Curves of stationary acceleration in SE(3)

^** Email: seligjm{at}lsbu.ac.uk The concept of curves of minimal acceleration seems to havebeen introduced by efran and Kumar and independently by Noakes,Heinzinger and Paden. In part, the motivation was to extendthe notion of spline curves to curves in groups, specificallythe groups associated with robotics. A curve in the rigid-bodymotion group SE(3), e.g. can be thought of as a trajectory ofa rigid body. Hence, these ideas have applications to motionplanning and interpolation. In this work, the analysis is repeatedbut using bi-invariant metrics on the group. Since these metricsare not positive definite, the curves specified by the equationsderived are only stationary, not minimal. It is possible tosolve these non-linear coupled differential equations in somesimple cases. However, these simple cases turn out to be highlyrelevant to robotics and mechanism theory.