Related papers: An Analytic Solution to the Optimal Spherical Dubi…
This paper introduces an exact algorithm for the construction of a shortest curvature-constrained network interconnecting a given set of directed points in the plane and an iterative method for doing so in 3D space. Such a network will be…
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,…
A fundamental problem in computational geometry is to compute an obstacle-avoiding Euclidean shortest path between two points in the plane. The case of this problem on polygonal obstacles is well studied. In this paper, we consider the…
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…
This article studies the time-optimal path planning problem for a convexified Reeds-Shepp (CRS) vehicle on a unit sphere, capable of both forward and backward motion, with speed bounded in magnitude by 1 and turning rate bounded in…
The Shortest-Path Problem in Graph of Convex Sets (SPP in GCS) is a recently developed optimization framework that blends discrete and continuous decision making. Many relevant problems in robotics, such as collision-free motion planning,…
In recent years, high-order finite element methods on high-order meshes have attracted considerable attention. This work investigates the isoparametric upwind discontinuous Galerkin method for the radiation transport equation on a bounded…
The control of a Dubins Vehicle when subjected to a loss of control effectiveness in the turning rate is considered. A complex state-space representation is used to model the vehicle dynamics. An adaptive control design is proposed, with…
Path planning is a major problem in autonomous vehicles. In recent years, with the increase in applications of Unmanned Aerial Vehicles (UAVs), one of the main challenges is path planning, particularly in adversarial environments. In this…
The problem of maneuvering a vehicle through a race course in minimum time requires computation of both longitudinal (brake and throttle) and lateral (steering wheel) control inputs. Unfortunately, solving the resulting nonlinear optimal…
This work presents a trajectory planning method based on composite Bernstein polynomials for autonomous systems navigating complex environments. The method is implemented in a symbolic optimization framework that enables continuous paths…
The trajectory optimization of the atmospheric entry of a reusable launch vehicle is studied. The objective is to maximize the crossrange of the vehicle subject to two control-inequality path constraints, two state-inequality path…
This paper investigates the problem of planning a minimum-length tour for a three-dimensional Dubins airplane model to visually inspect a series of targets located on the ground or exterior surface of objects in an urban environment.…
Vehicle trajectory optimization is essential to ensure vehicles travel efficiently and safely. This paper presents an infrastructure assisted constrained connected automated vehicles (CAVs) trajectory optimization method on curved roads.…
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…
This paper investigates an efficient algorithm for trajectory planning problem of autonomous unmanned aerial vehicles which fly over three-dimensional terrains. The proposed algorithm combines convex optimization with disjunctive…
This paper presents the problem of lateral interception by a Dubins car of a target that moves along an a priori known trajectory. This trajectory is given by two coordinates of a planar location and one angle of a heading orientation,…
We present a novel algorithm that fuses the existing convex-programming based approach with heuristic information to find optimality guarantees and near-optimal paths for the Shortest Path Problem in the Graph of Convex Sets (SPP-GCS). Our…
We give new rounding schemes for SDP relaxations for the problems of maximizing cubic polynomials over the unit sphere and the $n$-dimensional hypercube. In both cases, the resulting algorithms yield a $O(\sqrt{n/k})$ multiplicative…
The paper develops a novel motion model, called Generalized Multi-Speed Dubins Motion Model (GMDM), which extends the Dubins model by considering multiple speeds. While the Dubins model produces time-optimal paths under a constant speed…