Jake McGrath Final Defense

Abstract: Biological systems execute a remarkable variety of dynamical behaviors—including development, repair, motor control, sensing, signaling, and adaptation—powered by the transduction of stored energy. These behaviors span orders of magnitude in space and time, from nanometer-scale molecular motors to kilometer-scale migrations, and from millisecond reflexes to evolutionary adaptations. While physical forces govern the dynamics of these systems, they alone cannot explain how living systems sense, decide, and coordinate mechanical function. Here, I argue that control theory provides a unifying framework for understanding the regulation of biological systems across scales, from molecular actuators to macroscopic performance.

A central focus of this dissertation is nonlinear actuation in muscle-inspired systems as a model of these control theory concepts. In biological muscles, force generation follows Hill-type hyperbolic force–velocity relationships, characterized by a dimensionless nonlinearity parameter, alpha. I first construct a bioinspired electromagnetic motor, HillBot, that reproduces Hill-type dynamics via PID-controlled actuation. This platform demonstrates that nonlinear force production can reduce the energetic cost of actuation compared to conventional linear force–velocity systems, revealing generalizable principles of energy economy through nonlinearity. 

Extending to the molecular scale, I develop an analytical model linking myosin unbinding dynamics to macroscale muscle energetics. Together with the robophysical HillBot platform, I show that the degree of nonlinearity, alpha, governs a performance–efficiency tradeoff, and that the characteristic nonlinearity observed in-vivo, alpha*~4, balances power output and energetic efficiency, potentially explaining its prevalence in nature.

To explore long-term evolutionary consequences and fitness of alpha*, I built agent-based Monte Carlo simulations to show that populations of agents with varying alpha evolve toward alpha*, highlighting how nonlinear actuation shapes adaptability, robustness, and resource allocation across timescales. These results suggest that fundamental features of the actomyosin nonlinearity observed in nature can be understood as optimal solutions for energy management and performance in biological systems.

Additionally, I extend these control theoretic ideas by investigating two biologically inspired robophysical model systems and NBA player performance in free-throw shooting. The first robophysical model evaluates the efficiency of different control strategies in performing nonlinear, out-of-equilibrium tasks, providing insight into the principles of control in complex dynamical systems. The second investigates how muscle's embedded viscoelastic structure supports stabilization against perturbations. Finally, I apply data-driven methods to quantify skill and control in complex human systems, using NBA free-throw tracking data as a case study. By developing metrics that capture precision, consistency, and robustness, this work illustrates the broader applicability of control- and performance-focused frameworks to biological, engineered, and human systems.

Together, this dissertation provides a multiscale, mechanistic understanding of nonlinear actuation, energy management, and control in complex biological systems.