Human like trajectory generation for a biped robot with a four-bar linkage for the knees

• Simulation the locomotion of a planar biped robot equipped with four-bar knees.
• Walking trajectories with phases of double support, single support and impacts.
• In single support the biped can be fully actuated and under actuated respectively.
• A sthenic criterion to compare a four-bar knee with revolute knees.
• Numerical results show that the four-bar linkage could be a good technological way.

The design of a knee joint is a key issue in robotics to improve the locomotion and the performances of the bipedal robots. We study a design for the knee joints of a planar bipedal robot, based on a four-bar linkage. We design walking reference trajectories composed of double support phases, single support phases and impacts. The single support phases are divided in two sub-phases. During the first sub-phase the stance foot has a flat contact with the ground. During the second sub-phase the stance foot rotates on its toes. In the double support phase, both stance feet rotate. This phase is ended by an impact on the ground of the toe of the forward foot, the rear foot taking off. The single support phase is ended by an impact of the heel of the swing foot, the other foot keeping contact with the ground through its toes. A parametric optimization problem is presented for the determination of the parameters corresponding to the optimal cyclic walking gaits. In the optimization process this novel bipedal robot is successively, overactuated (double support with rotation of both stance feet), fully actuated (single support sub-phase with a flat foot contact), and underactuated (single support sub-phase with a rotation of the stance foot). A comparison of the performances with respect to a sthenic criterion is proposed between a biped equipped with four-bar knees and another with revolute joints. Our numerical results show that the performances with a four-bar linkage are bad for the smaller velocities and better for the higher velocities. These numerical results allows us to think that the four-bar linkage could be a good technological way to increase the speed of the future bipedal robots.