Path planning in a Riemannian manifold using optimal control
2020 ◽
Vol 17
(12)
◽
pp. 2050181
Keyword(s):
We consider the motion planning of an object in a Riemannian manifold where the object is steered from an initial point to a final point utilizing optimal control. Considering Pontryagin Minimization Principle we compute the Optimal Controls needed for steering the object from initial to final point. The Optimal Controls were solved with respect to time [Formula: see text] and shown to have norm [Formula: see text] which should be the case when the extremal trajectories, which are the solutions of Pontryagin Principle, are arc length parametrized. The extremal trajectories are supposed to be the geodesics on the Riemannian manifold. So we compute the geodesic curvature and the Gaussian curvature of the Riemannian structure.
2019 ◽
Vol 20
(2)
◽
pp. 132-141
Keyword(s):
2020 ◽
Vol 2020
◽
pp. 1-12
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2018 ◽
Vol 36
(3)
◽
pp. 779-833
2018 ◽
Vol 2018
◽
pp. 1-10
◽
Keyword(s):
2016 ◽
Vol 13
(03)
◽
pp. 1650010
Keyword(s):