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 nor dynamics-based, poor performance may occur in applications where high speed tracking is required Use of high gains also,worsens performance, especially in the presence of noise. fn addition, lack of a systematic gain selection makes it difficult to apply, 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 the step, resulting in improved performance. The gains of the modified algorithm do nod 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 bath terrestrial and space applications show that tracking performance of this new algorithm is comparable to that of computed torque algorithms, although it does not require a prior knowledge of plant dynamics.