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In biped locomotion, the energy minimization problem is a challenging topic. This problem cannot be solved analytically since modeling the whole robot dynamics is intractable. Using the inverted pendulum model, researchers have defined the Zero Moment Point (ZMP) target trajectory and derived the corresponding Center of Mass (CoM) motion trajectory, which enables a robot to walk stably. A changing vertical CoM position has proved to be crucial factor in reducing mechanical energy costs and generating an energy efficient walk [1]. The use of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) on a Fourier basis representation, which models the vertical CoM trajectory, is investigated in this paper to achieve energy efficient walk with specific step length and period. The results show that different step lengths and step periods lead to different learned energy efficient vertical CoM trajectories. For the first time, a generalization approach is used to generalize the learned results, by using a programmable Central Pattern Generator (CPG) on the learned results. Online modulation of the trajectory is performed while the robot changes its walking speed using the CPG dynamics. This approach is implemented and evaluated on the simulated and real NAO robot.

Generalized Learning to Create an Energy Efficient ZMP-Based Walking