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Solving trajectory optimization problems via nonlinear programming: the brachistochrone case study

Jean-Pierre Dussault(Jean-Pierre.Dussault***at***usherbrooke.ca)

Abstract: This note discusses reformulations the brachistochrone problem suitable for solution via NLP. The availability of solvers and modeling languages such as AMPL makes it tempting to formulate discretized optimization problems and get solutions to the discretized versions of trajectory optimization problems. We use the famous brachistochrone problem to warn that the resulting solutions may be far different from the true optimal trajectory. Actually, we use our knowledge of the brachistochrone to argue that without this knowledge, we could not distinguish the true solution (a cycloid) from spurious solutions obtained by a natural discretization.

Keywords: trajectory optimization - unconstrained optimization

Category 1: Nonlinear Optimization


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Entry Submitted: 02/22/2012
Entry Accepted: 02/22/2012
Entry Last Modified: 02/22/2012

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