Guaranteed solution of direct kinematic problems for general configurations of parallel manipulators

Author

Didrit, Olivier ; Petitot, Michel ; Walter, Eric

Author_Institution

Lab. des Signaux et Syst., CNRS, Gif-sur-Yvette, France

Volume

14

Issue

2

fYear

1998

fDate

4/1/1998 12:00:00 AM

Firstpage

259

Lastpage

266

Abstract

Finding all possible positions of a Stewart platform from the knowledge of the lengths of its limbs amounts to solving a set of nonlinear equations, the number of real solutions of which is, in the general case, unknown a priori. This paper shows how Hansen´s algorithm (1992), based upon interval analysis, can be used to get all solutions in an approximate but guaranteed way even when the platform is nonplanar and the equations are nonpolynomial and with real coefficients. Computation is simple enough to be performed on a personal computer

Keywords

manipulator kinematics; nonlinear equations; PC; Stewart platform; direct kinematic problems; general configurations; interval analysis; nonlinear equations; nonplanar platform; nonpolynomial equations; parallel manipulators; personal computer; Algorithm design and analysis; Arithmetic; Closed-form solution; Computational geometry; Concurrent computing; Jacobian matrices; Kinematics; Microcomputers; Mobile computing; Nonlinear equations;

fLanguage

English

Journal_Title

Robotics and Automation, IEEE Transactions on

Publisher

ieee

ISSN

1042-296X

Type

jour

DOI

10.1109/70.681244

Filename

681244