Date of Award

5-10-2026

Date Published

June 2026

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mechanical and Aerospace Engineering

Advisor(s)

Zhenyu Gan

Keywords

Animal locomotion;Dynamics;Learning for Dynamics and Control;Legged Robotics;Symmetry

Subject Categories

Computer Engineering | Engineering | Robotics

Abstract

Legged locomotion in animals and robots is naturally modeled as a hybrid dynamical system: smooth body evolution is repeatedly interrupted by discrete contact events such as touchdown and liftoff. Although symmetry is a powerful organizing principle in smooth dynamical systems, a comparably systematic symmetry framework for hybrid legged locomotion remains underdeveloped. This dissertation develops such a framework for a scoped class of periodic hybrid locomotion models and uses it to relate theoretical gait analysis, animal locomotion studies, and robotic gait generation. The dissertation first extends symmetry notions from autonomous dynamics to hybrid legged systems and distinguishes symmetries of the hybrid laws from symmetries retained by periodic hybrid solutions, with particular emphasis on the spatio-temporal organization of locomotion. Within this viewpoint, gaits are treated as structured periodic hybrid solutions of shared hybrid models or nearby parameterized model families, enabling locomotor patterns to be compared, classified, and related through symmetry rather than only through descriptive labels. Using this framework, the dissertation analyzes how symmetry and symmetry breaking organize quadrupedal gait diversity. Loss of solution-level symmetry gives rise to distinct gait families, whereas symmetry changes in the model alter the set of dynamically admissible gaits. This distinction provides a principled interpretation of gait transitions and clarifies the relative roles of state-dependent gait selection and changes in morphology, loading, or other model structure. The framework is then applied to animal locomotion. In jerboa locomotion, it explains gait transitions through model-based analysis of symmetric and asymmetric parameter variations. In load-pulling sled dogs, a unified quadrupedal model reproduces transverse and rotary galloping patterns and supports limb-specific swing-stiffness modulation as a plausible transition mechanism. Finally, the dissertation transfers these ideas to robotics by incorporating temporal, morphological, and time-reversal symmetry into reinforcement learning for quadrupedal locomotion, enabling a single learned policy to generate and transition among multiple gaits. Taken together, these results show that, within the class of systems studied here, symmetry and symmetry breaking provide a common language for describing, explaining, and synthesizing legged locomotion across theory, biology, and robotics.

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