%0 Book Section
%T Computing capture tubes
%+ Lab-STICC_ENSTAB_CID_IHSEV
%+ Pôle STIC_OSM
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%+ University Of Manchester Institute (UMIST/Department of Process Integration)
%+ MBDA France (MBDA)
%+ IMT Atlantique (IMT Atlantique)
%A Jaulin, Luc
%A Daniel, Lopez
%A Vincent Le, Doze
%A Stéphane Le, Menec
%A Jordan, Ninin
%A Chabert, Gilles
%A Mohamed Saad, Ibnseddik
%A Alexandru, Stancu
%@ 978-3-319-31768-7
%B Scientific Computing, Computer Arithmetic, and Validated Numerics
%I Springer
%V 9553
%P 209-224
%8 2016-04-09
%D 2016
%R 10.1007/978-3-319-31769-4_17
%K Capture tube Contractors Interval arithmetic Robotics Stability
%Z Engineering Sciences [physics]/Automatic
%Z Mathematics [math]Book sections
%X Many mobile robots such as wheeled robots, boats, or plane are described by nonholonomic differential equations. As a consequence, they have to satisfy some differential constraints such as having a radius of curvature for their trajectory lower than a known value. For this type of robots, it is difficult to prove some properties such as the avoidance of collisions with some moving obstacles. This is even more difficult when the initial condition is not known exactly or when some uncertainties occur. This paper proposes a method to compute an enclosure (a tube) for the trajectory of the robot in situations where a guaranteed interval integration cannot provide any acceptable enclosures. All properties that are satisfied by the tube (such as the non-collision) will also be satisfied by the actual trajectory of the robot.
%G English
%L hal-01326533
%U https://hal.science/hal-01326533
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