipulator | |
| CN112276947B (en) | Robot motion simulation method, device, equipment and storage medium | |
| Ardiani | Contribution to the parametric identification of dynamic models: application to collaborative robotics | |
| Wang et al. | Reference trajectory generation for force tracking impedance control by using neural network-based environment estimation | |
| Lee et al. | Optimized System Identification of Humanoid Robots with Physical Consistency Constraints and Floating-based Exciting Motions | |
| Dash et al. | A inverse kinematic solution of a 6-dof industrial robot using ANN | |
| CN116796636A (en) | RBFN-based positive dynamic analysis method and system containing sliding friction mechanism | |
| Yu et al. | Physical-Parameter-Free Learning of Inverse Dynamics for Multi-DOF Industrial Robots via Sparsity and Feature Learning |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |