Thesis (M.Sc.Eng.) PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / Legged robots offer significant advantages over their wheeled and treaded counterparts, enabling access to huge sectors of otherwise non-navigable terrain. To develop these walkers many engineers have looked to nature for inspiration, but the field of bipedal research has been focused almost exclusively on human locomotion. Other than Homo sapiens, the only regularly bipedal walkers are members of Theropoda, a clade that includes modern day birds as well as all the carnivorous dinosaurs. Whereas birds evolved extensively for flying, their ancestors, e.g. Velociraptor and Tyrannosaurus Rex, were much more specialized for dynamic terrestrial motion. We submit that there is good reason to look to theropod body geometry for an efficient alternative walking model. In this thesis, a novel model was developed in order to examine the mechanics of such specialized bipedal motion. Instead of a traditional anthropomorphic model maintaining a vertically balanced torso, this research synthesized a dinomorphic model that consists of a horizontal spine with counterbalanced torso and tail masses pivoting around the hip joint. The system model developed herein was an extension of the simple rimless wheel representation and aimed to capture critical events in the cycle of bipedal motion while avoiding chaotic regimes. Mathematical models and computer simulations were designed iteratively and in parallel. Once the system dynamics and the energy losses from inelastic impact were derived, then all the equations were nondimensionalized. Theoretical bounds on efficiency were found, and an attempt was made to experimentally quantify the effects of each geometric system parameter. A region of improved performance was identified, indicating non-negligible benefits to tailed morphologies over tail-less ones. It is suggested that further research might adapt and apply this model to the more complex bipedal compass gait. Ideally these findings will enable and encourage the design of legged robots with a horizontal load-bearing frame, demonstrating advantage over anthropomorphic walkers. / 2031-01-01

Human walking is dynamic, stable, and energy efficient. To achieve such remarkable legged locomotion in robots, engineers have explored bipedal robots developed based on two paradigms: trajectory-controlled and passive-based walking. Trajectory-controlled bipeds often deliver energy-inefficient gaits. The reason is that these bipeds are controlled via high-impedance geared electrical motors to accurately follow predesigned trajectories. Such trajectories are designed to keep a biped locally balanced continually while walking. On the other hand, passive-based bipeds provide energy-efficient gaits. The reason is that these bipeds adapt to their natural dynamics. Such gaits are stable limit-cycles through entire walking motion, and do not require being locally balanced at every instant during walking. However, passive-based bipeds are often of round/point foot bipeds that are not capable of achieving and experiencing standing, stopping, and some important bipedal gait phases and events, such as the double support phase. Therefore, the goals of this thesis are established such that the aforementioned limitations on trajectory-controlled and passive-based bipeds are resolved. Toward the above goal, comprehensive simulation and experimental explorations into bipedal walking have been carried out. Firstly, a novel systematic trajectory-controlled gait-planning framework has been developed to provide mechanical insights into bipedal walking in terms of gait characteristics and energy efficiency. For the same purpose, a novel mathematical model of passive-based bipedal walking with compliant hip-actuation and compliant-ankle flat-foot has been developed. Finally, based on mechanical insights that have been achieved by the aforementioned passive-based model, a physical prototype of a passive-based bipedal robot has been designed and fabricated. The prototype experimentally validates the importance of compliant hip-actuation in achieving a highly dynamic and energy efficient gait.

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This 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.