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We develop a family of cut finite element methods of different orders based on the discontinuous Galerkin framework, for hyperbolic conservation laws with stationary interfaces in both one and two space dimensions, and for moving interfaces…

The low-temperature driven or thermally activated motion of several condensed matter systems is often modeled by the dynamics of interfaces (co-dimension-1 elastic manifolds) subject to a random potential. Two characteristic quantitative…

Learning human-like, robust bipedal walking remains difficult due to hybrid dynamics and terrain variability. We propose a lightweight framework that combines a gait generator network learned from human motion with Proximal Policy…

Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…

Invariant manifolds play an important role in organizing global dynamical behaviors. For example, it is found that in multi-well conservative systems where the potential energy wells are connected by index-1 saddles, the motion between…

In the first part of this thesis, we present our efforts on experimental validation of the predictive performance of mechanics-based mathematical models on a physical one-legged hopping robot platform. We extend upon a recently proposed…

Legged robot locomotion is hindered by a mismatch between applications where legs can outperform wheels or treads, most of which feature deformable substrates, and existing tools for planning and control, most of which assume flat, rigid…

Learning-based approaches have recently shown notable success in legged locomotion. However, these approaches often lack accountability, necessitating empirical tests to determine their effectiveness. In this work, we are interested in…

Computing stabilizing and optimal control actions for legged locomotion in real time is difficult due to the nonlinear, hybrid, and high dimensional nature of these robots. The hybrid nature of the system introduces a combination of…

While Reinforcement Learning (RL) has achieved remarkable progress in legged locomotion control, it often suffers from performance degradation in out-of-distribution (OOD) conditions and discrepancies between the simulation and the real…

This work introduces a geometric framework and a novel network architecture for creating correspondences between samples of different conditions. Under this formalism, the latent space is a fiber bundle stratified into a base space encoding…

Robotic adaptation to unanticipated operating conditions is crucial to achieving persistence and robustness in complex real world settings. For a wide range of cutting-edge robotic systems, such as micro- and nano-scale robots, soft robots,…

Quadrupeds transition spontaneously to various gait patterns (e.g., walk, trot, pace, gallop) in response to the locomotion speed. The generation of these gait patterns has been the subject of debate for a long time. We propose a coupled…

We discuss the relation between particle number conservation and topological phases. In four spatial dimensions, we find that systems belonging to different topological phases in the presence of a U(1) charge conservation can be connected…

Most passivity based trajectory tracking algorithms for mechanical systems can only stabilise reference trajectories that have constant energy. This paper overcomes this limitation by deriving a single variable Hamiltonian model for the…

A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear…

While modular robots offer versatility, excessive joint torque during locomotion poses a significant risk of mechanical failure, especially for detachable joints. To address this, we propose an optimization framework using the NSGA-III…

Legged robots have the potential to traverse complex terrain and access confined spaces beyond the reach of traditional platforms thanks to their ability to carefully select footholds and flexibly adapt their body posture while walking.…

This work tries to contribute to the design of legged robots with capabilities boosted through thruster-assisted locomotion. Our long-term goal is the development of robots capable of negotiating unstructured environments, including land…

As a unique biometric that can be perceived at a distance, gait has broad applications in person authentication, social security, and so on. Existing gait recognition methods suffer from changes in viewpoint and clothing and barely consider…