Journal of Chongqing University (English Edition) [ISSN 1671-8224]
Vol. 10 No. 2
June 2011
60
Article ID: 1671-8224(2011)02-0060-08
To cite this article: ZHAO Yong-jie. Inverse displacement analysis of the general six degree-of-freedom serial robot based on optimization method [J]. J Chongqing Univ: Eng
Ed [ISSN 1671-8224], 2011, 10(2): 60-67.
Inverse displacement analysis of the general six degree-of-freedom
serial robot based on optimization method
ZHAO Yong-jie
†
Department of Mechatronics Engineering, Shantou University, Guangdong 515063, P. R. China
Received 11 February 2011; received in revised form 27 March 2011
Abstract: The paper presents a new solution of inverse displacement analysis of the general six degree-of-freedom serial robot.
The inverse displacement analysis of the general serial robot is transformed into a minimization problem and then the
optimization method is adopted to solve the nonlinear least squares problem with the analytic form of new Jacobian matrix. In this
way, joint variables of the general serial robot can be searched out quickly under the desired precision when positions of the three
non-collinear end effector points are given. Compared with the general Newton iterative method, the proposed algorithm can
search out the solution when the robot is at the singular configuration and the initial configuration used in the optimization method
may also be the singular configuration. So the convergence domain is bigger than that of the general Newton iterative method.
Another advantage of the proposed algorithm is that positions of the three non-collinear end effector points are usually much
easier to be measured than the orientation of the end effector. The inverse displacement analysis of the general 6R (six-revolute-
joint) serial robot is illustrated as an example and the simulation results verify the efficiency of the proposed algorithm. Because
the three non-collinear points can be selected at random, the method can be applied to any other types of serial robots.
Keywords: inverse displacement analysis; general serial robot; optimization method
CLC number: TP242 Document code: A
1 Introduction
a
A robot is a reprogrammable multifunctional
manipulator designed to move material, parts, tools, or
specialized devices through variable programmed
motions for the performance of a variety of tasks. For a
robot to perform a specific task, the location of the end
effector relative to the base should be established first.
This is the displacement analysis problem. There are two
kinds of displacement problems, namely, direct
†
ZHAO Yong-jie (赵永杰): meyjzhao@yahoo.com.cn.
Funded by National Natural Science Foundation of China (No.
50905102), the Natural Science Foundation of Guangdong
Province (Nos. 10151503101000033 and 8351503101000001),
and the Building Fund for the Academic Innovation Team of
Shantou University (No. ITC10003).
displacement analysis and inverse displacement
analysis
[1]
. For the direct displacement analysis, joint
variables are given and the problem is to find the pose of
the end effector. For the inverse displacement analysis,
the pose of the end effector is given and the problem is to
find the joint variables necessary to bring the end
effector to the desired pose. Inverse displacement
analysis has been one of the main problems in robotics
research. For the serial robot, which consists of serial
links connected in series by various types of joints,
typically revolute and prismatic joints, the inverse
displacement analysis is quite difficult. The inverse
displacement problem of robot is fundamental for the
design, trajectory planning, motion control and
workspace analysis while the direct displacement
problem is usually used for simulation. There are two
main approaches, namely, the algebraic method and the
numerical method addressed in literatures on the inverse
displacement problem. The basic idea of the algebraic