International Conference on Robotics and Automation c 1996 IEEEMinneapolis , MN

This paper addresses the general problem of generating smooth trajectories between an initial and a nal position and orientation. A functional depending on velocity and its higher derivatives involving a left invariant Riemannian metric on SE(3) is used to measure the smoothness of a trajectory. The problem of determining a smooth trajectory between two points is formulated as a variational problem on SE(3). We derive necessary conditions for the shortest distance and minimum jerk trajectories and solve the resulting two-point boundary value problem.