## Invitation to Topological Robotics |

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admissible configuration affine function An~l assume bars cell coefficients cohomology class collinear collinear configurations cone configuration space Consider continuous section Corollary 4.40 critical points defined denote diffeomorphic disjoint edges equals equation equilibrium stress Euler characteristic exists expansive motion fibration finite G R2 G Xe given graph Hence homeomorphic homology homotopy inequality integer intersection involution knot theory Lemma length vector lens spaces linkages long subset lying manifold median subset moduli space Morse index motion planning algorithms navigation function neighborhood nonzero obtain open cover open subset pair path pi+i polyhedron problem proof of Theorem result satisfying Schwarz genus sequence short subsets shown on Figure simplex statement strut submanifold subset J C tangent vector TC(X TC(Y Theorem Theorem 2.3 topological complexity topological space torus total Betti number unstable manifolds vector field vertex vertices zero-divisors