Development of a humanoid robot state estimator robust to modeling uncertainty

Abstract

This study proposes a novel estimator framework for the humanoid robot state estimation. Most existing studies adopted the original Kalman filter framework for the humanoid robot state estimation problem. However, the conventional Kalman filter guarantees optimal estimation solutions only when the nominal equations of the model and measurement include zero-mean, state-uncorrelated, white Gaussian noise. Because a humanoid robot is a complex system with multiple degrees of freedom, its mathematical model is limited in terms of expressing the system accurately, resulting in the generation of non-zero-mean, non-Gaussian, correlated modeling errors. Therefore, it is difficult to obtain accurate state estimates if the conventional Kalman filter-based approaches are used with such inexact simplified humanoid models. To overcome these drawbacks of the existing humanoid robot state estimators, a new robust state estimator scheme is proposed. The proposed modified Kalman filter framework consists of two loops: a loop to estimate the state, and a loop to estimate the state-correlated disturbance generated by the modeling errors (a dual-loop Kalman filter). The disturbance values estimated by the disturbance estimation loop are provided as feedback to the state estimation loop, thereby improving the accuracy of the model-based prediction process. By considering the correlation between the state and disturbance in the estimation process, the disturbance can be accurately estimated. Therefore, the proposing estimator allows the use of a simple model, even if it implies the presence of a large modeling error. In addition, it can estimate the humanoid state more accurately than the conventional Kalman filter. Furthermore, the proposing filter has a simpler structure than the existing robust Kalman filters, which require the solution of complex Riccati equations

hence, it can facilitate recursive online implementation. It is proved that the proposing estimator is the unbiased estimator for the state and the modeling disturbance and is the optimal filter in minimum variance sense. Along with the new estimator, a novel humanoid robot model is presented that can reflect key physical characteristics of the humanoid robot. The new model can reflect the undesired flexibility feature and the swing-leg-dynamics effect of the humanoid robot. Based on the forementioned estimator and model, the humanoid robot state estimation framework is configured. The performance and characteristics of the proposed humanoid robot state estimation framework are verified by comparison with other existing linear/nonlinear estimators using simple examples and simulations. Furthermore, the feasibility of the proposing state estimator scheme is verified by implementing it on a real humanoid robot platform.