Journal of Dynamical and Control Systems

, Volume 21, Issue 1, pp 47–80 | Cite as

Lyapunov and Minimum-Time Path Planning for Drones

  • Thibault Maillot
  • Ugo Boscain
  • Jean-Paul Gauthier
  • Ulysse SerresEmail author


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 predesigned admissible circular trajectory around the target which is itself a fixed point in the space. Our strategy is presented for both high altitude long endurance (HALE) and medium altitude long endurance (MALE) types of UAVs. A UAV flying at a constant altitude (HALE type) is modeled as a Dubins vehicle (i.e., a planar vehicle with constrained turning radiusand 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 \(\mathbb {R}^{3}\). 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 is very rich, although much simpler than the point-to-point time-optimal strategy studied in the 1990s. Finally, we propose control strategies to provide supervision of a moving target, which are based upon theprevious ones.


Optimal control Path planning Aircraft navigation Unmanned aerial vehicles Rigid-body dynamics Under-actuated systems Nonlinear control Trajectory tracking 

Mathematics Subject Classifications (2010)

93D15 49J15 34H05 



This research has been supported by the French FUI SHARE project (see [3]), supported by a consortium of companies and research labs (Opéra Ergonomie, ONERA, Thales Alénia Space, Eurocopter, Adetel group) and by the European Research Council, ERC StG 2009 “GeCoMethods”, contract number 239748.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Thibault Maillot
    • 1
  • Ugo Boscain
    • 2
    • 3
  • Jean-Paul Gauthier
    • 1
    • 3
  • Ulysse Serres
    • 4
    Email author
  1. 1.Université de Toulon, LSIS, UMR CNRS 7296La Garde CedexFrance
  2. 2.CNRS, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), UMR CNRS 7641Palaiseau CedexFrance
  3. 3.INRIA GECO ProjectLa Garde CedexFrance
  4. 4.Université Claude Bernard Lyon 1, LAGEP, UMR CNRS 5007VilleurbanneFrance

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