TY - GEN A1 - Landry, Chantal A1 - Welz, Wolfgang A1 - Gerdts, Matthias T1 - A coupling of discrete and continuous optimization to solve kinodynamic motion planning problems N2 - 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. KW - Trajectory planning, optimal control problem, collision avoidance, KW - graph search algorithm, initialization, robotics Y1 - 2014 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1295 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-12950 ER -