Intelligent passive control in robotic assembly

It is clear that if a bean drops in a bowl, the bean would approach to the bottom of the bowl (a unique state) with its gravity, if the frictional coefficient is not very large. This provides an example of eliminating positional uncertainty with a unique constant input. From another point of view, the height of the bean in the bowl can be considered as an energy function V of position X of the bean in the horizontal plane when the bean touches the bowl. V is a proper function of ||X||. The gravity input decreases V in all the region of the bowl. Therefore the system is asymptotically stable at the bottom of the bowl, because V is a Lyapunov function. In practice, if the motion region of the system in the configuration space has one or more bowl-like region, a unique constant input can be designed to reduce the uncertainty of the system state. In this paper, the works in two important traditional areas are shown. It proves that there are always some attractive regions in the motion regions of a general peg-hole system with a fixed angle and also of the polyhedral part in 3D. Therefore, it is possible to design a unique constant sensorless input to reduce the uncertainty of the systems with no additional advice.