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This work presents algorithms for the feedback-stabilised walking of bipedal humanoid robotic platforms, along with the underlying theoretical and sensorimotor frameworks required to achieve it. Bipedal walking is inherently complex and difficult to control due to the high level of nonlinearity and significant number of degrees of freedom of the concerned robots, the limited observability and controllability of the corresponding states, and the combination of imperfect actuation with less-than-ideal sensing. The presented methods deal with these issues in a multitude of ways, ranging from the development of an actuator control and feed-forward compensation scheme, to the inclusion of filtering in almost all of the gait stabilisation feedback pipelines. Two gaits are developed and investigated, the direct fused angle feedback gait, and the tilt phase controller. Both gaits follow the design philosophy of leveraging a semi-stable open-loop gait generator, and extending it through stabilising feedback via the means of so-called corrective actions. The idea of using corrective actions is to modify the generation of the open-loop joint waveforms in such a way that the balance of the robot is influenced and thereby ameliorated. Examples of such corrective actions include modifications of the arm swing and leg swing trajectories, the application of dynamic positional and rotational offsets to the hips and feet, and adjustments of the commanded step size and timing. Underpinning both feedback gaits and their corresponding gait generators are significant advances in the field of 3D rotation theory. These advances include the development of three novel rotation representations, the tilt angles, fused angles, and tilt phase space representations. All three of these representations are founded on a new innovative way of splitting 3D rotations into their respective yaw and tilt components.