Motion planning for a steering-constrained robot through moderate obstacles
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Proceedings of the twelfth annual symposium on Computational geometry
Curvature-constrained shortest paths in a convex polygon (extended abstract)
Proceedings of the fourteenth annual symposium on Computational geometry
The complexity of the two dimensional curvature-constrained shortest-path problem
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Approximation algorithms for curvature-constrained shortest paths
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Curvature-bounded traversals of narrow corridors
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Optimal Trajectories of Curvature Constrained Motion in the Hamilton---Jacobi Formulation
Journal of Scientific Computing
Approximating minimum bending energy path in a simple corridor
Computational Geometry: Theory and Applications
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We describe an algorithm to find a unit-curvature path between specified configurations in an arbitrary polygonal domain. Whenever such a path exists, the algorithm returns an explicit description of one such path in time that is polynomial in n (the number of features of the domain), m (the precision of the input) and k (the number of segments on the simplest obstacle-free Dubins path connecting the specified configurations). Our algorithm is based on a new normal form for unit-curvature paths and a dynamic path filtering argument that exploits a separation bound for distinct paths in this normal form.The best result known for the feasibility of bounded-curvature motion in the presence of arbitrary polygonal obstacles involves a reduction to the first-order theory of the reals. It just determines if a feasible path exists (it does not return a path) and requires exponential time and space.