Both quadrupedal and bipedal robots have their own advantages. In order for some quadrupedal robots, such as Jet Propulsion Laboratory's RoboSimian, to act as bipedal robots, a transition motion is often needed. In this thesis, we present a ZMP based bang-bang control method to solve for a minimum time transition trajectory for a simplified dynamic model. Also, we explore two different quadratic programming problem formulations to plan for a fast pitching up robot trajectory from being horizontal in hope that the robot can be balanced when it's near an upright position. We also investigate different ways to improve the speed a body trajectory given a limited physical capability of a robot.