Departmental Papers (MEAM)

Document Type

Journal Article

Subject Area


Date of this Version



Suggested Citation:
Belta, Calin and Vijay Kumar. (2002). An SVD-Based Projection Method for Interpolation on SE3. IEEE Transactions on Robotics and Automation, Vol. 18(3) p. 334-345.

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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+(n), a subgroup of the affine group in IRn 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+(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.


Interpolation, Lie groups, trajectory generation



Date Posted: 01 September 2010

This document has been peer reviewed.