Related papers: A Decomposition-Based Approach to Reasoning about …
CAT(0) metric spaces constitute a far-reaching common generalization of Euclidean and hyperbolic spaces and simple polygons: any two points x and y of a CAT(0) metric space are connected by a unique shortest path {\gamma}(x,y). In this…
We consider the problem of connected coordinated motion planning for a large collective of simple, identical robots: From a given start grid configuration of robots, we need to reach a desired target configuration via a sequence of…
For motion planning in high dimensional configuration spaces, a significant computational bottleneck is collision detection. Our aim is to reduce the expected number of collision checks by creating a belief model of the configuration space…
Contact involving soft materials often combines dry adhesion, sliding friction, and large deformations. At the local level, these three aspects are rarely captured simultaneously, but included in the theoretical models by Mergel et al.…
Despite the attention that the problem of path planning for tethered robots has garnered in the past few decades, the approaches proposed to solve it typically rely on a discrete representation of the configuration space and do not exploit…
We consider the feedback design for stabilizing a rigid body system by making and breaking multiple contacts with the environment without prespecifying the timing or the number of occurrence of the contacts. We model such a system as a…
We study a natural geometric variant of the classic Knapsack problem called 2D-Knapsack: we are given a set of axis-parallel rectangles and a rectangular bounding box, and the goal is to pack as many of these rectangles inside the box…
With the explosive growth of web-based cameras and mobile devices, billions of photographs are uploaded to the internet. We can trivially collect a huge number of photo streams for various goals, such as 3D scene reconstruction and other…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…
A practical autonomous driving system urges the need to reliably and accurately detect vehicles and persons. In this report, we introduce a state-of-the-art 2D object detection system for autonomous driving scenarios. Specifically, we…
In this paper, we address the problem of road segmentation and free space detection in the context of autonomous driving. Traditional methods either use 3-dimensional (3D) cues such as point clouds obtained from LIDAR, RADAR or stereo…
A critical task for developing safe autonomous driving stacks is to determine whether an obstacle is safety-critical, i.e., poses an imminent threat to the autonomous vehicle. Our previous work showed that Hamilton Jacobi reachability…
Object functionality is often expressed through part articulation -- as when the two rigid parts of a scissor pivot against each other to perform the cutting function. Such articulations are often similar across objects within the same…
In this contribution I summarize the achievements of separation of variables in integrable quantum systems from the point of view of path integrals. This includes the free motion on homogeneous spaces, and motion subject to a potential…
Avoiding collisions between obstacles and vehicles such as cars, robots or aircraft is essential to the development of automation and autonomy. To simplify the problem, many collision avoidance algorithms and proofs consider vehicles to be…
We present an anytime algorithm that generates a collision-free configuration-space path that closely follows a desired path in task space, according to the discrete Frechet distance. By leveraging tools from computational geometry, we…
This paper provides an introduction to decomposition spaces and 2-Segal spaces, unifying the two perspectives. We begin by defining decomposition spaces using the active-inert factorization system on the simplicial category, and show their…
The paper surveys topological problems relevant to the motion planning problem of robotics and includes some new results and constructions. First we analyse the notion of topological complexity of configuration spaces which is responsible…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
The motion of a mechanical system can be defined as a path through its configuration space. Computing such a path has a computational complexity scaling exponentially with the dimensionality of the configuration space. We propose to reduce…