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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. INDEX TERMS Triple link rotary inverted pendulum (TLRIP), neuro-fuzzy friction estimation and modelling.

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Most of mechanical robotic systems include nonnegligible nonlinearities due to the complex dynamic behaviors of frictions. In this study, joint frictions of Rotary Triple Inverted Pendulums (RTIP) are examined based on its experimental and simulation dynamic responses. RTIP might be considered as the most appropriate mechanical setup to investigate friction phenomena and understand the frictions' influence in the dynamics of any mechanical system. In this paper, three different friction estimation models such as Non-Conservative, Linear and Non-linear friction models are compared to estimate the joint frictions of the RTIP developed in our laboratory. Non-Conservative friction estimation model considers only viscous frictions. Linear friction model is dependent on Coulomb and viscous frictions. The Non-Linear friction model is the sum of five types of frictions: the zero drift error of friction, the Coulomb friction, the viscous friction, and the experimental friction. Based on comparative experimental friction analysis, the joint frictions of the RTIP are estimated more effectively using a Non-Linear friction model. 