Related papers: A note on synthesizing geodesic based contact curv…
Although the kinematics and dynamics of spherical robots (SRs) on flat horizontal and inclined 2D surfaces are thoroughly investigated, their rolling behavior on generic 3D terrains has remained unexplored. This paper derives the kinematics…
This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of…
We give bounds on the number of non-simple closed curves on a negatively curved surface, given upper bounds on both length and self-intersection number. In particular, it was previously known that the number of all closed curves of length…
This paper investigates the problem of efficient computation of physically consistent multi-contact behaviors. Recent work showed that under mild assumptions, the problem could be decomposed into simpler kinematic and centroidal dynamic…
Let $\Sigma$ be a compact, orientable surface of negative Euler characteristic, and let $h$ be a complete hyperbolic metric on $\Sigma$. A geodesic curve $\gamma$ in $\Sigma$ is filling, if it cuts the surface into topological disks and…
Parameterizing finger rolling and finger-object contacts in a differentiable manner is important for formulating dexterous manipulation as a trajectory optimization problem. In contrast to previous methods which often assume simplified…
We consider a system of self-avoiding polygons interacting through a potential that penalizes or rewards the number of mutual touchings and we provide an exact computation of the critical curve separating a regime of long polygons from a…
This paper tackles the problem of physics-aware human motion synthesis in a dynamic scene. Unlike existing works which mainly tend to generate physically unrealistic motions due to limited contact modeling, typically restricted to hands, in…
We introduce an operation that measures the self intersections of paths on a surface. As applications, we give a criterion of the realizability of a generalized Dehn twist, and derive a geometric constraint on the image of the Johnson…
The surface of a liquid near a moving contact line is highly curved owing to diverging viscous forces. Thus, microscopic physics must be invoked at the contact line and matched to the hydrodynamic solution farther away. This matching has…
Connecting curves have been shown to organize the rotational structure of strange attractors in three-dimensional dynamical systems. We extend the description of connecting curves and their properties to higher dimensions within the special…
In this paper, we develop a principled method to model line and surface contact with point contact (we call this point, equivalent contact point) that is consistent with physics-based models of surface (line) contact. Assuming that the set…
Physics simulation is ubiquitous in robotics. Whether in model-based approaches (e.g., trajectory optimization), or model-free algorithms (e.g., reinforcement learning), physics simulators are a central component of modern control pipelines…
In a wide range of practical problems, such as forming operations and impact tests, assuming that one of the contacting bodies is rigid is an excellent approximation to the physical phenomenon. In this work, the well-established dual mortar…
In this work we study the general system of geodesic equations for the case of a massive particle moving on an arbitrary curved manifold. The investigation is carried out from the symmetry perspective. By exploiting the parametrization…
Gradient-based methods can efficiently optimize controllers by leveraging differentiable simulation and physical priors. However, contact-rich manipulation remains challenging because hybrid contact dynamics often produce discontinuous or…
We investigate the vertex curve, that is the set of points in the hyperbolic region of a smooth surface in real 3-space at which there is a circle in the tangent plane having at least 5-point contact with the surface. The vertex curve is…
Soft robots can safely interact with environments because of their mechanical compliance. Self-collision is also employed in the modern design of soft robots to enhance their performance during different tasks. However, developing an…
A general definition of the curves and geodesics associated with a given connection on a quantized manifold is given. In the particular case of the functional quantization we define geodesics in the same way as in the classical case and we…
A numerical method is described for studying how elastic waves interact with imperfect contacts such as fractures or glue layers existing between elastic solids. These contacts have been classicaly modeled by interfaces, using a simple…