Related papers: Optimal Geodesic Curvature Constrained Dubins' Pat…
We give a metric characterization of the Euclidean sphere in terms of the lower bound of the sectional curvature and the length of the shortest closed geodesics.
We study the motion-planning problem for a car-like robot whose turning radius is bounded from below by one and which is allowed to move in the forward direction only (Dubins car). For two robot configurations $\sigma, \sigma'$, let…
A time-optimal problem for redundantly actuated robots moving on a specified path is a challenging problem. Although the problem is well explored and there are proposed solutions based on phase plane analysis, there are still several…
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…
We study the problem of planning paths for $p$ distinguishable pebbles (robots) residing on the vertices of an $n$-vertex connected graph with $p \le n$. A pebble may move from a vertex to an adjacent one in a time step provided that it…
In this short note, we consider the problem of prescribing the Gauss curvature and image of the Gauss map for the graph of a function over a domain in Euclidean space. The prescription of the image of the Gauss map turns this into a second…
This paper investigates the problem of computing the shortest path between two states under resource constraints in environments with resource-replenishment regions. Namely, the length of the path is limited by a budget that can be restored…
The geodesic between two points $a$ and $b$ in the interior of a simple polygon~$P$ is the shortest polygonal path inside $P$ that connects $a$ to $b$. It is thus the natural generalization of straight line segments on unconstrained point…
We propose a combination of a bounding procedure and gradient descent method for solving the Dubins traveling salesman problem, that is, the problem of finding a shortest curvature-constrained tour through a finite number of points in the…
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…
We present a decoupled algorithm for motion planning for a collection of unit-balls moving among polyhedral obstacles in $\mathbb{R}^d$, for any $d \ge 2$. We assume that the robots have revolving areas in the vicinity of their start and…
The problem of finding the shortest path for a vehicle visiting a given sequence of target points subject to the motion constraints of the vehicle is an important problem that arises in several monitoring and surveillance applications…
We give an accessible introduction and elaboration on the methods used in obtaining a geodesic, which is the curve of shortest length connecting two points lying on the surface of a function. This is found through computing what's known as…
Navigating our physical environment requires changing directions and turning. Despite its ecological importance, we do not have a unified theoretical account of non-straight-line human movement. Here, we present a unified optimality…
Multi-mobile robot systems show great advantages over one single robot in many applications. However, the robots are required to form desired task-specified formations, making feasible motions decrease significantly. Thus, it is challenging…
Using a path integral approach, we derive an analytical solution of a nonlinear and singular Langevin equation, which has been introduced previously by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion of a solid…
Navigating mobile robots through environments shared with humans is challenging. From the perspective of the robot, humans are dynamic obstacles that must be avoided. These obstacles make the collision-free space nonconvex, which leads to…
We consider $L^2$ minimizing geodesics along the group of volume preserving maps $SDiff(D)$ of a given 3-dimensional domain $D$. The corresponding curves describe the motion of an ideal incompressible fluid inside $D$ and are (formally)…
The paper is concerned with elongating the shortest curvature-bounded path between two oriented points to an expected length. The elongation of curvature-bounded paths to an expected length is fundamentally important to plan missions for…
Optimal path planning is prone to convergence to local, rather than global, optima. This is often the case for mobile manipulators due to nonconvexities induced by obstacles, robot kinematics and constraints. This paper focuses on planning…