The minimum-energy trajectory generation problem of cornering with a fixed heading is solved for three-wheeled omni-directional mobile robots (TOMRs). To maximize the total operation time of a mobile robot with carried batteries having finite energy, we have chosen a practical cost function to be the total energy drawn from the batteries. Then, we formulate the minimum-energy trajectory generation problem of executing a cornering motion with a fixed heading for TOMRs with given dynamics including actuator motors. The optimal control theory using a Hamiltonian function and a numerical method are used to obtain the minimum-energy trajectory, which gives the velocity profile in analytic form. Performance analyses are conducted with various simulations and the consumed energy using obtained minimum-energy trajectory is compared with a typical conventional trajectory with a trapezoidal velocity profile, which reveals that an energy savings of up to 18.7 % is achieved. To validate the actual performance of our trajectory, we implemented and tested an accurate trajectory following system which utilizes a resolved acceleration controller.