Frequency criteria for the grasping control of a hyper-redundant robot

The paper focuses on hyper-redundant arms with continuum elements that perform the grasping function by coiling. First, there is concern with the dynamic model of the continuum arm for the position control during non-contact operations with the environment. A frequency stability criterion based on the Kahman - Yakubovich - Popov Lemma and P and PD control algorithms is proposed. Then, the grasping control of the arm in contact with a load is analyzed. The dynamics of the system are discussed and an extension of the Popov criterion is endorsed. The control algorithms based on SMA actuators are introduced. Numerical simulations and experimental results of the arm motion toward an imposed target are presented.