We extend a result of Dubins (Ann Probab 3:89–99, 1975) from bounded to unbounded random variables. Dubins showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectat...

In this letter, a variation of the classical Markov-Dubins problem is considered, which deals with curvature-constrained least-cost paths in plane prescribed initial and final configurations, different bounds for sinistral dextral curvatures, penalties $\mu _{L}$<...

Visiting and observing specified locations is a fundamental task for various applications including environmental monitoring military operations. The Orienteering Problem (OP) variant of routing problems in which the goal to maximize objective function by visiting most rewarding while respecting limited travel budget (e.g., distance or time). However, traditional formulations generally neglect ...

We present an approximation algorithm for the Traveling Salesman Problem when the vehicle is constrained to move forward along paths with bounded curvature (Dubins’ vehicle). A deterministic algorithm returns in time O(n3) a tour within (( 1 + max { 8πρ Dmin , 14 3 }) log n ) of the optimum tour, where n is the number of points to visit, ρ is the minimum turning radius and Dmin is the minimum E...

We present an approximation algorithm for the traveling salesman problem when the vehicle is constrained to move forward along paths with bounded curvatures (Dubins’ vehicle). A deterministic algorithm returns in time O(n3) a tour within (( 1 + max { 8πρ Dmin , 14 3 }) log n ) of the optimum tour, where n is the number of points to visit, ρ is the minimum turn radius and Dmin is the minimum Euc...

We extend a result of Dubins (1975) from bounded to unbounded random variables. Dubins (1975) showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectations (conglom...

Motivated by a fixed-speed, fixed-altitude Unmanned Aerial Vehicle (UAV), we seek to control the turning rate of a planar Dubins vehicle that tracks an unpredictable target at a nominal standoff distance. To account for all realizations of the uncertain target kinematics, we model the target motion as a planar random walk. A Bellman equation and an approximating Markov chain that is consistent ...

Microlight aircraft are increasingly becoming the most popular segment of private aviation. In the United Kingdom the majority (about 2500 of a total fleet of 3500) of these aircraft are of the weightshift class, also known as flexwings or trikes. This paper introduces the main issues involved in the design and operation of this class of aeroplane.