Curves of stationary acceleration in SE(3)

The concept of curves of minimal acceleration seems to have been introduced by Žefran and Kumar and independently by Noakes, Heinzinger and Paden. In part, the motivation was to extend the notion of spline curves to curves in groups, specifically the groups associated with robotics. A curve in the rigid-body motion group SE(3), e.g. can be thought of as a trajectory of a rigid body. Hence, these ideas have applications to motion planning and interpolation. In this work, the analysis is repeated but using bi-invariant metrics on the group. Since these metrics are not positive definite, the curves specified by the equations derived are only stationary, not minimal. It is possible to solve these non-linear coupled differential equations in some simple cases. However, these simple cases turn out to be highly relevant to robotics and mechanism theory. © 2007 Oxford University Press. This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Mathematical Control and Information following peer review. The version of record is available online at: http://dx/doi/org/10.1093/imamci/dnl017