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Mathematical Control and Related Fields (MCRF)
 

Minimal time synthesis for a kinematic drone model

Pages: 259 - 288, Volume 7, Issue 2, June 2017      doi:10.3934/mcrf.2017009

 
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Marc-Aurèle Lagache - Université de Toulon, CNRS, LSIS, UMR 7296, F-83957 La Garde, France (email)
Ulysse Serres - Univ. Lyon, Universit´e Claude Bernard Lyon 1, CNRS, LAGEP, UMR 5007, 43 bd du 11 novembre 1918, F-69100 Villeurbanne, France (email)
Vincent Andrieu - Univ. Lyon, Universit´e Claude Bernard Lyon 1, CNRS, LAGEP, UMR 5007, 43 bd du 11 novembre 1918, F-69100 Villeurbanne, France (email)

Abstract: In this paper, we consider a (rough) kinematic model for a UAV flying at constant altitude moving forward with positive lower and upper bounded linear velocities and positive minimum turning radius. For this model, we consider the problem of minimizing the time travelled by the UAV starting from a general configuration to connect a specified target being a fixed circle of minimum turning radius. The time-optimal synthesis is presented as a partition of the state space which defines a unique optimal path such that the target can be reached optimally.

Keywords:  Nonlinear control systems, optimal control, optimal synthesis, Pontryagin Maximum Principle, feedback stabilization.
Mathematics Subject Classification:  93D15, 49J15, 34H05, 49K15, 93C15, 93C10, 34D23.

Received: April 2016;      Revised: October 2016;      Available Online: April 2017.

 References