Date of Award

Fall 10-1-2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mechanical Engineering & Materials Science (ENAS)

First Advisor

Venkadesan, Madhusudhan

Abstract

Mechanical stability is vital for the fitness and survival of animals and is a crucial aspect of robot design and control. Stability depends on multiple factors, including the body's intrinsic mechanical response and feedback control. But feedback control is more fragile than the body's innate mechanical response or open-loop control strategies because of sensory noise and time-delays in feedback. This thesis examines the overarching hypothesis that stability demands have played a crucial role in how animal form and function arise through natural selection and motor learning. In two examples, finger contact and overall body stability, we investigated the relationship between morphology, open-loop control, and stability. By studying the stability of the internal degrees of freedom of a finger when pushing on a hard surface, we find that stability limits the force that we can produce and is a dominant aspect of the neural control of the finger's muscles. In our study on whole body lateral stability during locomotion in terrestrial animals, we find that the overall body aspect ratio has evolved to ensure passive lateral stability on the uneven terrain of natural environments. Precisely gripping an object with the fingertips is a hallmark of human hand dexterity. In Chapter 2, we show how human fingers are intrinsically prone to a buckling-type postural instability and how humans use careful neural orchestration of our muscles so that the elastic response of our muscles can suppress the intrinsic instability. In Chapter 3, we extend these findings further to examine the nature of neuromuscular variability and how the nervous system deals with the need for muscle-induced stability. We find that there is structure to neuromuscular variability so that most of the variability lies within the subspace that does not affect stability. Inspired by the open-loop stable control of our index fingers, in Chapter 4, we derive open-loop stability conditions for a general mechanical linkage with arbitrary joint torques subjected to holonomic constraints. The solution that we derive is physically realizable as cable-driven active mechanical linkages. With a user-prescribed cable layout, we pose the problem of actuating the system to maintain stability while subject to goals like energy minimization as a convex optimization problem. We are thus able to use efficient optimization methods available for convex problems and demonstrate numerical solutions in examples inspired by the finger. Chapter 5 presents a general formulation of the stability criteria for active mechanical linkages subject to Pfaffian holonomic and non-holonomic constraints. Active mechanical linkages subject to multiple constraints represent the mechanics of systems spanning many domains and length scales, such as limbs and digits in animals and robots, and elastic networks like actin meshes in microscopic systems. We show that a constrained mechanical linkage with regular stiffness and damping, and circulation-free feedback, can only destabilize by static buckling when subject to holonomic constraints. In contrast, the same mechanical linkage, subject to a non-holonomic constraint, such as a skate contact, can exhibit either static buckling or flutter instability. Chapter 6 moves away from neural control and studies the shape of animal bodies and their relationship to stability in locomotion. We investigate why small land animals tend to have a crouched or sprawled posture, whereas larger animals are generally more upright. We propose a new hypothesis that the scaling of body aspect ratio with size is driven by the scale-dependent unevenness of natural terrain. We show that the scaling law arising from the need for stability on rough natural terrain correctly predicts the frontal aspect ratio scaling law across 335 terrestrial vertebrates and invertebrates, spanning eight orders of magnitude in mass so that smaller animals have a wider aspect ratio. We also carry out statistical analyses that consider the phylogenetic relationship among the species in our dataset to show that the scaling is not due to gradual changes of the traits over time. Thus, stability demands on natural terrain may have driven the macroevolution of body aspect ratio across terrestrial animals. Interrogating unstable and marginally stable behaviors has helped us identify the morphological and control features that allow animals to perform robustly in noisy environments where perfect sensory feedback cannot be assumed. Although the thesis identifies the `what' and `why,' further studies are needed to understand `how' mechanics and development intertwine to give rise to control and form in growing and adapting biological organisms.

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