Candidate Name: Hamidreza Moradi
Program: Mechanical Engineering​​​​​​​
Committee Chairs: Dr. Scott David Kelly​​​​​​​
Committee Members: Dr. Artur Wolek, Dr. Russell Keanini, Dr. Wesley Williams
Abstract:

This work investigates how agents can influence one another and their environment purely through physical interactions, without explicit communication channels, inspired by coordination mechanisms observed in biological systems. For this purpose, snake robots operating on shared moving platforms are adopted as a canonical model system, given their rich nonholonomic structure, internal actuation-driven locomotion, and strong coupling between shape changes and global motion. These features make them particularly well-suited for studying indirect, physically mediated coordination.

Snake robots represent a fundamental class of nonholonomic locomotion systems whose motion is generated entirely through internal shape changes subject to nonholonomic contact constraints. Despite extensive prior research, existing modeling approaches often ignore modeling complexity and in some cases their ability in capturing force-level actuation and reduced-order dynamics in a unified framework.
This thesis develops a comprehensive dynamical modeling and analysis framework for snake robots by systematically comparing classical and geometric formulations, including constrained Euler–Lagrange equations, symmetry-based Lagrangian reduction, Hamiltonian methods, and Gibbs–Appell dynamics. Building on this comparison, a novel Iterated Lagrangian Reduction–Gibbs–Appell (ILR–GA) framework is introduced, combining geometric reduction with acceleration-level dynamics expressed directly in admissible coordinates. This approach enables the derivation of closed, low-dimensional models without Lagrange multipliers while preserving full dynamical fidelity.

The proposed framework is applied to the underactuated two-link snake robot, a system characterized by intrinsic drift and singular configurations. Leveraging the structure imposed by nonholonomic constraints, a novel reduction combined with dynamical modeling is developed, enabling the study of the system’s motion directly in admissible coordinates. A novel formulation is introduced for N-link snake robots, where a new reduction and modeling approach exploits the constraint geometry to collapse the full dynamics into only two second-order differential equations. The remaining system behavior is recovered through explicit reconstruction, allowing consistent incorporation of distributed actuation, elastic forces, and joint torques within a unified reduced-order framework.
Building on the single-agent formulation, the thesis investigates the interaction between snake robots and dynamically evolving environments, revealing bidirectional coupling between internal actuation and platform dynamics. A new reduction is developed for this coupled system, enabling tractable analysis of the combined robot–platform dynamics. Furthermore, a feedback linearization controller is introduced to steer the heading angle of the robot through platform actuation, producing motion patterns reminiscent of undulatory swimming induced by wavy platform excitations.

Finally, the framework is extended to multi-agent systems, including both one-dimensional and planar configurations of interacting robots on a shared moving platform. Using newly developed reduction techniques, the coupled dynamics of these systems are derived and analyzed to study how agents influence one another through the platform. This formulation provides new insights into mechanically mediated interaction, coordination, and collective behavior arising from nonholonomic constraints and shared dynamic environments.
Overall, this work establishes a unified geometric and dynamical framework for modeling, reduction, and control of snake robot systems, and provides a foundation for understanding mechanical communication and coordination in nonholonomic multi-agent systems.