Related papers: On the Reachability of 3-Dimensional Paths with a …
This paper presents a reachability-based approach to finite-time transition problem of nonlinear systems between two stationary points (i.e., the point-to-point steering problem). When the target state is reachable, we prove that a solution…
Markov-Dubins path is the shortest planar curve joining two points with prescribed tangents, with a specified bound on its curvature. Its structure, as proved by Dubins in 1957 nearly 70 years after Markov posed the problem of finding it,…
Let $B$ be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most one, and let $P$ be a convex polygon with $n$ vertices. Given a starting configuration (a location and a direction of travel)…
In this paper, we present strategies for designing curvature-bounded trajectories of any desired length between any two given oriented points. The proposed trajectory is constructed by the concatenation of three circular arcs of varying…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
The Dubins interval problem aims to find the shortest path of bounded curvature between two targets such that the departure angle from the first target and the arrival angle at the second target are constrained to two respective intervals.…
This paper presents an enhanced direct-method-based approach for the real-time solution of optimal control problems to handle path constraints, such as obstacles. The principal contributions of this work are twofold: first, the existing…
This paper deals with the problem of point-to-point reachability in multi-linear systems. These systems consist of a partition of the Euclidean space into a finite number of regions and a constant derivative assigned to each region in the…
The reachability problem in 3-dimensional vector addition systems with states (3-VASS) is known to be PSpace-hard, and to belong to Tower. We significantly narrow down the complexity gap by proving the problem to be solvable in…
This paper is concerned with characterizing the shortest path of a Dubins vehicle from a position with a prescribed heading angle to a target circle with the final heading tangential to the target circle. Such a shortest path is of…
A realistic generalization of the Markov--Dubins problem, which is concerned with finding the shortest planar curve of constrained curvature joining two points with prescribed tangents, is the requirement that the curve passes through a…
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…
We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that subset. In particular, we recover and extend the results of…
A bounded curvature path is a continuously differentiable piece-wise $C^2$ path with bounded absolute curvature connecting two points in the tangent bundle of a surface. These paths have been widely considered in computer science and…
The kinematic approximation of Dubin's Vehicle has been largely exploited in the formulation of various motion planning methods. In the majority of these methods, planning and control phases are decoupled, and the burden of rejecting…
In this article, a new model for 3D motion planning, applicable to aerial vehicles, is proposed to connect an initial and final configuration subject to pitch rate and yaw rate constraints. The motion planning problem for a…
Computing shortest paths for curvature-constrained Dubins vehicles on the unit sphere is fundamental to many engineering applications, including long-range flight planning, persistent surveillance patterns, and global routing problems where…
Reachability queries ask whether there exists a path from the source vertex to the target vertex on a graph. Recently, several powerful reachability queries, such as Label-Constrained Reachability (LCR) queries and Regular Path Queries…
A Dubins path is a shortest path with bounded curvature. The seminal result in non-holonomic motion planning is that (in the absence of obstacles) a Dubins path consists either from a circular arc followed by a segment followed by another…
Given a graph $G$ and two vertices $s$ and $t$ in it, {\em graph reachability} is the problem of checking whether there exists a path from $s$ to $t$ in $G$. We show that reachability in directed layered planar graphs can be decided in…