Energy of wheeled mobile robot is usually supplied by batteries. In order to extend operation time of mobile robots, it is necessary to minimize the energy consumption. The energy is dissipated mostly in the motors, which strongly depends on the velocity profile. This paper investigates various 3-step (acceleration - cruise - deceleration) speed control methods to minimize a new energy object function which considers the practical energy consumption dissipated in motors related to motor control input, velocity profile, and motor dynamics. We performed an analysis on the energy consumption various velocity profile patterns generated by standard control input such as step input, ramp input, parabolic input, and exponential input. Based on these standard control inputs, we analyzed the six 3-step velocity profile patterns: E-C-E, P-C-P, R-C-R, S-C-S, R-C-S, and S-C-R (S means a step control input, R means a ramp control input, P means a parabolic control input, and E means an exponential control input, C means a constant cruise velocity), and suggested an efficient iterative search algorithm with binary search which can find the numerical solution quickly. We performed various computer simulations to show the performance of the energy-optimal 3-step speed control in comparison with a conventional 3-step speed control with a reasonable constant acceleration as a benchmark. Simulation results show that the E-C-E is the most energy efficient 3-step velocity profile pattern, which enables wheeled mobile robot to extend working time up to 50%.