This thesis presents a ZMP based motion planning using a simplified model of RoboSimian, a quadruped disaster response robot by Jet Propulsion Laboratory (JPL) and Stanford University that is to compete in the DARPA Robotics Challenge (DRC), along with a method of planning for a swing trajectory for a limb using value iteration to optimize the walking speed of RoboSimian. The ZMP based planning is shown to be difficult for large step sizes because of the joint velocity limit. However, the value iteration for planning a swing trajectory was effective in finding an optimal trajectory which improves the overall walking speed of RoboSimian. Lastly, comparing the two methods, we show that when the joint velocity limit is low it is better to use the value iteration based gait but if the joint velocity limit is increased, the ZMP based method will generate a faster gait.