A new motion planning algorithm for the so-called Dubins Travelling Salesperson Problem is derived, and compared via simulations with a number of existing algorithms from the literature. In its general form, the new algorithm is dubbed “k-step look-ahead algorithm” and stems naturally from the formulation of the Dubins Travelling Salesperson Problem as a minimum-time control problem. When the m...

This paper investigates the task assignment and path planning problem for multiple AUVs in three dimensional (3D) underwater wireless sensor networks where nonholonomic motion constraints of underwater AUVs in 3D space are considered. The multi-target task assignment and path planning problem is modeled by the Multiple Traveling Sales Person (MTSP) problem and the Genetic Algorithm (GA) is used...

We consider a planar continuous robotic manipulator and determine the reachable set of its end-e ector with and without prescribed terminal direction. To do so we use optimal control and geometric techniques similar to those used in solving Dubins` problem. We also solve the synthesis problem of Dubins` problem with free terminal direction.

In this paper, a simplified aircraft system model is developed correctly emulating the nonlinear dynamics of complex aircraft models under closed-loop control. The simplified model is based on Dubins models used in optimization algorithms for trajectory control of multiple Unmanned Aeriel Vehicles (UAVs). Algorithms optimizing area coverage for reconnaissance based on UAV capabilities, fuel rem...

Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti (1974) and Dubins (1975), subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­‐ additive has conditional probabilities that fail to be conglomerable i...

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 constant speed along paths with bounded curvature without reversing direction. For this version of the classic Traveling Salesperson Problem, our algorithm closes...

A shortest path joining two specified endpoint configurations that is constrained to have mean curvature at most ς on every non-zero length sub-path is called a ς-geodesic. A seminal result in non-holonomic motion planning is that (in the absence of obstacles) a 1-geodesic consists of either (i) a (unit-radius) circular arc followed by a straight segment followed by another circular arc, or (ii...

Safe and simultaneous arrival of constant speed, constant altitude unmanned air vehicles (UAVs) on target is solved by design of paths of equal lengths. The starting point for our solution is the well-known Dubins path, which is composed of circular arc and line segments, thus requiring only one simple maneuver—constant rate turn. An explicit bound can be imposed on the rate during the design a...