Contact State and Extremal Configuration Identification for Force Guided Assembly

The reliable automation of assembly is important for improved product manufacture. One approach to achieving reliable automated assembly is known as force assembly. A robot\u27s motion response to a contact force is determined by its mechanical admittance. An admittance is the relationship between the applied force and the resulting motion. The force assembly approach uses the manipulator admittance to compensate for part misalignment. The design strategy is that by imposing a set of sufficient conditions on the admittance at some sample configurations (a configuration describes the relative position between two objects), misalignment reduction is achieved for all the possible intermediate configurations. The number of configurations for a general assembly task is infinite; whereas, the number of contact states, which characterize the contact status between two object, is finite. Therefore, the approach to identifying the sample configurations contains the following two issues: 1) all contact states for an assembly task are first obtained; 2) a finite number of extremal configurations (the configurations that have extreme values in misalignment) are extracted within each contact state. These finite number of extremals are selected as the set of representative configurations. The approach to identifying contact states and the associated extremal configurations is from the less constrained contact states (the contact states that constrain less degrees of freedom for the parts) to the more constrained contact states (the contact states that constrain more degrees of freedom for the parts). The approach has the following three components: Obtains the unique contact state description by considering topological and geometrical conditions. This component eliminates the redundant description for the same contact features. Identifies whether a contact state description is valid for an assembly task. The procedure first uses simple topological and geometrical conditions to evaluate the existence of a contact state description. Then a optimization procedure is applied to evaluate the existence of the contact state by finding whether there is valid configuration within the contact state. Determine the extremal configurations for the contact states by involving constrained optimizations. In the approach, a strategy based on the contact state generation procedure, extremal configurations and the topological relationships among contact states is used to improve the robustness of the algorithm