Identification and Compensation for Nonlinear Friction of Integrated Spherical Joint Based on Hippopotamus Optimization Algorithm

Abstract

The integrated spherical joint is a multi-DOF motion component with strong potential for humanoid robot actuation. However, nonlinear friction at low velocities leads to hysteresis and vibrations, limiting its use in high-precision applications such as medical and rescue tasks. This article proposes a friction model identification method based on the hippopotamus optimization (HO) algorithm to address these challenges. Experimental friction-velocity data are used to identify static parameters, while dynamic parameters are obtained by linearizing the motor’s presliding region, forming a complete LuGre dynamic friction model. The LuGre model is selected for its ability to capture key nonlinear friction behaviors such as presliding, hysteresis, and the Stribeck effect while maintaining a relatively simple structure suitable for real-time applications. To validate the model, a backstepping adaptive sliding mode control (BASMC) is applied for friction compensation. The BASMC adaptively estimates friction model errors and disturbances, effectively reducing low-speed nonlinear effects and enhancing robustness. Experimental results confirm that the proposed method significantly improves tracking performance, making it suitable for high-precision applications.