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In this paper, the effects of the addition of an active toe joint on a 2D humanoid robot with heel-off and toe-off motions are studied. To this end, the trajectories of joints and links are designed firstly. After gait planning, the dynamic model of the humanoid robot in different phases of motion is derived using Kane and Lagrange methods. Then, the veracity of the derived dynamic model is demonstrated by two different methods. The under-study model, is in accordance with the features of SURENA III, which is a humanoid robot designed and fabricated at the Center of Advanced Systems and Technologies (CAST) located in University of Tehran. Afterward, the optimization procedure is done by selection of two different goal functions; one of them minimizes the energy consumption and the other maximizes the stability of the robot. At last, the obtained results are presented. According to the results, there is an optimum value for heel-off and toe-off angles in each velocity which minimizes the consumption of energy. The results also show that, the heel-off angle does not have any significant effects on the stability of the robot while increasing the toe-off angle improves the stability of motion. Finally, the effects of mass and length of the toe joint is inspected. These inspections suggest that heavier toe joints cause an increase in both energy consumption and stability of the robot while increasing the length of the toe joint does not have any effects on both goal functions.

Keywords: Humanoid robot, Active toe joint, Heel-off and toe-off motions, Path planning optimization

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