Output excitation via second-order sliding-modes to generate periodic motion for underactuated systems

Generation of periodic motion for underactuated manipulator is done through the second-order sliding-mode (SOSM) algorithms, particularly via the twisting algorithm. This study is motivated by the recent results which show that the SOSM algorithm may generate a periodic motion if the relative degree of the plant is higher than two. To obtain the desired amplitude and velocity of oscillations we use the describing function and the locus of a perturbed relay system approach. Performance issue of the controllers is illustrated in a simulation study made for a three-link underactuated robot