CN102320043A - Static and dynamic identification method for dynamic parameter for robot - Google Patents

Abstract

The invention discloses a static and dynamic identification method for a dynamic parameter for a robot, which needs to provide a robot substrate six-axis force as well as the driving torque, the angular velocity and the angular acceleration of each joint. During static identification, a multidimensional matrix is built by the rotation transformation relationship between connecting rod coordinate systems of the robot by changing the configuration of a mechanical arm, a static identification model is built, and the product of the quality of each connecting rod and the coordinate of the centroid is solved with a least square method. According to a static identification result, a mechanical arm dynamics equation of a dynamics parameter decoupling form is deduced on the basis of the Newton-Euler algorithm. In the dynamic identification, each joint is planned to move in a specific combination mode, and the inertia tensor and the coordinate of the centroid from a tail-end connecting rod to a connecting rod 1 are successively identified with a pseudo inverse method so as to the full identification of the dynamic parameter for the robot. The parameter identification result disclosed by the invention comprises the mechanical arm joint characteristics, and therefore, the inertia parameter value in the practical work of the robot can be reflected.

Description

A kind of sound attitude discrimination method of robot dynamics's parameter

Technical field

The present invention relates to the technical field of robot parameter identification, relate in particular to a kind of sound attitude substep discrimination method that is used for each connecting rod kinetic parameter of identification robot.

Background technology

The development of Robot Control Technology is determining the development level of Robotics.Aspect robot dynamics's modeling, because actual measurement and modeling is inaccurate, add the existence of load variations, external disturbance and a large amount of uncertain factors, we are difficult to obtain actual accurate, the complete motion model of robot.The expansion of robot application scope and Robotics develop the further raising with automaticity rapidly, to the demands for higher performance of robot.At first, in the practical application of robot, operating efficiency and quality are to weigh robot performance's important indicator.Improve the operating efficiency of industrial robot, reduce motion and power error in the practical operation, improve stability and become the critical problem that in robot application, needs to be resolved hurrily.Secondly, robot must have the more dynamic role and the flexibility of height, has more wide reached at space, and this just requires the quite high control algolithm of precision.Kinetic model identification and system modelling are the bases of Control System Design, and the acquisition of model parameter accurately to a certain extent, can be accelerated design process, improve control accuracy.Therefore the accuracy of modeling also becomes the problem that the various countries scholar is studying, and has introduced more advanced, novel modeling method, for robot control provides good premise.

Accurate kinetic model is the precondition of robot control and emulation, needs each connecting rod kinetic parameter of robot accurately and set up accurate kinetic model.Robot is after assembling is accomplished; We generally can't obtain the kinetic parameter of true mechanical arm; Or can only estimate the kinetic parameter value after the assembling according to the individual parameter of each joint of robot and connecting rod, the estimation result of obvious this method can not reflect the dynamic characteristic that robot is whole.

Summary of the invention

The present invention proposes a kind of discrimination method of robot arm kinetic parameter, and the identification thinking of sound attitude is adopted in this identification, to overcome since the coupled problem of parameter can't all connecting rods of identification the difficult problem of kinetic parameter value.The present invention need provide the driving moment in the sextuple power of robot base and each joint under the known situation of robot motion's mathematic(al) parameter, the pedestal six-dimension force sensor is installed on the junction in a robot base and a joint.The kinetic parameter of the identification of wanting comprises quality, center-of-mass coordinate and the inertial tensor of each connecting rod of robot.

Technical solution of the present invention comprises following step:

1) sets up the static identification model of robot dynamics's parameter;

2) find the solution each connecting rod quality of mechanical arm and center-of-mass coordinate product based on least square method;

3) set up the dynamic identification model of robot dynamics's parameter;

4) make robot that each connecting rod moves according to the specific combined mode, the inertial tensor of each connecting rod of identification and center-of-mass coordinate;

5), calculate inertial tensor, quality and the center-of-mass coordinate of each connecting rod of robot successively through the identification result in second step and the 4th step.

Further:

In static identification process,, close series structure multi-dimensional matrix Q according to the rotation transformation between each link rod coordinate system through changing the configuration of mechanical arm _{3n * 3a}(n is the free degree of mechanical arm; A is the configuration number of the mechanical arm of institute's conversion); Utilize the sextuple power of pedestal to obtain the gross mass of mechanical arm system and the center-of-mass coordinate of every group of configuration indirectly, based on the quality of each connecting rod of thought identification of least square method and the product of center-of-mass coordinate.

Further:

Utilize quality and the product of center-of-mass coordinate of each connecting rod of static identification gained; The mechanical arm kinetics equation of derivation kinetic parameter decoupling zero form; The quadratic component of identified parameters and the coupling product term of parameter are treated in cancellation, make joint moment in the mechanical arm kinetics equation form linear relation with treating identified parameters;

Further:

In dynamic identification process, at first all joints of planning robot (joint 1 to joint n) moves simultaneously, the kinetic parameter of identification tail end connecting rod n; Planning robot joint 1 to joint n-1 moves simultaneously then, and joint n is locked, with connecting rod n and connecting rod n-1 integral body as tail end connecting rod; Its whole kinetic parameter of identification; With get final product the kinetic parameter of connecting rod n-1, according to same thinking, plan joint 1 to joint i motion successively; Joint i+1 to the joint n locked, the kinetic parameter of an order identification connecting rod.

The invention has the advantages that:

1) adopts static and dynamic substep discrimination method, at first obtain the product of mechanical arm quality and center-of-mass coordinate, for dynamic identification process cancellation is treated the quadratic component of identified parameters, the complexity of reduction identification by static identification;

2) the sextuple power/torque sensor of pedestal is static measurement in identification process, can effectively reduce the dynamic measurement error of six-dimension force sensor;

3) comprise the joint of mechanical arm characteristic in the kinetic parameter identification result of connecting rod, can react the inertial parameter value in the robot real work.

Description of drawings

Fig. 1 is the illustraton of model of the mechanical arm of the n free degree;

Fig. 2 is robot dynamics's parameter sound attitude identification flow chart.

The specific embodiment

Below in conjunction with accompanying drawing the inventive method is done further explain.

At first describe with reference to 1 pair of symbol that occurs hereinafter of accompanying drawing.c _nRepresent the n of robot connecting rod barycenter, ⁿp _N+1Represent the coordinate of n+1 joint under the n coordinate system, ∑ _nRepresent the n joint coordinate system, Representative coordinates is the rotation transformation matrix of n to coordinate system n+1, θ _n

Represent joint angles, angular speed, the angular acceleration in n joint, ⁿω _n ⁿα _nRepresent angular speed, the angular acceleration of n connecting rod under current coordinate system, ⁿv _n ⁿa _nRepresent linear velocity, the linear acceleration of n joint under current coordinate system, ⁿf _nRepresentative acts on the power on the n connecting rod at n-1 connecting rod under the n coordinate system, ⁿn _nRepresentative acts on the moment on the n connecting rod at n-1 connecting rod under the n coordinate system, τ _nRepresent the driving moment in n joint, ⁿz _nRepresent under the n coordinate z to unit vector.

The static identification of each connecting rod quality of robot and center-of-mass coordinate product

Robot with n free degree, each connecting rod quality and center-of-mass coordinate exist following relation:

$\mathrm{MC}={\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="HSA00000511843800012.png"\; state="\{\{state\}\}">m</figure-callout>}}_1\mathrm{<figure-callout\; id="1"\; label="Rc"\; filenames="HSA00000511843800012.png"\; state="\{\{state\}\}">Rc</figure-callout>}_1^0{}_1+m_2\mathrm{Rc}_2^0{}_2+m_3\mathrm{Rc}_3^0{}_3+......+m_n\mathrm{Rc}_n^0{}_n---\left(1\right)$

Wherein: M is the mechanical arm gross mass; C is the barycenter of mechanical arm system;

c ₁c ₂c ₃... c _nBarycenter for each connecting rod;

is tied to the rotation transformation matrix of basis coordinates system for each joint coordinates;

Six-dimension force sensor required for the present invention is installed between first joint and pedestal of robot, and then whole quality and the center-of-mass coordinate of mechanical arm system can be tried to achieve through six-dimension force sensor:

F＝-Mg (2)

N＝F×C

If the suffered sextuple power of pedestal is F ₆=[F _xF _yF _zN _xN _yN _z].Then there is following relation:

[N _xN _yN _z]＝-Mg[cosαcosβcosγ]×C (3)

Wherein,

α=arccos (F _x/ Mg), β=arccos (F _y/ Mg), γ=arccos (F _z/ Mg).

The present invention needs planning mechanical arm A group configuration in the static identification process of robot dynamics's parameter, the configuration group number of planning need be greater than the free degree of mechanical arm.Each joint should turn an angle at random when changing configuration at every turn, to guarantee not occur the problem of linear correlation.Then can construct following matrix equation:

Y＝Q·ψ (4)

Wherein: Y=[MC ₁MC ₂MC ₃... MC _A] ^T

$Q=\left[\begin{array}{c}\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000511843800012.png"\; state="\{\{state\}\}">R</figure-callout>}_1^0{}_1\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000511843800012.png"\; state="\{\{state\}\}">R</figure-callout>}_1^0{}_2\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000511843800012.png"\; state="\{\{state\}\}">R</figure-callout>}_1^0{}_3......\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="HSA00000511843800012.png"\; state="\{\{state\}\}">R</figure-callout>}_1^0{}_n\\ R_2^0{}_{1}R_2^0{}_{2}R_2^0{}_3......R_2^0{}_n\\ .\\ .\\ .\\ R_A^0{}_{1}R_A^0{}_{2}R_A^0{}_3......R_A^0{}_n\end{array}\right];$

ψ＝[m ₁c ₁m ₂c ₂m ₃c ₃......m _nc _n]。

The present invention is in the static identification of robot dynamics's parameter; Utilize the pedestal six-dimension force sensor at first to obtain the quality and the center-of-mass coordinate of entire system; Through the configuration structure multi-dimensional matrix of planning mechanical arm, then the least square solution of the product of the quality of each connecting rod of robot and center-of-mass coordinate is:

ψ＝[Q ^T·Q] ^-1Q ^-1Y (5)

The dynamic identification of each connecting rod kinetic parameter of robot

(1) discrimination method of connecting rod two to tail end connecting rod kinetic parameter

The present invention at first need set up the mechanical arm kinetics equation of kinetic parameter decoupling zero form in the dynamic identification process of robot dynamics's parameter.The power of each connecting rod of robot and moment is according to the reverse transmission of formula of formula (6), for tail end connecting rod, because ^N+1f _N+1And ^N+1n _N+1Be zero, but the form of the power of tail end connecting rod and moment relation formula of reduction (7) then.Simultaneous formula (6), (7) merge the quality of connecting rod and the product term of center-of-mass coordinate, and it is designated as mc _n, can get formula (8) after the arrangement.

$f_i^i=R_{i+1}^{i}f_{i+1}^{i+1}+f_{\mathrm{ci}}^i$

$n_i^i=R_{i+1}^{i}n_{i+1}^{i+1}+n_{\mathrm{ci}}^i+r_{\mathrm{ci}}^i\&times;f_{\mathrm{ci}}^i+P_{i+1}^i\&times;R_{i+1}^{i}f_{i+1}^{i+1}---\left(6\right)$

τ _i＝′n _i′Z _i

ⁿn _n＝ ⁿn _n+ ⁿr _cn× ⁿf _cn (7)

ⁿn _n-mc _n× ⁿa _n＝ ^cnI _n ⁿα _n+ ⁿω _n×( ^cnI _n ⁿω _n)+mc _n×( ⁿα _n×c _n) (8)

+mc _n×( ⁿω _n×( ⁿω _n×c _n))

With the further abbreviation of formula (8), can obtain the form of the matrix equation shown in the formula (9).

N＝H·Φ+K·Γ (9)

Wherein: Φ=[I _Xx, I _Yy, I _Zz, I _Xy, I _Xz, I _Yz] ^TΓ=[c _Ix, c _Iy, c _Iz] ^T

The present invention at first makes joint of robot 1 n motion to the joint in dynamic identification, in the run duration in each joint, extract B (B >=9) group data constantly as sample, comprises the driving moment in each joint, the speed and the acceleration in each joint.Joint of robot driving moment τ is a joint moment z durection component, extracts matrix equation (9) the third line, adopts the pseudoinverse technique identification to obtain the tail end connecting rod kinetic parameter.

[ΦΓ] ^T＝[H(B)E(B)] ⁺·N(B) (10)

The present invention is in dynamic identification; After obtaining the identification of tail end connecting rod kinetic parameter; Tail end connecting rod and time tail end connecting rod is whole as the object of treating identification; Identification process is identical with said method, obtains the kinetic parameter of time terminal mechanical arm then according to transformational relation between the coordinate system of kinetic parameter.With this successively recursion accomplish the identification of robot second connecting rod to the kinetic parameter of tail end connecting rod to second connecting rod.

(2) identification of connecting rod one kinetic parameter

The present invention is in dynamic identification because the robot first connecting rod is the rotatablely moving of one axis around the joint, so its exist self coordinate system z to speed and acceleration.Consider the particularity of connecting rod one motion, need carry out independent analysis the method for its kinetic parameter identification.Connecting rod one in the process of motion, the moment that joint one is suffered and three parameter (I in the connecting rod inertial tensor _1xx, I _1yy, I _1xy) have no operation relation, so above-mentioned three inertial tensors of connecting rod one all belong to can't identification kinetic parameter.Make robot one joint motions, then can know that according to newton's euler dynamical equations the moment in a joint representes shown in formula (11):

¹n ₁＝ ¹I _c ¹α+ ¹ω×( ¹I _c ¹ω)+MC×( ¹α×C)

(11)

+MC×( ¹ω×( ¹ω×c _n))+MC× ¹a

C in the formula (11) * ( ¹α * C) and C * ( ¹ω * ( ¹ω * c _n)) the quadratic component that is the connecting rod barycenter, it can change through the translation of connecting rod inertial tensor between coordinate system and carry out abbreviation.By the transforming relationship of inertial tensor under different coordinates, formula (11) is done further to simplify, finally can push away the inertial tensor of connecting rod shown in formula (12) (in the formula ¹I is the inertial tensor of connecting rod with respect to coordinate origin).

[I _zzI _xzI _yz]T＝{H ₁} ⁺· ¹n ₁ (12)

Wherein: ${\mathrm{<figure-callout\; id="1"\; label="H"\; filenames="HSA00000511843800012.png"\; state="\{\{state\}\}">H</figure-callout>}}_1=\left[\begin{array}{ccc}0& -\mathrm{\&alpha;}_{1\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HSA00000511843800012.png"\; state="\{\{state\}\}">z</figure-callout>}}^1& {\mathrm{\&omega;}}_{1z}_2^1\\ 0& -{\mathrm{\&omega;}}_{1z}_2^1& -\mathrm{\&alpha;}_{1\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HSA00000511843800012.png"\; state="\{\{state\}\}">z</figure-callout>}}^1\\ \mathrm{\&alpha;}_{1\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HSA00000511843800012.png"\; state="\{\{state\}\}">z</figure-callout>}}^1& 0& 0\end{array}\right].$

The inertial tensor I of connecting rod one _1zz, I _1xz, I _1yzWith trying to achieve.So far, quality that the quality of the inertial tensor of each connecting rod of robot, second connecting rod to tail end connecting rod and center-of-mass coordinate and mechanical arm system are whole and center-of-mass coordinate are all to obtain identification, and the quality of connecting rod one and center-of-mass coordinate can directly be obtained by formula (1).The overview flow chart of mechanical arm kinetic parameter discrimination method is as shown in Figure 2.

Claims (3)

1. the sound attitude discrimination method of robot dynamics's parameter; It is characterized in that; The substep identification process of said method through the sound attitude solves parameter coupling problems in the mechanical arm kinetic model, through static the identification at first quality of each connecting rod of identification motion arm and the product of center-of-mass coordinate; Avoid in the process of dynamically identification, the quadratic component of identified parameters and the coupling product term of parameter occurring treating, make that joint moment forms linear relation with treating identified parameters in the mechanical arm kinetics equation.

2. the sound attitude discrimination method of robot dynamics's parameter as claimed in claim 1; It is characterized in that; In the identification process of static state; Through the many groups configuration structure multi-dimensional matrix of planning mechanical arm, utilize the sextuple power of pedestal to obtain the gross mass of mechanical arm system and the center-of-mass coordinate of every group of configuration indirectly, based on the quality of each connecting rod of thought identification mechanical arm of least square method and the product of center-of-mass coordinate.

3. the sound attitude discrimination method of robot dynamics's parameter as claimed in claim 1 is characterized in that, in dynamic identification process; At first all joints of planning robot (joint 1 to joint n) moves simultaneously, the kinetic parameter of identification tail end connecting rod n, and planning robot joint 1 to joint n-1 moves simultaneously then; Joint n is locked, with connecting rod n and connecting rod n-1 integral body as tail end connecting rod, its whole kinetic parameter of identification; With get final product the kinetic parameter of connecting rod n-1, according to same thinking, plan joint 1 to joint i motion successively; Joint i+1 to the joint n locked, the kinetic parameter of order identification each connecting rod.

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