To maximize energy efficiency, we suggest minimum-energy trajectory planning and online trajectory modification algorithms for three-wheeled omni-directional mobile robots (TOMRs). First, minimum-energy multisection trajectory planning for various constraints is performed using Pontryagin's minimum principle. Two strategies are established to formulate an efficient minimum-energy, multisection trajectory generation algorithm: an online trajectory modification and a control algorithm that maintains energy efficiency are investigated using novel heuristic functions. Compared with the conventional trajectory using the trapezoidal velocity profile, the generated transport trajectory can save energy.