Self-Motion Manifolds of Redundant Manipulators

Self-motion manifolds are introduced in a new approach to the characterization of self-motions of a robotic manipulator that has redundant degrees of freedom. Self motions, which are made possible by the redundancy, are those motions of the robot joints that leave the position of the end effector unchanged. In much of the previous research on redundant manipulators, the approach has been to resolve the redundancy by optimizing the redundant motions of the joints with respect to additional criterion functions while commanding the end effector to follow the desired trajectory. The previous approach has involved the use of a pseudoinverse of the Jacobian matrix (which consists of derivatives of the coordinates of the end effector with respect to the coordinates of the joints) in optimizing locally Q that is, within a small range of redundant motions. In the alternative approach, the kinematics of the robot are reformulated via a manifold mapping that stresses global, rather than local, kinematic analysis. Within this theoretical framework, the infinite number of redundant solutions of the inverse kinematic problem (the problem of finding the trajectories of the joints as functions of the desired trajectory of the end effector) are naturally interpreted as a set of self-motion manifolds (see figure) rather than in terms of the Jacobian null space. This approach is useful in the study of redundant manipulator kinematics. In addition, the problem of the resolution of redundancy can be posed equivalently in this approach as the problem of the control of self-motions, and the self-moti on manifolds are useful in investigating, interpreting, and formulating both local a nd global techniques for the resolution of redundancy. Redundancy can be resolved by direct control of a set of self-motion parameters, by direct control of a rela ted set of kinematic functions defined by the user and the use of these functions to construct an augmented Jacobian, or by optimization with an objective function.

More details can be found in:

Kreutz, K., Long, M. and Seraji, H.: "Kinematic analysis of 7 DOF manipulators," Intern. Journal of Robotics Research, 1992, 11(5), pp. 469-481.

Point of Contact:
Joel Burdick,
Homayoun Seraji,
Mail Stop 198-219
Jet Propulsion Laboratory
4800 Oak Grove Drive
Pasadena, CA 91109
seraji@telerobotics.jpl.nasa.gov

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Last updated: May 10, 1996