Related papers: Elongation of Curvature-Bounded Path
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…
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…
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…
This paper investigates the problem of computing a two-dimensional optimal curvature straight line (CS) shortest path for an unmanned aerial vehicle (UAV) to intercept a moving target, with both the UAV (pursuer) and target travelling at…
In this paper, we consider the tracking of arbitrary curvilinear geometric paths in three-dimensional output spaces of unmanned aerial vehicles (UAVs) without pre-specified timing requirements, commonly referred to as path-following…
Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable…
Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for the minimum-weight subset of the obstacles separating the two points.…
Motion prediction of surrounding vehicles is one of the most important tasks handled by a self-driving vehicle, and represents a critical step in the autonomous system necessary to ensure safety for all the involved traffic actors. Recently…
This paper presents a method of finding the shortest path for an unmanned aerial vehicle (UAV) flying from an initial point to a target line at a constant altitude. The length of a Dubins path is derived as a function of the final position…
We consider the problem of finding collision-free paths for curvature-constrained systems in the presence of obstacles while minimizing execution time. Specifically, we focus on the setting where a planar system can travel at some range of…
We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with…
Given two points in the plane, a set of obstacles defined by closed curves, and an integer $k$, does there exist a path between the two designated points intersecting at most $k$ of the obstacles? This is a fundamental and well-studied…
Minimum-time speed profiles are constructed for planar paths with smooth strictly-monotonic signed curvature, subject to constraints on velocity, normal acceleration and tangential acceleration. The construction is explicit and exact, and…
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…
In many mobile robotics scenarios, such as drone racing, the goal is to generate a trajectory that passes through multiple waypoints in minimal time. This problem is referred to as time-optimal planning. State-of-the-art approaches either…
A bounded curvature path is a continuously differentiable piecewise $C^2$ path with a bounded absolute curvature that connects two points in the tangent bundle of a surface. In this work, we analyze the homotopy classes of bounded curvature…
This paper presents the reachability analysis of curves in $\mathbb{R}^3$ with a prescribed curvature bound. Based on Pontryagin Maximum Principle, we leverage the existing knowledge on the structure of solutions to minimum-time problems,…
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…
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…
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…