This paper develops a method for generating smooth trajectories for mobile robots in formation. The problem of trajectory generation is cast in terms of designing optimal curves on the Euclidean group, SE(3). Specifically, the method generates the trajectory that minimizes the total energy associated with the translations and rotations of the robots, while maintaining a rigid formation. When the mobile robots are nonholonomic, trajectories that allow rigid formations to be maintained must satisfy appropriate constraints. An efficient non-iterative algorithm to obtain near-optimal trajectories is described. Finally, the approach is illustrated with examples involving formations of aircrafts.