Browsing by Subject "hybrid systems"
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Item Hybrid Geometric Feedback Control of Three-Dimensional Bipedal Robotic Walkers with Knees and Feet(2012-07-16) Sinnet, Ryan WesleyThis thesis poses a feedback control method for obtaining humanlike bipedal walking on a human-inspired hybrid biped model. The end goal was to understand better the fundamental mechanisms that underlie bipedal walking in the hopes that this newfound understanding will facilitate better mechanical and control design for bipedal robots. Bipedal walking is hybrid in nature, characterized by periodic contact between a robot and the environment, i.e., the ground. Dynamic models derived from Lagrangians modeling mechanical systems govern the continuous dynamics while discrete dynamics were handed by an impact model using impulse-like forces and balancing angular momentum. This combination of continuous and discrete dynamics motivated the use of hybrid systems for modeling purposes. The framework of hybrid systems was used to model three-dimensional bipedal walking in a general setup for a robotic model with a hip, knees, and feet with the goal of obtaining stable walking. To achieve three-dimensional walking, functional Routhian reduction was used to decouple the sagittal and coronal dynamics. By doing so, it was possible to achieve walking in the two-dimensional sagittal plane on the three-dimensional model, restricted to operate in the sagittal plane. Imposing this restriction resulted in a reduced-order model, referred to as the sagittally-restricted model. Sagittal control in the form of controlled symmetries and additional control strategies was used to achieve stable walking on the sagittally-restricted model. Functional Routhian reduction was then applied to the full-order system. The sagittal control developed on the reduced-order model was used with reduction to achieve walking in three dimensions in simulation. The control schemes described resulted in walking which was remarkably anthropomorphic in nature. This observation is surprising given the simplistic nature of the controllers used. Moreover, the two-dimensional and three-dimensional dynamics were completely decoupled inasmuch as the dynamic models governing the sagittal motion were equivalent. Additionally, the reduction resulted in swaying in the lateral plane. This motion, which is generally present in human walking, was unplanned and was a side-effect of the decoupling process. Despite the approximate nature of the reduction, the motion was still almost completely decoupled with respect to the sagittal and coronal planes.Item Nonlinear dynamics of hysteretic oscillators(2009-05-15) Shekhawat, AshivniThe dynamic response and bifurcations of a harmonic oscillator with a hysteretic restoring force and sinusoidal excitation are investigated. A multilinear model of hysteresis is presented. A hybrid system approach is used to formulate and study the problem. A novel method for obtaining exact transient and steady state response of the system is discussed. Simple periodic orbits of the system are analyzed using the KBM method and an analytic criterion for existence of bound and unbound resonance is derived. Results of KBM analysis are compared with those from numerical simulations. Stability and bifurcations of higher period orbits are studied using Poincar?e maps. The Poincar?e map for the system is constructed by composing the corresponding maps for the individual subsystems of the hybrid system. The novelty of this work lies in a.) the study of a multilinear model of hysteresis, and, b.) developing a methodology for obtaining the exact transient and steady state response of the system.