Abstract. This paper discusses the POP-2 language and Multipop time-sharing system developed during the second half of the 1960s. POP-2's expressiveness spanned numeric and symbolic programming and supported experiments in logic of programming languages (by Boyer and Moore) and programming language concepts (for example, Michie's memoisation). The paper also discusses how the goals of POP-2 might be achieved in a successor language.

A fitting relationship in an assembly implies that the relative location of the bodies belongs to a coset of the symmetry group of the mating feature pair. When a symmetry group is continuous, there are infinitesimal displacements which preserve the relationship. Assembly of two bodies normally involves the establishment of successively more constraining relations, many of which are fitting relations. The continuous topological structure of the associated group determines possible directions of assembly at any state in the assembly process. To accommodate to errors, it is necessary to choose a stiffness matrix appropriate to a given assembly state, which allows the robot to comply with wrenches normal to the possible assembly directions. The derivation of such matrices from a computational geometric representation of the mating feature symmetry group is considered.>

The use of symmetry groups in analysis of the kinematics aspects of assembly is described. The goal is to find how to assemble a product from a characterization of its final assembly configuration. From such an assembly configuration, a contact state lattice expressed in terms of the contacting faces of mating assembly components is generated. This contact state lattice contains all the partially ordered assembly motion sets (POAMS) that describe the intermediate contact states of an assembly component and the translational motions leading from one contact state to another. POAMS form a detailed task specification for a robot task-level planner and can be used for generating compliant control strategies. The work described forms part a kinematic assembly planning system that reasons about how parts with multiple contacting features fit together and generates assembly task specifications automatically from solid models using symmetry groups.>

When planning or describing an assembly, statements about how features should (or might) relate spatially can be expressed in terms of the symmetry groups of the features. The same is true of the interpretation of sense data. The authors show how to associate symmetry groups with features of body models created by the PADL2 system of A.A.G. Requicha and Voelcker (1982), and how to perform reasoning about spatial relationships between features of bodies occurring in an assembly in this group-theoretic context. Techniques for implementing this approach in numerical algorithms are described, with a focus on its extension to include finite rotational symmetries.>

The authors describe how to use geometric boundary models of assembly components to find mating features, thereby permitting simpler task specifications to be used. To mitigate the combinatorics of searching for a feasible correspondence between features of different bodies, boundary models produced by PADL2 (the geometric modeler) are matched against a library of standard compound features. The feasibility of mating compound features is analyzed using the symmetry groups of features.>

The paper is concerned with the use of symmetry groups as descriptors for surfaces-such symmetry groups can be used to characterise the constraints imposed between two bodies by areal contact between their surfaces. A method is presented for combining constraints imposed by spatial relationships between features (infinite geometric entities) of bodies. It consists of an algorithm for computing the intersections of infinite symmetry groups from their characteristic invariants. It is demonstrated that invariants of symmetry groups for these combined features can be computed in an efficient and practical way.>

The Edinburgh Designer System provides a high level of integration of knowledge about function and form for Mechanical Engineering Design. In this paper I discuss the extensions required to make this system suitable for assembly planning, showing that interface modules (eg. a seated-bearing) give rise to the basic acts of assembly, and that, with the provision of a suitable temporal formalism, the detailing of these actions can be accomplished within the Designer System framework.

Integrated systems have become prominent in the research programmes of a number of artificial intelligence laboratories. The Edinburgh machine intelligence group here defines its research and development philosophy in reply to questions put by Japanese robot engineers.