Nano-robotic manipulation using a RRP nanomanipulator: Part A – Mathematical modeling and development of a robust adaptive driving mechanism

A three degree of freedom (3 DOF) nanomanipulator with revolute revolute prismatic (RRP) actuator structure, named here MM3A, can be utilized for a variety of nanomanipulation tasks. This first paper in the series presents the mathematical modeling and development of a memory-based robust adaptive controller for the nanomanipulator driving principle. Unlike widely used Cartesian-structure nanomanipulators, the MM3A is equipped with revolute-piezoelectric actuators which result in outstanding performance in controlling the nanomanipulator’s tip alignment during the nanomanipulation. However, the RRP structure of the nanomanipulator introduces complexity in kinematic and dynamic equations of the system which needs to be addressed in order to control the nanomanipulation process. Dissimilar to the ordinary piezoelectric actuators which provide only a couple of micrometers working range, the piezoelectric actuators utilized in MM3A, namely Nanomotors®, provide wide range of action (120° in revolute actuators and 12 mm in prismatic actuator) with nanoscale precision (0.1 μrad in revolute actuators and 0.25 nm in prismatic actuator). This wide range of action combined with nanoscale precision is achieved using a special stick/slip moving principle of the Nanomotors®. However, such stick/slip motion results in stepping movement of the MM3A. Hence, due to the RRP structure and stepping movement principle of the MM3A nanomanipulator, development and implementation of an appropriate controller for such nanomanipulation process is not a trivial task. In this paper, a novel memory-based robust adaptive controller is proposed to overcome such shortfalls. Following the development the controller, numerical simulations are preformed to demonstrate the positioning performance capability of the controller in a variety of nanomanipulation tasks.