Legged locomotion is a discrete event system (DES) due to the ever changing contact states of each leg. As such, it requires a nonlinear modelling method to predict the trajectory of a legged robot. One such robot has been focused on throughout this thesis; the six legged "Zebro''. With its half-circular legs, the Zebro is well suited for traversing uneven terrain and even climbing up small steps, making it the robot of choice for a lunar mission in the near future. A previous attempt at modelling the trajectory of a Zebro kinematically fell short when it came to modelling a curved path, with the reasoning behind this being how the Zebro's legs can visibly be seen slipping over the ground as it walks, the effect of which is never taken into account. A combination of kinematics and dynamics was used for the model in this thesis. The reason for this is that the Zebro's legs are actuated using position controlled motors, so the information available is the leg's angle and the speed at which the leg is rotating, rather than the torque. Therefore, kinematics were used to estimate the vertical motion of the Zebro due to the rotational speed of each leg, which could then be used to estimate the normal contact force on each leg. The traction forces could then be estimated using the normal force and a slippage model which has been experimentally identified in collaboration with a different research team at the TU Delft. With these forces, and the Newton-Euler equations of motion, the Zebro's path could be predicted. Applying a slippage model to a half-circular leg, rather than a wheel, required a new method of calculating the slip ratios which was based on Pacejka's formula, but adapted to also account for the case where a leg is standing on its toe. Furthermore, a contact detection algorithm was designed to kinematically predict which leg(s) lift off of the ground during a touchdown event. This was used to kinematically model the orientation of the Zebro during a tetrapod gait and was shown to correctly predict the complicated contact transitions during said gait. Another product of the research in this thesis is a new and improved algorithm for a turning tripod gait, which achieves smoother turning than beforehand by guaranteeing a smooth contact transition between two leg groups. That being said, it cannot yet be applied to the tetrapod gait, so the current gait scheduling algorithm is still required for a turning tetrapod gait. The results of the simulations showed the Zebro walking as expected, both in a straight line and when turning, but the simulations could not be validated quantitatively due to current events regarding COVID-19. For a qualitative review of the model, photographs were taken of the Zebro during walking gaits to compare to the simulations and showed that, while straightforward walking was predicted well, the turning circle of the model was significantly sharper than in reality. The reason for this is most likely a problem in the calculation of the slip ratios, since they were consistently unrealistically low, therefore requiring further research in future.