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This paper proposes a steady-state genetic algorithm for trajectory generation used in the imitation of a partner robot interacting with a human. Various types of genetic algorithms have been applied for the trajectory generation of robot manipulators. In this paper, we propose a trajectory generation method for the partner robot by a steady-state genetic algorithm based on the human motions pattern, and compare the proposed method with its related methods. Finally, we show experimental results of trajectory generation through interaction with a human.