book - Jean-Paul Laumond (Editor) Robot Motion Planning and...

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Jean-Paul Laumond (Editor) Robot Motion Planning and Control Laboratoire d’Analye et d’Architecture des Syst` emes Centre National de la Recherche Scientifique LAAS report 97438 Previoulsy published as: Lectures Notes in Control and Information Sciences 229. Springer, ISBN 3-540-76219-1, 1998, 343p.
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Foreword How can a robot decide what motions to perform in order to achieve tasks in the physical world ? The existing industrial robot programming systems still have very limited motion planning capabilities. Moreover the field of robotics is growing: space exploration, undersea work, intervention in hazardous environments, servicing robotics ... Motion planning appears as one of the components for the neces- sary autonomy of the robots in such real contexts. It is also a fundamental issue in robot simulation software to help work cell designers to determine collision free paths for robots performing specific tasks. Robot Motion Planning and Control requires interdisciplinarity The research in robot motion planning can be traced back to the late 60’s, during the early stages of the development of computer-controlled robots. Nev- ertheless, most of the effort is more recent and has been conducted during the 80’s ( Robot Motion Planning , J.C. Latombe’s book constitutes the reference in the domain). The position (configuration) of a robot is normally described by a number of variables. For mobile robots these typically are the position and orientation of the robot (i.e. 3 variables in the plane). For articulated robots (robot arms) these variables are the positions of the different joints of the robot arm. A motion for a robot can, hence, be considered as a path in the configuration space. Such a path should remain in the subspace of configurations in which there is no collision between the robot and the obstacles, the so-called free space. The motion planning problem asks for determining such a path through the free space in an efficient way. Motion planning can be split into two classes. When all degrees of freedom can be changed independently (like in a fully actuated arm) we talk about holonomic motion planning . In this case, the existence of a collision-free path is characterized by the existence of a connected component in the free config- uration space. In this context, motion planning consists in building the free configuration space, and in finding a path in its connected components. Within the 80’s, Roboticians addressed the problem by devising a variety of heuristics and approximate methods. Such methods decompose the config- uration space into simple cells lying inside, partially inside or outside the free space. A collision-free path is then searched by exploring the adjacency graph of free cells.
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VI In the early 80’s, pioneering works showed how to describe the free config- uration space by algebraic equalities and inequalities with integer coefficients (i.e. as being a semi-algebraic set). Due to the properties of the semi-algebraic
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book - Jean-Paul Laumond (Editor) Robot Motion Planning and...

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