Related papers: RM-Dijkstra: A surface optimal path planning algor…
This paper addresses path planning of an unmanned aerial vehicle (UAV) with remote sensing capabilities (or wireless communication capabilities). The goal of the path planning is to find a minimum-flight-time closed tour of the UAV visiting…
This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…
We give the first parallel algorithm with optimal $\tilde{O}(m)$ work for the classical problem of computing Single-Source Shortest Paths in general graphs with negative-weight edges. In graphs without negative edges, Dijkstra's algorithm…
A major challenge with off-road autonomous navigation is the lack of maps or road markings that can be used to plan a path for autonomous robots. Classical path planning methods mostly assume a perfectly known environment without accounting…
We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…
Global Route-Planning Algorithms (GRPA) are required to compute paths between several points located on Earth's surface. A geodesic algorithm is employed as an auxiliary tool, increasing the precision of distance calculations. This work…
In this paper, we propose a new global analysis framework for a class of low-rank matrix recovery problems on the Riemannian manifold. We analyze the global behavior for the Riemannian optimization with random initialization. We use the…
Safe and efficient path planning is crucial for autonomous mobile robots. A prerequisite for path planning is to have a comprehensive understanding of the 3D structure of the robot's environment. On MAVs this is commonly achieved using…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
We present a novel approach called Optimized Directed Roadmap Graph (ODRM). It is a method to build a directed roadmap graph that allows for collision avoidance in multi-robot navigation. This is a highly relevant problem, for example for…
The Wasserstein metric or earth mover's distance (EMD) is a useful tool in statistics, machine learning and computer science with many applications to biological or medical imaging, among others. Especially in the light of increasingly…
Many robotics applications benefit from being able to compute multiple locally optimal paths in a given configuration space. Examples include path planning for of tethered robots with cable-length constraints, systems involving cables,…
Motion planning is a fundamental problem in autonomous robotics that requires finding a path to a specified goal that avoids obstacles and takes into account a robot's limitations and constraints. It is often desirable for this path to also…
Path planning for a robot is one of the major problems in the area of robotics. When a robot is given a task in the form of a Linear Temporal Logic (LTL) specification such that the task needs to be carried out repetitively, we want the…
We propose a new Riemannian gradient descent method for computing spherical area-preserving mappings of topological spheres using a Riemannian retraction-based framework with theoretically guaranteed convergence. The objective function is…
Motion planning in the presence of multiple dynamic obstacles is an important research problem from the perspective of autonomous vehicles as well as space-constrained multi-robot work environment. In this paper, we address the motion…
With the development of robotics, ground robots are no longer limited to planar motion. Passive height variation due to complex terrain and active height control provided by special structures on robots require a more general navigation…
Dijkstra's algorithm for the Single-Source Shortest Path (SSSP) problem is notoriously hard to parallelize in $o(n)$ depth, $n$ being the number of vertices in the input graph, without increasing the required parallel work unreasonably.…
Distributed optimization has gained substantial interest in recent years due to its wide applications in machine learning. However, most of existing algorithms are designed for Euclidean spaces, leaving composite optimization on Riemannian…
Trajectory retiming is the task of computing a feasible time parameterization to traverse a path. It is commonly used in the decoupled approach to trajectory optimization whereby a path is first found, then a retiming algorithm computes a…