Person:

Tsiotras, Panagiotis

Permanent Link

https://hdl.handle.net/1853/71790

Associated Organization(s)

Organizational Unit

Daniel Guggenheim School of Aerospace Engineering

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Now showing 1 - 10 of 12

Optimal 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, Panagiotis

The 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.
The Markov-Dubins Problem in the Presence of a Stochastic Drift Field

(Georgia Institute of Technology, 2012-12) Anderson, Ross P. ; Bakolas, Efstathios ; Milutinovic, Dejan ; Tsiotras, Panagiotis

We consider the problem of navigating a small Dubins-type aerial or marine vehicle to a prescribed destination set in minimum expected time and in the presence of a stochastic drift field induced by local winds or currents. First, we present a deterministic control law that is independent of the local winds/currents and their statistics. Next, by employing numerical techniques from stochastic optimal control, we compute an optimal feedback control strategy that incorporates the stochastic variation in the wind when driving the Dubins vehicle to its destination set in minimum expected time. Our analyses and simulations offer a side-by-side comparison of the optimal deterministic and stochastic optimal feedback control laws for this problem, and they illustrate that the deterministic control can, in many cases, capture the salient features of structure of the stochastic optimal feedback control.
Relay Pursuit of a Maneuvering Target Using Dynamic Voronoi Diagrams

(Georgia Institute of Technology, 2012-08) Bakolas, Efstathios ; Tsiotras, Panagiotis

This 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.
Optimal Synthesis of the Zermelo–Markov–Dubins Problem in a Constant Drift Field

(Georgia Institute of Technology, 2012-01-16) Bakolas, Efstathios ; Tsiotras, Panagiotis

We 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.
Feedback Navigation in an Uncertain Flow Field and Connections with Pursuit Strategies

(Georgia Institute of Technology, 2012) Bakolas, Efstathios ; Tsiotras, Panagiotis

This 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
Optimal Pursuit of Moving Targets using Dynamic Voronoi Diagrams

(Georgia Institute of Technology, 2010) Bakolas, Efstathios ; Tsiotras, Panagiotis

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.
The Zermelo-Voronoi Diagram: a Dynamic Partition Problem

(Georgia Institute of Technology, 2010) Bakolas, Efstathios ; Tsiotras, Panagiotis

We 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.
Minimum-Time Paths for a Light Aircraft in the Presence of Regionally-Varying Strong Winds

(Georgia Institute of Technology, 2010) Bakolas, Efstathios ; Tsiotras, Panagiotis

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.
On the Generation of Nearly Optimal, Planar Paths of Bounded Curvature and Curvature Gradient

(Georgia Institute of Technology, 2009) Bakolas, Efstathios ; Tsiotras, Panagiotis

We present a numerically efficient scheme to generate a family of path primitives that can be used to construct paths that take into consideration point-wise constraints on both the curvature and its derivative. The statement of the problem is a generalization of the Dubins problem to account for more realistic vehicle dynamics. The problem is solved by appropriate concatenations of line segments, circular arcs and pieces of clothoids, which are the path primitives in our scheme. Our analysis reveals that the use of clothoid segments, in addition to line segments and circular arcs, for path generation introduces significant changes on issues such as path admissibility and length minimality, when compared with the standard Dubins problem.
The Asymmetric Sinistral/Dextral Markov-Dubins Problem

(Georgia Institute of Technology, 2009) Bakolas, Efstathios ; Tsiotras, Panagiotis

We consider a variation of the classical Markov-Dubins problem dealing with curvature-constrained, shortest paths in the plane with prescribed initial and terminal positions and tangents, when the lower and upper bounds of the curvature are not necessarily equal. The motivation for this problem stems from vehicle navigation applications when the vehicle may be biased in taking turns at a particular direction due to hardware failures or environmental conditions. We employ optimal control to characterize the structure of the shortest path and we resort to geometric techniques to provide sufficient conditions for optimality of the resulting path.