Mobile robots can be used in many applications, such as exploration, search and rescue, reconnaissance, security, and cleaning. Mobile robots usually carry batteries as their energy source and their operational time is restricted by the finite energy available from the batteries. Therefore, energy constraints are critical to the service time of mobile robots. This paper investigates the minimum-energy control problem for translational trajectory generation, which minimizes the energy drawn from the batteries. Optimal control theory is used to find the optimal velocity trajectory in analytic form. To demonstrate energy efficiency obtainable, we performed simulations of minimum-energy velocity control and compared the results with loss-minimization control and energy-optimal trapezoidal velocity profiles. Simulation results showed that significant energy savings can be achieved, of up to 9% compared with loss-minimization control and up to 10% compared with energy-optimal trapezoidal velocity profile, We also performed an actual robot experiment using Pioneer 3-AT platform to show the validity of the proposed minimum-energy velocity control. The experimental results revealed that the proposed minimum-energy velocity control can save the battery energy up to 10% compared with loss-minimization control.