Control of space free-flyers using the modified transpose Jacobian algorithm

Transpose Jacobian control is one of the simplest algorithms used in manipulator control. However, since it is not dynamics-based, poor performance may occur in applications where high speed tracking is required. In this paper, a modified transpose Jacobian algorithm is presented and applied to control of space free-flyers. This new algorithm employs stored data of the control command in the previous time step, resulting in improved performance. The gains of the modified algorithm do not need to be large, hence the noise rejection characteristics of the algorithm are improved. Stability analysis, based on Lyapunov´s theorems, shows that both the standard and the modified transpose Jacobian algorithms are asymptotically stable. Simulations of both terrestrial and space applications show that the tracking performance of this new algorithm is comparable to that of computed torque algorithms, although it does not require a priori knowledge of plant dynamics