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A time optimal control problem for the collision‐free robot motion planning
Author(s) -
Landry Chantal,
Gerdts Matthias,
Henrion René,
Hömberg Dietmar
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110352
Subject(s) - polyhedron , trajectory , collision avoidance , robot , optimal control , collision , motion planning , regular polygon , mathematical optimization , state (computer science) , linear programming , computer science , motion (physics) , control theory (sociology) , mathematics , control (management) , algorithm , artificial intelligence , physics , geometry , computer security , astronomy
A time optimal control problem for the computation of the fastest collision‐free trajectory of a robot surrounded by obstacles is presented. The dynamics of the robot is governed by ordinary differential equations. To build the collision avoidance criterion, the robot and the obstacles are represented as finite unions of convex polyhedra. Each polyhedron is described by a system of linear inequalities. This description combined with linear programming arguments allows us to include the collision avoidance as linear state constraints in the optimal control problem. The resulting system is then solved by a sequential quadratic programming method. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)