Related papers: Sampling-based Roadmap Planners are Probably Near-…
We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…
Applying robust optimization often requires selecting an appropriate uncertainty set both in shape and size, a choice that directly affects the trade-off between average-case and worst-case performances. In practice, this calibration is…
For a variety of regularized optimization problems in machine learning, algorithms computing the entire solution path have been developed recently. Most of these methods are quadratic programs that are parameterized by a single parameter,…
We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…
This article presents a novel approach, named MCMP (Monte Carlo Motion Planning), to the problem of motion planning under uncertainty, i.e., to the problem of computing a low-cost path that fulfills probabilistic collision avoidance…
We devise a method to exactly compute the length of the longest simple path in factored state spaces, like state spaces encountered in classical planning. Although the complexity of this problem is NEXP-Hard, we show that our method can be…
This paper studies motion planning of a mobile robot under uncertainty. The control objective is to synthesize a {finite-memory} control policy, such that a high-level task specified as a Linear Temporal Logic (LTL) formula is satisfied…
A new path planning method for Mobile Robots (MR) has been developed and implemented. On the one hand, based on the shortest path from the start point to the goal point, this path planner can choose the best moving directions of the MR,…
By utilizing only depth information, the paper introduces a novel but efficient local planning approach that enhances not only computational efficiency but also planning performances for memoryless local planners. The sampling is first…
Time Optimal Path Parametrization is the problem of minimizing the time interval during which an actuation constrained agent can traverse a given path. Recently, an efficient linear-time algorithm for solving this problem was proposed.…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
This work considers a Motion Planning Problem with Dynamic Obstacles (MPDO) in 2D that requires finding a minimum-arrival-time collision-free trajectory for a point robot between its start and goal locations amid dynamic obstacles moving…
Autonomous technology, which has become widespread today, appears in many different configurations such as mobile robots, manipulators, and drones. One of the most important tasks of these vehicles during autonomous operations is path…
Probabilistic analysis for metric optimization problems has mostly been conducted on random Euclidean instances, but little is known about metric instances drawn from distributions other than the Euclidean. This motivates our study of…
We study the path planning problem for continuum-arm robots, in which we are given a starting and an end point, and we need to compute a path for the tip of the continuum arm between the two points. We consider both cases where obstacles…
With the pervasiveness of Stochastic Shortest-Path (SSP) problems in high-risk industries, such as last-mile autonomous delivery and supply chain management, robust planning algorithms are crucial for ensuring successful task completion…
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a…
Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently…
Path planners that can interpret free-form natural language instructions hold promise to automate a wide range of robotics applications. These planners simplify user interactions and enable intuitive control over complex semi-autonomous…