MATLAB Robotics Toolbox：Puma560运动示例与注意事项

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《Robotic Toolbox 使用说明书》是一份针对MATLAB机器人大规模应用软件包的详细指南，特别适用于 Robotics Toolbox 的Release 6 版本。这份文档由Peter I. Corke撰写，他是CSIRO Manufacturing Science and Technology部门的研究人员，主要关注于机器人技术领域。该手册的核心内容围绕MATLAB环境下Robotic Toolbox的功能展开，旨在帮助用户理解和操作复杂的机器人系统，包括但不限于运动规划、仿真、控制和分析。章节可能涵盖了基础概念，如坐标系变换、关节空间与笛卡尔空间的转换，以及如何使用toolbox中的各种函数和工具来创建、操纵和分析机器人模型，如Puma 560示例所示。图中的数据展示了Puma 560机器人的位置和姿态变量（x, y, z 和旋转关节q2, q3），以及可能涉及的其他内部参数I11。这些数据可用于展示如何在实际任务中操作和理解机器人的运动范围和工作空间。在手册中，Corke强调了虽然他尽可能确保信息准确，但用户应自行核实并寻求专业意见，因为该出版物不提供任何形式的担保或责任声明。这意味着在使用Robotic Toolbox时，用户需要对自己的决策负责，特别是当依赖于其中的建议或信息进行操作时。此外，书中还可能包含如何编写有效的脚本和函数，以及如何利用MATLAB的图形用户界面（GUI）进行交互式操作的指导。对于学习者和开发者来说，这是一份宝贵的参考资料，可以帮助他们深入理解并掌握基于MATLAB的机器人工程实践。《Robotic Toolbox 使用说明书》为MATLAB用户提供了全面的工具和技术支持，无论是在教学、研究还是工业应用中，都是不可或缺的资源，它能帮助读者设计、测试和优化机器人系统，提高工作效率和理论理解。

REFERENCES

the direct, integral or forward dynamic formulation is required giving joint motion in terms

of input torques.

Walker and Orin[23] describe several methods for computing the forward dynamics, and

all make use of an existing inverse dynamics solution. Using the RNE algorithm for in-

verse dynamics, the computational complexity of the forward dynamics using ‘Method 1’

is O

for an n-axis manipulator. Their other methods are increasingly more sophisticated

but reduce the computational cost, though still O n

. Featherstone[24] has described the

“articulated-body method” for O n computation of forward dynamics, however for n 9

it is more expensive than the approach of Walker and Orin. Another O n approach for

forward dynamics has been described by Lathrop[25].

3.3 Rigid-body inertial parameters

Accurate model-based dynamic control of a manipulator requires knowledge of the rigid-

body inertial parameters. Each link has ten independent inertial parameters:

link mass, m

;

three ﬁrst moments, which may be expressed as the COM location, s

, with respect to

some datum on the link or as a moment S

;

six second moments, which represent the inertia of the link about a given axis, typi-

cally through the COM. The second moments may be expressed in matrix or tensor

form as

(33)

where the diagonal elements are the moments of inertia, and the off-diagonals are

products of inertia. Only six of these nine elements are unique: three moments and

three products of inertia.

For any point in a rigid-body there is one set of axes known as the principal axes of

inertia for which the off-diagonal terms, or products, are zero. These axes are given

by the eigenvectors of the inertia matrix (33) and the eigenvalues are the principal

moments of inertia. Frequently the products of inertia of the robot links are zero due

to symmetry.

A 6-axis manipulator rigid-body dynamic model thus entails

60 inertial parameters. There

may be additional parameters per joint due

to friction and motor armature inertia. Clearly,

establishing numeric values for this number of parameters is a difﬁcult task. Many parame-

ters cannot be measured without dismantling the robot and performing careful experiments,

though this approach was used by Armstrong et al.[26]. Most parameters could be derived

from CAD models of the robots, but this information is often considered proprietary and

not made available to

researchers.

References

[1] R. S. Hartenberg and J. Denavit, “A kinematic notation for lower pair mechanisms

based on matrices,” Journal of Applied Mechanics, vol. 77, pp. 215–221, June 1955.

REFERENCES

[2] R. P. Paul, Robot Manipulators: Mathematics, Programming, and Control. Cam-

bridge, Massachusetts: MIT Press, 1981.

[3] K. S. Fu, R. C. Gonzalez, and C. S. G. Lee, Robotics. Control, Sensing, Vision and

Intelligence. McGraw-Hill, 1987.

[4] C. S. G. Lee, “Robot arm kinematics, dynamics and control,” IEEE Computer, vol. 15,

pp. 62–80, Dec. 1982.

[5] J. J. Craig, Introduction to Robotics. Addison Wesley, second ed., 1989.

[6] D. Whitney and D. M. Gorinevskii, “The mathematics of coordinated control of pros-

thetic arms

and manipulators,” ASME Journal of Dynamic Systems, Measurement and

Control, vol. 20, no. 4, pp. 303–309, 1972.

[7] R. P. Paul, B. Shimano, and G. E. Mayer, “Kinematic control equations for simple

manipulators,” IEEE Trans. Syst. Man Cybern., vol. 11, pp. 449–455, June 1981.

[8] J. M. Hollerbach, “Dynamics,” in Robot Motion - Planning and Control (M. Brady,

J. M. Hollerbach, T. L. Johnson, T. Lozano-Perez, and M. T. Mason, eds.), pp. 51–71,

MIT, 1982.

[9] C. S. G. Lee, B. Lee, and R. Nigham, “Development of the generalized D’Alembert

equations of motion for mechanical manipulators,” in

Proc. 22nd CDC, (San Antonio,

Texas), pp. 1205–1210, 1983.

[10] T. Kane and D. Levinson, “The use of Kane’s dynamical equations in robotics,” Int. J.

Robot. Res., vol. 2, pp. 3–21, Fall 1983.

[11] J. Uicker, On the Dynamic Analysis of Spatial Linkages Using 4 by 4 Matrices. PhD

thesis, Dept. Mechanical Engineering and Astronautical Sciences, NorthWestern Uni-

versity, 1965.

[12] M. Kahn, “The near-minimum time control of open-loop articulated kinematic link-

ages,” Tech. Rep. AIM-106,

Stanford University, 1969.

[13] M. H. Raibert and B. K. P. Horn, “Manipulator control using the conﬁguration space

method,” The Industrial Robot, pp. 69–73, June 1978.

[14] A. Bejczy, “Robot arm dynamics and control,” Tech. Rep. NASA-CR-136935, NASA

JPL, Feb. 1974.

[15] R. Paul, “Modelling, trajectory calculation and servoing of a computer controlled

arm,” Tech. Rep. AIM-177, Stanford University, Artiﬁcial Intelligence Laboratory,

1972.

[16] D. Orin, R. McGhee, M. Vukobratovic, and G. Hartoch, “Kinematics and kinetic

analysis of open-chain linkages utilizing Newton-Euler methods,” Mathematical Bio-

sciences. An International Journal, vol. 43, pp. 107–130, Feb. 1979.

[17] W. Armstrong, “Recursive solution to the equations of motion of an n-link manipula-

tor,” in Proc. 5th World Congress on Theory of Machines and Mechanisms, (Montreal),

pp. 1343–1346, July 1979.

[18] J. Y. S. Luh, M. W. Walker, and R. P. C. Paul, “On-line computational scheme for me-

chanical manipulators,” ASME Journal of Dynamic Systems, Measurement and Con-

trol, vol.

102, pp. 69–76, 1980.

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