Modified Transpose Effective Jacobian control of underactuated manipulators

The modified transpose Jacobian (MTJ) algorithm is a recently proposed algorithm used in manipulator control. Based on an approximated feedback linearization approach the MTJ does not need to a priori knowledge of the plant dynamics. In this paper, this scheme is extended to the complicated control problem of underactuated robots in Cartesian space. Based on the notion of transpose effective Jacobian, this new proposed algorithm is called modified transpose effective Jacobian (MTEJ) algorithm. The MTEJ control law employs stored data of the control command in the previous time step, as a learning tool to yield an improved performance, with a bit need to a priori knowledge of the plant dynamics. Therefore, unlike a model-based algorithm, it is not so affected by inaccuracies in mass properties. The gains of MTEJ can be selected more systematically, and do not need to be large, hence the noise rejection characteristics of the algorithm are improved. Finally, a proposition is presented about the manipulability measure of underactuated manipulators. Obtained results show an improved performance compared to that of the transpose effective Jacobian and even model-based algorithms in the presence of uncertainties and noises.