Thesis Dissertation Defense

Abstract: Biological systems can use seemingly simple rhythmic body and/or limb undulations to traverse their natural terrains. We are particularly interested in the regime of locomotion in highly damped environments, which we refer to as geometric locomotion. In geometric locomotion, net translation is generated from properly coordinated self-deformation to counter drag forces. The scope of geometric locomotion is broad across scales with diverse morphologies. For example, at the macroscopic scale, legged animals such as fire salamanders (Salamandra salamandra), display high maneuverability by properly coordinating their body bending and leg movements. At the microscopic scale, nematode worms, such as C. elegans, can manipulate body undulation patterns to facilitate effective locomotion in diverse environments. These movements often require proper coordination of animal limbs and body; more importantly, such coordination patterns are environment dependent. In robotic locomotion, however, the state-of-the-art gait design and feedback control algorithms are computationally costly and typically not transferable across platforms (body-morphologies and environments), thus limiting the versatility and performance capabilities of engineering systems. While it is challenging to directly replicate the success in biological systems to robotic systems, the study of biological locomotors can establish simple locomotion models and principles to guide the robotics control process. The overarching goal of this thesis is to connect the observations in biological systems to the optimization problems in robotics applications. In the last 30 years, a framework called “geometric mechanics” has been developed as a general scheme to link locomotor performance to the patterns of “self-deformation”. This geometric approach replaces laborious calculation with illustrative diagrams. Unfortunately, this geometric approach was limited to low degree-of-freedom systems while assuming idealized contact models with the environment. This thesis develops and advances the geometric mechanics framework to overcome both of these limitations; and thereby throws insights into understanding a variety of animal behaviors as well as controlling robots, from short-limb elongate quadrupeds to body-undulatory multi-legged centipedes.