An SVD-based projection method for interpolation on SE(3)
- 7 August 2002
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Robotics and Automation
- Vol. 18 (3) , 334-345
- https://doi.org/10.1109/tra.2002.1019463
Abstract
This paper develops a method for generating smooth trajectories for a moving rigid body with specified boundary conditions. Our method involves two key steps: 1) the generation of optimal trajectories in GA/sup +/ (n), a subgroup of the affine group in R/sup n/ and 2) the projection of the trajectories onto SE(3), the Lie group of rigid body displacements. The overall procedure is invariant with respect to both the local coordinates on the manifold and the choice of the inertial frame. The benefits of the method are threefold. First, it is possible to apply any of the variety of well-known efficient techniques to generate optimal curves on GA/sup +/ (n). Second, the method yields approximations to optimal solutions for general choices of Riemannian metrics on SE(3). Third, from a computational point of view, the method we propose is less expensive than traditional methods.Keywords
This publication has 18 references indexed in Scilit:
- 3D recovery of polyhedra by rectangularity heuristicsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Interpolation in Lie GroupsSIAM Journal on Numerical Analysis, 1999
- Interpolation schemes for rigid body motionsComputer-Aided Design, 1998
- The Geometry of Algorithms with Orthogonality ConstraintsSIAM Journal on Matrix Analysis and Applications, 1998
- Computer-Aided Design With Spatial Rational B-Spline MotionsJournal of Mechanical Design, 1996
- Splines of class Ck on non-euclidean spacesIMA Journal of Mathematical Control and Information, 1995
- The dynamic interpolation problem: On Riemannian manifolds, Lie groups, and symmetric spacesJournal of Dynamical and Control Systems, 1995
- Be´zier Curves on Riemannian Manifolds and Lie Groups with Kinematics ApplicationsJournal of Mechanical Design, 1995
- Cubic Splines on Curved SpacesIMA Journal of Mathematical Control and Information, 1989
- Animating rotation with quaternion curvesACM SIGGRAPH Computer Graphics, 1985