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Variational Obstacle Avoidance with Applications to Interpolation Problems in Hybrid Systems (2108.13238v1)
Published 30 Aug 2021 in math.OC, cs.SY, and eess.SY
Abstract: We study variational obstacle avoidance problems on complete Riemannian manifolds and apply the results to the construction of piecewise smooth curves interpolating a set of knot points in systems with impulse effects. We derive the dynamical equations for extrema in the variational problem, and show the existence of minimizers by using lower-continuity arguments for weak convergence on an infinite-dimensional Hilbert manifold. We then provide conditions under which it is possible to ensure that the extrema will safely avoid a given obstacle within some desired tolerance.