软件：matlab2014a

工具箱：Matlab Robotic Toolbox v9.8

这里感谢枫箫提供的机器人工具箱：http://blog.sina.com.cn/u/2707887295

本次连载主要以机器人工具箱附带的使用例子为主，提供注释和翻译。希望可以帮助大家更好使用机器人工具箱。

安装好Matlab

Robotic Toolbox

v9.8后，打开MATLAB，查看附带的例子输入rtbdemo,回车，就可以看到简介菜单。

这里逐次介绍每个的使用简介

rtbdemo

------------------------------------------------------------

Many of these demos print tutorial text and MATLAB commmands in the

console window.

Read the text and press to move on to the next command

At the end of the tutorial/demo you can choose the next one from

the graphical menu.

--- runscript

D:\matlab\toolbox\robot\rvctools\robot\demos\rotation.m

% In the field of robotics there are many possible ways of

representing

% orientations of which the most common are:

% - orthonormal【正交】rotation matrices (3x3),正交旋转矩阵

% - three angles (1x3), and

% - quaternions.【四元数】表示法可以参考http://blog.sina.com.cn/u/2707887295

% A rotation of pi/2 about the x-axis can be represented as an

orthonormal rotation

% matrix【绕x轴旋转pi/2的正交旋转矩阵】

>> R = rotx(pi/2)

R =

1.0000  0

0

0  0.0000  -1.0000

0  1.0000  0.0000

% which we can see is a 3x3 matrix.

% Such a matrix has the property that it's columns【列】 (and rows【行】)

are sets of orthogonal

% unit vectors【单位向量】.  The determinant of such a

matrix is always 1

>> det(R)

ans =

1

% Let's create a more complex rotation【创作一个更复杂的旋转】

>> R = rotx(30, 'deg') * roty(50, 'deg') * rotz(10,

'deg')

R =

0.6330  -0.1116  0.7660

0.5276  0.7864  -0.3214

-0.5665  0.6076  0.5567

% where this time we have specified the rotation angle in

degrees.【度数】

% Any rotation can be expressed in terms of a single rotation about

some axis

% in space【任何旋转都可以表达为绕空间某一特定轴的单独旋转】

>> [theta,vec] = tr2angvec(R)

theta

1.0610

vec =

0.5322  0.7634  0.3662

% where theta is the angle (in radians【弧度】) and vec is unit vector

representing the

% direction of the rotation

axis【旋转轴方向】.【这里theta是角度(以弧度表示)，vec是代表旋转轴方向的单位向量】

% Commonly rotations are represented by Euler angles【欧拉角】

>> eul = tr2eul(R)

eul =

-0.3972  0.9804  0.8204

% which are three angles such that R = rotz(a)*roty(b)*rotz(c), ie.

the rotations

% required about the Z, then then the Y, then the Z axis.

% Rotations are also commonly represented by roll-pitch-yaw

angles

>> rpy = tr2rpy(R)

rpy =

0.5236  0.8727  0.1745

% which are three angles such that R = rotx(r)*roty(p)*rotz(y), ie.

the rotations

% required about the X, then then the Y, then the Z axis.

% We can investigate the effects of rotations about different

axes

% using this GUI based demonstration.  The menu

buttons allow the rotation

% axes to be varied【我们可以查看不同轴的旋转效果，通过使用演示的GUI。菜单按钮可以使旋转轴改变】

% close the window when you are done.

>> tripleangle('rpy', 'wait')

% The final useful form is the quaternion which comprises 【包含】4

numbers.  We can create

% a quaternion from an orthonormal matrix

>> q = Quaternion(R)

q =

0.86256 < 0.26926, 0.38622, 0.18526 >

% where we can see that it comprises a scalar【标量】 part and a

vector【向量】 part.  To convert back【向后转换】

>> q.R

ans =

0.6330  -0.1116  0.7660

0.5276  0.7864  -0.3214

-0.5665  0.6076  0.5567

% which is the same of the value of R we determined

above.【这和我们上面所推算的R是一样的】

% Quaternions are a class and the orientations they represent can

be compounded【复合的】, just

% as we do with rotation matrices by multiplication【乘法运算】.

% First we create two quaternions

>> q1 = Quaternion( rotx(pi/2) )

q1 =

0.70711 < 0.70711, 0, 0 >

>> q2 = Quaternion( roty(pi/2) )

q2 =

0.70711 < 0, 0.70711, 0 >

% then the rotation of q1 followed【跟随的】 by q2 is simply

>> q1 * q2

ans =

0.5 < 0.5, 0.5, 0.5 >

% We can also take the inverse【逆的，反的】 of a Quaternion

>> q1 * inv(q1)

ans =

1 < 0, 0, 0 >

% which results in a null【零位的】 rotation (zero vector part)

------ done --------