FEEDBACK LINEARIZATION CONTROL OF FLEXIBLE JOINT ROBOTS

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 = f(x) + g(x)u +J(T)(X)f(e)(x). (a) 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), (f(x) + J(T)f(e)(x))]) (b) where u is an outer loop control signal and v = T(x) is a diffeomorphism that transforms (a) into a 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.