Generation of the destination for a mating action in the presence of uncertainty

An assembly planning system that takes the CAD model description of a product as input and automatically generates executable plans not only can automate assembly processes, but also can provide assembly properties of the product through the simulation of all possible assembly plans. Yet, to achieve such automation, the necessary information required in describing the executable action must be automatically generated from the model of a product so that the effective simulation of the assembly process is possible. In this paper, the generation of the destination of a mating action in the presence of uncertainty is presented. When a mating action in an assembly process is required to be executed, the action description developed from the model of a product usually only specifies the mating properties of the action, like “peg in hole”. Thus, with the purpose of effective simulation, a set of locations must be derived from the mating property to identify the acceptable region of the goal of the action such that the uncertainties occurring in the representation of object dimensions, action motions, and sensory information can be incorporated in the assembly process. In the authors´ previous work, a systematic procedure has been proposed to automatically generate such a goal region. However, goal regions can only provide the information of the acceptable goals of the corresponding moving objects. In specifying a goal in a planning process or in the description of an executable action, a point is required to define the destination of a mating action in order that the system can know how to perform the action. In this paper, with the concept of reliability indices, the destination of a goal region, which is assumed to be a convex polygon, is considered to be the point from which the minimal distance to the edges of the polygon is the maximum, and then the destination can yield the maximal estimated success probability on executing the mating action. An algorithm with the time complexity of O(NlogN) is proposed to find the point from which the minimal distance to the edges of the polygon is the maximum