At a platform singularity, a parallel manipulator loses constraint. Adding redundant actuation in an existing leg or new leg can eliminate these types of singularities. However, redundant manipulators have been designed with little attention to frame invariant techniques. In this dissertation, physically meaningful measures for closeness to singularities in non-redundant manipulators are developed. Two such frameworks are constructed. The first framework is a constrained optimization problem that unifies seemingly unrelated existing measures and facilitates development of new measures. The second is a clearance propagation technique based on workspace generation. These closeness measures are expanded to include redundancy and thus can be used as objective functions for designing redundant actuation. The constrained optimization framework is applied to a planar three degree of freedom redundant parallel manipulator to show feasibility of the technique.

This thesis seeks to advance the field of microrobotics by leveraging Bayesian principles and computational tools to design system parameters for information gain and microrobot propulsion. Inspired by living cells, the development of mobile robots on the micron scale (microrobots) promises new capabilities for advancing human health, renewable energy, and environmental sustainability. To help pave the way towards this goal we develop practical recipes for applying computational and analytical tools to physics-based dynamical models of our microrobot experiments. We apply methods of criticism and validation to identify robust models for the motion of magnetic particles at curved interfaces, and identify optimal conditions for propulsion in our model system. We then develop tools for identifying optimal experimental conditions for most efficiently learning model parameters. By studying microscale actuation in depth, we seek to provide a roadmap of how to apply these computational tools to other microrobot design challenges, accelerating the scientific process. In Chapter 1, we focus on the actuation of magnetic particles adsorbed at curved liquid interfaces by external fields, a phenomenon that can be utilized for applications such as droplet mixing or propulsion. To optimize these behaviors, the development and validation of predictive models are essential. We employ Bayesian data analysis as a principled approach to infer model parameters from experimental observations, assess the capabilities of candidate models, and select the most plausible among them. Specifically, we identify and validate a dynamical model which accounts for the effects of gravity and tilting of the particle, a Janus sphere, at the interface. We show how this favored model can predict complex particle trajectories with micron-level accuracy across the range of driving fields considered. Chapter 2 builds on this modeling to develop the optimal properties of a mobile liquid droplet, driven by an adsorbed magnetic particle. This configuration enables the design of responsive emulsions, which can be actuated by a magnetic field. This work develops the properties of such a swimmer and validates our findings with an experimental realization of a ferromagnetic ellipsoid adsorbed onto a stationary water droplet in decane. Accounting for geometric differences, the model developed in the previous chapter is demonstrated to be accurate for this new system. We find that the configuration of the magnetic moment of our ellipsoid prohibits swimming of the assembly, but if it can be modified during fabrication, propulsion is possible. In Chapter 3 we show how automated experiments based on Bayesian inference and design can accurately and efficiently characterize another microscale propulsion system, the acoustic field within resonant chambers used to propel acoustic nanomotors. Repeated cycles of observation, inference, and design are guided by a physical model that describes the rate at which levitating particles approach the nodal plane. We show how this iterative process serves to discriminate between competing hypotheses and efficiently converges to accurate parameter estimates using only a few automated experiments. This work demonstrates how Bayesian methods can learn the parameters of nonlinear hierarchical models used to describe video microscopy data of active colloids. Finally, the forward-looking perspective in Chapter 4 illustrates how best to leverage these techniques and models to provide a path forward for self-guided microrobots. Existing microrobots based on field-driven particles rely on knowledge of the particle position and the target destination to control particle motion through fluid environments. These external control strategies are challenged by limited information and global actuation, where a common field directs multiple robots with unknown positions. We discuss how time-varying magnetic fields can be used to encode self-guided behaviors of magnetic particles conditioned on local environmental cues. Programming these behaviors is framed as a design problem: we seek to identify the design variables (e.g. particle shape, magnetization, elasticity, stimuli-response) that achieve the desired performance in a given environment. We discuss strategies for accelerating the design process using the methods developed in this thesis—including automated experiments, computational models, and statistical inference—as well as other approaches such as machine learning. Based on the current understanding of field-driven particle dynamics and existing capabilities for particle fabrication and actuation, we argue that self-guided microrobots with potentially transformative capabilities are close at hand. This research offers a unique contribution by demonstrating the practicality and efficiency of Bayesian computational methods in microrobot design, and provides a template that is applicable anywhere that physics-based dynamical models can be used to guide experimental effort.