Manipulation and propagation of uncertainty and verification of applicability of actions in assembly tasks

A systematic methodology of manipulating and propagating spatial uncertainties in the form of homogeneous transforms and in a probabilistic sense is presented. Uncertainties are represented by covariance matrices and the manipulation of uncertainties focuses on the spatial uncertainty propagation and the uncertainty fusion. To integrate the uncertainty information into a task plan that consists of a sequence of primitive actions, the propagation of uncertainty before and after a primitive action such as moving action, perception action, and contact action is developed. A simple and optimal solution for maintaining the consistency in the world state is proposed for perception actions. To determine the applicability of an action, forward propagation and backward propagation are proposed to verify the success of an action in the presence of uncertainties. It is shown that the backward propagation method can be used to determine an admissible set of an action with a specified acceptable success confidence and/or to efficiently apply perception actions to reduce the uncertainty