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Abstract This paper addresses the problem of algorithmic prediction of protein folding pathways, namely, the transient three-dimensional conformations of protein molecules during folding, under constrained rates of entropy change. We formulate the physics-based prediction of folding pathways as a control synthesis problem, where the control inputs guide the protein folding simulations. These folding control inputs are obtained from largescale trust-region subproblems (TRS) utilizing a computationally efficient algorithm with no need for outer iterations. The proposed control synthesis approach, which leverages the solutions obtained from a special generalized eigenvalue problem, avoids potentially cumbersome and unpredictable iterative computations at each protein conformation. Moreover, the TRS-based control inputs align the closed-loop dynamics closely with the kinetostatic compliance method (KCM) reference vector field while satisfying ellipsoidal constraints on the folding control inputs. Finally, we provide conditions for existence and uniqueness of the resulting closed-loop solutions, which are the protein folding pathways under constraints on the rate of entropy change. Numerical simulations utilizing the KCM approach on protein backbones confirm the effectiveness of the proposed framework. 

Numerical simulations of protein folding enable the design of protein-based nanomachines and nanorobots by predicting folded three-dimensional protein structures with high accuracy and revealing the protein conformation transitions during folding and unfolding. In the kinetostatic compliance method (KCM) for folding simulations, protein molecules are represented as ensembles of rigid nano-linkages connected by chemical bonds, and the folding process is driven by the kinetostatic influence of nonlinear interatomic force fields until the system converges to a free-energy minimum of the protein. Despite its strengths, the conventional KCM framework demands an excessive number of iterations to reach folded protein conformations, with each iteration requiring costly computations of interatomic force fields. To address these limitations, this work introduces a family of sign gradient descent (SGD) algorithms for predicting folded protein structures. Unlike the heuristic-based iterations of the conventional KCM framework, the proposed SGD algorithms rely on the sign of the free-energy gradient to guide the kinetostatic folding process. Owing to their faster and more robust convergence, the proposed SGD-based algorithms reduce the computational burden of interatomic force field evaluations required to reach folded conformations. Their effectiveness is demonstrated through numerical simulations of KCM-based folding of protein backbone chains. 

Effective human-robot interaction is increasingly vital across various domains, including assistive robotics, emotional communication, entertainment, and industrial automation. Visual feedback, a common feature of current interfaces, may not be suitable for all environments. Audio feedback serves as a critical supplementary communication layer in settings where visibility is low or where robotic operations generate extensive data. Sonification, which transforms a robot's trajectory, motion, and environmental signals into sound, enhances users' comprehension of robot behavior. This improvement in understanding fosters more effective, safe, and reliable Human-Robot Interaction (HRI). Demonstrations of auditory data sonification's benefits are evident in real-world applications such as industrial assembly, robot-assisted rehabilitation, and interactive robotic exhibitions, where it promotes cooperation, boosts performance, and heightens engagement. Beyond conventional HRI environments, auditory data sonification shows substantial potential in managing complex robotic systems and intricate structures, such as hyper-redundant robots and robotic teams. These systems often challenge operators with complex joint monitoring, mathematical kinematic modeling, and visual behavior verification. This dissertation explores the sonification of motion in hyper-redundant robots and teams of industrial robots. It delves into the Wave Space Sonification (WSS) framework developed by Hermann, applying it to the motion datasets of protein molecules modeled as hyper-redundant mechanisms with numerous rigid nano-linkages. This research leverages the WSS framework to develop a sonification methodology for protein molecules' dihedral angle folding trajectories. Furthermore, it introduces a novel approach for the systematic sonification of robotic motion across varying configurations. By employing localized wave fields oriented within the robots' configuration space, this methodology generates auditory outputs with specific timbral qualities as robots move through predefined configurations or along certain trajectories. Additionally, the dissertation examines a team of wheeled industrial/service robots whose motion patterns are sonified using sinusoidal vibratory sounds, demonstrating the practical applications and benefits of this innovative approach. 

Sonification is a method to represent data and convey information using sound. Just like the Geiger counter, humans can use sound to better understand complex sets of data that are either unable to be seen or visualized or that are too complex to understand with visual displays. Sonification research and learning have been predominantly conducted at the higher education level. However, as STEM-related programs and activities continue to be increasingly important in secondary school education, it is possible to expose high school students to university-level research through project-based learning (PBL) activities in the classroom. Using a physical snake robot prototype that was built and programmed with low-cost materials, high school students are introduced to the field of sonification and its applications to snake robots. This dissertation demonstrates the feasibility of using project-based learning to teach university level research in secondary school education. Using the sonification of snake robot movement, students learned advanced topics in robotics with the goal of realizing that university level research is accessible and understandable through PBL. This paper will begin by discussing the concept of human-robot interaction, introduce sonification, and give a brief overview of project-based learning. A detailed discussion of how the snake robot prototype was constructed and programmed, an in-depth explanation of the sonification algorithm that was used, and how sonification was taught in a high school classroom using PBL is presented along with student feedback and suggestions for future work. 

The development of Unmanned Aerial Vehicles (UAVs) can be enhanced through the use of sonification, an emerging field within Human-Robot Interaction (HRI). This dissertation introduces UAVSonification, a computational algorithm that maps simulation data to musical notes using the Musical Instrument Digital Interface (MIDI). By integrating UAVSonification with Formation Flight Simulation in Simulink, this study explores the sonification of UAV trajectories under environmental conditions. The function transforms simulation data into auditory signals, allowing users to discern key dynamics through sound. Specifically, the data series for multiple UAVs is mapped to piano notes via MIDI on MATLAB, providing auditory insights into UAV trajectories, environmental conditions, and control errors. A well-controlled flight path and stable heading controller produce harmonious sounds, while disruptions and deviations result in dissonance. UAVSonification offers a unique auditory approach to understanding UAV behavior in relation to control dynamics and environmental conditions. The sonification of UAVs has the potential to aid in the planning and analysis of UAV trajectories and controllers, as well as in creative endeavors. The effectiveness of the proposed method is shown through MATLAB numerical simulations. 

Tweezers-based nanorobots, optical tweezers in particular, are renowned for their exceptional precision, and among their biomedical applications are cellular manipulation, unzipping DNAs, and elongating polypeptide chains. This thesis introduces a series of Lyapunov-based feedback control frameworks that address both stability and controlled instability for biological manipulation, applied within the context of optical tweezers. At the core of this work are novel controllers that stabilize or destabilize specific molecular configurations, enabling fine manipulation of particles like polystyrene beads and tethered polymers under focused laser beams. Chapter 1 covers the foundational principles and surveys existing literature on the modeling and control of optical tweezers, emphasizing gaps in the stability and instability control of molecular systems. Chapter 2 presents a robust Control Lyapunov Function (CLF) approach, designed to stabilize spherical particles under optical trapping. By formulating a smooth, norm-bounded feedback controller, we achieve lateral stabilization despite external disturbances, using a real-time, static nonlinear programming (NLP) solution. Simulations verify the effectiveness of this CLF framework, even with significant initial displacements from the laser focus and under thermal forces modeled as a white Gaussian noise. Chapter 3 addresses controlled instability through a Control Chetaev Function (CCF) framework, specifically targeting protein unfolding applications. Linearization with respect to the control input facilitates the application of destabilizing universal controls for affine- in-control system dynamics. The resulting CCF-based norm-bounded feedback controller induces system instability by laterally extending the trapped DNA handle, thereby increasing the molecular extension and providing insights into protein denaturation and unfolding pathways. This controller is robust to stochastic thermal forces and optimized for real-time computational efficiency. These Lyapunov and Chetaev-based control designs collectively expand the capabilities of optical tweezers, advancing single-molecule manipulation under both stable and unstable conditions. These findings advance precision nanomanipulation, opening new avenues for exploring the molecular mechanics of protein unfolding and DNA elasticity. 

The kinetostatic compliance method (KCM) models protein molecules as nanomechanisms consisting of numerous rigid peptide plane linkages. These linkages articulate with respect to each other through changes in the molecule dihedral angles, resulting in a kinematic mechanism with hyper degrees of freedom. Within the KCM framework, nonlinear interatomic forces drive protein folding by guiding the molecule’s dihedral angle vector towards its lowest energy state in a kinetostatic manner. This paper proposes a numerical integrator that is well suited to KCM-based protein folding and overcomes the limitations of traditional explicit Euler methods with fixed step size. Our proposed integration scheme is based on pseudo-transient continuation with an adaptive step size updating rule that can efficiently compute protein folding pathways, namely, the transient three-dimensional configurations of protein molecules during folding. Numerical simulations utilizing the KCM approach on protein backbones confirm the effectiveness of the proposed integrator. 

Despite the inherent need for enhancing human-robot interaction (HRI) by non-visually communicating robotic movements and intentions, the application of sonification (the translation of data into audible information) within the field of robotics remains underexplored. This paper investigates the problem of designing sonification algorithms that translate the motion of teams of industrial mobile robots to non-speech sounds. Our proposed solution leverages the wave space sonification (WSS) framework and utilizes localized wave fields with specific orientations within the system configuration space. This WSS-based algorithm generates sounds from the motion data of mobile robots so that the resulting audio exhibits a chosen timbre when the robots pass near designated configurations or move along desired directions. To demonstrate its versatility, the WSS-based sonification algorithm is applied to a team of OMRON LD series autonomous mobile robots, sonifying their motion patterns with pure tonal sounds. 

Considering the non-affine-in-control system governing the motion of a spherical particle trapped inside an optical tweezer, this paper investigates the problem of stabilization of the particle position at the origin through a control Lyapunov function (CLF) framework. The proposed CLF framework enables nonlinear optimization-based closed-loop control of position of tiny beads using optical tweezers and serves as a first step towards design of effective control algorithms for nanomanipulation of biomolecules. After deriving necessary and sufficient conditions for having smooth uniform CLFs for the optical tweezer control system under study, we present a static nonlinear programming problem (NLP) for generation of robustly stabilizing feedback control inputs. Furthermore, the NLP can be solved in real-time with no need for running computationally demanding algorithms. Numerical simulations demonstrate the effectiveness of the proposed control framework in the presence of external disturbances and initial bead positions that are located far away from the laser beam. 

This paper proposes a sign gradient descent (SGD) algorithm for predicting the three-dimensional folded protein molecule structures under the kinetostatic compliance method (KCM). In the KCM framework, which can be used to simulate the range of motion of peptide-based nanorobots/nanomachines, protein molecules are modeled as a large number of rigid nano-linkages that form a kinematic mechanism under motion constraints imposed by chemical bonds while folding under the kinetostatic effect of nonlinear interatomic force fields. In a departure from the conventional successive kinetostatic fold compliance framework, the proposed SGD-based iterative algorithm in this paper results in convergence to the local minima of the free energy of protein molecules corresponding to their final folded conformations in a faster and more robust manner. KCM-based folding dynamics simulations of the backbone chains of protein molecules demonstrate the effectiveness of the proposed algorithm.