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This paper addresses an optimization problem of trajectories for a biped robot with a new modelled structure of knees which is called rolling knee (RK). The first part of article is to present the new kinematic knee on a biped robot and the different models used to know the dynamic of the robot during a walking step. The gait is cyclic and simplified by a Single Support Phase (SSP) followed by an impact. The second part is a comparison of the influence of the gait trajectory on the control, using cubic spline functions as well as the Bézierfunctions. The energetic criterion is minimized through optimization while using the simplex algorithm and the Lagrange penalty functions to meet the constraints of stability and deflection of mobile foot. The main result is the using of Bézierfunctions permit to improve the energy gain in slow walking speeds. These trajectories permit to the biped robot to walk progressively without energy disturbance unlike those with cubic spline functions.

Gait Optimization of a Rolling Knee Biped at Low Walking Speeds