Departmental Papers (MEAM)

Document Type

Journal Article

Subject Area


Date of this Version

June 2002


Copyright 2002 IEEE. Reprinted from IEEE Transactions on Robotics and Automation, Volume 18, Issue 3, June 2002, pages 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 Rn 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: 15 November 2004

This document has been peer reviewed.