This thesis 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.

中文翻译：

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倾斜相空间中具有融合角度和校正作用的解析式双足行走

本文提出了用于双足类人机器人平台的反馈稳定行走的算法，以及实现它所需的基础理论和感觉运动框架。由于相关机器人的高度非线性和大量自由度，相应状态的可观察性和可控性有限以及不完美的驱动力与不理想的驱动力相结合，因此双足行走固有地复杂且难以控制感应。所提出的方法以多种方式处理这些问题，从执行器控制和前馈补偿方案的开发，到几乎所有步态稳定反馈管道中都包含滤波。研究和研究了两种步态，直接融合角反馈步态，和倾斜相位控制器。两种步态均遵循以下设计理念：利用半稳定的开环步态发生器，并通过所谓的纠正措施来通过稳定反馈来扩展它。使用纠正措施的想法是修改开环关节波形的生成，以使机器人的平衡受到影响，从而得到改善。这种纠正措施的示例包括手臂摆动和腿部摆动轨迹的修改，对臀部和脚部的动态位置和旋转偏移的应用以及命令步长和时机的调整。反馈步态及其相应步态发生器的基础是3D旋转理论领域的重大进步。这些进步包括开发了三种新颖的旋转表示，倾斜角，熔融角和倾斜相空间表示。所有这三种表示形式均基于将3D旋转分解为各自的偏航和倾斜分量的新创新方式。