Parts entropy methods for robotic assembly system design

Assembly tasks require the feeding, acquisition, orientation, and mating of parts subject to contact forces. Positional entropy provides an efficient tool for describing an assembly task and its system implementation in terms of the uncertainty in position and orientation of parts as the assembly sequence progresses. A parts entropy measure HQ(X) may be calculated from the probability distribution of parts positions and orientations at a given assembly step defined over an ensemble of repeated assembly tasks. The part entropy may be reduced mechanically by containerization, fixturing, manipulation, or product redesign. The part entropy may also be reduced using sensors (typically vision or tactile) by reducing the conditional entropy HQ(X/Y) due to the sensory measurement. The information obtained about part position may be defined in terms of the mutual information I(X;Y). In these terms, the goal of an assembly system is to reduce the joint entropy among parts by mating them in stable configurations. The positional entropy concept provides a unifying tool for assessing the relative effectiveness of systems designs which incorporate both mechanical and sensor-based techniques. The approach may also provide a useful ingredient for quantitative assessment of product designs, complexity of assembly procedures, and flexibility of assembly systems. An example of the use of positional entropy for analysis of an electronic assembly task is given.