called interval method (or interval analysis).
In the last 20 years, both of the algorithmic components of interval arithmetic and their relation on computers were further developed. However, overestimation of an interval function is still a major drawback in interval analysis.
By representing uncertain geometric parameters as interval numbers, this paper presents a novel approach to compute the forward kinematics of robot by solving a series of interval functions. And a reliable approach to evaluate the interval functions’ values was proposed also to obviate overestimation, the major drawback in interval computation. In this approach, these interval functions were estimated by solving a series of global optimization problems. An intellective algorithm named as real-code genetic algorithm was used to solve the optimization problems also. Numerical examples were given to illustrate the feasibility and the efficiency.
the interval computational model to compute the forward kinematics of robot with uncertain geometric parameters
(1) Determinate computational model of robot
Fig. 1 D-H convention for robot link coordinate system
The robot kinematic model is based on the Denavit-Hartenberg (DH) convention. The relative translation and rotation between link coordinate frame i-1 and i can be described by a homogenous transformation matrix, which is a function of four kinematic parameters , , and as shown in Fig. 1.
The homogen英语论文网 【http://www.51lunwen.org】ous transformation Ai is given in Eq. (1)
(1)
Using the homogenous transformation matrix the relationship of the end-effector frame with respect to the robot base frame can be represented as in Eq. (2):
(2)
(2) The robot kinematic model using parameters with interval uncertainty
When the kinematic parameters θi, di, αi, ai have no fixed value but having the values falling in the intervals [θi], [di], [αi], [ai] randomly, expanding the Eq. (2) with the intervals, we get,
(3)
with
solution of the interval computational model of robot with uncertain geometric parameters
(1) Brief review of some definitions and properties in interval mathematics [7-8]
For two interval number and , ( , is the set of real compact intervals), the interval arithmetic was defined as follows. , , and (for ).
If , then the interval degenerates to a real number a, i.e. . In this way, interval mathematics can be considered as a generation of real numbers mathematics. However, only some of the algebraic laws, valid for real numbers, remain valid for intervals. The other laws hold only in a weaker form. For example, a non-degenerate interval has no inversion with respect to addition or multiplication. Even the distributive law has to be replaced by the so-called subdistributivity
(4)
Let be given by a mathematical expression , which is composed by finitely many elementary operations an
本文来自：英语论文网 【http://www.51lunwen.org】 |
论文编号：
lw200708061140494387 
