  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.
