Adaptive Practical Tracking Control for a Class of Uncertain Flexible Joint Robots with Variable Stiffness Actuators

This paper is devoted to the tracking control of a class of uncertain flexible joint robots with variable stiffness actuators (VSAs). Compared with the related literature, more serious system uncertainties are allowed since the disturbances exist in all the three subsystems but only in one or two subsystems in those of the related literature. Moreover, more wide class of reference signals can be tracked since which are only first order continuously differentiable rather than higher order (more than two) continuously differentiable in the related literature. To solve the control problem, a novel adaptive practical tracking control design scheme is proposed by skillfully incorporating the adaptive dynamic compensation technique into the vectorial backstepping framework. Then, adaptive tracking controllers are explicitly designed which ensure that all the states of the resulting closed-loop system are bounded while the system outputs practically track the reference signals, i.e., the tracking errors arrive and then stay at an arbitrary neighborhood of the origin after some time. It is worth strengthening that the proposed controllers do not require the measurements of the derivatives for reference signals but those of the related literature must do, and hence is much more applicable. Finally, simulation is provided to validate the proposed theoretical results.