Related papers: A note on synthesizing geodesic based contact curv…
We consider the problem of finding embedded closed geodesics on the two-sphere with an incomplete metric defined outside a point. Various techniques including curve shortening methods are used.
This paper is concerned with the computation of an optimal matching between two manifold-valued curves. Curves are seen as elements of an infinite-dimensional manifold and compared using a Riemannian metric that is invariant under the…
With the maturation of differentiable physics, its role in various downstream applications: such as model predictive control, robotic design optimization, and neural PDE solvers, has become increasingly important. However, the derivative…
Designing planners and controllers for contact-rich manipulation is extremely challenging as contact violates the smoothness conditions that many gradient-based controller synthesis tools assume. Contact smoothing approximates a non-smooth…
This paper presents a novel contact-implicit trajectory optimization method using an analytically solvable contact model to enable planning of interactions with hard, soft, and slippery environments. Specifically, we propose a novel contact…
This paper presents a novel approach to the problem of almost global attitude stabilization. The reduced attitude is steered along a geodesic path on the n-sphere. Meanwhile, the full attitude is stabilized on SO(n). This action,…
We apply contact homology to obtain new results in the problem of distinguishing immersed plane curves without dangerous self-tangencies.
We apply a local systolic-diastolic inequality for contact forms and odd-symplectic forms on three-manifolds to bound the magnetic length of closed curves with prescribed geodesic curvature (also known as magnetic geodesics) on an oriented…
Any finite configuration of curves with minimal intersections on a surface is a configuration of shortest geodesics for some Riemannian metric on the surface. The metric can be chosen to make the lengths of these geodesics equal to the…
We study the geodesic motion in Godel's universe, using conserved quantities. We give a necessary and sufficient condition for curves to be geodesic curves in terms of conserved quantities, which can be computed from the initial values of…
We present Jade, a differentiable physics engine for articulated rigid bodies. Jade models contacts as the Linear Complementarity Problem (LCP). Compared to existing differentiable simulations, Jade offers features including…
In this paper, we investigate collision orbits of two identical bodies placed on the surface of a two-dimensional sphere and interacting via an attracting potential of the form $V(q)=-\cot(q)$, where $q$ is the angle formed by the position…
Scalable sensor simulation is an important yet challenging open problem for safety-critical domains such as self-driving. Current works in image simulation either fail to be photorealistic or do not model the 3D environment and the dynamic…
This paper proves an elementary topological fact about closed curves on surfaces, namely that by carefully smoothing an intersection point, one can reduce self-intersection by exactly $1$. This immediately implies a positive answer to a…
This paper addresses the problem of computing optimal impedance schedules for legged locomotion tasks involving complex contact interactions. We formulate the problem of impedance regulation as a trade-off between disturbance rejection and…
The existence of the limiting pair correlation for angles between reciprocal geodesics on the modular surface is established. An explicit formula is provided, which captures geometric information about the length of reciprocal geodesics, as…
We present a computational framework for simulating filaments interacting with rigid bodies through contact. Filaments are challenging to simulate due to their codimensionality, i.e., they are one-dimensional structures embedded in…
This paper outlines a methodology for constructing a geometrically smooth interpolatory curve in $\mathbb{R}^d$ applicable to oriented and flattenable points with $d\ge 2$. The construction involves four essential components: local…
Ruled surface is widely used in engineering design such as parting surface design of injection mold and checking surface design of checking fixture, which are usually generated by offsetting 3D curves. However, in 3D curve offset, there…
A common way to manipulate heavy objects is to maintain at least one point of the object in contact with the environment during the manipulation. When the object has a cylindrical shape or, in general, a curved edge, not only sliding and…