A Foot Placement Strategy for Robust Bipedal Gait Control

This thesis introduces a new measure of balance for bipedal robotics called the foot placement estimator (FPE). To develop this measure, stability first is defined for a simple biped. A proof of the stability of a simple biped in a controls sense is shown to exist using classical methods for nonlinear systems. With the addition of a contact model, an analytical solution is provided to define the bounds of the region of stability. This provides the basis for the FPE which estimates where the biped must step in order to be stable. By using the FPE in combination with a state machine, complete gait cycles are created without any precalculated trajectories. This includes gait initiation and termination. The bipedal model is then advanced to include more realistic mechanical and environmental models and the FPE approach is verified in a dynamic simulation. From these results, a 5-link, point-foot robot is designed and constructed to provide the final validation that the FPE can be used to provide closed-loop gait control. In addition, this approach is shown to demonstrate significant robustness to external disturbances. Finally, the FPE is shown in experimental results to be an unprecedented estimate of where humans place their feet for walking and jumping, and for stepping in response to an external disturbance

Theorizing the Westphalian system of states: international relations from absolutism to capitalism

This article provides a new approach, revolving around contested property relations, for theorizing the constitution, operation and transformation of geopolitical systems, exemplified with reference to early modern international relations. Against the cross-paradigmatic IR consensus that equates the Westphalian Settlement with the codification of modern international relations, the article shows to which degree 17th and 18th century European geopolitics remained tied to rather unique pre-modern practices. These cannot be understood on the basis of realist or constructivist premises. In contrast, the theoretical argument is that the proprietary and personalized character of dynastic sovereignty was predicated on pre-capitalist property relations. Dynasticism, in turn, translated into historically specific patterns of conflict and cooperation that were fundamentally governed by the competitive logic of geopolitical accumulation. The decisive break to international modernity comes with the rise of the first modern state — England. After the establishment of a capitalist agrarian property regime and the transformation of the English state in the 17th century, post-1688 Britain starts to restructure international relations in a long-term process of geopolitically combined and socially uneven development