Geometric modeling of biological and robotic locomotion in highly damped environments

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Zhong, Baxi
Goldman, Daniel I.
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Biological systems can use seemingly simple rhythmic body and limb undulations to traverse their complex 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, the net translation is generated from properly coordinated self-deformation to counter the drag forces, as opposed to inertia-dominated systems where inertial forces dominate over frictional forces (thus coasting/gliding is possible). The scope of geometric locomotion include locomotors with diverse morphologies across scales in various environments. For example, at the macroscopic scale, legged animals such as fire salamanders (S. 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 bodies and/or limbs; 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 and scenarios (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 robotics control processes. The overarching goal of this thesis is to (1) connect the observations in biological systems to the optimization problems in robotics applications, and (2) use robotics as tools to analyze locomotion behaviors in various biological systems. 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. Historically, this geometric approach was limited to low degree-of-freedom systems while assuming an idealized contact model with the environment. This thesis develops and advances the geometric mechanics framework to overcome both of these limitations; and thereby generates insight into understanding a variety of animal behaviors as well as controlling robots, from short-limb elongate quadrupeds to body-undulatory multi-legged centipedes in highly-damped environments.
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