Manipulation planning: building paths on constrained manifolds

Joseph Mirabel (1) , Florent Lamiraux (1)

1 LAAS-GEPETTO - Équipe Mouvement des Systèmes Anthropomorphes

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.

Domaines: Automatique / Robotique; Robotique [cs.RO]

Joseph Mirabel, Florent Lamiraux. Manipulation planning: building paths on constrained manifolds. 2016. ⟨hal-01360409v2⟩