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Tsiotras, Panagiotis

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    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.
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    Multiresolution Path Planning Via Sector Decompositions Compatible to On-Board Sensor Data
    (Georgia Institute of Technology, 2008) Bakolas, Efstathios ; Tsiotras, Panagiotis
    In this paper we present a hybrid local-global path planning scheme for the problem of operating a moving agent inside an unknown environment in a collision-free manner. The path planning algorithm is based on information gathered on-line by the available on-board sensor devices. The solution minimizes the total length of the path with respect to a metric that includes actual path length along with a risk-induced metric. We use a multi-resolution cell decomposition of the environment in order to solve the path-planning problem using the wavelet transform in conjunction with a conformal mapping to polar coordinates. By performing the cell decomposition in polar coordinates we can naturally incorporate sector-like cells that are adapted to the data representation collected by the on-board sensor devices. Simulations are presented to test the efficiency of the algorithm using a non trivial scenario.
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    A Hierarchical On-Line Path-Planning Scheme Using Wavelets
    (Georgia Institute of Technology, 2007-07) Tsiotras, Panagiotis ; Bakolas, Efstathios
    We present an algorithm for solving the shortest (collision-free) path planning problem for an agent (e.g., wheeled vehicle, UAV) operating in a partially known environment. The agent has detailed knowledge of the environment and the obstacles only in the vicinity of its current position. Far away obstacles or the final destination are only partially known and may even change dynamically at each instant of time. We obtain an approximation of the environment at different levels of fidelity using a wavelet approximation scheme. This allows the construction of a directed weighted graph of the obstacle-free space in a computationally efficient manner. In addition, the dimension of the graph can be adapted to the on-board computational resources. By searching this graph we find the desired shortest path to the final destination using Dijkstra's algorithm, provided that such a path exists. Simulations are presented to test the efficiency of the algorithm using non trivial scenarios.