Manipulation planning: building paths on constrained manifolds
Résumé
Constrained motion planning and Manipulation planning, for generic non-linear constraints, highly rely on the ability of solving non-linear equations. The Newton-Raphson method is often used in this context. This work tackles the problem of continuity that arises when projecting paths point wise with such method. A theoretical proof of an interval of continuity for the Newton-Raphson iteration function is given. This interval requires to bound from above the norm of the Hessian of the constraints. A method to compute this bound for constraints involving joint positions and orientations is proposed. Then, this theoretical result is used in two path projection algorithm to give a certicate of continuity of the continuously projected path. Finally, simulations are run on several problems.
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Origine | Fichiers produits par l'(les) auteur(s) |
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