Feedback linearization control of flexible joint robots

Abstract

In this paper, the control of a two link, flexible joint manipulator is examined. Among external forces, an exogenous constraint force acting on the end-effector is included. The manipulator dynamics are described by: x ̇ =ƒ( x)+ g(x)u+J T( x)ƒ e( x) . On the assumption that f(x), g(x) and J T f e(x) are smooth vector fields, it is shown that the inner loop control u is of the form: u= 1 〈dT n,g〉 ( v−〈dT n,(ƒ( x)+J Tƒ e( x))〉) where u is an outer loop control signal and y = T(x) is a diffleomorphism that transform (a) into linear system. As the position control scheme is adopted, the value of the contact force is not controlled. The results for the inner loop control are substantiated by simulation of a two-link robot model. The robustness of the control method is examined and a Lyapunov-based control correction, similar to that of the free motion case, is implemented. Results are obtained for parametric errors of up to 50%. In the simulation, the manipulator is required to follow a specified joint trajectory such that the end-effector traces a sinusoidal path along a constraint surface. The results obtained illustrate the tracking of the link reference trajectory and indicate that the inner loop corrections are valid.