Numerical examples
The nominal parameters for MOTOMAN SV3 industrial robot were shown in Table 1.
Table1 Design parameters of MOTOMAN SV3 robot
|
Link coordinate system |
a /mm |
α /℃ |
d /mm |
θi / ° |
|
1 |
150 |
-90 |
0 |
-170~ 170 |
|
2 |
260 |
0 |
0 |
-45~ 150 |
|
3 |
60 |
-90 |
0 |
-70~ 190 |
|
4 |
0 |
90 |
260 |
-180~ 180 |
|
5 |
0 |
-90 |
0 |
-135~ 135 |
|
6 |
0 |
0 |
90 |
-350~ 350 |
Based on the nominal (design) kinematic parameters those were shown in Table 1, the end-effector working envelope can be calculated as follows by the presented method in this paper.
Due to the tolerance and manufacturing error, 0.1% of the design value is taken for every kinematic parameter as the parameter deviation from the nominal one, that is, the value is fall in the interval [1-0.05%,1+0.05%] after normalization. The actual working envelop for the robot end-effector could be obtained as following shows by using the presented method.
Conclusion and remarks
By representing all uncertain geometric parameters, a new approach to determine the static pose (position and orientation) of the robot end effector in space was proposed through evaluating interval functions. A reliable computation strategy to is proposed also to overcome overestimation, the major drawback in conventional interval computation.
Parameters with interval uncertainties instead of fixed values are used to compute the forward kinematic. In this way, the actual robot end-effector envelop can be determined, which is essential for the robot off-line programming, obstacle autonomous avoidance, etc.
In most cases, the error distribution should be identified, that is, with known end-effector position error to determine the robot kinematic parameter deviation. It is important for the robot calibration and robot production. Using the interval theory to solve this problem inversely is ongoing.
ACKNOWLEDGEMENTS
The research reported in this paper was supported by China Postdoctoral Science Foundation and the National Nature Science Foundation of China (10072014).
Reference
1 Xu W L. Monte Carlo technique for workspace analysis of robot manipulator. Journal of Southeast University, 1990, 20(1): 1-8.
2 Gong C H. Nongeometric error identification and compensation for robotic system by inverse calibration, International Journal of Machine Tools & Manufacturing, 2000,40: 2119-2137.
3 Wang D G. Nonlinear inversion algorithms and their applications (Ph. D Dissertation). Dalian: Dalian university of technology, 2001. (in Chinese)
4 Chen S H, Yang X W. Interval finite element method for beam structures. Finite elements in analysis and design, 2000, 34:75-88.
5 Zhang J Y, Shen S F. Interval analysis method for determining kinematic solutions of mechanisms. Chinese Journal of Mechanical Engineering, 1991,27(2):75-99. (in Chinese)
6 Alefeld G, Herzberger J. Introduction to interval computations. Academic Press, New York. 1983.
7 Alefeld G, Claudio D. The basic properties of interval arithmetic, its software realizations and some applications. Computers and Structures, 1998, 67:3-8.
8 Goldberg D E. Genetic algorithms in search, optimization and machine learning. Reading, MA: Addison－Wesley, 1989.
9 Michalewicz Z. Genetic Algorithm+Data Structures=Evolution Programs. Springer-Verlag, Berlin Heidelberg. 1996.