Moving horizon for friction state and parameter estimation

Efficient on-line state and parameter estimation is essential for model-based friction compensation in order to track changes of friction characteristics in time and space. This paper presents a moving horizon estimation (MHE) algorithm for on-line friction state and parameter estimation using a smoothed (analytic) version of the Generalized Maxwell-Slip (GMS) model, a multi-state friction model known to describe all essential friction characteristics in presliding and sliding motion. In contrast to the GMS model, which consists of a switching structure to accommodate for its hybrid nature, the Smoothed GMS (S-GMS) model consists of an analytic set of differential equations well suited for gradient-based state and parameter estimation, as in MHE or in extended Kalman filtering (EKF). Moreover, MHE is known to better handle model nonlinearities, disturbances and constraints than EKF. This paper discusses the implementation of an MHE algorithm for the S-GMS friction model and experimentally compares its performance to an EKF implementation for joint state and parameter estimation.