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@MISC{Mirrazavi Salehian2016-ID956,
author = {Mirrazavi Salehian, S. S. and Khoramshahi, M. and Billard, A.},
title = {A Dynamical System Approach for Catching Softly a Flying Object: Theory and Experiment},
howpublished = {in IEEE Transactions on Robotics, vol. 32, no. 2, pp. 462-471, April 2016.},
year = {2016},
abstract = {Catching a fast flying object is particularly challenging as
consists of two tasks: it requires extremely precise estimation of the
object?s motion and control of the robot motion. Any small imprecision
may lead the fingers to close too abruptly and let the object fly away from
the hand before closing. We present a strategy to overcome for sensori-
motor imprecision by introducing softness in the catching approach. Soft
catching consists of having the robot moves with the object for a short
period of time, so as to leave more time for the fingers to close on the
object. We use a dynamical systems (DS) based control law to generate
the appropriate reach and follow motion, which is expressed as a Linear Parameter Varying (LPV) system. We propose a method to approximate the parameters of LPV systems using Gaussian Mixture Models, based on a set of kinematically feasible demonstrations generated by an off-line optimal control framework. We show theoretically that the resulting DS will intercept the object at the intercept point, at the right time with the desired velocity direction. Stability and convergence of the approach are assessed through Lyapunov stability theory. The proposed method is validated systematically to catch three objects that generate elastic contacts and demonstrate important improvement over a hard catching approach.},

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