This thesis explores the application of reorientation manoeuvres to an articulated and a mobile robot architecture. These manoeuvres are often attributed to cats that are said to always land on their feet, but have also been observed in other animals and used by humans in certain sports. However, these manoeuvres are more than just a curiosity and have seen some use in the field of robotics. Indeed, reorientation manoeuvres are used for orientation control in falling robots, such as rescue robots deployed in dangerous environments, and in jumping robots. With such applications in mind, this thesis aims to develop and demonstrate fast (180-degree reorientation about one axis — the worst-case scenario — within the time of a one-metre fall), multi-axis reorientation manoeuvres. Firstly, an articulated architecture, along with two different manoeuvres, are designed in order to attain the desired reorientation capabilities and are tested in simulated conditions. The results obtained show that, although multi-axis reorientation is achieved, the required motor torques to reach the desired reorientation speeds are not feasible for the proposed architecture. Secondly, an omnidirectional mobile robot architecture is designed to address the limitations of the first architecture. A prototype of this mobile architecture is developed and is used to demonstrate a reorientation of 179 degrees about the pitch axis in 0.44 seconds as well as a reorientation about multiple axes. Therefore, with this prototype, the desired reorientation capabilities are achieved. Finally, the use of sensor fusion methods based on extended Kalman filtering in the context of estimation of the orientation of a free-floating platform is studied. The results obtained from this study support the viability of using such methods for on-board trajectory planning in future iterations of the developed prototype.