A discrete event controller (DEC) synthesis methodology for the successful convergence of assembly is presented. The modelling of an assembly process as a hybrid dynamic system (HDS) has been shown to be a very effective strategy to incorporate the interaction between the workpiece and its environment. In addition, this modelling has allowed the derivation of realistic conditions on the DEC for the convergence to the full assembly, known as p-convergence. In this paper the authors propose a DEC synthesis methodology resulting in an optimal p-convergence by combining the maintaining and enabling conditions proposed by McCarragher and Asada and dynamic programming. The applicability of the proposed synthesis methodology is then demonstrated for a dual peg insertion task.

A new approach to the planning and analysis of the successful convergence of assembly is presented. The convergence is referred to as p-convergence, since it is derived within a probability framework. The assembly is modeled as a hybrid dynamic system (HDS) accounting for the presence of the discrete change of contact and the continuous movement during the process. The continuous property is then employed to represent an assembly DES as a Markov chain such that p-convergence can be proposed. To derive conditions for p-convergence of the full assembly, methods for estimating the transition probability matrix are derived for the perfect case, the tracking error case, and the case of parameter uncertainty. It is shown that p-convergence for an assembly DES requires a control effort which is significantly more realistic for practical implementation than current methods presented in the literature.

Sufficient conditions for the success of the robotic control of assembly are presented. The assembly is modelled as a discrete event system using Petri nets. The abstraction of assembly to the discrete event system highlights the changes in the state of contact as the key points to control in the assembly process. Using this abstraction, sufficient conditions on the velocity commands are developed which guarantee successful parts mating. A method to derive robot velocity commands satisfying these conditions is derived. The method is then applied to a dual peg-in-the-hole problem.>