Applications of Heisenberg Geometry
A very intuitive way to think of the sub-Riemannian Heisenberg group is as a medium in which motion is only possible along a given set of directions, changing from point to point. If the constraints are too tight, then it may be impossible to join any two points with an admissible trajectory, hence one needs to find conditions on the constraints implying “horizontal accessibility”.
KeywordsPath Planning Heisenberg Group Pseudoconvex Domain Carnot Group Jacobi Elliptic Function
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