Displaying similar documents to “Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane”

Maxwell strata in sub-Riemannian problem on the group of motions of a plane

Igor Moiseev, Yuri L. Sachkov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The left-invariant sub-Riemannian problem on the group of motions of a plane is considered. Sub-Riemannian geodesics are parameterized by Jacobi's functions. Discrete symmetries of the problem generated by reflections of pendulum are described. The corresponding Maxwell points are characterized, on this basis an upper bound on the cut time is obtained.

Projective Reeds-Shepp car on with quadratic cost

Ugo Boscain, Francesco Rossi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Fix two points x , x ¯ ∈ S 2 and two directions (without orientation) η , η ¯ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost J [ γ ] = ∫ 0 T γ ( t ) ( γ ˙ ( t ) , γ ˙ ( t ) ) + K γ ( t ) 2 γ ( t ) ( γ ˙ ( t ) , γ ˙ ( t ) ) d t along all smooth curves starting from x with direction η and ending in x ¯ with direction η ¯ . Here g is the standard Riemannian metric on S 2...