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Locomotion is typically studied either in continuous media where bodies and legs experience forces generated by the flowing medium, or on solid substrates dominated by friction. In the former, centralized coordination is believed to…

We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…

Many forms of locomotion, both natural and artificial, are dominated by viscous friction in the sense that without power expenditure they quickly come to a standstill. From geometric mechanics, it is known that for swimming at the…

This paper presents an optimization-based motion planning methodology for snake robots operating in constrained environments. By using a reduced-order model, the proposed approach simplifies the planning process, enabling the optimizer to…

Gaits engineered for snake-like robots to rotate in-place instrumentally fill a gap in the set of locomotive gaits that have traditionally prioritized translation. This paper designs a Turn-in-Place gait and demonstrates the ability of a…

Human mobility, enabled by diverse transportation modes, is fundamental to urban functionality. Studying these movements across scales-from microscopic to macroscopic-yields valuable insights into urban dynamics. Local adaptation and…

This paper describes a novel numerical model aiming at solving moving-boundary problems such as free-surface flows or fluid-structure interaction. This model uses a moving-grid technique to solve the Navier--Stokes equations expressed in…

We examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod that is able to control its spontaneous curvature. Using a Cosserat model we derive, through variational principles, the…

Motivated by a possible convergence of terrestrial limbless locomotion strategies ultimately determined by interfacial effects, we show how both 3D gait alterations and locomotory adaptations to heterogeneous terrains can be understood…

We address the problem to infer physical material parameters and boundary conditions from the observed motion of a homogeneous deformable object via the solution of an inverse problem. Parameters are estimated from potentially unreliable…

Locomotion by shape changes (spermatozoon swimming, snake slithering, bird flapping) or gas expulsion (rocket firing) is assumed to require environmental interaction, due to conservation of momentum. As first noted in (Wisdom, 2003) and…

Systems whose movement is highly dissipative provide an opportunity to both identify models easily and quickly optimize motions. Geometric mechanics provides means for reduction of the dynamics by environmental homogeneity, while the…

As a mathematical model of high-speed flow and shock wave propagation in a complex multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes, advection-dominated solutions, and moving shock fronts with sharp…

Advances in the variational approach to the $n$-body problem have led to significant progress in celestial mechanics, uncovering new types of possible orbits. In this paper, critical points of the Lagrangian action associated with the…

A key problem in robotic locomotion is in finding optimal shape changes to effectively displace systems through the world. Variational techniques for gait optimization require estimates of body displacement per gait cycle; however, these…

Robotic motion optimization often focuses on task-specific solutions, overlooking fundamental motion principles. Building on Riemannian geometry and the calculus of variations (often appearing as indirect methods of optimal control), we…

In this paper, we present an intrinsic derivation of the equations ruling the dynamics motion of a snake robot dynamics. Based on a Cosserat beam model, we first show that the extended configuration space is a Lie group. Endowing it with an…

Coastal erosion describes the displacement of sand caused by the movement induced by tides, waves or currents. Some of its wave phenomena are modeled by Helmholtz-type equations. Our purposes, in this paper are, first, to study optimal…

This paper is about the construction of displacement interpolations on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence…

In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories. Model reduction methods exploit this for simplifying chemical kinetics via a time scale…