This paper deals with the depth observability problem of a hand-eye robot system. In contrast to earlier works, this paper presents a complete study of this observability problem. The velocity of the active camera in the handeye robot system is considered as the input. The observability of depth estimation is then related to the velocity of the camera. A necessary and sufficient condition for the types of camera velocities necessary to ensure observability is found. This compensates for the results of earlier works, in which the velocity of camera was estimated. The theory is also verified by both simulations and experiments in this paper. Furthermore, a modified LQ visual servo control law is proposed to vary the weighting matrices so that depth estimation is improved while the level of control performance is still retained.
This article summarizes four formulations of the composite body method for the inertia matrix of a manipulator in the earlier works and presents a new formulation. These five formulations all use the first moments and the inertia tensors of composite bodies about the origin of the local frame. This paper also presents an algorithm for computing these first moments and inertia tensors. This algorithm utilizes a set of minimal linear combinations of inertia parameters instead of the natural inertia parameters, so that a number of redundant computations are saved. It is found that the new algorithm for the first moments and the inertia tensors of composite bodies is computationally superior to the others in the literature. On the other hand, two among the five formulations for the inertia matrix are more efficient than the other three as well as the others in the literature. The new formulation is one of these two most efficient formulations, and is specially adequate to a manipulator with some translational joints.
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