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Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in…
Cross-lingual or cross-domain correspondences play key roles in tasks ranging from machine translation to transfer learning. Recently, purely unsupervised methods operating on monolingual embeddings have become effective alignment tools.…
A geometrical pattern is a set of points with all pairwise distances (or, more generally, relative distances) specified. Finding matches to such patterns has applications to spatial data in seismic, astronomical, and transportation…
Path planning for 3D solid objects is a challenging problem, requiring a search in a six-dimensional configuration space, which is, nevertheless, essential in many robotic applications such as bin-picking and assembly. The commonly used…
We address the problem of planning robot motions in constrained configuration spaces where the constraints change throughout the motion. The problem is formulated as a fixed sequence of intersecting manifolds, which the robot needs to…
We address the problem of motion planning for a robotic manipulator with the task to place a grasped object in a cluttered environment. In this task, we need to locate a collision-free pose for the object that a) facilitates the stable…
We present a unified approach for constraint displacement problems in which a robot finds a feasible path by displacing constraints or obstacles. To this end, we propose a two stage process that returns locally optimal obstacle…
The formulas for the 3-dimensional distance and the velocity modulus in the 4-dimensional linear space with the Berwald-Moor metrics are obtained. The used algorithm is applicable both for the Minkowski space and for the arbitrary…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
Conformant planning is the problem of finding a sequence of actions for achieving a goal in the presence of uncertainty in the initial state or action effects. The problem has been approached as a path-finding problem in belief space where…
The Gauss-Minkowski correspondence in $\mathbb{R}^2$ states the existence of a homeomorphism between the probability measures $\mu$ on $[0,2\pi]$ such that $\int_0^{2\pi} e^{ix}d\mu(x)=0$ and the compact convex sets (CCS) of the plane with…
Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…
In this paper we prove new lower bounds for the minimum distance of a toric surface code defined by a convex lattice polygon P. The bounds involve a geometric invariant L(P), called the full Minkowski length of P which can be easily…
This paper develops an algorithm that guides a multi-robot system in an unknown environment in search of fixed targets. The area to be scanned contains an unknown number of convex obstacles of unknown size and shape. The algorithm covers…
Object rearrangement has recently emerged as a key competency in robot manipulation, with practical solutions generally involving object detection, recognition, grasping and high-level planning. Goal-images describing a desired scene…
Location modeling, or determining where non-existing objects could feasibly appear in a scene, has the potential to benefit numerous computer vision tasks, from automatic object insertion to scene creation in virtual reality. Yet, this…
The task of "relative placement" is to predict the placement of one object in relation to another, e.g. placing a mug onto a mug rack. Through explicit object-centric geometric reasoning, recent methods for relative placement have made…
Robotic grasping is facing a variety of real-world uncertainties caused by non-static object states, unknown object properties, and cluttered object arrangements. The difficulty of grasping increases with the presence of more uncertainties,…
In task and motion planning (TAMP), the ambiguity and underdetermination of abstract descriptions used by task planning methods make it difficult to characterize physical constraints needed to successfully execute a task. The usual approach…
There is a complex conformal transformation, which maps the $D$ - dimensional real Minkowski space on a bounded set in the $D$ - dimensional complex vector space. It generalizes the Cayley map from $D=1$ dimensions to higher space-time…