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An optimum internal model with constraints is proposed and discussed for the control of a speech robot, which is based on the human-like behavior. The main idea of the study is that the robot movements are carried out in such a way that the length of the path traveled in the internal space, under external acoustical and mechanical constraints, is minimized. This optimum strategy defines the designed internal model, which is responsible for the robot task planning. First, an exact analytical way to deal with the problem is proposed. Next, by using some empirical findings, an approximate solution for the designed internal model is developed. Finally, the implementation of this solution, which is applied to the control of a speech robot, yields interesting results in the field of task-planning strategies, task anticipation (namely, speech coarticulation), and the influence of force on the accuracy of executed tasks.