# Learning Global Properties of Nonredundant Kinematic Mappings

@article{DeMers1998LearningGP, title={Learning Global Properties of Nonredundant Kinematic Mappings}, author={David DeMers and Kenneth Kreutz-Delgado}, journal={The International Journal of Robotics Research}, year={1998}, volume={17}, pages={547 - 560} }

The kinematic mapping x = f(θ) is generally many to one. For nonredundant manipulators, this means that there are a finite num ber of configurations (joint angles) that will place the end-effector at a target location in the workspace. These correspond to pos tures of the manipulator, and each configuration lies on a specific solution branch. It is shown that for certain classes of revolute joint regional manipulators (those with no joint limits and having almost everywhere a constant number of…

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## References

SHOWING 1-10 OF 28 REFERENCES

Learning Global Topological Properties of Robot Kinematic Mappings for Neural Network-based Configuration Control

- Mathematics
- 1993

We examine the topology of the kinematics mapping and propose methods for resolving redundancy and the multiplicity of disjoint pre-image manifolds, resulting in a global regularization of the…

Canonical parameterization of excess motor degrees of freedom with self-organizing maps

- EngineeringIEEE Trans. Neural Networks
- 1996

A method is presented for solving the nonlinear inverse kinematics problem for a redundant manipulator by learning a natural parameterization of the inverse solution manifolds with self-organizing maps.

Learning Global Direct Inverse Kinematics

- MathematicsNIPS
- 1991

A bootstrap method for construction of an inverse function for the robot kinematic mapping using only sample configuration--space/ workspace data is introduced and a global inverse kinematics solution for the wristless Puma manipulator is developed.

THE KINEMATICS OF MANIPULATORS UNDER COMPUTER CONTROL

- Computer Science
- 1968

A set of heuristics is developed for moving a six degree-of-freedom manipulator from an initial position to a final position through a space containing obstacles, which results in a computer program shown to be able to direct a manipulator around obstacles.

Kinematic analysis of the 6R manipulator of general geometry

- Geology
- 1991

This paper presents a new solution to the inverse kinematics problem for the 6R series manipulator of general geometry, which has 6 revolute (R) joints arranged in series.

Adaptive visual-motor coordination in multijoint robots using parallel architecture

- Computer ScienceProceedings. 1987 IEEE International Conference on Robotics and Automation
- 1987

This article derives and simulates a neural-like network architecture that adaptively controls a visually guided, two-jointed robot arm to reach spot targets in three dimensions. The architecture…

Three-dimensional neural net for learning visuomotor coordination of a robot arm

- Computer ScienceIEEE Trans. Neural Networks
- 1990

An extension of T. Kohonen's (1982) self-organizing mapping algorithm together with an error-correction scheme based on the Widrow-Hoff learning rule is applied to develop a learning algorithm for…

Some topological problems in robotics

- Materials Science
- 1990

This paper is intended to be an exposition for mathematicians on some problems in engineering, and, before introducing these problems, it seems worthwhile to first arm the reader with at least one…