In order to enhance the omnidirectional maneuverability of outdoor wheeled mobile robots, a mobile robot driven by a common wheel is proposed, which realizes four-wheel steering (4WS), oblique motion mode, and spot turn modes according to different power distribution and angle of leg rotation. A dual-mode hybrid controller is designed based on the oblique and 4WS modes, in which multipoint prescanning trajectory tracking control is used for the oblique mode, and incremental linear time-varying model predictive control (ILTV-MPC) is used for the 4WS mode. The constraints required for the dual-mode controller are obtained by experimenting with the test prototype’s transverse and longitudinal tracking performance. A joint MATLAB/CARSIM simulation platform is used to compare and verify the performance of each mode controller under two operating conditions. In the first condition, the tracking accuracy of the 4WS mode can be achieved by using the oblique motion mode, and the transverse sway angle variation is significantly reduced. In the second working condition, the oblique motion mode is better than the tracking effect of the 4WS mode overall. The results show that the oblique motion mode can be used instead of the 4WS mode for trajectory tracking under a small-curvature reference trajectory.