We derive a near-time-optimal trajectory for wheeled mobile robots (WMRs) satisfying the following: 1) initial and final postures/velocities as well as 2) battery voltage and armature current constraints, under assumptions of simplified dynamics and constant translational/rotational velocity sections. We use a simplified dynamic model for WMRs neglecting inductances of motor armatures and divide our trajectory generation algorithm for cornering motion into three sections, We specify a path-deviation requirement for obstacle avoidance. Transforming dynamics into uncorrelated form with regard to translational and rotational velocities, we make extreme control possible. By splining rotational section with translational sections and determining the velocity scale factor, a near-time-optimal trajectory can be obtained. Simulation results along with inverse control of path-following are given to validate the generated trajectory.