New Fixed-Time Observer-Based Model-Free Fixed-Time Sliding Mode of Joint Angle Commanded NAO Humanoid Robot

In this article, we present a new fixed-time observer (FTO) with time delay estimation (TDE)-based model-free fixed-time sliding mode for the problem of robust walking of the NAO robot. The proposed technique ensures convergence in fixed time, regardless of initial conditions, thereby enhancing both convergence speed and robustness. This method allows for precise tracking of the joint angles’ positions without depending on the robot’s dynamic models while reducing the chattering via a modified exponential reaching law (MERL). To address the complexities of stabilizing the walking dynamics of the NAO robot, which include highly nonlinear dynamics and limited computational process, the proposed strategy utilizes the TDE technique for system model estimation. To mitigate estimation errors, a novel observer with guaranteed fixed-time stability is proposed. This last helps to enhance the tracking performance. Using the Lyapunov theory and experimental validation, within the proposed composite control method, the proposed nonsingular terminal sliding surface’s fixed-time stability along with the system state’s stability is verified. Significantly improved stability and accuracy in the robot’s joint movements are demonstrated through experimental results, validating the efficacy of the tracking trajectory for robotic systems such as the NAO humanoid robot.