Dubin's problem on surfaces. I: Nonnegative curvature

DOI10.1007/BF02922245zbMath1090.53042OpenAlexW2046583247MaRDI QIDQ816222

Yacine Chitour, Mario Sigalotti

Publication date: 21 February 2006

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: http://www.mathjournals.org/jgan/2005-015-004/2005-015-004-002.html

zbMATH Keywords

controllabilitygeodesic curvaturenonnegative curvature

Mathematics Subject Classification ID

Related Items (10)

Error-based control systems on Riemannian state manifolds: properties of the principal pushforward map associated to parallel transport ⋮ Optimal synthesis in the Reeds and Shepp problem with a free final direction ⋮ Markov-Dubins path via optimal control theory ⋮ Optimal geodesic curvature constrained Dubins' paths on a sphere ⋮ Optimal trajectories of curvature constrained motion in the Hamilton-Jacobi formulation ⋮ Optimal synthesis of the Zermelo-Markov-Dubins problem in a constant drift field ⋮ Optimal synthesis of the asymmetric sinistral/dextral Markov-Dubins problem ⋮ Projective Reeds-Shepp car onS²with quadratic cost ⋮ Extension of PID Regulators to Dynamical Systems on Smooth Manifolds (M-PID) ⋮ Lyapunov and minimum-time path planning for drones

Cites Work

• On subharmonic functions and differential geometry in the large
• Proof of the soul conjecture of Cheeger and Gromoll
• On the minimum time problem for driftless left-invariant control systems on \(SO(3)\).
• On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents
• Dubins' Problem on Surfaces II: Nonpositive Curvature
• Volumes of Small Balls on Open Manifolds: Lower Bounds and Examples
• Dubins' problem is intrinsically three-dimensional
• Controllability of Nonlinear Systems on Compact Manifolds
• Time-Optimal Synthesis for Left-Invariant Control Systems on SO(3)
• Contrôlabilité des Systèmes non Linéaires
• A Generalization of Chow’s Theorem and the Bang-Bang Theorem to Nonlinear Control Problems
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