A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Approximation algorithms for curvature-constrained shortest paths
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
Nonuniform Discretization for Kinodynamic Motion Planning and its Applications
SIAM Journal on Computing
A level set approach for computing discontinuous solutions of Hamilton-Jacobi equations
Mathematics of Computation
Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations
Journal of Computational Physics
Fast Sweeping Methods for Static Hamilton--Jacobi Equations
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
An anti-diffusive scheme for viability problems
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Planning Algorithms
A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
Journal of Computational Physics
Finding curvature-constrained paths that avoid polygonal obstacles
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
From Dubins’ car to Reeds and Shepp’s mobile robot
Computing and Visualization in Science
Dynamic Programming
SIAM Journal on Control and Optimization
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We propose a PDE approach for computing time-optimal trajectories of a vehicle which travels under certain curvature constraints. We derive a class of Hamilton---Jacobi equations which models such motions; it unifies two well-known vehicular models, the Dubins' and Reeds---Shepp's cars, and gives further generalizations. Numerical methods (finite difference for the Reeds---Shepp's car and semi-Lagrangian for the Dubins' car) are investigated for two-dimensional domains and surfaces.