Related papers: An Analytic Solution to the Optimal Spherical Dubi…
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…
The main contribution of this paper is a novel method for planning globally optimal trajectories for dynamical systems subject to polygonal constraints. The proposed method is a hybrid trajectory planning approach, which combines graph…
Time-optimal path planning in high winds for a turning-rate constrained UAV is a challenging problem to solve and is important for deployment and field operations. Previous works have used trochoidal path segments comprising straight and…
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…
As UAV popularity soars, so does the mission planning associated with it. The classical approaches suffer from the triple problems of decoupled of task assignment and path planning, poor real-time performance and limited adaptability.…
We present a partial-differential-equation-based optimal path-planning framework for curvature constrained motion, with application to vehicles in 2- and 3-spatial-dimensions. This formulation relies on optimal control theory, dynamic…
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,…
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…
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 a robust tracking controller for tracking curvature-constrained paths by vehicles/robots with uncertain Dubins dynamics. Although Dubins paths have been widely used in vehicular and robotic applications, robust and…
Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced…
Dubins tours represent a solution of the Dubins Traveling Salesman Problem (DTSP) that is a variant of the optimization routing problem to determine a curvature-constrained shortest path to visit a set of locations such that the path is…
Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…
This article proposes the first known algorithm that achieves a constant-factor approximation of the minimum length tour for a Dubins' vehicle through $n$ points on the plane. By Dubins' vehicle, we mean a vehicle constrained to move at…
Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…
We investigate the problem of finding paths that enable a robot modeled as a Dubins car (i.e., a constant-speed finite-turn-rate unicycle) to escape from a circular region of space in minimum time. This minimum-time escape problem arises in…
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…
Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to…
In this paper, we present a new method to solve a certain type of Semidefinite Programming (SDP) problems. These types of SDPs naturally arise in the Quadratic Convex Reformulation (QCR) method and can be used to obtain dual bounds of…
Preliminary mission design requires an efficient and accurate approximation to the low-thrust rendezvous trajectories, which might be generally three-dimensional and involve multiple revolutions. In this paper, a new shaping method using…