Wheeled-legged (hybrid) robots have the potential for highly agile and versatile locomotion in any real-world application requiring rapid, long-distance mobility skills on challenging terrain. The ability to walk and drive simultaneously is an attractive feature of these hybrid systems, but is unexplored in literature. This thesis work presents an online trajectory optimization framework for high-dimensional wheeled-legged quadrupedal robots where the feet and base trajectories are generated in a model predictive control fashion for robustness against disturbances. Our feet optimization employs a unique parameterization that captures the velocity constraints of the wheels’ rolling and our base optimization uses a ZMP-based balance criterion. Our approach is verified on a torque-controlled quadrupedal robot with nonsteerable wheels. The robot performs hybrid locomotion with different gait sequences on flat and rough terrain. Moreover, our optimization framework generates base trajectories at a rate of about 100 Hz and feet trajectories at 1000 Hz or higher. In addition, we validated the robotic platform at the Defense Advanced Research Projects Agency (DARPA) Subterranean Challenge, where the robot rapidly maps, navigates, and explores dynamic underground environments.