Abstract—Most of mechanical robotic systems include non-negligible 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.
 

Index Terms—Rotary Triple Inverted Pendulums (RTIP), Linear Friction Estimation, Non-linear Friction Estimation, Non- Conservative Friction Estimation, Gradient Descent (GD) algorithm, Pattern Search (PS) algorithm