Pythagorean Hodograph (PH) Path Planning for Tracking Airborne Contaminant using Sensor Swarm

Subchan, S.; White, Brian; Tsourdos, Antonios; Shanmugavel, Madhavan; Żbikowski, Rafał

doi:10.1109/imtc.2008.4547087

Cited by 22 publications

(16 citation statements)

References 13 publications

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“…The theory of rational adapted RMFs on general spatial PH curves yields results analogous to (32) and (33), but without the sin θ factor in (33). In the absence of this factor, the rotation matrix in (32) is rational in ξ, and hence the RMF (f 1 , f 2 , f 3 ) is rational.…”

mentioning

confidence: 79%

“…There has recently been considerable interest in using Pythagorean-hodograph (PH) curves to specify paths for swarms of unmanned aerial vehicles (UAVs) or other autonomous or remotely-operated vehicles [1,3,4,6,20,21,23,24,25,26,27,28,29,30,31,33]. A polynomial PH curve r(ξ) = (x(ξ), y(ξ), z(ξ)) incorporates a special algebraic structure [9], ensuring that the components of the hodograph (derivative) r ′ (ξ) = (x ′ (ξ), y ′ (ξ), z ′ (ξ)) satisfy a Pythagorean condition -i.e., x ′2 (ξ)+y ′2 (ξ)+z ′2 (ξ) is equal to the perfect square of a single polynomial.…”

Section: Introductionmentioning

confidence: 99%

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Helical polynomial curves interpolating G 1 data with prescribed axes and pitch angles

Farouki

2017

Computer Aided Geometric Design

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A helical curve, or curve of constant slope, offers a natural flight path for an aerial vehicle with a limited climb rate to achieve an increase in altitude between prescribed initial and final states. Every polynomial helical curve is a spatial Pythagorean-hodograph (PH) curve, and the distinctive features of the PH curves have attracted growing interest in their use for Unmanned Aerial Vehicle (UAV) path planning. This study describes an exact algorithm for constructing helical PH paths, corresponding to a constant climb rate at a given speed, between initial and final positions and motion directions. The algorithm bypasses the more sophisticated algebraic representations of spatial PH curves, and instead employs a simple "lifting" scheme to generate helical PH paths from planar PH curves constructed using the complex representation. In this context, a novel scheme to construct planar quintic PH curves that interpolate given end points and tangents, with exactly prescribed arc lengths, plays a key role. It is also shown that these helical paths admit simple closed-form rotation-minimizing adapted frames. The algorithm is simple, efficient, and robust, and can accommodate helical axes of arbitrary orientation through simple rotation transformations. Its implementation is illustrated by several computed examples.

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mentioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Helical polynomial curves interpolating G 1 data with prescribed axes and pitch angles

Farouki

2017

Computer Aided Geometric Design

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“…In (11) the paths are allowed to intersect, but the vehicles are time separated and hence do not arrive at the intersection point simultaneously. If either Equation (10) or (11) is satisfied, then the generated trajectories are spatially deconflicted and therefore form a set of feasible paths. In this paper, feasible paths are generated by imposing the spatial separation constraint (Equation (10)); ensuring minimal spatial clearance E between the paths through temporal separation is part of ongoing research.…”

Section: Trajectory Generationmentioning

confidence: 99%

“…subject to boundary conditions (6), dynamic constraints of the aircraft (8), mission-specific constraints, for example Equation (9), Equation (10) or (11) for spatial deconfliction,…”

Section: Trajectory Generationmentioning

confidence: 99%

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A Trajectory-Generation Framework for Time-Critical Cooperative Missions

Choe

Cichella

Xargay

et al. 2013

AIAA Infotech@Aerospace (I@A) Conference

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This paper introduces a heuristic planar trajectory-generation framework for multiple vehicles. Desired feasible trajectories are generated using Pythagorean Hodograph Bézier curves that satisfy the dynamic constraints of the vehicles, and guarantee spatial separation between the paths for safe operation. It is shown that the trajectory generation framework can be cast into a constrained optimization problem where a set of (sub)optimal desired trajectories are obtained by minimizing a cost function. To show the efficiency of the algorithm, a simulation example is given, where three fixed-wing Unmanned Aerial Vehicles are following and coordinating along feasible trajectories that are generated by the algorithm.

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Robust adaptive neural network control for environmental boundary tracking by mobile robots

Sun

Pei

Pan

et al. 2011

Intl J Robust & Nonlinear

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SUMMARY The paper addresses the problem of environmental boundary tracking for the nonholonomic mobile robot with uncertain dynamics and external disturbances. To do environmental boundary tracking, a reference velocity is designed for the nonholonomic mobile robot. In this paper, a radial basis function neural network (NN) is used to approximate a nonlinear function containing the uncertain model terms and the elements of the Hessian matrix of the environmental concentration function. Then, the NN approximator is combined with a robust control to construct a robust adaptive NN control for the mobile robot to track the desired environment boundary. It is proved that the tracking error can be guaranteed to converge to zero in the ultimate. Simulation results are presented to illustrate the stability of the robust adaptive control. Copyright © 2011 John Wiley & Sons, Ltd.

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Pythagorean Hodograph (PH) Path Planning for Tracking Airborne Contaminant using Sensor Swarm

Cited by 22 publications

References 13 publications

Helical polynomial curves interpolating G 1 data with prescribed axes and pitch angles

Helical polynomial curves interpolating G 1 data with prescribed axes and pitch angles

A Trajectory-Generation Framework for Time-Critical Cooperative Missions

Robust adaptive neural network control for environmental boundary tracking by mobile robots

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