Metrics and connections for rigid-body kinematics
- California Inst. of Tech., Pasadena, CA (United States)
- Univ. of Pennsylvania, Philadelphia, PA (United States)
The set of rigid-body motions forms a Lie group called SE(3), the special Euclidean group in three dimensions. In this paper, the authors investigate possible choices of Riemannian metrics and affine connections on SE(3) for applications to kinematic analysis and robot-trajectory planning. In the first part of the paper, they study metrics whose geodesics are screw motions. They prove that no Riemannian metric can have such geodesics, and they show that the metrics whose geodesics are screw motions from a two-parameter family of semi-Riemannian metrics. In the second part of the paper, they investigate affine connections which through the covariant derivative give the correct expression for the acceleration of a rigid body. They prove that there is a unique symmetric connection with this property. Furthermore, they show that there is a family of Riemannian metrics that are compatible with such a connection. These metrics are products of the bi-invariant metric on the group of rotations and a positive-definite constant metric on the group of translations.
- OSTI ID:
- 346804
- Journal Information:
- International Journal of Robotics Research, Vol. 18, Issue 2; Other Information: PBD: Feb 1999
- Country of Publication:
- United States
- Language:
- English
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