Walking Control Using TDE-Based Backstepping SM of Position-Commanded NAO Biped Robot with Matched and Unmatched Perturbations

This paper tackles the problem of high-precision joint position trajectory tracking in the presence of matched and unmatched perturbations of the humanoid NAO robot that has not direct drive joints. The proposed solution consists of combining a backstepping sliding mode with time delay estimation. Since the processor on-board has low computational power, the time delay estimation will alleviate the heavy computations while ensuring an effective approximation of the global robot dynamics. On the other hand, the backstepping method will allow the rejection of the mismatched perturbations, while the sliding mode will guarantee fast convergence and will deal with the estimation error. Moreover, the sliding mode will be based on the exponential reaching law in order to reduce the problem of chattering. The controller is designed step-by-step using recursive Lyapunov functions to ensure the stability. The last step in the design procedure consists of a modification based on the NAO’s proportional-derivative regulator to convert the computed torque inputs into a position command for the robot’s servo actuators. Finally, experimental work was carried out to validate the proposed control architecture and to verify its performance.