By Takeo Igarashi, Mike Stilman (auth.), David Hsu, Volkan Isler, Jean-Claude Latombe, Ming C. Lin (eds.)
Robotics is on the cusp of dramatic transformation. more and more complicated robots with extraordinary autonomy are discovering new functions, from clinical surgical procedure, to building, to domestic companies. by contrast historical past, the algorithmic foundations of robotics have gotten extra an important than ever, which will construct robots which are speedy, secure, trustworthy, and adaptive. Algorithms allow robots to understand, plan, keep watch over, and study. The layout and research of robotic algorithms bring up new primary questions that span machine technological know-how, electric engineering, mechanical engineering, and arithmetic. those algorithms also are discovering purposes past robotics, for instance, in modeling molecular movement and developing electronic characters for games and architectural simulation. The Workshop on Algorithmic Foundations of Robotics (WAFR) is a hugely selective assembly of best researchers within the box of robotic algorithms. considering the fact that its construction in 1994, it has released many of the field’s most crucial and lasting contributions. This publication includes the lawsuits of the ninth WAFR, hung on December 13-15, 2010 on the nationwide collage of Singapore. The 24 papers integrated during this e-book span a large choice of themes from new theoretical insights to novel applications.
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Extra info for Algorithmic Foundations of Robotics IX: Selected Contributions of the Ninth International Workshop on the Algorithmic Foundations of Robotics
5. The overlapping swaths of appropriate paths p1 and p2 cover a continuum of intermediate swaths between the two paths. Eqn. (5) is a proper equivalence relation because it possesses each of three properties: • reflexivity. μH (p, p) = 0; p is trivially deformable to itself. • symmetry. The Hausdorff metric is symmetric. • transitivity. Given μH (p1 , p2 ) ≤ d and μH (p2 , p3 ) ≤ d, a continuous deformation from p1 to p3 passes through p2 . 2 Equivalence Relation Having presented the set of conditions under which (5) holds, we now prove that they are sufficient to ensure the existence of a continuous deformation between two neighboring paths.
1 The projections from X onto its components Z and G are denoted πZ and πG respectively. Common examples of such invariantly acting Lie groups arising from the system’s symmetry group, are translations (Rn ), rotations (SO(2), SO(3)) or combinations thereof (SE(2), SE(3), R3 × SO(2), . . ). 1 For the decomposition to exist, the Lie group’s action has to be free. That is, for all x ∈ X and g, h ∈ G it has to be true that gx = hx implies g = h. If G is a symmetry group of the system, this is usually the case.
A GVD curve generated by two constant-curvature sets forms a conic section . Table 1 reflects that the curvature of pc is everywhere bounded with the maximum possible curvature being bounded by 43 κmax . For the full proofs, see . Lemma 2. Given safe, appropriate guard paths pi , p j ∈ F(s f , κmax ) separated by μH (pi , p j ) ≤ d, any path pc ⊂ F(s−f , 43 κmax ) between them is safe. Proof. We prove this lemma by contradiction. Assume an obstacle lies between pi and p j . We show that this assumption imposes lower bounds on v and w.
Algorithmic Foundations of Robotics IX: Selected Contributions of the Ninth International Workshop on the Algorithmic Foundations of Robotics by Takeo Igarashi, Mike Stilman (auth.), David Hsu, Volkan Isler, Jean-Claude Latombe, Ming C. Lin (eds.)