Published: 30 September 2008

A linear optimization approach to inverse kinematics of redundant robots with respect to manipulability

W. Lalo1
T. Brandt2
D. Schramm3
M. Hiller4
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Abstract

The solution of the inverse kinematics is required in many technical applications. In this contribution a concept is proposed which reformulates the inverse kinematics (IK) of kinematically redundant manipulators as a linear programming (LP) problem. This formulation enables the explicit consideration of technical constraints as for example mechanical end-stops, velocity and, if necessary, acceleration limits as linear inequality constraints. Besides that, automatic collision avoidance within the workspace of the manipulator can be included. The kinematic redundancy is resolved with respect to quadratic criteria. As the LP problem at hand belongs to the small-size problems, the optimal solution can be found numerically in appropriate time using standard algorithms such as the simplex algorithm or interior point methods. This article closes with a numerical example of the LP-IK of a planar 4-link manipulator

About this article

Received
08 September 2008
Accepted
16 September 2008
Published
30 September 2008
Keywords
redundancy
inverse kinematics
linear programming
manipulability
manipulator