On the l1 Optimal State Estimator with Applications to Bipedal Robots

Motivated by the fact that a number of present state estimations require some presumed conditions and could not lead to a desired accuracy when they are applied to real systems, this paper is concerned with providing a new framework for the state estimation. We first introduce some existing methods of state estimations and describe their weaknesses for unknown bounded persistent elements. Aiming at taking into account more practical situations of real systems, which cannot be treated by the existing methods, this paper provides a new state estimation method by using the l1 optimal control theory. More precisely, the new state estimation method called the l1 optimal state estimation considers unknown bounded persistent elements such as external disturbances and measurement noises, which often occur in the systems and make the estimation difficult. The problem of minimizing the effect of the bounded persistent elements on the corresponding state estimation error could be mathematically formulated by using the arguments on l1 optimal state estimation introduced in this paper. Finally, the effectiveness of the l1 optimal state estimation is demonstrated through some simulation results associated with the center of mass (CoM) estimation for a bipedal robot on its linear inverted pendulum model (LIPM).