Related papers: Efficient Probabilistic Collision Detection for No…
In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal…
This paper introduces a new technique for learning probabilistic models of mass and friction distributions of unknown objects, and performing robust sliding actions by using the learned models. The proposed method is executed in two…
Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this…
We revisit the computation of a probability of collision in the context of automotive collision avoidance (also referred to as conflict detection in other contexts). After reviewing existing approaches to the definition and computation of a…
Online generation of collision free trajectories is of prime importance for autonomous navigation. Dynamic environments, robot motion and sensing uncertainties adds further challenges to collision avoidance systems. This paper presents an…
This study presents an integrated framework for enhancing the safety and operational efficiency of robotic arms in laparoscopic surgery by addressing key challenges in collision detection and minimum distance estimation. By combining…
This paper presents an algorithm for local motion planning in environments populated by moving elliptical obstacles whose velocity, shape and size are fully known but may change with time. We base the algorithm on a collision avoidance…
Given an even number of points in a plane, we are interested in matching all the points by straight line segments so that the segments do not cross. Bottleneck matching is a matching that minimizes the length of the longest segment. For…
With the development of robotics, there are growing needs for real time motion planning. However, due to obstacles in the environment, the planning problem is highly non-convex, which makes it difficult to achieve real time computation…
We present a novel learning-based approach for computing correspondences between non-rigid 3D shapes. Unlike previous methods that either require extensive training data or operate on handcrafted input descriptors and thus generalize poorly…
This draft summarizes some basics about geometric computer vision needed to implement efficient computer vision algorithms for applications that use measurements from at least one digital camera mounted on a moving platform with a special…
We present complexity and numerical results for a new asynchronous parallel algorithmic method for the minimization of the sum of a smooth nonconvex function and a convex nonsmooth regularizer, subject to both convex and nonconvex…
Real-time safety systems are crucial components of intelligent vehicles. This paper introduces a prediction-based collision risk assessment approach on highways. Given a point mass vehicle dynamics system, a stochastic forward reachable set…
Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…
We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in…
In this study, we investigate the problem of tracking objects with unknown shapes using three-dimensional (3D) point cloud data. We propose a Gaussian process-based model to jointly estimate object kinematics, including position,…
We propose new algorithms for topic modeling when the number of topics is unknown. Our approach relies on an analysis of the concentration of mass and angular geometry of the topic simplex, a convex polytope constructed by taking the convex…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and…
Collision-free mobile robot navigation is an important problem for many robotics applications, especially in cluttered environments. In such environments, obstacles can be static or dynamic. Dynamic obstacles can additionally be…