## “Iterative Solutions to the Inverse Geometric Problem for Manipulators with no Closed Form Solution”Authors: Pål J. From and Jan T. Gravdahl,
Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 2008, Vol 29, No 3, pp. 77-92. |

**Keywords:**Robotics, Kinematics, Inverse Kinematics

**Abstract:**A set of new iterative solutions to the inverse geometric problem is presented. The approach is general and does not depend on intersecting axes or calculation of the Jacobian. The solution can be applied to any manipulator and is well suited for manipulators for which convergence is poor for conventional Jacobian-based iterative algorithms. For kinematically redundant manipulators, weights can be applied to each joint to introduce stiffness and for collision avoidance. The algorithm uses the unit quaternion to represent the position of each joint and calculates analytically the optimal position of the joint when only the respective joint is considered. This sub-problem is computationally very efficient due to the analytical solution. Several algorithms based on the solution of this sub-problem are presented. For difficult problems, for which the initial condition is far from a solution or the geometry of the manipulator makes the solution hard to reach, it is shown that the algorithm finds a solution fairly close to the solution in only a few iterations.

PDF (275 Kb) DOI: 10.4173/mic.2008.3.1

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**BibTeX:**

@article{MIC-2008-3-1,

title={{Iterative Solutions to the Inverse Geometric Problem for Manipulators with no Closed Form Solution}},

author={From, Pål J. and Gravdahl, Jan T.},

journal={Modeling, Identification and Control},

volume={29},

number={3},

pages={77--92},

year={2008},

doi={10.4173/mic.2008.3.1},

publisher={Norwegian Society of Automatic Control}

};