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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. 

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. 

This paper investigates development of an efficient numerical integrator for forward dynamics simulation of the protein folding process, where protein molecules are modeled as robotic mechanisms consisting of rigid nano-linkages with many degrees-of-freedom. To address the computational burden associated with fixed step-size explicit Euler methods, we develop a fast numerical scheme with an adaptive step-size strategy for computing the folding pathway of protein molecules.