相关论文: Hexapods with a small linear span
The article presents an analysis of the trends in the development of kinematic structures of modern machine-building technological equipment. The prospects of using machines with parallel kinematics in processing, measuring and handling…
We study the geometry of the moduli space of planes in a general cubic 5-fold and its deformation. We show that this moduli space is a smooth projective surface whose canonical bundle is ample. We also show that the variation of degree 1…
We study invariant surfaces generated by one-parameter subgroups of simply and pseudo isotropic rigid motions. Basically, the simply and pseudo isotropic geometries are the study of a three-dimensional space equipped with a rank 2 metric of…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
We compare two representations used to define the morphology of legs for a hexapod robot, which are subsequently 3D printed. A leg morphology occupies a set of voxels in a voxel grid. One method, a direct representation, uses a collection…
Backward compatible representation learning enables updated models to integrate seamlessly with existing ones, avoiding to reprocess stored data. Despite recent advances, existing compatibility approaches in Euclidean space neglect the…
Graphs and hypergraphs combine expressive modeling power with algorithmic efficiency for a wide range of applications. Hedgegraphs generalize hypergraphs further by grouping hyperedges under a color/hedge. This allows hedgegraphs to model…
Traditional approaches to quadruped control frequently employ simplified, hand-derived models. This significantly reduces the capability of the robot since its effective kinematic range is curtailed. In addition, kinodynamic constraints are…
We provide an account of the construction of the moduli stack of elliptic curves as an analytic orbifold. While intimately linked to Thurston's point of view on the subject (discrete groups acting properly and effectively on differentiable…
The quest for the efficient adaptation of multilegged robotic systems to changing conditions is expected to render new insights into robotic control and locomotion. In this paper, we study the performance frontiers of the enumerative…
Tracked vehicles distribute their weight continuously over a large surface area (the tracks). This distinctive feature makes them the preferred choice for vehicles required to traverse soft and uneven terrain. From a robotics perspective,…
A tetrahedral curve is a space curve whose defining ideal is an intersection of powers of monomial prime ideals of height two. It is supported on a tetrahedral configuration of lines. Schwartau described when certain such curves are ACM,…
This paper discusses the construction of local bounded commuting projections for discrete subcomplexes of the gradgrad complexes in two and three dimensions, which play an important role in the finite element theory of elasticity (2D) and…
By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via…
Learning motion planners to move robot from one point to another within an obstacle-occupied space in a collision-free manner requires either an extensive amount of data or high-quality demonstrations. This requirement is caused by the fact…
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…
We classify rational cuspidal curves of degrees 6 and 7 in the complex projective plane, up to symplectic isotopy. The proof uses topological tools, pseudoholomorphic techniques, and birational transformations.
A kinematic chain in three-dimensional Euclidean space consists of $n$ links that are connected by spherical joints. Such a chain is said to be within a closed configuration when its link lengths form a closed polygonal chain in three…
It is well known that a rigid motion of the Euclidean plane can be written as the composition of at most three reflections. It is perhaps not so widely known that a similar result holds for Euclidean space in any number of dimensions. The…
We introduce the Study variety of conformal kinematics and investigate some of its properties. The Study variety is a projective variety of dimension ten and degree twelve in real projective space of dimension 15, and it generalizes the…