Adaptive Practical Tracking Control For Multi-class Of Uncertain Robot Systems With Flexible Joints

Robots with flexible joint have been widely used in industrial and social practice whose tracking control has been a hot topic in modern control theory and engineering.However,due to the presence of strong nonlinearities,multiple freedoms,serious coupling and system uncertainties,their control design and analysis are usually challenging,many control problems of great scientific significance and practical application value remain unsolved yet.Noting the constrains of the existing theoretical results,practical tracking control for three classes of robots with flexible joint is investigated in the paper.Different from the related literature where strong constraints are required on the generality and measurability of reference signals as well as the severity of the system uncertainties,in the paper,disturbances exist in all the three systems,most of the dynamic matrices are unknown without known nominal parts,while the reference signal is not necessarily to be high-order continuously differentiable without its derivatives being available for feedback.Besides the weaken assumptions on system uncertainties and reference signals,dead-zone nonlinearity and input saturation are considered for the robots with flexible joint so as to improve the security of the theoretical results,and in turn to establish the novel framework for the practical tracking control of the robots with flexible joint.Specifically,a class of uncertain flexible joint robots with variable stiffness actuators is first considered.By incorporating the adaptive dynamic compensation technique into vectorial backstepping framework with the smart choices of adaptive law and virtual controls(without measurements of the derivatives for reference signals),the severe constraints on system uncertainties and reference signals are overcome.Based on this,practical tracking control for an uncertain free-flying flexible-joint space robot with dead-zone nonlinearities and serious uncertainties.Then,a class of flexible-joint robotic manipulators driven by DC motors under actuator saturation is investigated.By skillfully incorporating adaptive dynamic compensation technique,constructive methods of command filters and an auxiliary system for the compensation of actuator saturation into the backstepping framework,the serious system uncertainties is compensated while the explosion of complexity of the traditional backstepping method is avoided.It is proven that the tracking controllers designed for the three typical systems under investigation ensure that all the states of the resulting closed-loop system are bounded while the system output practically tracks the reference signal.Finally,numerical examples are provided to validate the validity of the proposed theoretical results.