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ItemOptimal Feedback Guidance of a Small Aerial Vehicle in the Presence of Stochastic Wind(Georgia Institute of Technology, 2013) Anderson, Ross P. ; Bakolas, Efstathios ; Milutinović, Dejan ; Tsiotras, PanagiotisThe navigation of a small unmanned aerial vehicle is challenging due to a large influence of wind to its kinematics. When the kinematic model is reduced to two dimensions, it has the form of the Dubins kinematic vehicle model. Consequently, this paper addresses the problem of minimizing the expected time required to drive a Dubins vehicle to a prescribed target set in the presence of a stochastically varying wind. First, two analytically-derived control laws are presented. One control law does not consider the presence of the wind, whereas the other assumes that the wind is constant and known a priori. In the latter case it is assumed that the prevailing wind is equal to its mean value; no information about the variations of the wind speed and direction is available. Next, by employing numerical techniques from stochastic optimal control, feedback control strategies are computed. These anticipate the stochastic variation of the wind and drive the vehicle to its target set while minimizing the expected time of arrival. The analysis and numerical simulations show that the analytically-derived deterministic optimal control for this problem captures, in many cases, the salient features of the optimal feedback control for the stochastic wind model, providing support for the use of the former in the presence of light winds. On the other hand, the controllers anticipating the stochastic wind variation lead to more robust and more predictable trajectories than the ones obtained using feedback controllers for deterministic wind models.
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ItemRelay Pursuit of a Maneuvering Target Using Dynamic Voronoi Diagrams(Georgia Institute of Technology, 2012-08) Bakolas, Efstathios ; Tsiotras, PanagiotisThis paper addresses the problem of the pursuit of a maneuvering target by a group of pursuers distributed in the plane. This pursuit problem is solved by associating it with a Voronoi-like partitioning problem that characterizes the set of initial positions from which the target can be intercepted by a given pursuer faster than any other pursuer from the same group. In the formulation of this partitioning problem, the target does not necessarily travel along prescribed trajectories, as it is typically assumed in the literature, but, instead, it can apply an “evading” strategy in an effort to delay or, if possible, escape capture. We characterize an approximate solution to this problem by associating it with a standard Voronoi partitioning problem. Subsequently, we propose a relay pursuit strategy, that is, a special group pursuit scheme such that, at each instant of time, only one pursuer is assigned the task of capturing the maneuvering target. During the course of the relay pursuit, the pursuer-target assignment changes dynamically with time based on the (time varying) proximity relations between the pursuers and the target. This proximity information is encoded in the solution of the Voronoi-like partitioning problem. Simulation results are presented to highlight the theoretical developments.
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ItemOptimal Synthesis of the Zermelo–Markov–Dubins Problem in a Constant Drift Field(Georgia Institute of Technology, 2012-01-16) Bakolas, Efstathios ; Tsiotras, PanagiotisWe consider the optimal synthesis of the Zermelo–Markov–Dubins problem, that is, the problem of steering a vehicle with the kinematics of the Isaacs–Dubins car in minimum time in the presence of a drift field. By using standard optimal control tools, we characterize the family of control sequences that are sufficient for complete controllability and necessary for optimality for the special case of a constant field. Furthermore, we present a semi-analytic scheme for the characterization of a (nearly) optimal synthesis of the minimum-time problem. Finally, we establish a direct correspondence between the optimal syntheses of the Markov–Dubins and the Zermelo–Markov–Dubins problems by means of a discontinuous mapping.
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ItemFeedback Navigation in an Uncertain Flow Field and Connections with Pursuit Strategies(Georgia Institute of Technology, 2012) Bakolas, Efstathios ; Tsiotras, PanagiotisThis paper presents several classes of control laws for steering an agent, that is, an aerial or marine vehicle, in the presence of a both temporally and spatially varying drift field induced by local winds/currents. The navigation problem is addressed assuming various information patterns about the drift field in the vicinity of the agent. In particular, three cases are considered, namely when the agent has complete information about the local drift, when the drift field is partially known, and when the drift field is completely unknown. By first establishing a duality between the navigation problem and a special class of problems of pursuit of a maneuvering target, several navigation schemes are presented, which are appropriately tailored to the fidelity of the information about the local drift available to the agent. The proposed navigation laws are dual to well-known pursuit strategies, such as pure pursuit, parallel guidance/navigation, line-of-sight guidance, motion camouflage, and pursuit with neutralization. Simulation results are presented to illustrate the theoretical developments
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ItemThe Zermelo-Voronoi Diagram: a Dynamic Partition Problem(Georgia Institute of Technology, 2010) Bakolas, Efstathios ; Tsiotras, PanagiotisWe consider a Voronoi-like partition problem in the plane for a given finite set of generators. Each element in this partition is uniquely associated with a particular generator in the following sense: An agent that resides within a set of the partition at a given time will arrive at the generator associated with this set faster than any other agent that resides anywhere outside this set at the same instant of time. The agent’s motion is affected by the presence of a temporally-varying drift, which is induced by local winds/currents. As a result, the minimum-time to a destination is not equivalent to the minimum-distance traveled. This simple fact has important ramifications over the partitioning problem. It is shown that this 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 first reducing it to a standard Voronoi Diagram by means of a time-varying coordinate transformation. We then extend the approach to solve the dual problem where the generators are the initial locations of a given set of agents distributed over the plane, such that each element in the partition consists of the terminal positions that can be reached by the corresponding agent faster than any other agent.