Balancing control is important for biped locomotion. In spite of large efforts, it is extremely difficult to design balancing control strategies for a standing biped satisfying the following three requirements simultaneously: maintaining postural stability, improving energy efficiency and guaranteeing satisfaction of the constraints between the biped feet and the ground. In this paper, a proportional-derivative (PD) controller developed from the genetic algorithm (GA) satisfying all three requirements is proposed for a standing biped, which is simplified as a two-link inverted pendulum with one additional rigid foot-link. The simulation results show that with the proposed controller the biped can be maintained at the upright position with the minimal energy consumption, and the constraints between the foot-link and the ground are satisfied during quiet standing. By using the concept of Lyapunov exponents (LEs), the stability analysis of the controlled biped is provided. Morever, structural stability of the biped subject to the different control gains is also investigated, and parts of the stability regions in the parametric space of control gains are identified. The paper contributes to the biped balancing control, which is significant to the development of biped robots.

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