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In this paper, the imitation of human captured motions by a humanoid robot is considered. The main objective is to reproduce an imitated motion which should be as close as possible to the original human captured motion. To achieve this goal, the imitation problem is formulated as an optimization problem and the physical limits of the humanoid robot are considered as constraints. The optimization problem is then solved recursively by using an efficient dynamics algorithm, which allows the calculation of the gradient function with respect to the control parameters analytically. The simulation results using OpenHRP platform, which is a dynamical simulator for humanoid robot motions, have pointed out that the imitated motions preserve the salient characteristics of the original human captured motion. Moreover the optimization procedure converges well thanks to the analytical calculation of the gradient function.