Oscillation, orientation, and locomotion of mechanical rectifier systems

Animal locomotion possesses advantageous characteristics in animal morphology, motion efficiency and environment adaptivity, hence furnishing a natural learning template for design and optimization of robotic vehicles. Inspired by their natural analogues, the increasing number of animal-like robots have emerged in recent years. This thesis considers a class of mechanical rectifiers arising from dynamics of animal locomotion. The thesis starts with introduction of the general system modeling method of the mechanical rectifiers, followed by the description of three typical robotic implementations, namely fliptail, snake-like and flapping-wings locomotors. The dynamics of mechanical rectifiers then is revealed to be under-actuated and essentially have three components: oscillation, orientation and locomotion dynamics. The oscillation dynamics describes how the oscillatory motion of the body shape results from the interaction with environment and body actuation. The orientation dynamics shows the under-actuation property of the locomotion system where the system orientation does not receive direct control. But it is coupled with oscillation dynamics. The locomotion dynamics demonstrates the effect of the mechanical rectification where the periodic body motion is converted to the movement on the mass center. Regarding three components, the main achievement of this work has three folds. For oscillation dynamics, we introduce the natural oscillation patterns for body shape and proposed a biologically inspired controller to make the closed-loop system exactly entrain the oscillation. For orientation dynamics, we construct a orientation controller on top of the entrainment controller manipulating the average orientation to be aligned with locomotion direction, though at price of the accuracy of body oscillation. The oscillation accuracy however can be tuned by controller parameters. For locomotion dynamics, we prove that the induced body oscillation and orientation can globally achieve a specific locomotion velocity at mass center which is called natural velocity. This three efforts compose a control design framework for mechanical rectifiers. Throughout the thesis, these three aspects of the framework would be detailed by applications to the three aforementioned robotic locomotors. The effectiveness of control design framework is supported theoretically by rigorous proof and practically validated by numerical simulation.