# Lyapunov and minimum-time path planning for drones

3 GECO - Geometric Control Design
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : In this paper, we study the problem of controlling an unmanned aerial vehicle (UAV) to provide a target supervision and/or to provide convoy protection to ground vehicles. We first present a control strategy based upon a Lyapunov-LaSalle stabilization method to provide supervision of a stationary target. The UAV is expected to join a pre-designed admissible circular trajectory around the target which is itself a fixed point in the space. Our strategy is presented for both HALE (High Altitude Long Endurance) and MALE (Medium Altitude Long Endurance) types UAVs. A UAV flying at a constant altitude (HALE type) is modeled as a Dubins vehicle (i.e. a planar vehicle with constrained turning radius and constant forward velocity). For a UAV that might change its altitude (MALE type), we use the general kinematic model of a rigid body evolving in $\R^3$. Both control strategies presented are smooth and unlike what is usually proposed in the literature these strategies asymptotically track a circular trajectory of exact minimum turning radius. We also present the time-optimal control synthesis for tracking a circle by a Dubins vehicle. This optimal strategy, although much simpler than the point-to-point time-optimal strategy obtained by P. Souéres and J.-P. Laumond in the 1990s (see [45]), is very rich. Finally, we propose control strategies to provide supervision of a moving target, that are based upon the previous ones.
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https://hal.archives-ouvertes.fr/hal-00847812
Contributor : Ulysse Serres <>
Submitted on : Wednesday, July 24, 2013 - 2:44:07 PM
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• HAL Id : hal-00847812, version 1

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Thibault Maillot, Ugo Boscain, Jean-Paul Gauthier, Ulysse Serres. Lyapunov and minimum-time path planning for drones. 2013. ⟨hal-00847812⟩

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