A coupling of discrete and continuous optimization to solve kinodynamic motion planning problems

Please always quote using this URN:urn:nbn:de:0296-matheon-12950
  • This paper studies the relationship between the material derivative method, the shape derivative method, the min-max formulation of Correa and Seeger, and the Lagrange method introduced by Cea. A theorem is formulated which allows a rigorous proof of the shape differentiability without the usage of material derivative; the domain expression is automatically obtained and the boundary expression is easy to derive. Furthermore, the theorem is applied to a cost function which depends on a quasi-linear transmission problem. Using a Gagliardo penalization the existence of optimal shapes is established.

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Metadaten
Author:Chantal Landry, Wolfgang Welz, Matthias Gerdts
URN:urn:nbn:de:0296-matheon-12950
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2014/05/20
Release Date:2014/05/20
Tag:Trajectory planning, optimal control problem, collision avoidance,; graph search algorithm, initialization, robotics
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J15 Optimal control problems involving ordinary differential equations
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M25 Discrete approximations
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Nxx Miscellaneous topics / 49N90 Applications of optimal control and differential games [See also 90C90, 93C95]
70-XX MECHANICS OF PARTICLES AND SYSTEMS (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX) / 70Exx Dynamics of a rigid body and of multibody systems / 70E60 Robot dynamics and control [See also 68T40, 70Q05, 93C85]
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C30 Nonlinear programming
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C35 Programming involving graphs or networks [See also 90C27]
Preprint Number:1063
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