机器人机械臂线性运动学参数识别方法

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"本文介绍了一种针对机器人机械臂运动学参数辨识的线性方法，旨在从末端执行器的位置测量和已知测量配置下的关节位置读数中确定机械臂未知的运动学模型参数。该方法无需依赖名义模型或线性误差模型，而是利用特殊的机器人运动学建模约定——CPC模型，以及特定的机器人姿态测量序列来直接求解未知的运动学参数。首先，通过递归方式在条件约束下确定各旋转关节的CPC定向参数，然后结合测量数据求解其余参数，实现高精度的机械臂参数辨识。" 本文是 IEEE Transactions on Robotics and Automation 杂志1993年4月刊的一篇文章，由 Hanqi Zhuang 和 Zvi S. Roth 共同撰写。文章的核心内容围绕机器人运动学参数的辨识问题，这是基于模型的机器人校准过程中的关键步骤。传统的参数辨识方法往往需要先建立名义模型或考虑线性化误差模型，但这种方法提出了一种新颖的线性解决方案。该线性解决方案的关键在于采用CPC（Closed-Chain Passive Coordinate）模型，这是一种特殊的运动学建模方法。在CPC模型中，独立的CPC链参数线性地出现在待求解的方程系统中，简化了参数辨识的过程。此外，通过精心设计的机器人姿态测量序列，可以进一步优化参数估计的准确性和效率。在实际应用中，首先根据条件约束递归地计算各个旋转关节的CPC定向参数，这一步有助于消除不确定性并提高计算稳定性。然后，结合末端执行器的位姿测量数据，解算其他未确定的运动学参数，如连杆长度、关节轴的位置等。这种方法的优势在于其线性特性，使得计算过程更为简洁，且对初始估计的敏感度较低，有利于提高整体的辨识精度。这项研究提供了一种高效、精确的机械臂运动学参数辨识方法，对于机器人系统的校准和控制具有重要的理论和实践价值，尤其适用于需要高精度运动控制的工业应用场景。

I76

IEEE

TRANSACTIONS ON ROBOTICS AND AUTOMATION,

VOL.

NO.

APRIL

1993

The origin of

{i}

is at the intersection point of the

is in the direction of the

lth joint axis.

If the projection of

37-1

on the &-plane does not vanish,

is chosen to be parallel to the projection of

zi-1

the Bi-plane, and

is taken to form an orthonormal

right-hand coordinate system; otherwise,

is parallel

to the projection of

Remark:

Since the projections of

xi-1

and

yiP1

on the Bi-

plane do not vanish simultaneously, the link coordinate frames

assigned based on the above convention are unique.

The assignment of link frames for

“simple” robot (i.e., in

which each two consecutive joint axes are either perpendicular

or parallel one to another) can,

in the

D-H

model, be done

by inspection using the following convenient assignment rules.

4’)

is perpendicular to

zi-1,

then let

have the same

direction

21-1;

otherwise since

is parallel to

zi-1

(this

time the projection of

z,-1

on the Bi-plane vanishes), let

have the same direction as

yi-l.

Vi,

which transforms the

lth frame to the ith frame while

the ith joint is kept zero, consists of a rotation transformation

followed by

translation transformation. Let

[0,

1IT,

and

[z~,~,z~,~,z;,,]~.

and

feature the coordinates

of the ith and

lth joint axes direction vectors in

l}.

Link frame

can be brought to be parallel to

{i}

the following rotation:

B,-plane with the

lth joint axis.

on the Bi-plane.

rot(k,,

a,)

(4)

where

is the familiar twist angle (see Fig.

and

where

denotes the Euclidian norm

(k,

is not shown in

Fig.

1).

is undefined from

(6)

whenever

However,

it can be defined without an explicit reference to

zL.

Substitution of

(5)

and

(6)

into the general rotation matrix

formula of

(4)

(refer to

[23])

yields

[24], [lo]

the following

rotation representation:

-z,>Y

(7)

is always nonsingular since, by definition,

z,,~

The origin of the rotated

can then be brought to be

coincident with that of

{i}

through translations along the

and

axes

{i}

(refer to Fig.

I),

which is the transformation

Trans(l,,,.

0).

For

prismatic joint

l,,,,

and

l,,y

are set

to zero. This is similar to the construction of the

D-H

model,

in which prismatic joint offset distance and link length

are

set

to zero.

The link transformation

for a revolute joint is then given

Q,R,trans(l,,,,

0,1,.

(Sa)

For

prismatic joint,

Q,&

O,l,...,rt

1. (Sb)

Finally,

Q,R,rot(z, P,)trans(l,,,,

L).

(8~)

The additional parameter

l,,z

allows an arbitrary placement of

the tool frame origin, and the parameter

allows an arbitrary

orientation of the tool frame. If the nth joint is prismatic,

In some applications, it may be convenient to let the

structure of

be the same

that of

B,.

In such cases,

and

0,1,

. . . ,

are redundant link parameters.

l,,,

ln.v

Remarks

The CPC model is complete

it has

independent link parameters.

The model is never singular for any orientation of two

consecutive axes since the matrices

are well defined

by restricting the

axis to point upwards.

The orientation parameter vector

is unique

the

direction vector of the

lth joint axis in link frame

is unique at the zero-joint-reading position.

In this case, the translation parameter vector

{li,x,

li,z}

is also unique if

li.z

is kept zero for the

internal link transformations.

Example:

Consider two consecutive link transformations

with revolute joints (see Fig.

2).

Let the ith joint axis be

nominally perpendicular to the

lth axis, and the

lth

joint axis be nominally parallel to the ith axis.

this case,

zi-1

[-1,

OIT

and

[O,O,

1IT.

Assume that link frame

has been assigned

shown in Fig.

According

to the CPC modeling convention, the

yip]

axis is taken to

be parallel to the

yiPz

axis since

zi-1

is parallel to

zi-2.

Also, the

axis is taken to be parallel to the

zi-1

axis

since

is perpendicular to

zi-1.

Translational parameters

are then assigned accordingly. Since

zi-2

intersects with

zi-l,li-~,~

1i-1,~

and since

yi-]

aligns with

yi,

111.

PROBLEM

FORMULATION

AND

SOLUTION

STRATEGY

The following notation will be used thereafter:

the zth joint variable,

iot,

d,}

the joint variable vector,

[q~.

q2,

q,lT

the link (kinematic) parameter vector,

[zr

IT,

. .

‘T3

homogeneous transformation relating link frame

{

‘R,

the upper-left

submatrix (the Orientation part)

2:.

IT,

,&IT

for the CPC model

to link frame

{j}

‘TJ

-1

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