相关论文: Separation-Sensitive Collision Detection for Conve…

Optically-levitated dielectric objects are promising for precision force, acceleration, torque, and rotation sensing due to their extreme environmental decoupling. While many levitated opto-mechanics experiments employ spherical objects,…

In this paper we compare the different phenomena that occur when intersecting geometric objects with random geodesics on the unit sphere and inside convex bodies. On the high dimensional sphere we see that with probability bounded away from…

During about 30 years, a lot of research teams have worked on the big challenge of detection of moving objects in various challenging environments. First applications concern static cameras but with the rise of the mobile sensors studies on…

This paper discusses improvements to the numerical robustness of the algorithm described in Kasper Fauerby's "Improved Collision Detection and Response." The algorithm addresses a common collision detection query: a moving sphere or…

Parallel robots (PRs) allow for higher speeds in human-robot collaboration due to their lower moving masses but are more prone to unintended contact. For a safe reaction, knowledge of the location and force of a collision is useful. A novel…

We first prove a new separating hyperplane theorem characterizing when a pair of compact convex subsets $K, K'$ of the Euclidean space intersect, and when they are disjoint. The theorem is distinct from classical separation theorems. It…

Object detection and classification of traffic signs in street-view imagery is an essential element for asset management, map making and autonomous driving. However, some traffic signs occur rarely and consequently, they are difficult to…

The motion of robots and objects in our world is often highly dependent upon contact. When contact is expected but does not occur or when contact is not expected but does occur, robot behavior diverges from plan, often disastrously. This…

In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection…

Deep learning-based visual perception models lack robustness when faced with camera motion perturbations in practice. The current certification process for assessing robustness is costly and time-consuming due to the extensive number of…

This paper studies the problem of object discovery -- separating objects from the background without manual labels. Existing approaches utilize appearance cues, such as color, texture, and location, to group pixels into object-like regions.…

We revisit the notion of WSPD (i.e., well-separated pairs-decomposition), presenting a new construction of WSPD for any finite metric space, and show that it is asymptotically instance-optimal in size. Next, we describe a new WSPD…

Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…

For a set $\mathcal{D}$ of disks in the plane, its disk graph $G(\mathcal{D})$ is the graph with vertex set $\mathcal{D}$, where two vertices are adjacent if and only if the corresponding disks intersect. Given a set $\mathcal{D}$ of $n$…

Real-time robot motion planning in complex high-dimensional environments remains an open problem. Motion planning algorithms, and their underlying collision checkers, are crucial to any robot control stack. Collision checking takes up a…

We explore the separability of point sets in the plane by a restricted-orientation convex hull, which is an orientation-dependent, possibly disconnected, and non-convex enclosing shape that generalizes the convex hull. Let $R$ and $B$ be…

Spontaneous self-assembly of hard convex polyhedra are known to form orientationally disordered crystalline phases, where particle orientations do not follow the same pattern as the positional arrangement of the crystal. A distinct type of…

The separation of two sets (or more specific of two cones) plays an important role in different fields of mathematics such as variational analysis, convex analysis, convex geometry, optimization. In the paper, we derive some new results for…

Obstacle Detection is a central problem for any robotic system, and critical for autonomous systems that travel at high speeds in unpredictable environment. This is often achieved through scene depth estimation, by various means. When fast…

Robotic manipulation can greatly benefit from the data efficiency, robustness, and predictability of model-based methods if robots can quickly generate models of novel objects they encounter. This is especially difficult when effects like…