Optimal Balancing Control of a Standing Biped Subject to Constraints

Yuming Sun and Qiong Wu


Biped balancing control, Lyapunov exponents, Genetic algorithm, Stability analysis


Balancing control is important for biped locomotion. In spite of much effort, 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 the satisfaction of the constraints between the biped feet and the ground. In this paper, an optimal proportional-derivative (PD) controller is proposed using the genetic algorithm (GA) 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 standing. More importantly, rigorous stability analysis of the controlled system is provided using the concept of Lyapunov exponents (LEs), and parts of the stable regions are determined. The paper contributes to the biped balancing control, which is significant to the development of bipedal robots.

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