Differential flatness of a class of n—DOF planar manipulators driven by an arbitrary number of actuators

This paper deals with the problem of feedback linearization, either by dynamic or static feedback, of a planar robot manipulator with n links and m inputs. The robot is pro-vided with a particular inertia distribution in order to reduce nonlinearities, and with n-m springs to keep controllability. Under these design conditions, the paper answers the question of where to place the actuators such that the system is static feedback linearizable. For those systems that there are not static feedback linearizable, the paper shows that are linearizable by prolongations and, therefore, dynamic feedback linearizable.