Modified Transpose Effective Jacobian Law for Control of Underactuated Manipulators

摘要

Underactuated manipulators consist of active and passive joints, and developing a control technique that can manage such systems is an attractive, challenging problem. Most works in this area present model-based control laws that require a full dynamics model, and are consequently affected from uncertainties and time delays due to massive computations. Non-model-based control approaches provide an efficient alternative for practical implementation. The Modified Transpose Jacobian (MTJ) algorithm is one of these controllers that has been recently proposed for fully actuated manipulators with a square matrix Jacobian. Based on an approximated feedback linearization approach, the MTJ does not need 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. To this end, the notion of the Transpose Effective Jacobian (TEJ) is presented and so the proposed algorithm is called the Modified TEJ (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. Therefore, the proposed law needs just to a portion of mass matrix that corresponds to passive joint(s), and it is much less affected by inaccuracies in system properties. The gains of the proposed MTEJ can be selected more systematically and do not need to be large; hence, the noise rejection, characteristics of the algorithm are improved. Also, no need for the pseudo-inversion of the Jacobian matrix in the proposed controller makes further convenience in the underactuated cases. In addition, the relationship between kinematic and dynamic manipulability measures is discussed for underactuated manipulators. Obtained results show its superior performance even compared to that of the model-based algorithms that need full dynamics models, while the proposed MTEJ requires much lower computation effort.