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We study oriented connected closed polyhedral surfaces with non-degenerate triangular faces in three-dimensional Euclidean space, calling them polyhedra for short. A polyhedron is called flexible if its spatial shape can be changed…
Dexterous manipulation requires careful reasoning over extrinsic contacts. The prevalence of deforming tools in human environments, the use of deformable sensors, and the increasing number of soft robots yields a need for approaches that…
This document explores structural controllability of polynomial dynamical systems or polysystems. We extend Lin's concept of structural controllability for linear systems, offering hypergraph-theoretic methods to rapidly assess strong…
Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…
High-fidelity simulation has become essential to the design and control of soft robots, where large geometric deformations and complex contact interactions challenge conventional modeling tools. Recent advances in the field demand…
Track systems effectively distribute loads, augmenting traction and maneuverability on unstable terrains, leveraging their expansive contact areas. This tracked locomotion capability also aids in hand manipulation of not only regular…
We introduce here a direct method to construct multivariate explicit B-spline bases. B-splines are piecewise polynomials, which are defined on adjacent tetrahedra and which are $C^{r}$ continuous throughout. The $C^{r}$ continuity is…
Soft robotics focuses on designing robots with highly deformable materials, allowing them to adapt and operate safely and reliably in unstructured and variable environments. While soft robots offer increased compliance over rigid body…
For the shape control of deformable free-form surfaces, simulation plays a crucial role in establishing the mapping between the actuation parameters and the deformed shapes. The differentiation of this forward kinematic mapping is usually…
Compared with traditional rigid-body robots, soft robots not only exhibit unprecedented adaptation and flexibility but also present novel challenges in their modeling and control because of their infinite degrees of freedom. Most of the…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
In applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical object can be manipulated through control points that…
Continuum and soft robots can transform diverse sectors, including healthcare, agriculture, marine, and space, thanks to their potential to adaptively interact with unstructured environments. These robots exhibit complex mechanics that pose…
This paper presents the design, modeling, and fabrication of 3D-printed, tendon-actuated continuum robots featuring a flexible, tapered backbone constructed from thermoplastic polyurethane (TPU). Our scalable design incorporates an…
This paper focuses on vertices of the master corner polyhedra $P(G,g_0),$ the core of the group-theoretical approach to integer linear programming. We introduce two combinatorial operations that transform each vertex of $P(G,g_0)$ to…
Polyhedral meshes (PM) - meshes having planar faces - have enjoyed a rise in popularity in recent years due to their importance in architectural and industrial design. However, they are also notoriously difficult to generate and manipulate.…
Soft pneumatic legged robots show promise in their ability to traverse a range of different types of terrain, including natural unstructured terrain met in applications like precision agriculture. They can adapt their body morphology to the…
By taking quotients of a certain tiling of hyperbolic plane / space by certain group actions, we obtain geometric polyhedra / cellulations with interesting symmetries and incidence structure.
We construct a phase space for a three dimensional cellular complex with decorations on edges and faces using crossed modules (strict 2-groups) equipped with a (non-trivial) Poisson structure. We do not use the most general crossed module,…
We introduce an elastic-driven self-folding approach that fabricates robots directly from flat 3D-printed conductive PLA nets. Elastic bands routed through printed hooks store energy that folds the sheet into programmed 3D geometries, while…