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The research presented herein aims to develop a bio-inspired swimming system for an autonomous underwater vehicle using Macro-Fiber Composite (MFC) actuators. The swimming system draws inspiration from the motion of carangiform fish, which limit their body motion while rapidly oscillating their caudal tail fin. The foundation for the bio-inspired swimming system is built upon a composite cantilever beam with MFC actuators in bimorph configuration. The MFC actuators excite the composite beam near its fundamental natural frequency to produce thrust as the vibration transfers momentum to the surrounding fluid. An analytical model that incorporates Euler-Bernoulli beam theory, linear piezoelectricity, and fluid mechanics is developed to predict the thrust generated by the beam vibration. Experimental testing is performed to verify aspects of, as well as recommend corrections to, the analytical model. A prototype carangiform swimmer is developed that employs a passive caudal tail fin to alter the vibratory motion of the system from a beam vibration mode to one more resembling carangiform swimming. This device is subjected to experimental testing to determine the swim speeds it is able to achieve. A maximum velocity of 90mm/s was observed when the system is excited at 900V. However, better performance may be achieved by increasing the excitation voltage. / Master of Science

This thesis explores the development of time-varying virtual constraint controllers that allow stable and agile gaits for full-order hybrid dynamical models of quadrupedal locomotion. Unlike time-invariant nonlinear controllers, time-varying controllers do not rely on sensor data for gait phasing and can initiate locomotion from zero velocity. Motivated by these properties, we investigate the stability guarantees that can be provided by the time-varying approach. More specifically, we systematically establish necessary and sufficient conditions that guarantee exponential stability of periodic orbits for time-varying hybrid dynamical systems utilizing the Poincar� return map. Leveraging the results of the presented proof, we develop time-varying virtual constraint controllers to stabilize bounding, trotting, and walking gaits of a 14 degree of freedom quadrupedal robot, Minitaur. A framework for selecting the parameters of virtual constraint controllers to achieve exponential stability is shown, and the feasibility of the analytical results is numerically validated in full-order model simulations of Minitaur. / Master of Science / This thesis extends a class of controllers designed to address the full dynamics of stable locomotion in quadrupedal robots. As of yet, there is no widely-accepted standard methodology for controlling the complex maneuvers of quadrupedal locomotion, as most strategies rely on simplified models to ease computational constraints. "Virtual constraint'' controllers - also known as Hybrid Zero Dynamics controllers - are a class of controllers designed to address the full dynamics of legged locomotion by coordinating the links of a legged robot model to follow a periodic trajectory representing the desired gait pattern. However, the formalized "time-invariant'' model of virtual constraint controllers relies on sensor data to track progress on the desired gait trajectory. This dependence on sensor data makes the resulting controllers unable to start from a state of zero velocity and sensitive to disturbances generated by high velocity impacts. The proposed "time-varying'' virtual constraints controllers utilize the elapsed time to track gait progress and do not have the previously mentioned limitations. Motivated by these benefits, we develop a formalized methodology for designing time-varying virtual constraint controllers for quadrupedal robots. This includes extending time-invariant means of mathematically validating the stability of the gait controllers to time-varying systems. With strategies of designing and validating time-varying virtual constraint controllers formalized, the methodology is implemented on numerical simulations of bounding, trotting, and walking gaits for the quadrupedal robot Minitaur which validates the stability and feasibility of the developed controllers.

Existing state-of-the-art legged robots often require complex mechanisms with multi-level controllers and computationally expensive algorithms. Part of this is owed to the multiple degrees of freedom (DOFs) these intricate mechanisms possess and the other is a result of the complex nature of dynamic legged locomotion. The underlying dynamics of this class of non-linear systems must be addressed in order to develop systems that perform natural human/animal-like locomotion. However, there are no stringent rules for the number of DOFs in a system; this is merely a matter of the locomotion requirements of the system. In general, most systems designed for dynamic locomotion consist of multiple actuators per leg to address the balance and locomotion tasks simultaneously. In contrast, this research hypothesizes the decoupling of locomotion and balance by omitting the DOFs whose primary purpose is dynamic disturbance rejection to enable a far simplified mechanical design for the legged system. This thesis presents a novel single DOF mechanism that is topologically arranged to execute a trajectory conducive to dynamic locomotive gaits. To simplify the problem of dynamic balancing, the mechanism is designed to be utilized in a quadrupedal platform in the future. The preliminary design, based upon heuristic link lengths, is presented and subjected to kinematic analysis to evaluate the resulting trajectory. To improve the result and to analyze the effect of key link lengths, sensitivity analysis is then performed. Further, a reference trajectory is established and a parametric optimization over the design space is performed to drive the system to an optimal configuration. The evolved design is identified as the Bio-Inspired One-DOF Leg for Trotting (BOLT). The dynamics of this closed kinematic chain mechanism is then simplified, resulting in a minimal order state space representation. A prototype of the robotic leg was integrated and mounted on a treadmill rig to perform various experiments. Finally, open loop running is implemented on the integrated prototype demonstrating the locomotive performance of BOLT. / MS / Existing state-of-the-art legged robots often require complex mechanisms with multi-level controllers and computationally expensive algorithms. Part of this is owed to the multiple degrees of freedom (DOFs) these intricate mechanisms possess and the other is a result of the complex nature of dynamic legged locomotion. The underlying dynamics of this class of non-linear systems must be addressed in order to develop systems that perform natural human/animal-like locomotion. However, the number of active DOF is merely a designers choice. To simplify the problem at both levels: design and controls of dynamic locomotion, we developed a novel mechanism that incorporates the benefits of higher DOF legs while accommodating the simplicity of single DOF leg. The preliminary design of the mechanism was designed with parameters (lengths of the femur,tibia) that were directly derived from a domestic dog. Synthesis of the mechanism suggested that the design was not suitable for an intended running-trot gait observed in biological counterparts. However, to gain a deeper understanding of the mechanism, it was necessary to perform a sensitivity analysis, as a result we arrived at a mechanism whose performance was better than the initial but still not satisfactory.With the insight gained through the analysis and an ideal gait design exercise, then an optimization on the design space was performed with carefully tuned bounds. The final result is a novel mechanism identified as Biologically inspired One DOF Leg for Trotting (BOLT) that is topologically arranged to execute a running-trot gait. Finally, the design choice presented with a challenge that has not been actively addressed. The dynamics of the mechanism can not be modeled using traditional methods due to presence of constraints that characterize the closed loops of the mechanism. We present an adaption of the Singularly perturbed dynamic model for systems that are hybrid in nature. The resulting dynamics are simplified, resulting in a minimal order state space representation, which is more amenable to model based control development in future. A prototype of the robotic leg was integrated and mounted on a treadmill rig to perform various experiments.Finally, open loop running is implemented on the integrated prototype demonstrating the locomotive performance of BOLT.