Finding the Position and Orientation of a Sensor on a Robot Manipulator Using Quaternions
- 1 June 1991
- journal article
- Published by SAGE Publications in The International Journal of Robotics Research
- Vol. 10 (3), 240-254
- https://doi.org/10.1177/027836499101000305
Abstract
The problem of finding the relative position and orientation between the reference frames of a link-mounted sensor and the link has been formulated as a kinematic equation of the form H l H x = H x H c in terms of homogeneous transformation matrices by Shiu and Ahmad (1987). In this article, normal ized quaternions (Euler parameters) are used to transform the kinematic equation into two simple and structured linear systems with rank-deficient coefficient matrices. Closed-form solutions to these systems are derived using the generalized inverse method with singular-value decomposition analysis. To obtain a unique solution, two distinct robot movements are required. This leads to an overdetermined system of equations. A criterion for selecting the independent set of equations is developed. A set of closed-form formulae for the solution of these equations are derived. The selection crite rion and the solution formulae can be easily incorporated in application programs that require the calculation of the rela tive position and orientation of the sensor.Keywords
This publication has 12 references indexed in Scilit:
- Closed-form solution of absolute orientation using unit quaternionsJournal of the Optical Society of America A, 1987
- Multi-body systems with open chains: Graph-theoretic modelsMechanism and Machine Theory, 1986
- Dynamics of 3-D isolated rigid-body systems: graph-theoretic modelsMechanism and Machine Theory, 1986
- Spatial Kinematic and Dynamic Analysis with Euler ParametersPublished by Springer Science and Business Media LLC ,1984
- Application of Euler Parameters to the Dynamic Analysis of Three-Dimensional Constrained Mechanical SystemsJournal of Mechanical Design, 1982
- Dynamics of Systems of Rigid BodiesPublished by Springer Science and Business Media LLC ,1977
- Singularity-free extraction of a quaternion from a direction-cosine matrixJournal of Spacecraft and Rockets, 1976
- A new method for performing digital control system attitude computations using quaternionsAIAA Journal, 1970
- Principles of a General Quaternion-Operator Method of Spatial Kinematic SynthesisJournal of Applied Mechanics, 1968
- Application of Dual-Number Quaternion Algebra to the Analysis of Spatial MechanismsJournal of Applied Mechanics, 1964