This paper develops a controller synthesis method for ensuring an admissible bound of external forces on biped robots in a desired level. We first introduce the authors’ preceding results on the norm-based stability criterion for a biped walking constructed on its linear inverted pendulum model (LIPM). More precisely, an induced norm can be taken to formulate the fact that the balance for a biped robot is achieved if its zero moment point (ZMP) always stays in the supporting region at each step. Based on this norm-based criterion, we aim at making the maximum energy of external forces admissible for balancing the biped robot be a pregiven desired bound γ(> 0). To achieve this objective, a robust controller is designed through the linear matrix inequality (LMI)-based approach. More importantly, a necessary and sufficient condition for the existence of a robust controller leading to the desired bound is characterized by some LMI conditions. The effectiveness of the overall arguments is validated through some comparative simulation results of a biped walking robot with external forces.

This paper proposes a new framework for the computed torque method (CTM) of robot manipulators without velocity measurements. We first introduce the Luenberger-observer-based CTM with only position measurements. We then clarify that the external disturbance affects not only the tracking performances with respect to the plant but also the estimation accuracies relevant to the state observer. To address this problem, we establish a new architecture for the so-called dual-loop control scheme, by which both the tracking performances and estimation accuracies can be simultaneously improved, in contrast to its existing structure. A guideline for taking control parameters corresponding to the proposed control structure is also provided with respect to the stabilization of the overall closed-loop systems. Finally, simulation and experimental results are provided to demonstrate the validity and practical feasibility of the developed structure.

This article proposes a new stability criterion for biped walking systems on the linear inverted pendulum model, in which the dynamic relationship between the center of mass (CoM) and the zero moment point (ZMP) is dealt with. More precisely, based on the fact that a biped walking robot is stable if its ZMP is always located in the supporting region, we consider whether the ZMP error between its reference and real values stays inside a certain area to guarantee the stability condition. To this end, a norm-based new stability criterion is introduced, in which the temporal supremum of the ZMP error is concerned. Regarding the applicability of the stability criterion, we propose two control approaches to biped walking systems with the consideration of the norm-based stability criterion. In other words, full-state and observer-based feedback control approaches are analyzed in this article, and the initial CoM conditions with respect to the stability criterion are obtained for the two control approaches. We call the sets derived by such conditions the stability regions. Toward a more practical significance, we also deal with the effect of unknown disturbances and sensor noises on the stability of biped walking systems. More importantly, even though computing stability regions intrinsically involves an infinite number of linear inequalities, all the stability regions are shown to be explicitly obtained through only finite numbers of computations in this article. Finally, some simulation results are provided to demonstrate the validity as well as the practical applicability of the developed computation methods.

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 l1optimal 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 l1optimal state estimation introduced in this paper. Finally, the effectiveness of the l1optimal 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).