Showing papers by "Efstathios Bakolas published in 2010"

Optimal pursuit of moving targets using dynamic Voronoi diagrams

Abstract: We consider Voronoi-like partitions for a team of moving targets distributed in the plane, such that each set in this partition is uniquely associated with a particular moving target in the following sense: a pursuer residing inside a given set of the partition can intercept this moving target faster than any other pursuer outside this set. It is assumed that each moving target employs its own “evading” strategy in response to the pursuer actions. In contrast to standard formulations of problems of this kind in the literature, the evading strategy does necessarily restrict the evader to be slower than its pursuer. In the special case when all moving targets employ a uniform evading strategy, the previous problem reduces to the characterization of the Zermelo-Voronoi diagram.

Time-optimal synthesis for the Zermelo-Markov-Dubins problem: The constant wind case

Abstract: We consider a combination of the classical Markov-Dubins problem and Zermelo's navigation problem. In particular, we consider the problem of characterizing minimum-time paths with prescribed positions and tangents for a vehicle with Dubins-type kinematics in the presence of uniform winds/currents. By utilizing optimal control theory, we characterize the structure of the optimal paths, and subsequently solve the time-optimal synthesis problem.

Minimum-Time Paths for a Small Aircraft in the Presence of Regionally-Varying Strong Winds

Abstract: We consider the minimum-time path-planning problem for a small aircraft flying horizontally in the presence of obstacles and regionally-varying strong winds. The aircraft speed is not necessarily larger than the wind speed, a fact that has major implications in terms of the existence of feasible paths. First, it is possible that there exist configurations in close proximity to an obstacle from which a collision may be inevitable. Second, it is likely that points inside the obstacle-free space may not be connectable by means of an admissible bidirectional path. The assumption of a regionally-varying wind field has also implications on the optimality properties of the minimum-time paths between reachable configurations. In particular, the minimum-time-to-go and minimum-time-to-come between two points are not necessarily equal. To solve this problem, we consider a convex subdivision of the plane into polygonal regions that are either free of obstacles or they are occupied with obstacles, and such that the vehicle motion within each obstacle-free region is governed by a separate set of equations. The equations of motion inside each obstacle-free region are significantly simpler when compared with the original system dynamics. This approximation simplifies both the reachability/accesibility analysis, as well as the characterization of the locally minimum-time paths. Furthermore, it is shown that the minimum-time paths consist of concatenations of locally optimal paths with the concatenations occurring along the common boundary of neighboring regions, similarly to Snell’s law of refraction in optics. Armed with this representation, the problem is subsequently reduced to a directed graph search problem, which can be solved by employing standard algorithms.

The Zermelo-Voronoi Diagram: a dynamic partition problem

Abstract: We consider a Dirichlet-Voronoi like partition problem for a small airplane operating in the horizontal plane in the presence of winds that vary uniformly with time. It is shown that the problem can be interpreted as a Dynamic Voronoi Diagram problem, where the generators are not fixed, but rather they are moving targets to be reached in minimum time. The problem is solved by reducing it to a standard Voronoi Diagram by means of a time-varying coordinate transformation.