CN117331311A - Robot dynamics parameter estimation method based on acceleration-free recursive filtering regression - Google Patents
Robot dynamics parameter estimation method based on acceleration-free recursive filtering regression Download PDFInfo
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Abstract
The invention discloses a robot dynamic parameter estimation method based on acceleration-free recursive filtering regression, which comprises the following steps: constructing a robot kinematics model; constructing a first robot dynamics model based on a recursive Newton-Euler algorithm, and carrying out linear parameterization on the first robot dynamics model to obtain a second robot dynamics model; modeling the second robot dynamics into a minimum parameter set form based on a recursive parameter zero-space algorithm to obtain a first calculation result; convolving the first calculation result with the impulse response of the low-pass filter, and carrying out linear parameterization and filtering on the convolution result to obtain acceleration-free second-order filtering regression; and determining a composite learning parameter update law according to the acceleration-free second-order filtering regression, and using the composite learning parameter update law for self-adaptive parameter estimation and control. According to the invention, the filter regression matrix can be solved without acceleration feedback, parameter estimation of index convergence under interval excitation is realized, the identification precision, tracking performance and robustness of the robot system are improved, and the method can be applied to the technical field of robot ginseng number identification and control.
Description
Technical Field
The invention relates to the technical field of automatic control of robots, in particular to a robot dynamics parameter estimation method based on acceleration-free recursive filtering regression.
Background
Robots are typically complex systems with high degrees of freedom, strong nonlinearities, and high coupling. The dynamics model parameters of the robot are difficult to accurately obtain through physical measurement or CAD model calculation, and only linear combinations composed of part of the dynamics model parameters are distinguishable, and a set composed of the linear combinations is called a minimum parameter set. Furthermore, the kinetic parameters of the robot may change in the environment, such as slow parameter time-variations due to equipment aging, and overall kinetic parameters of the robot change due to load changes.
For a robot with low degree of freedom (such as a planar two-link mechanical arm), a linear parameterized model in a minimum parameter set form is easy to deduce manually, and the acquisition of a filtering regression matrix can be realized by rewriting a filtering acceleration term in a common regression matrix into a filtering derivative form of speed, so that the use of an acceleration signal is avoided. However, for a robot with a high degree of freedom, the number of terms of the analytical expression of the regression matrix in the form of the minimum parameter set is so large that it is difficult to derive it manually, so that it is also difficult to obtain the filtered regression matrix in a similar manner to a robot with a low degree of freedom.
In addition, parameter convergence requires a regression matrix Φ (τ) ∈R in performing machine ginseng number estimation n×N A certain excitation condition is satisfied, wherein the continuous excitation condition is defined as: for any time t.gtoreq.0, there is a positive constant T, α such thatI represents a unit array. Whereas the interval excitation condition is defined as: there are positive constants T and T e In time interval [ T e ,T e +T]The presence of an incentive, i.e.)>
The existing self-adaptive parameter estimation and control method for the high-freedom robot mainly has the following two defects: (1) The calculation complexity of the regression matrix is high by using the dynamic modeling method of the analytical expression, and the calculation of the filtering regression matrix depends on the estimated joint acceleration signal; (2) The kinetic modeling method using the RNE algorithm does not transform the kinetic model into a minimum parameter set form, unrecognizable parameters exist in the parameter vector, and parameter convergence depends on strict continuous excitation conditions.
Disclosure of Invention
The present invention aims to solve at least one of the technical problems in the related art to some extent. Therefore, the invention provides a robot dynamics parameter estimation method based on an acceleration-free recursive filtering regression matrix.
In one aspect, an embodiment of the present invention provides a method for estimating a robot kinetic parameter based on acceleration-free recursive filtering regression, including:
constructing a robot kinematics model according to a space vector representation method;
constructing a first robot dynamics model based on the robot dynamics model, and performing linear parameterization on the robot dynamics model to obtain a second robot dynamics model;
converting the second robot dynamics model into a minimum parameter set form to obtain a first calculation result; the first calculation result comprises a minimum parameter set and a common regression matrix;
performing convolution processing on the first calculation result and impulse response of a first-order low-pass filter, performing linear parameterization processing on the convolution processing result to obtain a first-order filtering regression matrix, and then passing the first-order filtering regression matrix through the first-order low-pass filter to obtain an acceleration-free second-order recursive filtering regression matrix;
and determining a composite learning parameter update law according to the acceleration-free second-order recursive filtering regression matrix, and performing parameter estimation.
Optionally, the constructing a robot kinematic model according to the space vector representation includes:
establishing a connecting rod coordinate system, and determining the conversion relation of adjacent connecting rod coordinate systems;
constructing a space vector and a space transfer matrix of a mechanical arm connecting rod based on the connecting rod coordinate system, and generating a robot kinematic model; wherein the spatial transfer matrix satisfies a transfer property.
Optionally, the constructing a first robot dynamics model based on the robot dynamics model, and performing linear parameterization on the robot dynamics model to obtain a second robot dynamics model, including:
determining the number of degrees of freedom of the robot;
constructing a first robot dynamics model by adopting a space vector RNE algorithm according to the number of degrees of freedom;
and carrying out linear parameterization on the first robot dynamics model according to the physical properties of the robot to obtain a second robot dynamics model.
Optionally, the converting the second robot dynamics model into a minimum parameter set form, to obtain a first calculation result, includes:
adopting an RPN algorithm to solve the second robot dynamics model into a minimum parameter set;
calculating a common regression matrix corresponding to the minimum parameter set;
and taking the minimum parameter set and the common regression matrix as a first calculation result.
Optionally, the convolving the first calculation result and the impulse response of the first-order low-pass filter, performing linear parameterization on the convolved result to obtain a first-order filtering regression matrix, and passing the first-order filtering regression matrix through the first-order low-pass filter to obtain an acceleration-free second-order recursive filtering regression matrix, including:
carrying out convolution processing on the first calculation result, the first-order low-pass filter and the impulse response to obtain a convolution processing result;
converting the convolution processing result into a minimum parameter set form, and carrying out linear parameterization based on a space vector RNE algorithm to obtain a first-order filtering regression matrix;
and performing primary filtering on the primary filtering regression matrix to obtain an acceleration-free second-order recursive filtering regression matrix.
Optionally, the determining a composite learning parameter update law according to the acceleration-free second-order recursive filtering regression matrix is used for parameter estimation, and includes:
acquiring a joint expected position, expected speed and expected acceleration;
calculating a joint position error from the joint desired position, the desired velocity, and the desired acceleration;
calculating a filtered tracking error and a reference speed from the joint position error and the desired speed;
and determining a composite learning parameter updating law according to the filtering tracking error, the joint expected position, the expected speed and the expected acceleration.
Optionally, the expression of the complex learning parameter update law is:
wherein,representing a composite learning parameter update law; Γ represents a positive definite diagonal learning rate matrix; phi represents a normal regression matrix with a reference speed, T represents a matrix transpose; q represents a position; />Representing the speed; />Representing a reference speed; />Representing a reference acceleration; e, e f Representing a filtered tracking error; epsilon represents the prediction error; kappa represents the prediction error weight.
On the other hand, the embodiment of the invention also provides a robot dynamics parameter estimation system based on acceleration-free recursive filtering regression, which comprises the following steps:
the first module is used for constructing a robot kinematic model according to the space vector representation method;
the second module is used for constructing a first robot dynamics model based on the robot dynamics model, and carrying out linear parameterization on the robot dynamics model to obtain a second robot dynamics model;
the third module is used for converting the second robot dynamics model into a minimum parameter set form to obtain a first calculation result; the first calculation result comprises a minimum parameter set and a common regression matrix;
a fourth module, configured to perform convolution processing on the first calculation result and an impulse response of a first-order low-pass filter, perform linear parameterization processing on the convolution processing result to obtain a first-order filtering regression matrix, and then pass the first-order filtering regression matrix through the first-order low-pass filter to obtain an acceleration-free second-order recursive filtering regression matrix;
and a fifth module, configured to determine a composite learning parameter update law according to the acceleration-free second-order recursive filtering regression matrix, and perform parameter estimation.
It should be noted that the system may further include:
and the sixth module is used for planning the expected track of the joint of the arm robot according to the task requirement of the arm robot and obtaining the expected position, speed and acceleration of the joint. Obtaining a complex learning parameter updating law and a control law by using the expected data and the arm robot joint position, speed and moment sensing data to obtain a robust complex learning self-adaptive controller; the controller is adopted to drive the arm type robot to move according to the planned expected track.
In another aspect, an embodiment of the present invention further provides an electronic device, including: a processor and a memory; the memory is used for storing programs; the processor executes the program to implement the method as described above.
In another aspect, embodiments of the present invention also provide a computer storage medium in which a processor-executable program is stored, which when executed by a processor is configured to implement the method as described above.
The embodiment of the invention has the following beneficial effects: constructing a robot kinematic model according to a space vector representation method; constructing a first robot dynamics model based on the robot dynamics model, and performing linear parameterization on the robot dynamics model to obtain a second robot dynamics model; converting the second robot dynamics model into a minimum parameter set form to obtain a first calculation result; the first calculation result comprises a minimum parameter set and a common regression matrix; performing convolution processing on the first calculation result and impulse response of the first-order low-pass filter, performing linear parameterization processing on the convolution processing result to obtain a first-order filtering regression matrix, and then passing the first-order filtering regression matrix through the first-order low-pass filter to obtain an acceleration-free second-order recursive filtering regression matrix; the composite learning parameter update law is determined according to the acceleration-free second-order recursive filtering regression matrix and is used for carrying out the overall step of parameter estimation, the filtering regression matrix can be solved under the condition that acceleration feedback is not needed, the parameter estimation can be carried out without acceleration feedback, the performance and the robustness of the parameter estimation are improved, and the method can be applied to the self-adaptive parameter estimation of the high-freedom-degree arm robot.
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The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate and do not limit the invention.
FIG. 1 is a step diagram of a robot dynamics parameter estimation method based on acceleration-free recursive filtering regression provided by an embodiment of the present invention;
FIG. 2 is a schematic diagram of a set of modified DH parameter coordinate systems provided by an embodiment of the present invention;
FIG. 3 is a graph showing experimental results of the method of the present invention and the conventional method applied to simulation comparison of error norms of a mechanical arm according to the embodiment of the present invention;
FIG. 4 is a graph of simulation contrast of tracking error norms of a mechanical arm using the method of the present invention and a conventional method according to an embodiment of the present invention;
FIG. 5 is a block diagram of a robot dynamics parameter estimation system based on acceleration-free recursive filtering regression provided by an embodiment of the present invention;
fig. 6 is a block diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
It should be noted that although functional block diagrams are depicted as block diagrams, and logical sequences are shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the block diagrams in the system. The terms first/S100, second/S200, and the like in the description and in the claims and in the above-described figures, are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order.
Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment of the invention. The appearances of such phrases in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. Those of skill in the art will explicitly and implicitly appreciate that the embodiments described herein may be combined with other embodiments.
Unless otherwise indicated, the terms "acceleration-free recursive filter regression matrix" and "acceleration-free second order recursive filter regression matrix" are used herein to be understood as meaning the former for short. The symbology convention herein is: thickening the lower case vector; capitalization vectors, scalar quantities, and matrix are not bolded; i n Representing an n x n dimensional array of units.
The following describes a robot dynamics parameter estimation method based on acceleration-free recursive filtering regression according to an embodiment of the present invention, referring to fig. 1, the method includes the following steps S100 to S500:
s100, constructing a robot kinematic model according to a space vector representation method.
Specifically, step S100 includes the following steps S110 to S120.
S110, establishing a connecting rod coordinate system, and determining the conversion relation of adjacent connecting rod coordinate systems.
The coordinate system i is defined by three axes attached to the link i in pairs perpendicular and conforming to the right hand rule. As shown in FIG. 2, the coordinate system is established to meet the modified DH (Denavit-Hartenberg) parameter specification, α in FIG. 2 i-1 ,a i-1 ,d i ,θ i Representing link rotation angle (link offset), link length (link length), link offset (link offset) and joint angle (joint angle) associated with the transformation between coordinate system i and coordinate system i+1, respectively;representing a rotation matrix transformed from coordinate system i+1 to coordinate system i, wherein +.>Is the projection of three basis vectors of the coordinate system i on three axes of the coordinate system i+1; the rotation matrix is an orthonormal matrix with determinant 1, which satisfies the property +.>
S120, constructing a space vector and a space transfer matrix of a mechanical arm connecting rod based on a connecting rod coordinate system, and generating a robot kinematic model; wherein the spatial transfer matrix satisfies the transfer property.
The space vector is a six-dimensional vector formed by combining a rigid body (angular velocity or moment) and (linear velocity or force). For the link i (i e {0,1, …, n }) of the mechanical arm, its spatial velocity vector v i ∈R 6 The specific expression is:
wherein omega i A rotational angular velocity v of the link i about the z-axis of the coordinate system i as a rotational axis i Is the expression of the linear velocity of the origin of the coordinate system i on the coordinate system i. The spatial acceleration vector is defined as
For the connecting rod i of the mechanical arm, the space force vector f i ∈R 6 The expression is:
wherein τ i ∈R 3 And f si ∈R 3 The moment and the force exerted on the connecting rod i are expressed on a coordinate system i respectively.
Space transfer matrix for transforming a space velocity vector or a space acceleration vector from a coordinate system i-1 to iThe definition is as follows:
wherein r is i-1,i Is the expression on the coordinate system i-1 of a vector pointing from the origin of the coordinate system i-1 to the origin of the coordinate system i.
Space transfer matrix for transforming a space force vector from coordinate system i+1 to coordinate system iThe definition is as follows:
is obtained by the above method
In an embodiment of the present invention, there are the following definitions:
(1) For any three-dimensional vector a= [ a ] 1 ,a 2 ,a 3 ] T A x is a cross operator, defined as:
a＝[a 1 ,a 2 ,a 3 ] T for any three-dimensional vector b= [ b ] 1 ,b 2 ,b 3 ] T The method comprises the following steps:
(2) Space velocity vector for connecting rod iDefining a spatial cross-product operator applied to the forward recursion as:
and defining a spatial cross-product operator v to which backward recursion is applied i ×] * ＝-[v i ×] T 。
(3) The space transfer matrix satisfies the transfer property, and the space transfer matrix between the connecting rod i and the connecting rod j satisfies the relation:
wherein, the embodiment of the invention assumes i>j, and prescribe
S200, constructing a first robot dynamics model based on the robot dynamics model, and performing linear parameterization on the robot dynamics model to obtain a second robot dynamics model.
Specifically, step S200 includes the following steps S210 to S230.
S210, determining the number of degrees of freedom of the robot.
S220, constructing a first robot dynamics model by adopting a space vector RNE algorithm according to the number of degrees of freedom.
By way of example, assuming that an arm robot has n degrees of freedom, an open loop dynamics model of the robot in closed form, i.e. a first robot dynamics model, may be expressed as:
wherein,expressed as acceleration, velocity and angle of the robot joint, respectively, τ e R n Represents the driving moment of the joint, M epsilon R n×n Is the inertial matrix of the robot, C epsilon R n×n G epsilon R as centrifugal force family type force matrix n Force moment vector F E R n Is a friction torque.
The space vector RNE inverse dynamics algorithm is expressed as:
forward recursion:i＝1,2,…,n.g 0 ＝[0 0 0 0 0 9.81] T
backward recursion:i＝n,n-1,…,1.f n+1 ＝0
wherein s is i ∈R 6 The spatial axis vector representing the ith joint (determined by the joint type). In the case of a rotary joint,z∈R 3 at the ith coordinate for joint iAnd (5) tying an orientation vector. For a rotary joint with the z-axis as the rotation axis, z= [ 00 1] T . J in the above i ∈R 6×6 Representing the spatial inertia of the connecting rod i, defined as:
wherein J is Ci ∈R 3×3 To be in an inertia matrix relative to the mass center of the connecting rod, m i Is the mass of the connecting rod i, c i ＝C xi C yi C zi ] T Is the expression of a vector from the origin of the coordinate system i to the centroid of the link i on the coordinate system i. J (J) i The expansion of (2) is as follows:
definition W i ＝m i ,m i C xi ,m i C yi ,m i C zi ,J xxi ,J yyi ,J zzi ,J xyi ,J xzi ,J yzi ] T Is the parameter vector of the connecting rod i, wherein W i l E R is W i R is the first parameter of (2) l To indicate parameter W i l At J i Matrix of intermediate positions, W i l The position of occurrence is 1, and the remaining positions are 0. Then J i All can be expressed as 10R l Linear combination of matrices:
it should be noted that, the Recursive Newton-Euler (RNE) algorithm is a method capable of reducing the computational complexity of the regression matrix to O (n) 2 ) Is a robot dynamics modeling method.
S230, performing linear parameterization on the first robot dynamics model according to the physical properties of the robot to obtain a second robot dynamics model.
Generally, kinematic DH parameters (such as link length, link rotation angle, link offset and joint angle) of the robot are easy to obtain, and dynamic parameters (such as link centroid position, moment of inertia and mass) are difficult to accurately determine. The embodiment of the invention assumes that the robot modified DH parameters are known and the dynamics parameters are unknown. Depending on the physical properties of the robot, the part of the kinetic equation that does not contain friction can be parameterized linearly in the form of the following closures:
wherein W is link ∈R 10n Is a vector containing only kinetic parameters, and is composed of parameters W of n connecting rods i The composition is formed by the following steps:
W 1ink ＝[W 1 ,W 2 ,…,W n ] T
meanwhile, the parameterized model can be expressed in a generalization way as follows:
wherein,for the auxiliary variables introduced ∈ ->Is its derivative. Let->Generalizing the regression matrixLet go of->Function phi link For a regression matrix independent of unknown kinetic parameters, Φ according to the above generalized parameterized model and space vector RNE inverse dynamics algorithm link Can be expressed as:
wherein,H i ∈R 6×10 and regression matrix components corresponding to the connecting rods. H is given below i Is a solution process of (1):
forward recursion:
i＝1,2,…,n。g 0 ＝[0,0,0,0,0,9.81] T
wherein H is i,l ∈R 6 Components related to each parameter in the regression matrix;and->Respectively->And the ith element of q.
For the case where the friction is to be considered, assuming that the friction coefficient is unknown, the friction model using linear parameterization is as follows:
wherein F is v ,F c ∈R n×n ,F o ∈R n Respectively a diagonal viscous friction coefficient matrix, a diagonal coulomb friction coefficient matrix and coulomb frictionWiping the offset vector; c is a constant for determining the steepness of the tanh function; w (W) fric ∈R 3n Is a friction parameter vector, and the expression is as follows:
W frix ＝[f v1 ,f x1 ,f o1 ,f v2 ,f x2 ,f o2 ,…,f vn ,f cn ,f on ] T
wherein f vi ,f ci Is F v ,F c The i-th diagonal element, f oi Is F o Is selected from the group consisting of the (i) th element,the regression matrix, independent of the coefficient of friction, is as follows:
in summary, the linear parameterized kinetic model, i.e. the second kinetic model, can be expressed as:
s300, converting the second robot dynamics model into a minimum parameter set form to obtain a first calculation result; wherein the first calculation result includes a minimum parameter set and a common regression matrix.
S310, solving a second robot dynamics model into a minimum parameter set by adopting an RPN algorithm.
The RPN algorithm is an algorithm used in rigid body dynamics to calculate rigid body system motion. Based on Newton-Euler equation, the dynamic behavior of the whole system is obtained by recursively calculating the motion state and moment of each rigid body. The basic idea of the algorithm is to calculate the motion state and moment of each rigid body layer by layer, starting from the bottom. First, for each rigid body, its acceleration is calculated by newton's second law. Then, the angular acceleration and the angular velocity of the rigid body are calculated using the euler equation. Next, based on the mass of the rigid body, the inertia matrix, and the external moment, the resultant force and resultant moment of the rigid body are calculated. The scheme utilizes an RPN algorithm to solve a minimum parameter set of the high-freedom-degree arm robot and a regression matrix corresponding to the minimum parameter set. The kinetic equation of the minimum parameter set form (the variable of the minimum parameter set is identified by a base) is consistent and equivalent to the general kinetic equation form, and specifically:
wherein n is the degree of freedom of the arm robot, and if the minimum parameter set element number of the dynamic parameters of the connecting rod is m, thenW link,base ∈R m 。
S320, determining a common regression matrix corresponding to the minimum parameter set.
Three DH parameters (link rotation angle, link length and link offset) of the robot are used as input, and the PHI can be obtained by using RPN algorithm link Conversion to phi link,base Mapping matrix P of (2) m ∈R 10n×m And W is to link Conversion to W link,base Mapping matrix P of (2) p ∈R m×10n The method comprises the following steps:
Φ link,base ＝Φ link P m ,
W link,base ＝P p W link .
when friction is considered, the linear parameterized kinetic model in the form of a minimum parameter set is:
wherein,w E R as a common regression matrix N Is a minimum parameter set vector (toHereinafter referred to as parameter vectors), n=m+3n is the total number of identifiable parameters.
S330, taking the minimum parameter set and the common regression matrix as a first calculation result.
S400, carrying out convolution processing on the first calculation result and the impulse response of the first-order low-pass filter, carrying out linear parameterization processing on the convolution processing result, and carrying out first-order filtering on the first-order filtering regression matrix to obtain an acceleration-free second-order recursive filtering regression matrix.
When calculating the torque prediction error, the common regression matrix obtained in S300 is needed, wherein the input contains the accelerationFor most arm robots, +.>And often cannot be measured directly. The regression matrix can be eliminated by filteringThe effects of reducing noise influence and improving system parameter convergence, tracking performance and robustness are achieved. However, for the high-degree-of-freedom arm robot, the regression matrix analysis expression has a plurality of terms, so that a corresponding filtering regression matrix is difficult to obtain. The embodiment of the invention can effectively solve the elimination of +.>Is a filtered regression matrix of (a).
Specifically, step S400 includes the following steps S410 to S430.
S410, carrying out convolution processing on the first calculation result and the impulse response of the first-order filter to obtain a convolution processing result.
The essence of filtering is to convolve the input with the unit impulse response of the first order low pass filter in the time domain. Fractional integration of convolution operations and exploiting the antisymmetric nature of the robot dynamics equation (i.e.) Can be eliminated->The expression of (2) is as follows:
wherein the method comprises the steps ofFor a first order low pass filter operator, +.>For filtering moment +.>Is w (t) =λe -λt Wherein e refers to a natural base.
Description in space vector representationAnd the ith element of the gravity term G (q) can be expressed as:
where i=1, 2, …, n.
S420, converting the convolution processing result into a minimum parameter set form, and performing linear parameterization based on a space vector RNE algorithm to obtain a first-order filtering regression matrix.
The above is performed in a similar manner to the processing of the kinetic equation in step S200And G (q) are converted into a minimum parameter set form, and linear parameterization is carried out based on space vector RNE to obtain +.>Andso that the following formula holds:
G(q)＝Φ 3 (q)P m W ,
thus, there is a first order filtered regression matrix Φ that does not take friction terms into account as follows f,link, ∈R n×N ：
S430, performing primary filtering on the primary filtering regression matrix to obtain an acceleration-free second-order recursive filtering regression matrix.
Because the first term on the right of the above formula has a noisy speed term, the embodiment of the invention uses an additional first-order filter to act on the first-order filter regression matrix to obtain a second-order filter regression matrix, so as to reduce the influence of the noisy speed term on parameter convergence and tracking performance, and the corresponding acceleration-free second-order recursive filter regression matrix expression in the form of a minimum parameter set is as follows:
wherein,is a second order filter operator.
S500, determining a composite learning parameter updating law according to the acceleration-free second-order recursive filtering regression matrix, and performing parameter estimation.
Specifically, step S500 includes the following steps S510 to S540.
S510, acquiring a joint expected position, expected speed and expected acceleration.
Specifically, the desired joint position q is obtained d ∈R n Desired speedAnd desired acceleration->
S520, calculating joint position errors according to the joint expected positions, expected speeds and expected accelerations.
The calculation formula of the joint position error e is: e=q d Q, where q is the actual position of the joint.
S530, calculating a filter tracking error and a reference speed according to the joint position error and the expected speed.
The calculation formula of the filtering tracking error is as follows:
the calculation formula of the reference speed is:
wherein, lambda E R n×n And (5) determining a symmetrical matrix for the selected positive.
S540, determining a composite learning parameter updating law according to the filtered tracking error, the expected position of the joint, the expected speed and the expected acceleration.
Specifically, the expression of the complex learning parameter update law in the embodiment of the invention is:
wherein,representing a composite learning parameter update law; Γ ε R N×N Determining a diagonal learning rate matrix for positive; phi represents a common regression matrix containing reference speed, and T represents matrix transposition; q represents a position; />Representing the speed; />Representing a reference speed; />Representing a reference acceleration; e, e f Representing a filtered tracking error; kappa represents a constant, kappa is a positive value, and represents the weight occupied by the prediction error in parameter updating; e represents the prediction error.
The expression of the control law is:
wherein the reference accelerationIs reference speed +.>Derivative of K c ∈R n×n To right and left anglesMatrix (S)>Parameters are estimated for online. The regression expansion matrix of the embodiment of the invention is as follows:
wherein τ d ∈R + For the length of the integration interval,and S5, obtaining a filtered regression matrix. The prediction error of the compound learning is as follows: />
Wherein τ f Is the filtered measured torque. T (T) e Time t is when the interval excitation condition is satisfied e Is [ T ] e ,t]The minimum singular value of Θ (t) in the time period takes the maximum value.
In some embodiments, the method may further comprise:
and planning the expected track of the joint of the arm robot according to the task requirement of the arm robot, and obtaining the expected position, speed and acceleration of the joint. Obtaining the update law and the control law of the composite learning parameters by using the expected data and the joint position, speed and moment sensing data of the arm robot to obtain a robust composite learning self-adaptive controller; the controller is adopted to drive the arm type robot to move according to the planned expected track.
In another aspect, as shown in fig. 5, an embodiment of the present invention provides a robot dynamics parameter estimation system based on acceleration-free recursive filtering regression, including:
the first module is used for constructing a robot kinematic model according to the space vector representation method;
the second module is used for constructing a first robot dynamics model based on the robot dynamics model, and carrying out linear parameterization on the robot dynamics model to obtain a second robot dynamics model;
the third module is used for converting the second robot dynamics model into a minimum parameter set form to obtain a first calculation result; the first calculation result comprises a minimum parameter set and a common regression matrix;
a fourth module, configured to perform convolution processing on the first calculation result and the impulse response of the first-order low-pass filter, perform linear parameterization processing on the convolution processing result, and perform first-order filtering on the first-order filtering regression matrix to obtain an acceleration-free second-order recursive filtering regression matrix;
and a fifth module, configured to determine a composite learning parameter update law according to the acceleration-free second-order recursive filtering regression matrix, and perform parameter estimation.
It should be noted that, in some embodiments, the system may further include the following modules:
and the sixth module is used for planning the expected track of the joint of the arm robot according to the task requirement of the arm robot and obtaining the expected position, speed and acceleration of the joint. Obtaining a complex learning parameter updating law and a control law by using the expected data and the arm robot joint position, speed and moment sensing data to obtain a robust complex learning self-adaptive controller; the controller is adopted to drive the arm type robot to move according to the planned expected track.
On the other hand, as shown in fig. 6, an embodiment of the present invention further provides an electronic device, including: a processor and a memory; the memory is used for storing programs; the processor executes the program to implement the method as described above.
In another aspect, embodiments of the present invention also provide a computer storage medium in which a processor-executable program is stored, which when executed by a processor is configured to implement the method as above.
The embodiment of the invention has the following beneficial effects:
1. the space vector is used for representing the RNE algorithm to realize the linear parameterization of the dynamic model of the robot with high degree of freedom, and the dynamic model is decoupled into the product of the regression matrix and the minimum parameter set vector to be identified, so that the method has the advantage of small calculated amount.
2. And the minimum parameter set of the robot and the corresponding regression matrix thereof are obtained by utilizing an RPN algorithm, so that all parameters are distinguishable, and a foundation is laid for accurate convergence of model parameters.
3. The RNE algorithm is represented by using space vectors, and each part of the convolution result of the kinetic equation is respectively and linearly parameterized, so that a filtering regression matrix is solved under the condition of avoiding input acceleration feedback, the acceleration feedback in the parameter estimation process is not required to be acquired, second-order filtering is used, and the influence of noisy speed items and inaccurate estimated acceleration on parameter convergence and tracking performance is avoided. Therefore, the performance and the robustness of the high-freedom-degree robot adaptive parameter estimation and control can be improved.
4. The embodiment of the invention can be applied to on-line identification of the robot dynamic model parameters so as to realize self-adaptive control, not only can obtain excellent dynamic and steady-state control performance, but also can use the identified accurate robot model for upper-layer decisions such as motion planning, fault prediction and the like.
Embodiments of the invention are further described below in conjunction with experimental data:
referring to fig. 3 and 4, fig. 3 illustrates simulation comparison results of a robot dynamics parameter estimation method without acceleration state feedback and a conventional method requiring acceleration signals applied to a high-degree-of-freedom robot Franka Emika Panda according to an embodiment of the present invention. In the view of figure 3 of the drawings,the error norm is represented, and it can be seen that fig. 3 shows that the error norm of the method of the present invention is smaller than that of the conventional method, and has better parameter convergence result; in fig. 4, i e i indicates a tracking error, and it can be seen that fig. 4 shows that the tracking error of the method of the present invention is smaller than that of the conventional method, and has a better tracking effect. In the experimental process, gaussian white noise with average value of 0 and standard deviation of 1e-6 is added into the position feedback q of the two methods, and the method is traditionalThe method and the velocity feedback method of the embodiment of the invention are added with Gaussian white noise with the mean value of 0 and the standard deviation of 1e-4, and acceleration information of the traditional method is represented by ∈4>And (5) estimating.
In summary, compared with the existing robot adaptive parameter estimation and control method using the RNE algorithm to perform dynamic modeling, the method utilizes the RPN algorithm to model dynamics into a minimum parameter set form, all elements in a parameter vector are identifiable parameters, and exponential convergence of the parameters only depends on interval excitation conditions which are easy to meet.
In some alternative embodiments, the functions/acts noted in the block diagrams may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Furthermore, the embodiments presented and described in the flowcharts of the present invention are provided by way of example in order to provide a more thorough understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed, and in which sub-operations described as part of a larger operation are performed independently.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method of the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
Logic and/or steps represented in the flowcharts or otherwise described herein, e.g., a ordered listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). In addition, the computer readable medium may even be paper or other suitable medium on which the program is printed, as the program may be electronically captured, via, for instance, optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner, if necessary, and then stored in a computer memory.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.
While the preferred embodiment of the present invention has been described in detail, the present invention is not limited to the embodiments described above, and those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention, and these equivalent modifications or substitutions are included in the scope of the present invention as defined in the appended claims.
Claims (10)
1. The robot dynamics parameter estimation method based on acceleration-free recursive filtering regression is characterized by comprising the following steps of:
constructing a robot kinematics model according to a space vector representation method;
constructing a first robot dynamics model based on the robot dynamics model, and performing linear parameterization on the robot dynamics model to obtain a second robot dynamics model;
converting the second robot dynamics model into a minimum parameter set form to obtain a first calculation result; the first calculation result comprises a minimum parameter set and a common regression matrix;
performing convolution processing on the first calculation result and impulse response of a first-order low-pass filter, performing linear parameterization processing on the convolution processing result to obtain a first-order filtering regression matrix, and then passing the first-order filtering regression matrix through the first-order low-pass filter to obtain an acceleration-free second-order recursive filtering regression matrix;
and determining a composite learning parameter update law according to the acceleration-free second-order recursive filtering regression matrix, and performing parameter estimation.
2. The method for estimating a robot kinetic parameter based on acceleration-free recursive filtering regression according to claim 1, wherein the constructing a robot kinematic model from a spatial vector representation comprises:
establishing a connecting rod coordinate system, and determining the conversion relation of adjacent connecting rod coordinate systems;
constructing a space vector and a space transfer matrix of a mechanical arm connecting rod based on the connecting rod coordinate system, and generating a robot kinematic model; wherein the spatial transfer matrix satisfies a transfer property.
3. The method for estimating a robot dynamics parameter based on acceleration-free recursive filtering regression according to claim 1, wherein the constructing a first robot dynamics model based on the robot dynamics model and performing linear parameterization on the robot dynamics model to obtain a second robot dynamics model comprises:
determining the number of degrees of freedom of the robot;
constructing a first robot dynamics model by adopting a space vector RNE algorithm according to the number of degrees of freedom;
and carrying out linear parameterization on the first robot dynamics model according to the physical properties of the robot to obtain a second robot dynamics model.
4. The method for estimating robot dynamics parameters based on acceleration-free recursive filtering regression according to claim 1, wherein the converting the second robot dynamics model into a minimum parameter set form, to obtain a first calculation result, comprises:
adopting an RPN algorithm to solve the second robot dynamics model into a minimum parameter set;
calculating a common regression matrix corresponding to the minimum parameter set;
and taking the minimum parameter set and the common regression matrix as a first calculation result.
5. The method for estimating the robot dynamics parameters based on the acceleration-free recursive filter regression according to claim 1, wherein the convolution processing is performed on the first calculation result and the impulse response of the first-order low-pass filter, the linear parameterization processing is performed on the convolution processing result to obtain a first-order filter regression matrix, and the first-order filter regression matrix is passed through the first-order low-pass filter to obtain an acceleration-free second-order recursive filter regression matrix, comprising:
carrying out convolution processing on the first calculation result, the first-order low-pass filter and the impulse response to obtain a convolution processing result;
converting the convolution processing result into a minimum parameter set form, and carrying out linear parameterization based on a space vector RNE algorithm to obtain a first-order filtering regression matrix;
and performing primary filtering on the primary filtering regression matrix to obtain an acceleration-free second-order recursive filtering regression matrix.
6. The method for estimating robot dynamics parameters based on acceleration-free recursive filtering regression according to claim 1, wherein the determining a complex learning parameter update law for parameter estimation based on the acceleration-free second-order recursive filtering regression matrix comprises:
acquiring a joint expected position, expected speed and expected acceleration;
calculating a joint position error from the joint desired position, the desired velocity, and the desired acceleration;
calculating a filtered tracking error and a reference speed from the joint position error and the desired speed;
and determining a composite learning parameter updating law according to the filtering tracking error, the joint expected position, the expected speed and the expected acceleration.
7. The method for estimating a robot kinetic parameter based on acceleration-free recursive filtering regression according to claim 6, wherein the expression of the complex learning parameter update law is:
wherein,representing a composite learning parameter update law; Γ represents a positive definite diagonal learning rate matrix; phi represents a normal regression matrix with a reference speed, T represents a matrix transpose; q represents a position; />Representing the speed; />Representing a reference speed; />Representing a reference acceleration; e, e f Representing a filtered tracking error; epsilon represents the prediction error; kappa represents the prediction error weight.
8. Robot dynamics parameter estimation system based on exempt from recursive filtering regression of acceleration, characterized by comprising:
the first module is used for constructing a robot kinematic model according to the space vector representation method;
the second module is used for constructing a first robot dynamics model based on the robot dynamics model, and carrying out linear parameterization on the robot dynamics model to obtain a second robot dynamics model;
the third module is used for converting the second robot dynamics model into a minimum parameter set form to obtain a first calculation result; the first calculation result comprises a minimum parameter set and a common regression matrix;
a fourth module, configured to perform convolution processing on the first calculation result and an impulse response of a first-order low-pass filter, perform linear parameterization processing on the convolution processing result to obtain a first-order filtering regression matrix, and pass the first-order filtering regression matrix through the first-order low-pass filter to obtain an acceleration-free second-order recursive filtering regression matrix;
and a fifth module, configured to determine a composite learning parameter update law according to the acceleration-free second-order recursive filtering regression matrix, and perform parameter estimation.
9. An electronic device comprising a processor and a memory;
the memory is used for storing programs;
the processor executing the program implements the method of any one of claims 1 to 7.
10. A computer storage medium in which a processor executable program is stored, characterized in that the processor executable program is for implementing the method according to any one of claims 1 to 7 when being executed by the processor.
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