CN100561122C - A Calibration Method of Follow-up Measuring Manipulator Based on Distance Constraint - Google Patents

Abstract

The invention relates to a method for calibrating a follow-up measuring manipulator based on distance constraints, which is characterized in that it comprises the following steps: 1) fixing the measuring manipulator and a calibration ruler; 2) forming the configuration (G1) of the measuring manipulator; 3) Calculate the error coefficient matrix and minimum singular value of the measuring manipulator in configuration (G1); 4) form the configuration of the measuring manipulator (G2); 5) calculate the error coefficient matrix of the measuring manipulator in configuration (G2) and the minimum singular value; 6) Calculate the calibration equation according to the measurement data of the above two configurations (G1, G2); 7) Move the calibration ruler to a new attitude, repeat the above steps, and obtain the calibration in different configurations respectively equation; solve the calibration equation separately to obtain the deviation of each parameter of the measuring manipulator; 8) repeat for many times, and then average the multiple results, and use the average as the final calibration result. The invention has the characteristics of short measurement time, low cost and convenient operation.

Description

A kind of trailing type measurement mechanical arm calibration method based on distance restraint

Technical field

The present invention relates to the measurement mechanical arm calibration method, particularly relate to a kind of trailing type measurement mechanical arm calibration method based on distance restraint.Belong to robot and measure demarcation skill this area.

Background technology

The measurement mechanical arm is a kind of version in the robot.In the practical application,, can make up dummy robot's kinematics model according to actual parameter in view of the above, thereby obtain to approach the kinematics model of actual robot by the measurement mechanical arm is demarcated the actual value that can obtain robot architecture's parameter.

An important link was gathered nominal data exactly during robot was demarcated.In existing physics is demarcated, generally need to obtain nominal data by means of survey instrument, there is shortcomings such as demarcating complexity, time length, calibration cost height.In order to overcome these shortcomings, adopted a kind of scaling method (being called self-calibrating method again) in recent years based on constraint, this self-calibrating method is exactly to need not special survey instrument, utilize particular geometries such as some special point, line, surface, ring, retrain the motion of end effector, in the measurement, make end effector of robot contact or move through conversion configuration repeatedly along these particular geometries, and note corresponding data, utilize these data configuration calibration equations, and solving equation, thereby obtain real robot parameter.In these self-calibrating methods, its constraint type is a single-point constraint, for example: adopt conical bore to be the constraint calibration point for constraint calibration point or Tri-ball structure etc.But, adopting described single-point constraint timing signal, some structural parameters of robot must be known, and obviously, providing of this parameter still need be by means of measuring equipment.In the prior art, the someone has designed a cover physical test device that is applied to the single-point calibration method, comprises and demarcates ball and demarcate spherical pore.There is following shortcoming in this physical test device: (1) timing signal, need measure the robot construction parameter by measuring equipment, and Measuring Time is long, cost is high.(2) need to move the entire machine human arm by hand so that spherical pore is demarcated in the contact of demarcation ball, because the robot arm quality is big, therefore, manual operations is very difficult.(3) want accurately the shape of spherical pore and location, processing difficulties.

Summary of the invention

Purpose of the present invention is the shortcoming that Measuring Time is long, cost is high in order to overcome existing single-point calibration method, provides a kind of and utilizes a scaling ruler that distance restraint is provided, and realizes the trailing type measurement mechanical arm calibration method based on distance restraint.

For achieving the above object, the present invention takes following technical measures:

A kind of trailing type measurement mechanical arm calibration method based on distance restraint is characterized in that may further comprise the steps:

1) fixation measuring mechanical arm, fixedly scaling ruler, make it to keep static relatively with the measurement mechanical arm;

2) end of traction measurement mechanical arm makes first on the measuring head contact scaling ruler on the end demarcate the hole, forms the first configuration G1 of measurement mechanical arm;

3) use the error coefficient matrix of COMPUTER CALCULATION measurement mechanical arm under the first configuration G1, and calculate the minimum singular value of this error coefficient matrix;

4) with the characteristic of computing machine judgement minimum singular value, if this minimum singular value is bigger than normal, then note the reading of each joint code-disc, and carry out step 5); Otherwise, carry out step 2);

5) traction measurement mechanical arm end makes second on the measuring head contact scaling ruler on the end demarcate the hole, forms the second configuration G2 of measurement mechanical arm;

6) use the error coefficient matrix of COMPUTER CALCULATION measurement mechanical arm under the second configuration G2, and calculate the minimum singular value of this error coefficient matrix;

7) with the characteristic of computing machine judgement minimum singular value, if this minimum singular value is bigger than normal, then note the reading of each joint code-disc, and carry out step 8); Otherwise, carry out step 5);

8) calculate calibration equation according to above-mentioned two configurations (G1, G2) measurement data;

9) the extremely new attitude of mobile scaling ruler, and guarantee that the measurement mechanical arm can arrive the first demarcation hole of scaling ruler, any one the demarcation hole in the second demarcation hole;

10) repeating step 2)～8), draw the calibration equation under isomorphism type not respectively;

11) find the solution calibration equation at last respectively, obtain the deviation of each parameter of measurement mechanical arm;

12) above calibration process can repeat repeatedly, then result is repeatedly asked on average, with this mean value as final calibration result.

Purpose of the present invention can also reach by taking following measure:

One embodiment of the present invention are: the measurement mechanical arm is formed by connecting by measuring head, wrist joint, forearm, elbow joint, big arm, shoulder joint, waist joint and pedestal.

One embodiment of the present invention are: scaling ruler comprises the chi body, is respectively equipped with first at the two ends of chi body and demarcates the hole and the second demarcation hole.

One embodiment of the present invention are: during different station the mechanical arm basis coordinates be relative pose determine comprise the steps:

1) on workpiece, sets up several measurement key points and numbering;

2) at station for the moment, the key point of this station of proceeding measurement by these key points, is set up the station reference frame that a period of time, the mechanical arm basis coordinates was fastened;

3) mobile mechanical arm is to station two, proceeding measurement station key point, and by these key points, the reference frame that the mechanical arm basis coordinates is fastened when setting up station two;

The prerequisite that reference frame need overlap during 4) at last according to different station solves the relative pose that the mechanical arm basis coordinates is under the different station.

The present invention has following beneficial effect:

The present invention is owing to be the scaling method that adopts based on distance, therefore can avoid contrary the separating of kinematics in the prior art single-point calibration method, if carry out the scaling method l-G simulation test based on distance, then setting joint variable is different value, can obtain two not isomorphism types.End effector position when obtaining isomorphism type not by forward kinematics solution, thus distance between two points obtained.And in the existing single-point calibration method, two different measurement configurations must be arranged, could be listed as and write out at least one calibration equation.If carry out single-point constraint emulation rating test, once can carry out forward kinematics solution and obtain the calibration measurements data in twice measurement by given joint variable value, but the acquisition of another nominal data can only be separated by means of kinematics is contrary.Therefore, the present invention has that scaling method is simple, demarcation speed fast, demarcate effect accurately.

Description of drawings

Fig. 1 is the structural representation of the used measurement mechanical arm of the present invention.

Fig. 2 is the structural representation of the used scaling ruler of the present invention.

Fig. 3 is a mechanical arm mobile working synoptic diagram among the present invention.

Fig. 4 is each coordinate system synoptic diagram of mechanical arm in the mobile working of the present invention.

Embodiment

With reference to Fig. 1, the used measurement mechanical arm 1 of the present invention is formed by connecting by measuring head 11, wrist joint 12, forearm 13, elbow joint 14, big arm 15, shoulder joint 16, waist joint 17 and pedestal 18.

With reference to Fig. 2, the used scaling ruler 2 of the present invention comprises chi body 23, is respectively equipped with first at the two ends of chi body 23 and demarcates the hole 21 and the second demarcation hole 22.

With reference to Fig. 3, when doing staking-out work,

1) earlier measurement mechanical arm 1 is fixed on the next door of measured workpiece 3, then scaling ruler 2 is fixed on a certain position of measured workpiece 3, and makes both maintenances static relatively;

2) end of traction measurement mechanical arm 1 makes first on the measuring head 11 contact scaling rulers 2 on the end demarcate hole 21, forms the first configuration G1 of measurement mechanical arm;

3) use the error coefficient matrix of COMPUTER CALCULATION measurement mechanical arm 1 under the first configuration G1, and calculate the minimum singular value of this error coefficient matrix;

4) with the characteristic of computing machine judgement minimum singular value,, then note the reading of each joint code-disc, and carry out step 5 if this minimum singular value is bigger than normal; Otherwise, carry out step 2;

5) traction measurement mechanical arm 1 end makes second on the measuring head 11 contact scaling rulers 2 on the end demarcate hole 22, forms the second configuration G2 of measurement mechanical arm;

6) use the error coefficient matrix of COMPUTER CALCULATION measurement mechanical arm 1 under the second configuration G2, and calculate the minimum singular value of this error coefficient matrix;

7) with the characteristic of computing machine judgement minimum singular value,, then note the reading of each joint code-disc, and carry out step 8 if this minimum singular value is bigger than normal; Otherwise, carry out step 5;

8) calculate calibration equation according to above-mentioned two configuration G1, G2 measurement data;

9) mobile scaling ruler 2 is to new attitude, and guarantees that measurement mechanical arm 1 can arrive first of scaling ruler and demarcate any one of demarcating in the hole in hole, second and demarcate hole;

10) repeating step 2～8, draw the calibration equation under isomorphism type not respectively;

11) find the solution calibration equation at last respectively, obtain the deviation of each parameter of measurement mechanical arm;

12) above calibration process can repeat repeatedly, then result is repeatedly asked on average, with this mean value as final calibration result.

In the staking-out work process, mechanical arm 1 may run into the problem of flexible work space less than workpiece, at this moment, needs mobile mechanical arm to work on to new position, thereby finishes whole task.

After mechanical arm moved to reposition, its basis coordinates system must obtain this relative pose and can finish continuously to guarantee task with relative pose the unknown of world's coordinate system.

From computer graphics as can be known, the space arbitrarily not three of conllinear can set up a coordinate system.Based on this principle, the mechanical arm basis coordinates is definite method of relative pose in the time of can providing different station, the steps include:

1) on workpiece, sets up several measurement key points and numbering;

2) at station for the moment, the key point of this station of proceeding measurement by these key points, is set up the station reference frame that a period of time, the mechanical arm basis coordinates was fastened;

3) mobile mechanical arm is to station two, proceeding measurement station key point, and by these key points, the reference frame that the mechanical arm basis coordinates is fastened when setting up station two;

The prerequisite that reference frame need overlap during 4) at last according to different station solves the relative pose that the mechanical arm basis coordinates is under the different station.

Referring to Fig. 4, in the mechanical arm work space, be provided with 2 P ₁, P ₂, its corresponding configuration is respectively G ₁, G ₂The distance of point-to-point transmission is made as D _R2 position vectors with respect to mechanical arm world coordinate system (basis coordinates system) are:

$\left\{\begin{array}{c}{P}_1=(A_1+{\mathrm{dA}}_1){|}_{\mathrm{xyz}}\\ P_2=(A_2+{\mathrm{dA}}_2){|}_{\mathrm{xyz}}\end{array}\right.---(5-1)$

Wherein, A ₁Be P ₁The theoretical pose matrix of pairing mechanical arm end effector, dA ₁Be configuration G ₁Pairing error vector, ${\mathrm{dA}}_1=A_1^R{J}_{e1}\mathrm{\ΔX},$ A ₁ ^RBe A ₁Rotating part, J _E1Be configuration G ₁Under the error coefficient matrix, | _XyzFor obtaining the position vector of end effector pose matrix; A ₂Be P ₂Pairing theoretical pose matrix, dA ₂Be configuration G ₂Pairing error vector, ${\mathrm{dA}}_2=A_2^R{J}_{e2}\mathrm{\ΔX},$ A ₂ ^RBe A ₂Rotating part, J _E2Be configuration G ₂Under the error coefficient matrix.Then 2 distances are

D _R＝||(A ₁+dA ₁)| _xyz-(A ₂+dA ₂)| _xyz|| (5-2)

Expansion (5-2) has

$D_R^2={[(A_1+{\mathrm{dA}}_1){|}_x-(A_2+{\mathrm{dA}}_2){|}_x]}^2+$

${[(A_1+{\mathrm{dA}}_1){|}_y-(A_2+{\mathrm{dA}}_2){|}_y]}^2+$

${[(A_1+{\mathrm{dA}}_1){|}_z-(A_2+{\mathrm{dA}}_2){|}_z]}^2---(5-3)$

The right-hand vector of expansion (5-3) is ignored the second order error item item by item, can get

$\frac{D_R^2-D_I^2}{2}=\left(\begin{array}{ccc}{A}_{12x}& A_{12y}& A_{12z}\end{array}\right)\left(\begin{array}{c}{({\mathrm{dA}}_1-{\mathrm{dA}}_2)|}_x\\ {({\mathrm{dA}}_1-{\mathrm{dA}}_2)|}_y\\ {({\mathrm{dA}}_1-{\mathrm{dA}}_2)|}_z\end{array}\right)---(5-4)$

Wherein | _xBe the x component in the position vector of getting matrix; D _IBe the distance of 2 theoretical positions, A _12x=(A ₁-A ₂) | _x, A _12y=(A ₁-A ₂) | _y, A _12z=(A ₁-A ₂) | _zSubstitution formula (5-1) gets to formula (5-4)

$\frac{D_R^2-D_I^2}{2}=\left(\begin{array}{ccc}{A}_{12x}& A_{12y}& A_{12z}\end{array}\right)(A_1^R{J}_{e1}-A_2^R{J}_{e2})\mathrm{\ΔX}---(5-5)$

Formula (5-5) is the calibration equation based on distance.

The demarcation of mechanical arm basis coordinates system:

Each coordinate system pose synoptic diagram as shown in Figure 4 in this process.

In Fig. 4, P ₁, P ₂, P ₃For measuring key point; W is a world coordinate system; T _BBe station mechanical arm basis coordinates system for the moment, it overlaps with W, measures key point at T _BUnder position coordinates be P ₁, P ₂, P ₃O _cX _cY _cZ _cBe the reference frame of setting up according to the measurement key point, wherein O _cSame P ₁Overlap line O _cP ₂Be made as O _cX _cU _cZ _cX axle X _c, Z _cBe plane O _cP ₁P ₂Normal, determine Y then _CT _BCBe reference frame O _cX _cY _cZ _cAt T _BUnder conversion; T ' _BKey point is measured at T ' by mechanical arm basis coordinates system during for station two _BUnder the position be P ' ₁, P ' ₂, P ' ₃Copy O _cX _cY _cZ _cBuilding method, by a P ' ₁, P ' ₂, P ' ₃Construct reference frame O ' _cX ' _cY ' _cZ ' _cT ' _BCBe reference frame O ' _cX ' _cY ' _cZ ' _cAt T ' _BUnder conversion; T ' _BBMechanical arm basis coordinates when being station two ties up to the conversion under the W.

$T_{\mathrm{BC}}=\left(\begin{array}{cccc}{X}_C& Y_C& Z_C& P_1\\ 0& 0& 0& 1\end{array}\right)---(5-6)$

Wherein, $X_C=\frac{P_1-P_2}{\left|\right|P_1-P_2\left|\right|},$ $Z_C=\frac{(P_1-P_2)\×(P_1-P_3)}{\left|\right|P_1-P_2\left|\right|\×\left|\right|P_1-P_3\left|\right|},$ Y _C＝X _C×Z _C。(5-6) is similar to formula, can

Obtain

$T_{\mathrm{BC}}^{\′}=\left(\begin{array}{cccc}{X}_C^{\′}& Y_C^{\′}& Z_C^{\′}& P_1^{\′}\\ 0& 0& 0& 1\end{array}\right)---(5-7)$

Therefore finally obtain

T′ _BB＝T _BC*T′ _BC ^-1 (5-8)

In actual mechanical process, can set a plurality of measurement key points, thereby set up a plurality of reference frames, solve a plurality of T ' _BB, to these T ' _BBAsk average, drawing final mechanical arm basis coordinates is transformation matrix.Because in the measuring process, unavoidably have measuring error, as measuring noise etc., set up a plurality of reference frames and ask T ' _BBThe method of estimating can effectively be eliminated measuring error to T ' _BBInfluence.

The present invention is that the physics of trailing type mechanical arm is demarcated distance D _RCan be by one given with the scaling ruler of two conical bores, and two distance between borehole draw with the superhigh precision three coordinate measuring engine measurement.When adopting large-scale active mechanical arm to carry out timing signal, but the position of mechanical arm end effector this moment is measured in driving device arm position to the work space; The driving device arm is to the another location again, and measures the end effector position.Can calculate the distance of mechanical arm end effector under two configurations according to measurement data.

Among the present invention, the general type of robot inaccuracy model is:

e＝JΔx

The position and attitude error of wherein, e---gauge head; The matrix of coefficients of J---error, it is with robot architecture's parameter correlation, and when robot was in different configurations, J can be different; Δ x---various initial errors comprise structure and kinematic error, and it is caused by factors such as manufacturings.

Minimum singular value is meant a key concept commonly used in the mathematics (matrix theory).

According to the D-H of robot parameter model, each joint has defined a coordinate system on the measurement mechanical arm.If certain two or more X-axis or the parallel situation of Z axle are arranged in each coordinate system in the gage beam, this moment, the minimum singular value of error coefficient matrix can be less than normal, otherwise can be moderate or bigger than normal; Can whether draw moderate standard bigger than normal or less than normal by repeatedly measuring statistics in advance.

" each parameter " in the deviation of each parameter of mechanical arm that the 12nd step solved at last is meant:

The measurement mechanical arm includes 6 rod members, and each rod member has 4 D-H parameters, and each parameter refers to 6 * 4=24 (individual) parameter that the measurement mechanical arm is comprised.

Two configuration G1, G2 refer to:

During traction measurement mechanical arm, it can arrive another shape, and this shape just is configuration.Under the draw, mechanical arm can not arrive identical two kinds of configurations basically, therefore, we can say that in some sense any two configurations of measurement mechanical arm all can be different.Only measuring configuration needs the gauge head of measurement mechanical arm and a certain hole of scaling ruler to coincide.

Joint variable is meant:

Rod member includes 4 D-H parameters in the measurement mechanical arm, and wherein 3 parameters are to immobilize, and with the structurally associated of gage beam, another parameter is a variable, is the reading of joint code-disc.

" proceeding measurement key point " is meant:

Set key point when the measurement mechanical arm is in first station, it is numbered gets final product arbitrarily.When second station was worked, the number order during by first station was measured key point.

Claims (4)

1, a kind of follow-up type measurement mechanical arm calibration method based on distance constraint, it is characterized in that comprising the following steps: 1) Fix the measuring robot arm (1), fix the calibration ruler (2), and keep it relatively stationary with the measuring robot arm (1); 2) pulling the end of the measuring robot arm (1), so that the measuring head (11) on the end contacts the first calibration hole (21) on the calibration ruler (2), forming the first configuration (G1) of the measuring robot arm; 3) Calculate the error coefficient matrix of the measuring manipulator (1) under the first configuration (G1), and calculate the minimum singular value of the error coefficient matrix; 4) Judging the characteristics of the minimum singular value, if the minimum singular value is too large, record the readings of the code discs of each joint, and proceed to step 5); otherwise, return to step 2); 5) pulling the end of the measuring mechanical arm (1), so that the measuring head (11) on the end contacts the second calibration hole (22) on the calibration ruler (2), forming the second configuration (G2) of the measuring mechanical arm; 6) Calculate the error coefficient matrix of the measuring manipulator (1) under the second configuration (G2), and calculate the minimum singular value of the error coefficient matrix; 7) Judging the characteristics of the minimum singular value, if the minimum singular value is too large, record the readings of the code discs of each joint, and proceed to step 8); otherwise, return to step 5); 8) Calculate the calibration equation according to the measurement data of the above two configurations (G1, G2); 9) Move the calibration ruler (2) to a new attitude, and ensure that the measuring robot arm (1) can reach any one of the first calibration hole (21) and the second calibration hole (22) of the calibration ruler; 10) Repeat steps 2) to 8) to obtain calibration equations in different configurations respectively; 11) Finally, solve the calibration equations respectively to obtain the deviation of each parameter of the measuring manipulator; 12) The above calibration process is repeated several times, and then the results are averaged, and the average value is used as the final calibration result. 2. A distance-constrained follow-up measuring manipulator calibration method according to claim 1, characterized in that the measuring manipulator (1) consists of a measuring head (11), wrist joint (12), forearm ( 13), elbow joint (14), big arm (15), shoulder joint (16), waist joint (17) and base (18) are connected and form. 3. A method for calibrating a follow-up measuring manipulator based on distance constraints according to claim 1, characterized in that: the calibration ruler (2) includes a ruler body (23), and the two ends of the ruler body (23) are respectively A first calibration hole (21) and a second calibration hole (22) are provided. 4. A method for calibrating a follow-up measuring manipulator based on distance constraints according to claim 1, wherein the determination of the relative pose of the base coordinate system of the manipulator at different positions comprises the following steps: 1) Establish several measurement key points on the workpiece and number them; 2) At station one, measure the key points of the station sequentially, and establish a reference coordinate system on the base coordinate system of the manipulator at station one through these key points; 3) Move the manipulator to station 2, measure the key points of the station sequentially, and establish the reference coordinate system on the base coordinate system of the manipulator at station 2 through these key points; 4) Finally, according to the premise that the reference coordinate system needs to coincide at different positions, the relative pose of the base coordinate system of the manipulator at different positions is solved.

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