Singular perturbation approach to trajectory tracking of flexible robot with joint elasticity

Abstract

The control problem of a robot manipulator with flexures both in the links and joints was investigated using the singular perturbation technique. Owing to the combined effects of the link and joint flexibilities, the dynamics of this type of manipulator become more complex and under-actuated leading to a challenging control task. The singular perturbation being a successful technique for solving control problems with under-actuation was exploited to obtain simpler subsystems with two-time-scale separation,thus enabling easier design of subcontrollers. Furthermore, simultaneous tracking and suppression of vibration of the link and joint of the manipulator is possible by application of the composite controller, i.e. the superposition of both subcontrol actions. In the first instance, the design of a composite controller was based on a computed torque control for slow dynamics and linear-quadratic fast control. Later, to obtain an improved control performance under model uncertainty, the composite control action was achieved using the radial basis function neural network for the slow control and a linear-quadratic fast control. It was confirmed through numerical simulations that the proposed singular perturbation controllers suppress the joint and link vibrations of the manipulator satisfactorily while a perfect trajectory tracking was achieved.