Nao’s head modelling and control using discrete-time sliding mode algorith

In this work, it is designed and implemented a discrete-time sliding mode control algorithm applied to control head’s position of the Nao humanoid robot. This is done firstly, by obtaining the direct kinematics through the Denavit-Hartenberg criteria; secondly, the differential kinematics is computed by the relationship between joint velocities and the linear velocity of the two joints; finally, the dynamics model of the head is obtained by using the Euler Lagrange’s equations. Once the mathematical model is obtained, it is used a zero-order hold for obtaining the discretization and a block control transformation in order to design the sliding surface, also in discrete-time. To this sliding surface, it is applied the discrete-time sliding mode algorithm to control the angular positions of the Yaw and Pitch joints. The complete closed-loop system is simulated in Simulink/Matlab in order to probe the proposed methodology. To validate the control algorithm, the proposed methodology is implemented in the generic simulation system SimSpark Nao robot, where different tracking references are probed. The results obtained validate the proposed control algorithm applied to the Nao robot.