Book excerpt: Legged robots often need to move through different terrains as they function. This requires a change of gaits by the robot in order to move with better efficiency. There has been a lot of research done to find out which gait works better for a given terrain so that the robot can change its gait accordingly. A reliable analysis of when exactly should the transition take place in a walking robot is important, so that there can be an assurance of stability in the locomotion of the robot during the transition between different gaits. This work presents analysis performed on a hexapod robot that can walk in three different gaits: Tripod gait, Ripple gait, and Wave gait, all on a flat terrain. The goal is to optimize the transition of the robot between these gaits by analyzing its stability during motion as the transition is initiated at different times during the stride, called the phase here. A reliable phase at which each transition can be implemented is analyzed with the help of a calculated cost of transition, which is based on the roll and pitch of the robot, and the general body stability margin, which relies upon computation of the support polygon. The roll and pitch of the robot are obtained from simulation of the walking robot as it transitions between gaits, while the stability margin during walking is computed in MATLAB. These values are then combined to determine the cost of transition as the function of the phase at transition. Ultimately, this can be used in real-time walking to determine when transitions should be initiated.