Related papers: Geometric Contact Potential
This work presents a comprehensive three-dimensional third-medium contact framework for modeling complex contact interactions in hyperelastic solids and pneumatically actuated systems. The proposed third-medium formulation embeds a…
Physical strands or sheets that can be modelled as curves or surfaces embedded in three dimensions are ubiquitous in nature, and are of fundamental importance in mathematics, physics, biology and engineering. Often the physical…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
From serving a cup of coffee to positioning mechanical parts during assembly, stable object placement is a crucial skill for future robots. It becomes particularly challenging under geometric uncertainties, e.g., when the object pose or…
We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature. Specifically, we find isotropic,convex-repulsive…
Contact can be conceptualized as a set of constraints imposed on two bodies that are interacting with one another in some way. The nature of a contact, whether a point, line, or surface, dictates how these bodies are able to move with…
Robots will increasingly operate near humans that introduce uncertainties in the motion planning problem due to their complex nature. Typically, chance constraints are introduced in the planner to optimize performance while guaranteeing…
A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…
The ability to reason about and predict the outcome of contacts is paramount to the successful execution of many robot tasks. Analytical rigid-body contact models are used extensively in planning and control due to their computational…
We propose that the behavior of asymmetric binary fluid mixtures with a large class of attractive or repulsive interparticle interactions can be understood by mapping onto effective non-additive hard-sphere models. The latter are best…
The present contribution proposes a universal framework to formulate generalized section-section interaction potentials (SSIP) within the geometrically exact beam theory. By exploiting the fundamental kinematic assumption of undeformable…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
This article reviews recent inverse statistical-mechanical methodologies that we have devised to optimize interaction potentials in soft matter systems that correspond to stable "target" structures. We are interested in finding the…
Safety is one of the fundamental challenges in control theory. Recently, multi-step optimal control problems for discrete-time dynamical systems were formulated to enforce stability, while subject to input constraints as well as…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…
We develop two new continuum contact models for coupled adhesion and friction, and discuss them in the context of existing models proposed in the literature. Our new models are able to describe sliding friction even under tensile normal…
We present a framework for the simulation of rigid and deformable bodies in the presence of contact and friction. Our method is based on a non-smooth Newton iteration that solves the underlying nonlinear complementarity problems (NCPs)…
Interior-point methods (IPMs) are a cornerstone of Euclidean convex optimization, due to their strong theoretical guarantees and practical performance. Motivated by scaling problems, recent work by Hirai and the last two authors (FOCS'23)…
This paper proposes a novel discretization workflow for contact problems in which the discretization of the contact interface is decoupled from that of the bulk domain. This separation enables independently tailored meshes for the contact…
This paper proposes a new set of conditions for exactly representing collision avoidance constraints within optimization-based motion planning algorithms. The conditions are continuously differentiable and therefore suitable for use with…