In this paper, we propose an efficient algorithm to solve the time parameterization problem for a redundant robot such as an upper-body industrial manipulator robot. To cope with the physical limits of the robot while minimizing the execution time, the time parameterization problem is formulated as an optimization problem for which we propose an appropriate solver. The output of the algorithm is a feasible trajectory that can be safely executed by the robot. To assess the proposed method, we conducted a simulation scenario of an upper-body industrial manipulator robot (HIRO robot) executing a trajectory while avoiding the collision with some obstacles. The simulation experiment pointed out that the well- known ill-conditioning and divergence problems in numerical time parameterization algorithms has been overcome thanks to the analytical computation of the derivative of objective function and the constraints, it also revealed the effectiveness of the proposed method to deal with the challenging problem of time parameterization.
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