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Tsiotras, Panagiotis

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

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.

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Wavelets in control and optimization

2008-09-16 , Tsiotras, Panagiotis

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Multiresolution Path Planning with Wavelets: A Local Replanning Approach

2008 , Cowlagi, Raghvendra V. , Tsiotras, Panagiotis

A path planning algorithm based on multiresolution cell decomposition of the environment using wavelets is proposed. The environment is assumed to be given by an occupancy grid at fine resolution. The algorithm constructs a cell decomposition at several levels of resolution (cell sizes) and constructs an optimal path to the destination from the current location of the agent. At each step the algorithm iteratively refines a coarse approximation to the path through local replanning. The replanning process uses previous information to refine the original cell channel in the immediate area of the path. This is done efficiently using the wavelet coefficients. Numerical tests show a speed-up of an order of magnitude over the baseline algorithm with minimal impact on the overall optimality of the resulting path. A comparative study with the well-known D* algorithm is also provided.

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On-line Path Generation for Small Unmanned Aerial Vehicles using B-Spline Path Templates

2008 , Jung, Dongwon , Tsiotras, Panagiotis

In this study we investigate the problem of generating a smooth, planar reference path, given a family of discrete optimal paths. In conjunction with a path representation by a finite sequence of square cells, the generated path is supposed to stay inside a feasible channel, while minimizing certain performance criteria. Constrained optimization problems are formulated subject to geometric (linear) constraints, as well as boundary conditions in order to generate a library of B-spline path templates. As an application to the vehicle motion planning, the path templates are incorporated to represent local segments of the entire path as geometrically smooth curves, which are then joined with one another to generate a reference path to be followed by a closed-loop tracking controller. The on-line path generation algorithm incorporates the path templates such that continuity and smoothness are preserved when switching from one template to another along the path. Combined with the D∗-lite path planning algorithm, the proposed algorithm provides a complete solution to the obstacle-free path generation problem in a computationally efficient manner, suitable for real-time implementation.

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Real-time Implementation and Validation of a New Hierarchical Path Planning Scheme for UAVs via Hardware-in-the-Loop Simulation

2009 , Jung, Dongwon , Ratti, Jayant , Tsiotras, Panagiotis

We develop a hierarchical path planning and control algorithm for a small fixed-wing UAV. Incorporating the hardware-in-the-loop (HIL) simulation environment, the hierarchical path planning and control algorithm has been validated through on-board, real-time implementation on a small autopilot. We present two distinct real-time software framework for implementation of the overall control algorithms including path planning, path smoothing, and path following. We especially emphasize the use of a real-time kernel, which shows effectiveness and robustness in accomplishing non-trivial real-time software environment. By a seamless integration of the control algorithms with a help of real-time kernel, it has been demonstrated that the UAV equipped with a small autopilot having limited computational resources manages to autonomously accomplish the mission control objective of reaching the goal while avoiding obstacles without human intervention.

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Bank-to-Turn Control for a Small UAV using Backstepping and Parameter Adaptation

2008-07 , Jung, Dongwon , Tsiotras, Panagiotis

In this research we consider the problem of path following control for a small fixed-wing unmanned aerial vehicle (UAV). Assuming the UAV is equipped with an autopilot for low level control, we adopt a kinematic error model with respect to the moving Serret-Frenet frame attached to a path for tracking controller design. A kinematic path following control law that commands heading rate is presented. Backstepping is applied to derive the roll angle command by taking into account the approximate closed-loop roll dynamics. A parameter adaptation technique is employed to account for the inaccurate time constant of the closed-loop roll dynamics during actual implementation. The path following control algorithm is validated in real-time through a high-fidelity hardware-in-the-loop simulation (HILS) environment showing the applicability of the algorithm on a real system.

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Multiresolution On-Line Path Planning for Small Unmanned Aerial Vehicles

2008 , Jung, Dongwon , Tsiotras, Panagiotis

In this article we propose a new online multiresolution path planning algorithm for a small unmanned air vehicle (UAV) with limited on-board computational resources. The proposed approach assumes that the UAV has detailed information of the environment only in the vicinity of its current position. Information about far away obstacles is also available, albeit with less accuracy. The proposed algorithm uses an integer arithmetic implementation of the fast lifting wavelet transform (FLWT) to get a multiresolution cell decomposition of the environment, whose dimension is commensurate to the on-board computational resources. A topological graph representation of the multiresolution cell decomposition is constructed efficiently, directly from the approximation and detail wavelet coefficients. Hardware-in-the-loop simulation (HILS) results validate the applicability of the algorithm on a small UAV autopilot. Comparisons with the standard D∗-lite algorithm are also presented.

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The Asymmetric Sinistral/Dextral Markov-Dubins Problem

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.

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Coordinated resource allocation among multiple agents with application to autonomous refueling and servicing of satellite constellations

2008-03-01 , Tsiotras, Panagiotis , Elmaghraby, Wedad J.

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Multiresolution Path Planning Via Sector Decompositions Compatible to On-Board Sensor Data

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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