Related papers: Sampling-based Roadmap Planners are Probably Near-…
Sampling-based motion planners are an effective means for generating collision-free motion paths. However, the quality of these motion paths, with respect to different quality measures such as path length, clearance, smoothness or energy,…
Finding paths in graphs is a fundamental graph-theoretic task. In this work, we we are concerned with finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident…
Asymptotically-optimal motion planners such as RRT* have been shown to incrementally approximate the shortest path between start and goal states. Once an initial solution is found, their performance can be dramatically improved by…
We describe a general probabilistic framework to address a variety of Frechet-distance optimization problems. Specifically, we are interested in finding minimal bottleneck-paths in $d$-dimensional Euclidean space between given start and…
This paper presents a game-theoretic path-following formulation where the opponent is an adversary road model. This formulation allows us to compute safe sets using tools from viability theory, that can be used as terminal constraints in an…
Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so…
In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
Although recent provable methods have been developed to compute preimage bounds for neural networks, their scalability is fundamentally limited by the #P-hardness of the problem. In this work, we adopt a novel probabilistic perspective,…
Among the most prevalent motion planning techniques, sampling and trajectory optimization have emerged successful due to their ability to handle tight constraints and high-dimensional systems, respectively. However, limitations in sampling…
Compact representations of objects is a common concept in computer science. Automated planning can be viewed as a case of this concept: a planning instance is a compact implicit representation of a graph and the problem is to find a path (a…
In this paper, we consider the problem of generating inspection paths for robots. These paths should allow an attached measurement device to perform high-quality measurements. We formally show that generating robot paths, while maximizing…
In this paper, we introduce a new probabilistically safe local steering primitive for sampling-based motion planning in complex high-dimensional configuration spaces. Our local steering procedure is based on a new notion of a convex…
Path planners based on basic rapidly-exploring random trees (RRTs) are quick and efficient, and thus favourable for real-time robot path planning, but are almost-surely suboptimal. In contrast, the optimal RRT (RRT*) converges to the…
In this paper, we present a new algorithm that extends RRT* and RT-RRT* for online path planning in complex, dynamic environments. Sampling-based approaches often perform poorly in environments with narrow passages, a feature common to many…
Sampling-based motion planning is the predominant paradigm in many real-world robotic applications, but its performance is immensely dependent on the quality of the samples. The majority of traditional planners are inefficient as they use…
Randomized sampling based algorithms are widely used in robot motion planning due to the problem's intractability, and are experimentally effective on a wide range of problem instances. Most variants do not sample uniformly at random, and…
In this paper the computational challenges of time-optimal path following are addressed. The standard approach is to minimize the travel time, which inevitably leads to singularities at zero path speed, when reformulating the optimization…
In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path…
Many exciting robotic applications require multiple robots with many degrees of freedom, such as manipulators, to coordinate their motion in a shared workspace. Discovering high-quality paths in such scenarios can be achieved, in principle,…