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We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…

Singular theories, characterised by the presence of degeneracies in their Lagrangian or Hamiltonian descriptions, require the systematic implementation of constraints in order to obtain well-defined dynamics. While the symplectic framework…

This paper presents a gait optimization and motion planning framework for a class of locomoting systems with mixed kinematic and dynamic properties. Using Lagrangian reduction and differential geometry, we derive a general dynamic model…

Gait is increasingly recognized as a vital sign, yet current approaches treat it as a symptom of specific pathologies rather than a systemic biomarker. We developed a gait foundation model for 3D skeletal motion from 3,414 deeply phenotyped…

The evolution of communities in dynamic (time-varying) network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for…

We consider a bosonic two-legged ladder whose two-band energy spectrum can be tuned in the presence of a uniform gauge field, to four distinct scenarios: degenerate or non-degenerate ground states with gapped or gapless energy bands. We…

Efficiently handling time-triggered and possibly nondeterministic switches for hybrid systems reachability is a challenging task. In this paper we present an approach based on conservative set-based enclosure of the dynamics that can handle…

Stable gait generation is a crucial problem for legged robot locomotion as this impacts other critical performance factors such as, e.g. mobility over an uneven terrain and power consumption. Gait generation stability results from the…

Stable bipedal walking is a key prerequisite for humanoid robots to reach their potential of being versatile helpers in our everyday environments. Bipedal walking is, however, a complex motion that requires the coordination of many degrees…

A constraint correlation dynamics up to 4-point Green functions is proposed for SU(N) gauge theories which reduces the N-body quantum field problem to the two-body level. The resulting set of nonlinear coupled equations fulfills all…

Human motion is a continuous physical process in 3D space, governed by complex dynamic and kinematic constraints. Existing methods typically represent the human pose as an abstract graph structure, neglecting the intrinsic physical…

Both legged locomotion and slithering motions typically utilize periodic gaits -- repeating cycles of body shape change that produce a net motion through the world. Legged locomotion can be viewed from the perspective of piece-wise contact…

Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter, and quantum information science. Their local symmetries enforce the charge conservation observed in the laws of physics. Impressive…

We propose in this paper a motion planning method for legged robot locomotion based on Geometric Heat Flow framework. The motion planning task is challenging due to the hybrid nature of dynamics and contact constraints. We encode the hybrid…

Safe path and gait planning are essential for bipedal robots to navigate complex real-world environments. The prevailing approaches often plan the path and gait separately in a hierarchical fashion, potentially resulting in unsafe movements…

We apply the computational methodology of phase retrieval to the problem of folding heteropolymers. The ground state fold of the polymer is defined by the intersection of two sets in the configuration space of its constituent monomers: a…

For full-size humanoid robots, even with recent advances in reinforcement learning-based control, achieving reliable locomotion on complex terrains, such as long staircases, remains challenging. In such settings, limited perception,…

Functional autonomous systems often realize complex tasks by utilizing state machines comprised of discrete primitive behaviors and transitions between these behaviors. This architecture has been widely studied in the context of…

We present a unified gait-conditioned reinforcement learning framework that enables humanoid robots to perform standing, walking, running, and smooth transitions within a single recurrent policy. A compact reward routing mechanism…

Dynamical systems (DSs) provide a framework for high flexibility, robustness, and control reliability and are widely used in motion planning and physical human-robot interaction. The properties of the DS directly determine the robot's…