A Comparative Study of the Joint Neuro-Fuzzy Friction Models for a Triple Link Rotary Inverted Pendulum

In this paper, Neuro-Fuzzy Friction Estimation Models (NFFEM) are developed to estimate the joint friction coefficients in a Triple Link Rotary Inverted Pendulum (TLRIP) system and compared with an Adaptive Friction Estimation Models (AFEM). The different versions of AFEMs and NFFEMs are generated based on each of the following friction estimation models: Non-Conservative Friction Model (NCFM), Linear Friction Model (LFM), and Non-Linear Friction Model (NLFM). The aim of this study is to obtain joint friction models which depend on both velocity and acceleration in a large range of motion trajectory that involves difficult and sudden large changes. In the proposed NFFEMs, joint velocities and accelerations of the TLRIP are used as the input variables of the Neuro-Fuzzy system trained by using a Radial Basis Function Artificial Neural Network (RBANN). Several experiments are conducted on TLRIP system to verify the NFFEMs. In order to determine the estimation performance of the friction models, total Root Mean Squared Errors (RMSE) between position simulation results obtained from each joint friction model and encoders in the experimental setup are computed. Based on the position RMSEs, the NFFEMs produces much better estimation results than the AFEMs. Among NFFEMs, the neuro-fuzzy nonlinear friction model (NFNLM) gives the best results.